Financial Risk Management and Modeling (Risk, Systems and Decisions) 3030666905, 9783030666903

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Risk, Systems and Decisions

Constantin Zopounidis Ramzi Benkraiem Iordanis Kalaitzoglou   Editors

Financial Risk Management and Modeling

Risk, Systems and Decisions

Series Editors Igor Linkov U.S. Army ERDC, Vicksburg, MS, USA Jeffrey Keisler College of Management, University of Massachusetts Boston, MA, USA James H. Lambert University of Virginia, Charlottesville, VA, USA Jose Figueira University of Lisbon, Lisbon, Portugal

Health, environment, security, energy, technology are problem areas where manmade and natural systems face increasing demands, giving rise to concerns which touch on a range of firms, industries and government agencies. Although a body of powerful background theory about risk, decision, and systems has been generated over the last several decades, the exploitation of this theory in the service of tackling these systemic problems presents a substantial intellectual challenge. This book series includes works dealing with integrated design and solutions for social, technological, environmental, and economic goals. It features research and innovation in cross-disciplinary and transdisciplinary methods of decision analysis, systems analysis, risk assessment, risk management, risk communication, policy analysis, economic analysis, engineering, and the social sciences. The series explores topics at the intersection of the professional and scholarly communities of risk analysis, systems engineering, and decision analysis. Contributions include methodological developments that are well-suited to application for decision makers and managers.

More information about this series at http://www.springer.com/series/13439

Constantin Zopounidis • Ramzi Benkraiem Iordanis Kalaitzoglou Editors

Financial Risk Management and Modeling

Editors Constantin Zopounidis Technical University of Crete, Greece and Audencia Business School Nantes Cedex 3, France

Ramzi Benkraiem Audencia Nantes School of Management Nantes Cedex 3, France

Iordanis Kalaitzoglou Audencia Nantes School of Management Nantes Cedex 3, France

ISSN 2626-6717 ISSN 2626-6725 (electronic) Risk, Systems and Decisions ISBN 978-3-030-66690-3 ISBN 978-3-030-66691-0 (eBook) https://doi.org/10.1007/978-3-030-66691-0 © Springer Nature Switzerland AG 2021 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors, and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, expressed or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. This Springer imprint is published by the registered company Springer Nature Switzerland AG The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland

Risk Management and Modeling

Co-edited by: Professor Constantin ZOPOUNIDIS Professor Ramzi BENKRAIEM, and Professor Iordanis KALAITZOGLOU Risk is the main source of uncertainty for investors, debtholders, corporate managers, and other stakeholders. For all these actors, it is vital to focus on identifying and managing risk before making decisions. The success of their businesses depends on the relevance of their decisions and consequently, on their ability to manage and deal with different types of risks. Risk can come from diverse and different sources. For instance, risk can be associated with the project to finance. Fund providers such as investors or banks try to value the risk before making the decision to invest or lend their money. When they do not have the accurate information for the risk assessment, they request a high interest or return rate in order to incorporate a kind of additional premium covering the “non-assessed” risk due to the lack of accurate information. A situation where the risk is not properly valued and managed is likely to distort fund provider decisions. It may favor funding applicants presenting abnormally risky projects to the detriment of those with reliable projects. In other words, fund providers do not finance the “right” funding applicants and, thus, bear a significant risk of failure or insolvency. In this scenario, the interest rate is not an effective means of selection in the investing or lending process. The increase in the interest or return rate reflects the difficulty of fund providers in appropriately selecting the applicants and projects to finance. This increase may induce a direct raise in fund provider income but can aggravate at the same time the probability of non-reimbursement. Risk can also come from the information asymmetry gap that exists between the fund providers and the managers of funding applicant firms. More precisely, the manager’s opportunistic behavior after receiving the funding approval known as the asset substitution risk may be the source of this risk. Thus, the applicant manager v

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can submit a funding request to fund providers considered as being “normally risky” (that is to say presenting a risk acceptable by the fund providers). An increase in the requested interest or return rate may affect the funding applicant manager’s behavior. The latter would be tempted in this case to abandon the first submitted project in favor of a riskier second one that the fund providers would have initially refused. This behavior could be explained by a basic rule in finance that associates the expected return of a project with the incurred risk. The increase in the interest or return rate for the funding applicant manager may lead to an increase in the expenses. To absorb this surplus of costs, the manager seeks to increase the profitability of the projects to finance by implementing the most risky, supposed to be the most profitable ones. However, this managerial behavior has considerable consequences for the fund providers. The risk coming from asset substitution exposes them to a greater probability of failure or insolvency. For all these reasons and many others, risk management and valuation is vital for investors, debtholders, corporate managers, and other stakeholders to make accurate decisions. Accordingly, the main objective of this book is to promote scientific research in the different areas of risk management to help academics as well as professionals to better understand and assess different types of risks. Aiming at being transversal and dealing with different aspects of risk management related to corporate finance as well as market finance, this book is structured as follows:

Book Synopsis 1. Asset Pricing a. Kalaitzoglou (Microstructure, Time and Asset Pricing) b. Tselika (Herding and Asset Pricing) 2. Asset Allocation a. b. c. d. e.

Terraza (Ptf Management) Skrinjaric (Ptf Management) Masmoudi (Investor Heterogeneity/Sentiment) Verousis (Country of Domicile and Investment Strategy) Uppal (Indiosyncratic Risk)

3. Corporate Management/Governance Risk a. Barnetto (Hedge Accounting) b. Kassem (Corporate Fraud) c. Ramzi (SMEs and Financing) 4. Banking Risk a. Koutmos (Sovereign and Country CDS) b. Galariotis (Bank Failures) c. Chenet (Banks and Climate Change Risk)

Contents

Corporate Risk Management and Hedge Accounting Under the Scope of IFRS 9 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Yves Rannou and Pascal Barneto Corporate Fraud Risk Management . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Rasha Kassem

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Leverage Financing and the Risk-Taking Behavior of Small Business Managers: What Happened After the Crisis? . . . . . . . . . . . . . . . . . . . . . Nour Khairallah, Ramzi Benkraiem, and Catherine Deffains-Crapsky

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Credit Contagion Between Greece and Systemically Important Banks: Lessons for the Euro Area. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Dimitrios Koutmos

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Cluster Analysis for Investment Funds Portfolio Optimisation: A Symbolic Data Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163 Virginie Terraza and Carole Toque Grey Incidence Analysis as a Tool in Portfolio Selection . . . . . . . . . . . . . . . . . . . . 189 Tihana Škrinjari´c Investors’ Heterogeneity and Interactions: Toward New Modeling Tools . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 235 Souhir Masmoudi and Hela Namouri On the Underestimation of Risk in Hedge Fund Performance Persistence: Geolocation and Investment Strategy Effects . . . . . . . . . . . . . . . . . . 265 William Joseph Klubinski and Thanos Verousis Equal or Value Weighting? Implications for Asset-Pricing Tests . . . . . . . . . . . 295 Yuliya Plyakha, Raman Uppal, and Grigory Vilkov

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Contents

Bank Failure Prediction: A Comparison of Machine Learning Approaches . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 349 Georgios Manthoulis, Michalis Doumpos, Constantin Zopounidis, Emilios Galariotis, and George Baourakis From Calendar to Economic Time. Deciphering the Arrival of Events in Irregularly Spaced Time . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 367 Kalaitzoglou Iordanis Climate Change and Financial Risk . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 393 Hugues Chenet The Curious Case of Herding: Theories and Risk. . . . . . . . . . . . . . . . . . . . . . . . . . . . 421 Tselika Maria Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 471

Corporate Risk Management and Hedge Accounting Under the Scope of IFRS 9 Yves Rannou and Pascal Barneto

1 Introduction An important function of a corporate treasury is to protect the value generated from the underlying business against external market forces such as commodity price fluctuations, changes in the interest rates and in the exchange rates. In practice, corporates implement hedging strategies with the objective of protection of both cash flow margins and earnings against volatility of commodity prices, interest rates and foreign exchange rates. While corporates use derivatives instruments to hedge their economic exposures, they generally seek to apply the hedge accounting. Without this treatment, derivatives gains or losses associated with the risk to be hedged may significantly affect corporate earnings. The resulting income volatility reduces the utility of hedging in terms of risk reduction. Fortunately, under IFRS, IFRS 9 ‘Financial Instruments’ issued by the International Accounting Standards

Corrigendum We are grateful to participants and reviewers of the 34th International Conference of the French Finance Association and the 39th Annual Conference of the French Accounting Association for helpful comments and discussions. Special thanks are addressed to Professor Pascal Dumontier and Professor Bernard Raffournier for their suggestions on the earlier versions of this chapter. All remaining errors are our own. Y. Rannou () ESC Clermont Business School, CleRMa Laboratory, Clermont-Ferrand, France e-mail: [email protected] P. Barneto University of Bordeaux, IRGO Laboratory, Bordeaux, France e-mail: [email protected] © Springer Nature Switzerland AG 2021 C. Zopounidis et al. (eds.), Financial Risk Management and Modeling, Risk, Systems and Decisions, https://doi.org/10.1007/978-3-030-66691-0_1

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Board (IASB) offers the possibility to reduce considerably this excess volatility.1 To qualify for hedge accounting, the derivative results must be ‘highly effective’ in offsetting the changes in fair value or cash flow associated with the risk being hedged, so hedge effectiveness tests for qualifying derivatives as hedging instruments must be carried out. The purpose of this chapter is twofold. Our first motivation is to show that the hedge accounting requirements of IFRS 9 are more appropriate for firms that use commodity derivatives and better aligned with their risk management objective than these of IAS 39. The World Federation of Exchanges (WFE) has recently estimated that the amount of exchange-traded commodity derivatives has increased fivefold over the past decade to reach 5.8 billion contracts in 2017 (WFE 2018). Similar to any other commodity derivatives traded in exchanges, European carbon futures are subject to vagaries posed by the timing of compliance events that cause high price volatility risks (Medina and Pardo 2013; Ibikunle et al. 2016). Also, carbon prices are influenced by the fuel-switching decisions of power firms (Chevallier 2012) that have the most important carbon emissions exposure to be hedged (Schopp and Neuhoff 2013). By bringing the amount of their hedging carbon costs on to their balance sheet, a connection between the amount of carbon emissions and their value has emerged (Lovell et al. 2013) but also with their financial performance (Qian and Schaltegger 2017). However, the absence of a commonly accepted accounting standard has led to the use of various methods to account for carbon hedging instruments (Haupt and Ismer 2013) and restrain the willingness of power firms to disclose them. If it raises concerns about the comparability of their financial statements, the ability to inform on their cost of complying with their objective of carbon emission reductions may also be hindered. Lovell et al. (2013) attribute this lack of transparency to a diversity in reporting practices used and to the difficulty in applying hedge accounting under IFRS. Because the adoption of hedge accounting remains optional with IFRS 9, corporates should assess the costs and benefits of its implementation. A first main benefit offered by IFRS 9 is the removal of the arbitrary 80–125% boundaries for hedge ratios. A second main benefit is the abandonment of retrospective tests to assess hedging effectiveness that were required by IAS 39.2 Instead, the hedge effectiveness tests are only prospective. A third main improvement is that IFRS 9 allows companies to maintain their hedges by means of rebalancing without discontinuing the hedging relationship as is the case with IAS 39, driven by the objective to enhance the linkages between hedge accounting and corporate 1 Banks are obliged to comply with IFRS 9 Financial Instruments’ that have came in force from January 1, 2018 while non-financial firms may adopt voluntarily IFRS 9 for reporting financial instruments. 2 The prospective (resp. retrospective) hedge effectiveness test is a forward-looking (resp. backward-looking) evaluation of whether or not the changes in the fair value or cash flows of the hedging item are expected to be highly effective in offsetting the changes in the fair value or cash flows of the hedged item over the term of the relationship (resp. since the date of designation).

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risk management activities.3 Rebalancing allows firms to refine their hedge ratio i.e. adjust the quantities of either the hedged item or the hedging instrument. Rebalancing is, thus, consistent with the objective of avoiding an imbalance in weightings at inception of the hedge and at each reporting date and on a significant change in circumstances, whichever comes first. In the view of these benefits, the Climate Disclosure Board and the International Energy Trading Association (2013) have called European emitting firms to apply the IFRS 9 requirements to account for carbon hedges without, however, giving specific guidance. In addition, the IASB has only provided very broad guidelines for measuring hedge effectiveness. In the absence of clear and precise guidance, non-financial firms and especially power firms are, however, expected to devise, apply and defend their own hedge effectiveness tests. To bridge this gap, relevant and easy to implement methodologies of hedge effectiveness assessment are presented in this chapter. The issue of measuring hedge effectiveness has been largely explored in the case of energy markets but to a lesser extent in carbon markets probably due to its newness. In a minimum variance framework, Feng et al. (2016) show that carbon hedging strategies are increasingly efficient even though optimal hedge ratios are estimated at lower levels compared to energy and more mature markets. By contrast, Fan et al. (2014) estimate optimal hedge ratios using European Allowances (EUAs) futures, with values ranging from 0.5 to 1.0 using a 1-year horizon, in line with estimations previously found for more mature financial markets. In terms of hedge effectiveness, they find that OLS carbon hedges often provide the greatest variance reduction in comparison to timevarying carbon hedges based on a GARCH structure (VECM-GARCH and CCC GARCH). In contrast, Philip and Shi (2016) provide evidence of the superiority of time-varying Markov regime switching (MRS-LR-DCC) hedge.4 In a Value at Risk (VaR) framework, Feng et al. (2012) use the Extreme Value Theory (EVT) to estimate optimal hedge ratios and to assess effectiveness of hedging strategies as Kleindorfer and Li (2011) recommend for power companies.5 Their results indicate that the EVT VaR is a more effective tool to evaluate the hedging effectiveness than the minimum variance reduction measure (Harris and Shen 2006). Building on this prior literature, we focus on proven empirical methods to estimate optimal hedge ratios and associated hedging effectiveness. For that purpose, we proceed in three steps. First, we consider that the large EU ETS companies use rollover strategies to cover their long-term hedging needs (Schopp and Neuhoff 2013) so that we choose 1-year hedging horizon as in Fan et al. (2013). Second, we estimate hedge ratios using two static models (OLS, VECM) and three time-varying 3 As

rebalancing does not result in de- (or -re) designation of a hedge when it changes, the hedging relationship is maintained while hedge ineffectiveness is recognised immediately before adjusting the hedge relationship. 4 The MRS-LR-DCC model leads to estimate a long run relationship between spot and futures prices and DCC-GARCH errors to connect to the idea of a disequilibrium measured by a lagged basis with this of uncertainty modelled by DCC-GARCH, across market regimes. 5 Kleindorfer and Li (2011) model portfolio strategies of power firms that choose a portfolio of electricity and carbon derivatives to maximise their expected profit under the constraint of minimizing its VaR exposure.

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models (VECM-GARCH and VECM-GJR GARCH). Our results indicate that hedge ratios sometimes fall outside the range of 80–125% especially for hedging strategies based on CER derivatives. Third, we propose two optimisation methods to estimate hedge effectiveness: variance reduction (Ederington 1979) and the VaR measure (Harris and Shen 2006). We find that time-varying VECM-GJR GARCH hedges deliver superior hedging effectiveness in terms of variance reduction and of VaR reduction for both EUA and CER derivatives. Interestingly, these time-varying ratios may be used to rebalance carbon hedges and more generally to rebalance commodity hedges. Whichever IAS 39 or IFRS 9 rules for hedge accounting are applied by nonfinancial firms, they must follow the disclosure requirements of IFRS 7. These disclosures must provide detailed information about: (i) the risk management strategy of a given corporate and its style of managing risks; (ii) how its hedges can influence the amount, timing and uncertainty of its future cash flows; (iii) the effect that hedge accounting has had on its financial statements. In this respect, the second objective of this chapter is to give operating guidelines to disclose cash flow hedges involving commodity derivatives into financial statements. For that purpose, we propose a case study that illustrates how a given power company can use IFRS 7 formatted presentations to disclose a cash flow hedge that involves carbon futures in its financial statements provided that the IFRS 9 requirements have been met. The remainder of the chapter is organised as follows. Section 2 describes the hedge accounting requirements of IFRS 9 and its main advances from the perspective of non-financial firms. Next, proven methodologies to estimate static or time-varying hedge ratios and associated hedge effectiveness tests are outlined in Sect. 3. Section 4 is devoted to the presentation of a case study that explains how a carbon hedge qualified under IFRS 9 must be disclosed in the financial statements according to IFRS 7. Section 5 concludes.

2 Hedge Accounting with IFRS 9 and Corporate Risk Management: Toward a Greater Alignment If researchers tend to emphasise the economic rather than the accounting perspective in the context of hedging on futures markets, we focus, in this section, on the advances of IFRS 9 Financial Instruments to account for commodity hedges including derivatives.

2.1 Accounting for Financial Instruments with IFRS 9: Background Information The IASB issued an Exposure Draft (ED) Hedge Accounting in December 2010, which contains the proposals for the third part of IFRS 9 Financial instruments that replaces IAS 39 Financial instruments: Recognition and Measurement (IASB 2010). On 19 November 2013, after receiving comments on the ED, the IASB

Corporate Risk Management and Hedge Accounting Under the Scope of IFRS 9

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issued a new version of IFRS 9 Financial Instruments: Hedge Accounting and amendments to IFRS 9, IFRS 7 and IAS 39 (IASB 2013), which introduces a new hedge accounting model, with the aim at providing relevant information about risk management activities using financial instruments. Interestingly, most significant benefits may be realised by non-financial firms since hedge accounting will now be permitted for components of non-financial items such as commodities, provided certain criteria can be satisfied. But a first question has to be answered: why do firms apply hedge accounting? Under IFRS, standard derivative accounting rules imply that changes in the derivative’s value are reported in the Profit and Loss account (P&L) between the purchase date and the date of the future cash flow. Because the hedging instrument and the hedged item may be recognised in different reporting periods, the application of fair value measurement could induce a significant P&L mismatch between the hedging instrument and the hedged item. Hedge accounting may significantly reduce a such mismatch by considering both the hedging instrument and the hedged item as a single item. Thus, the gains and losses from the hedged item and the hedging instrument are reported in the same period so that the changes in their valuation are offset, leading to reduce corporates’ earnings volatility. Figure 1 displays the sequence of all steps required by IFRS 9 for designating a hedging relationship that consists of eligible hedging instruments (i.e. derivatives) and eligible hedged items (i.e. underlyings). Unlike IAS 39, IFRS 9 proposes three types of hedging relationships: a fair value hedge, a cash flow hedge or a hedge of a net investment in a foreign operation. To be qualified for hedge accounting, the hedging relationship must meet all of these requirements: • There is an economic relationship between the hedged item and the hedging instrument; • Companies must provide a formal designation and documentation on the hedging relationship at inception of the hedging relationship. • The value changes related to this economic relationship that could impact both the hedging instrument and the hedged item are not dominated by the credit risk effect;6 • The hedge ratio of the hedging relationship resulting from the quantity of hedged item actually hedged is identical to this resulting from the quantity of the hedging instrument used by the firm actually to hedge the quantity of the hedged item. The first requirement implies that the hedging instrument and the hedged item should move in opposite directions as a result of a variation in the hedged risk. When the critical terms of the hedging instrument and hedged item are not closely aligned, which is often the case for commodities, IFRS 9 suggests that “it might only be possible for an entity to conclude [that there is an economic relationship] on the basis of a quantitative assessment.” If IFRS 9 does not specify a method

6 The

risk.

credit risk can take the form of either the counterparty’s credit risk or the company’ credit

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Define the risk management strategy of the firms and its objectives.

Identify eligible hedged item(s) and eligible hedging instruments

No Is there an economic relationship between hedged item and hedging instrument?

Yes Yes

Is the effect of the credit risk superior to the fair value changes?

No Compute the hedge ratio with the actual quantities used for risk management

To avoid hedge ineffectiveness, the hedge ratio may differ from this used in risk management.

Yes

Does the hedge ratio reflect an imbalance that would create hedge effectiveness?

Formal designation of the hedging relationship and hedge documentation.

Fig. 1 Achieving hedge accounting under the scope of IFRS 9

for quantitative assessment, a possible method is a statistical (regression) analysis in order to obtain a suitable hedge ratio. The third requirement is that this hedge ratio, which is the ratio between the amount of hedged item and the amount of hedging instrument used for hedge accounting shall be identical to this used for risk management objectives.7 Like in IAS 39, the decision to apply hedge accounting remains optional for nonfinancial firms so that their management should consider the costs and benefits when deciding whether or not to use it. For instance, power firms will have to consider their commodity hedging activities and existing hedge accounting or why hedge accounting has not been achieved in the past in order to assess the benefits of the IFRS 9 requirements. This assessment encompasses operational aspects (such as the hedge effectiveness test) as well as the eligibility of items (such as risk components of non-financial items) that can be designated in hedging relationships.

7 For a hedging relationship with a correlation between the hedged item and the hedging instrument

that differs from the 1:1 relationship, risk managers will generally adjust the hedge ratio to improve its effectiveness.

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Table 1 Advantages and disadvantages of IFRS 9 hedge accounting requirements Advantages More opportunities to use hedge accounting: Ability to designate non-financial risk components to be hedged More flexibility to hedge group of items

Disadvantages Impossible to discontinue hedge accounting on a voluntary basis Need to rebalance continuously the hedge ratio when hedge effectiveness is too low; Cost and effort of measuring hedge effectiveness can remain important for small and mid-sized companies (albeit reduced)

Increase ability to hedge items Reduction of costs and effort to assess hedge effectiveness through the abandonment of the 80–125% retrospective tests. Introduction of fair value option for credit risk (removes accounting mismatch); New accounting treatments of time value of options and futures/forward contracts reduce the income statement volatility.

Table 1 stresses the advantages and drawbacks of the IFRS 9 principles against IAS 39 rules in terms of hedge accounting. In a preliminary study, Onali and Ginesti (2014) show that if most of IFRS non-financial firms welcome IFRS 9 improvements, they also expect that the use of hedge accounting will be extended to non-financial items including commodities. Quite importantly, IAS 39 requires that the hedge relationship must meet the 80–125% quantitative threshold both retrospectively and prospectively. This requirement is operationally onerous and prevents many economic hedging relationships from qualifying for hedge accounting. Conversely, IFRS 9 only requires prospective hedge effectiveness tests and removes the 80–125% threshold for hedge ratios. Moreover, the firm’s risk management strategy and its objective are more important under IFRS 9 because of the effect on discontinuation of hedge accounting and the hedge accounting related disclosures. IFRS 9 necessitates the documentation of both hedge ratio and potential sources of ineffectiveness. For instance, companies must report 25% of ineffectiveness in P&L if the hedge was 75% effective at the end of a reporting period. To avoid discontinuation, IFRS 9 allows companies to rebalance i.e. to refine their hedge ratio in order to reduce this source of ineffectiveness due to changes in the relationship between the hedged item and the hedging instrument. Rebalancing can be achieved by: (i) increasing (or decreasing) the volume of the hedged item or (ii) increasing (or decreasing) the volume of the hedging instrument. In the view of the advances made by IFRS 9, Kawaller (2015) argues that the hedging part of IFRS 9 is a more ambitious and less prescriptive approach than of its US GAAP equivalent: FAS 133. First, IFRS 9 allows benchmark hedging for commodities as well as for interest rates. Therefore, if a commodity price is tied to a benchmark price and if the derivative depends on this benchmark price,

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the hedge may be expected to perform with zero ineffectiveness. Second, IFRS removes the 80–125% threshold for qualifying hedge relationships. By contrast, FAS 133 imposes that the hedging strategy must be “highly effective” meaning that the hedge ratio must fall within the boundaries of 80–125%, otherwise this precludes hedge accounting in that period. Third, FAS 133 imposes a repetition of prospective effectiveness tests at least on a quarterly basis whereas IFRS 9 only enforces a prospective test that must be conducted at the start of the hedge relationship and on an ongoing basis. Fourth, retrospective tests of hedge effectiveness are required under FAS 133, while they are abandoned in IFRS 9. For all of these reasons, the application of the more liberal IFRS 9 model is expected to boost the use of hedge accounting by non-financial firms using financial instruments such as commodity derivatives (see also Onali and Ginesti 2014).8

2.2 Accounting for Financial Instruments with IFRS 9: The Case of Carbon Derivatives Accounting for financial instruments has been subject to much controversy in terms of accounting commodity derivatives including energy derivatives held for hedging purposes (Lopes 2007). More especially, the case of European carbon derivatives is an enlightening example of the difficulty to adopt a commonly international standard for hedge accounting. In January 2005, the advent of the EU Emission Trading Scheme (EU ETS) introduced European Allowances (EUAs) as a new class of financial assets (Medina and Pardo 2013). All combustion installations exceeding 20 MW are affected by the EU ETS including different kinds of industries like metal, cement, paper, glass, etc., as well as refineries or coke ovens. In total, the EU-ETS system comprises 13,000 installations responsible for approximately 45% of EU’s CO2 emissions and has given birth to the world’s largest GHG emissions trading system. Each EU Member States proposes a National Allocation Plan (NAP) including caps on greenhouse gas emissions for power plants and other large point sources that are then approved by the European Commission (EC hereafter). The EC evaluate and decide whether such NAP is or is not in line with what each Member State is expected to comply with. If the answer is positive, Member States are in charge of allocating the number of European Allowances (EUAs) among the installations involved. In the Phase I (2005–2007) and Phase II (2008–2012) of EU ETS, EUAs were granted free of charge for 98% of the total volume. Phase III (2013–2020) introduces the purchases of EUAs by means of auctions. On average, 20% of EUAs have been auctioned in 2013 with a gradual rise to 70% in 2020. The EU ETS forces companies to hold an adequate number of EUAs according to their carbon dioxide output. Failure

8 The

FASB considers a hedge relationship, which is rebalanced as a new relationship that implies a fresh start to hedge documentation and hedge effectiveness assessment.

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to submit a sufficient amount of allowances resulted in sanction payments of 100 EUR per missing ton of CO2 allowances in Phases II and III. Therefore, EU ETS companies develop dedicated risk management strategies to hedge against both the risks of sanction payments and of higher prices when they have to purchase additional EUAs if their carbon emissions are more than expected. Whilst the EU ETS represents the most important tool to meet Kyoto obligations, other measures built around the ‘Clean Development Mechanism (CDM) have emerged. This mechanism allows EU ETS companies to earn ‘Certified Emissions Reductions’ (CERs) when they invest in low-carbon intensive projects. Each CER represents a successful emission reduction of one tonne of CO2 . With a limit of 13.4% of annual volume on average, CERs can be converted in EUAs by companies for compliance purposes (Trotignon and Leguet 2009). The emergence of EU ETS and CDM has given birth to a new class of traders since EUA and CER assets and related derivatives may be used for both hedging and speculative purposes (Berta et al. 2017).9 They can trade either EUA and CER spot or derivatives contracts including futures, OTC forwards and options on dedicated exchanges like the European Climate Exchange (ECX). If 75% of EUA and CER trades are futures in Phase II, ECX monopolises the EU-ETS exchange-based carbon trading with 92% market share (Ibikunle et al. 2016). Carbon traders prefer to hold long futures positions to hedge their long-term commitment to purchase EUAs especially in Phase III (Trück et al. 2016). They notably focus their attention on the December maturity representing 76% of the futures contracts traded on ECX from 2009 (Ibikunle et al. 2016). Kalaitzoglou and Ibrahim (2013) point out that OTC EUA forwards are fewer than EUA futures but with a larger size indicating a high proportion of informed traders. Similarly, Medina et al. (2013) estimate a large concentration of informed trading in the CER futures market. They also show that the contribution of CER futures to price discovery is overly large in Phase II of EU ETS given their share in trading volume in comparison to EUA futures. In 2004, the International Financial Reporting Interpretations Committee (IFRIC) released an interpretation dealing with accounting for Emission Rights (IFRIC 3 ‘Emissions Rights’). Nonetheless, IFRIC 3 was unable to address the accounting issues for EUAs held by non-EU ETS firms for investment and speculative reasons. Besides, IFRIC 3 proposes any guidance on the accounting treatment of carbon derivatives as part of hedging strategies (Haupt and Ismer 2013). One year after its release, IFRIC 3 was withdrawn further to a negative notice of EFRAG (EFRAG 2005) and complaints of numerous EU ETS firms, leaving a gap in international accounting standards to report carbon assets and derivatives (Lovell et al. 2013). 9 Berta

et al. (2017) show that the distinction between hedging and speculation is irrelevant in the case of carbon derivatives. Every hedging position of EU ETS companies requires a speculative position to bear the risk as a counterparty; so every hedging transaction is simultaneously a speculative one. While speculation is regarded as necessary to help firms to hedge against price volatility, speculation creates price volatility. Accordingly, we consider that both hedging and speculative derivatives trades as financial instruments.

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Y. Rannou and P. Barneto

Interestingly, to better control the increasing financialization of the EU ETS, the EC has included both EUA and CER derivatives in the revised MiFID Directive voted on 20 October 2011 (Rannou and Barneto 2016), so that they are now classified as financial instruments. In the absence of a commonly accepted accounting standard, a survey of the International Energy Trading Association (IETA) (2007) indicated that 53% of respondents deem the EUA and CER derivatives to be within scope of IAS 39 Financial Instruments and 47% either fair value the contracts through the income statement or fair value through reserves. Since the own use exemption (under IAS 39) was rarely applied in the case of EUA and CER derivatives, Haupt and Ismer (2013) argue that the cash flow hedge accounting regime of IFRS 9 should be adequate to account for carbon hedges involving those derivatives. Accordingly, changes in the fair value of EUA and CER derivatives used for compliance purposes will be recorded as adjustments to a cash flow hedging reserve on the balance sheet and do not affect profits until the hedged transactions are recorded in the P&L through the OCI. In contrast, EUA and CER derivatives that companies held for trading purposes should be directly accounted for in P&L.

3 Methodology 3.1 Assessment of Hedging Needs of EU ETS Power Firms Given the newness of the EU ETS, it is not surprising to see that research on carbon futures market has started to focus on its relationship with energy related markets. Based on a CAPM framework, Chevallier (2012) show that introducing EUA and CER futures leads to reduce the idiosyncratic risk of a portfolio including energy (natural gas and coal), weather, bonds but not its systematic risk due to the dependency of all these assets to macroeconomic shocks since the advent of financial crisis in 2008. Unlike other energy markets that are directly affected by macroeconomic conditions, volatility risk factors on the carbon market are also closely related to the fuel-switching behaviour of power firms (Bangzhu and Chevallier 2017). Among the nine industrial sectors covered by the EU ETS, the sector ‘combustion’ where power firms are included provides the largest source of carbon emissions.10 Table 2 gives an overview of the annual EUA shortages of the ‘combustion’ sector splitted by EU Member States. Overall, these annual EUA shortages to be covered by 6,591 installations that belong to the sector ‘combustion’

10 The

nine sectors covered by the EU ETS are the following: combustion, cement, ceramics, coke ovens, glass, iron and steel, metal ore, paper and board, refineries. Power firms that hold individual factories and cogeneration plants belong to the ‘combustion’ sector.

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11

Table 2 Theoretical carbon hedging needs of the power sector per country (in volume and in value)

PHASE II (2008-12) Country Austria Belgium Bulgaria Croatia Czech Republic Denmark Estonia Finland France Germany Greece Hungary Ireland Italy Latvia Lithuania Luxembourg Netherlands Poland Portugal Romania Slovakia Slovenia Spain Sweden United Kingdom

Total

Number of Annual volume installations (in million tC02eq) 99 0.064 217 4.444 70 (0.209) 25 N/A 166 (6.033) 335 0.308 42 0.508 121 (0.545) 816 9.869 1,117 90.557 63 3.952 140 0.275 93 (1.046) 270 1.897 8 (0.053) 83 (1.163) 12 (0.155) 287 5.255 487 (1.234) 97 (2.170) 138 (7.191) 119 (7.242) 47 0.162 497 10.898 690 3.554 551 16.249

6,591

120.951

PHASE III (2013-15)

Annual value (in € million) 0.908 62.21 Long Position N/A Long Position 4.314 7.122 Long Position 138.165 1 267.795 55.34 3.845 Long Position 26.564 Long Position Long Position Long Position 73.57 Long Position Long Position Long Position Long Position 2.262 152.573 49.763 227.484

Annual volume (in million tC02eq) 4.071 12.211 16.299 2.793 21.829 7.822 6.734 2.761 25.004 309.213 38.001 8.839 11.839 18.751 (0.028) (0.671) 0.293 44.039 93.827 14.153 11.163 6.276 4.432 66.51 (1.923) 78.64

1 416.981

802.878

Annual value (in € million) 28.497 85.474 114.095 19.551 152.807 54.751 47.136 19.325 175.025 2 164.489 266.009 61.87 82.875 131.257 Long Position Long Position 2.049 308.277 656.788 99.073 78.143 43.933 31.024 465.546 Long Position 550.467

5 638.461

Note: ‘Long Position’ indicates that the company has a theoretical surplus of EUAs to cover their emissions. If not, the country has a ‘short position’ and figures express a negative difference between the amount of EUAs/CERs held and this of verified emissions observed. ‘N/A’ means that data are not available

has increased sevenfold (resp. fourfold) in volume (resp. in value) from Phase II to Phase III (2013–2015).11 An exhaustive research from the 6,591 installations to estimate their own hedging needs is a very difficult challenge, if not impossible (Lovell et al. 2013). For this reason, we constitute a panel of the 19 most representative European power 11 The

economic crisis, which reduced carbon emissions more than anticipated and high imports of CERs, has generated a 2 billion surplus of EUAs at the end of 2014. This has led a significant fall in carbon prices. In July 2015, the EC has decided to postpone the auctioning of 500 million EUAs in 2016 and 2017. Given that this decision reduces drastically the volume of EUAs auctioned, the spot (auction) EUA market becomes much less liquid than previously and EUA spot prices become artificially much more volatile. Therefore, the variance of spot (unhedged) and futures (hedged) EUA portfolio that we estimate would have been necessarily affected after 2015. In this respect, we have considered the period 2013–2015 in order to study the carbon hedging strategies in Phase III given a EUA spot market offering comparable conditions of liquidity and price volatility.

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Table 3 Theoretical carbon hedging needs of the most representative power companies (in value) COMPANY BEH BRITISH ENERGY CEZ DRAX EAST ENERGIA EDF EDP EDISON ENDESA ENEL EON ESSENT GROSSKRAFT WERK IBERDROLA NUON PPC PGE RWE TAURON

Hedging needs averaged Hedging needs averaged Number of over the period 2008-121 over the period 2013-152 installations (in € million) (in € million) Bulgaria 11 23.472 117.707 United Kingdom 11 100.270 128.869 Long Position 117.478 Czech Republic 19 United Kingdom 7 171.354 104.258 Italy 1 0.237 0.199 France 52 25.042 181.456 Spain 1 6.637 2.279 Italy 14 17.880 31.390 Spain 16 83.511 162.585 Italy 36 69.125 256.520 Germany 85 34.976 0.904 Netherlands 11 3.100 48.074 Germany 1 8.112 44.127 Spain 18 13.419 15.329 Netherlands 16 62.443 72.997 Long Position Long Position Slovakia 2 Poland 11 69.690 397.002 Germany 51 684.947 852.473 Poland 15 6.317 100.963 Country

Average annual value of hedging needs per company 1,117

81.208

146.367

Δ +401% +29% N/S -39% -16% +625% -66% +76% +95% +271% -97% +1451% +444% +14% +17% N/S +470% +24% +1498% +80.2%

Note: ‘Long Position’ indicates that the company has a theoretical surplus of EUAs to cover their emissions. If not, the company has a ‘short position’ and figures express a negative difference between the amount of EUAs/CERs held and this of verified emissions observed. ‘N/S’ means Non Significant, ‘N/A’ means that data are not available a The amount of hedging needs has been estimated on the basis of a mean spot price of A C14 per missing EUA (=1tC02eq ) b The amount of hedging needs has been estimated on the basis of a mean spot price of A C7 per missing EUA (=1tC02eq )

companies which mimics this of Lovell et al. (2013). We then proceed in two steps to estimate their respective carbon hedging needs. First, we use the database of the European Union International Transaction Log (EU ITL) to identify installations and their corresponding amounts of emissions and EUAs granted. Second, since the EU ITL provides only details of installations, and not EU ETS company data, we undertake a matching of installations by Internet searches to the 19 power companies. As a result of our searches, we find that these 19 companies collectively own 378 installations in the period 2008–2015. Third, we follow the methodology of Berta et al. (2017)12 to estimate their theoretical hedging needs. For each installation, we compute the difference between allocation of EUAs and verified emissions recorded in April the following year. These positions, when installations are ‘short’ i.e. have negative difference (resp. ‘long’ i.e. have positive difference), are aggregated to calculate the overall shortage (surplus) for all of the power companies. Table 3 presents a snapshot of theoretical hedging needs estimated for the 19 representative power companies. We calculate these hedging needs by subtracting the number of EUAs and CERs that have been surrendered back by companies to 12 We

follow the rules applied by Berta et al. (2017) to correct missing data related to verified emissions and new entrants when it impacts the short positions of installations. See Berta et al. (2017) for more details.

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the amount of verified emissions emitted by companies. We observe a noticeable change from Phase II, where two firms (CEZ and PPC) were long of quotas (number of EUAs and CERs held by annual year exceed the amount of yearly verified emissions), while in Phase III, there is only one (PPC) In fact, power firms need to purchase EUAs by auctions in Phase III (2013–2020) rather being granted freely as in Phase II (2008–2012). Based on an average carbon price of 14 Euros per tC02 eq. in Phase II, our calculation gives an annual average amount of 81.207 million euros per company that needs to be hedged. Given an average carbon price of 7 euros per tC02 eq. along the period 2013–2015, we obtain an annual average amount of 146.367 million euros per company that is required to be hedged. These two observations provide clear evidence on the necessity for these 19 representative power companies to carry out effective hedging strategies through the use of EUA and CER derivatives, which calls into question whether or not they could apply the IFRS 9 hedge accounting framework to report them.

3.2 Hedge Ratio Estimation Our empirical work consists of first estimating optimal hedge ratios using daily returns and then assessing hedging effectiveness based on these hedge ratios. We consider that the optimal hedge ratio is the number of futures per unit of the spot minimizing the variance of the hedged portfolio returns (see e.g., Ederington 1979; Fan et al. 2013, 2014). In order to estimate optimal hedge ratios, we use EUA and CER daily futures prices traded on ICE-ECX, Bluenext spot prices for the period: 2008–2012 and EEX auction spot prices for the period: 2013–2015.13 Panels A and B of Table 4 display the basic properties of the EUA and CER spot or futures continuously compounded rate of returns (first difference) averaged for the Phase II and Phase III (2013–2015). The variance of the EUA futures returns is lower than that of the CER futures returns, resulting in lower volatility of price risks. The skewness of the EUA (resp. CER) futures returns is −0.282 (resp. -0.216) reflecting a clear left-side feature. The kurtosis of the EUA (resp. CER) futures returns is on average 5.181 (resp. 5.611) higher than 3, indicating a clear departure from the normal distribution that is confirmed by the Jarque Bera tests. We then examine the possibility of cointegration between spot and futures price series.14 As shown in Panels A and B of Table 5, the assumption of no cointegration for both EUA and CER markets is rejected according to the Johansen trace test statistics. Looking at the estimated cointegrating vectors, we observe a long run 13 Since

Bluenext closed their activities in December 2012, we use EEX spot prices between 2013 and 2015. 14 Before using the Johansen trace test for detecting cointegration, we apply the Augmented Dickey-Fuller and Phillips-Perron unit root tests to all series. The results show that the series have a stochastic trend in their univariate time-series presentations (non-stationary), while first differences are stationary.

Mean Median Max. Min. Panel A: EUA (average continuously compounded rate of returns: spot and futures) Bluenext Spot (2008–2012) −0.0042 −0.0041 0.7462 −0.4113 EEX Auction Spot (2013–2015) 0.0012 0.0011 0.7506 −0.3303 ECX December Futures −0.0039 −0.0033 0.7784 −0.3424 Panel B: CER (average continuously compounded rate of returns: spot and futures) Bluenext Spot (2009–2013) −0.0041 −0.0043 0.8453 −0.4215 EEX Auction Spot (2013–2015) −0.0019 −0.002 0.6871 −0.3875 ECX December Futures −0.044 −0.0034 0.86 −0.0117

Table 4 Descriptive statistics of the EUA and the CER spot and futures series Kurtosis 4.736 6.355 5.181 5.339 6.012 5.611

Skewness −0.402 −0.531 −0.282 −0.424 −0.497 −0.316

St. Dev. 0.215 0.266 0.194 0.423 0.398 0.233

13.04 14.91 8.85

11.89 15.21 8.16

Jarque-Bera

0.000 0.000 0.008

0.000 0.000 0.01

Prob.

14 Y. Rannou and P. Barneto

Normalized Cointegrating Vectors (α; β) Futures (α = −0,239*; β = 1000) Spot (α = −0,109; β = 1003*) Futures (α = −0,206*; β = 1000) Spot (α = −0,092; β = 1002*) Futures (α = −0,210*; β = 1000) Spot (α = −0,095; β = 1002*) Futures (α = 0,160; β = 1000) Spot (α = 0,084; β = −1023*)

Trace 223.55* 3.855* 181.22* 3.647* 183.70* 3.288* 141.19* 1.747

Note: We apply the Schwartz Information Criterion (SIC) to select optimal ‘Lag’ length of the unrestricted VAR model in levels. The null hypothesis (H0 ) of trace statistics tests if the number of cointegrating vectors is less than or equal to r α, β are the normalized cointegration vector of spot and futures price series.* Indicates if they are significant at the 95% confidence level based on the calculated p-values

H0 H1 VAR lag Panel A: EUA (average Phase II: 2008–2012 and average Phase III: 2013–2015) Spot/Futures Phase II (2008–12) r=0 r>0 2 r≤1 r>1 Spot/Futures Phase III (2013–15) r=0 r>0 2 r≤1 r>1 Panel B: CER (average Phase II: 2009–2012 and average Phase III: 2013–2015) Spot/Futures Phase II (2009–12) r=0 r>0 2 r≤1 r>1 Spot/Futures Phase III (2013–15) r=0 r>0 2 r≤1 r>1

Table 5 Cointegration tests of spot and futures price series

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Y. Rannou and P. Barneto

relationship between spot and futures series showing that futures prices contains information that can help predict the spot prices. The β estimates inform whether spot and futures price series are nearly equal over time and the basis adjustments of substitutes. When cointegration exists, the vector of adjustment coefficients α informs how quickly the EUA or CER markets adjust. Overall, we confirm the findings of Fan et al. (2014) and Bangzhu and Chevallier (2017). Bangzhu and Chevallier (2017) detect cointegration among Bluenext spot and ECX December futures over the period January 2008–April 2009. Fan et al. (2013) also find cointegration between Bluenext spot and ECX futures in Phase II for CER markets. There are two broad categories of hedge ratios that we have considered: static (or time-invariant) and time-varying. A static hedging ratio implies that once the optimal hedging ratio is defined, the position in the futures market is constant until the end of the hedging period. A time-varying ratio may be used for the purpose of rebalancing allowed by IFRS 9, which consists of adjusting the designated quantities of either the hedged item or the hedging instrument.15 Few attempts to estimate hedge ratio have been made in the European carbon market to the noticeable exception of Fan et al. (2013) that have calculated hedge ratios and their respective performance for CER markets from 2008 to 2010. Before estimating hedge ratios, we have taken some of the EU ETS specificities into account. First, in Phase II of EU ETS, we have considered the spot contract traded on Bluenext as a proxy of the hedged instruments for the Phase II (2008–2012) during which EUAs were almost freely allocated. In Phase III, where an increasing proportion of EUAs (from 30% in 2013 to 100% in 2020) are purchased by auctions, we have studied the most liquid auction spot contract traded at EEX as a proxy of the hedged instrument since Bluenext has closed its activities in December 2012. Second, we have assumed that power companies may use either the front or the second nearest EUA (resp. CER) December futures traded on ECX to hedge their spot market positions. Indeed, the results of Lucia et al. (2015) suggest that the hedging demand dominates the activity of the second nearest December futures more than this of the front December futures due to the fact that speculative activity occurs mainly in the front contract. Third, we have considered that power firms trade EUA (resp. CER) December futures expiring at the end of the year to hedge against the price risk of buying EUA (resp. CER) on the spot market. This framework is consistent with the rollover hedging strategies of power firms (Schopp and Neuhoff 2013)16 and convenient from a reporting perspective as emissions are counted on the calendar year basis. Finally, we have supposed no daily marking-to market, so the different estimated hedge ratios via two time-invariant (naïve, OLS and 15 If

the position taken in the EUA or CER futures changes over time, the hedging strategy is dynamic implying that the optimal hedge ratio is time-varying and the position in the futures market continuously rebalanced. 16 After interviewing 13 experts and managers of power companies, Schopp and Neuhoff (2013) conclude that annual rollover strategies are largely employed to hedge long-term commitment through the purchase of EUA December futures on annual basis.

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17

VECM) methods and two time-varying methods (VECM GARCH and VECM GJRGARCH) are not tailed (see Fan et al. 2013).17

3.2.1

Static Hedging and Estimation of Time Invariant Hedge Ratios

The naïve model is used for comparison purposes due to its inability to be optimal. The naïve hedge ratio is always equal to one because each spot contract is offset by exactly one futures contract. We also run ordinary least squares (OLS) regression of the spot return on the futures return to obtain the slope coefficient that gives the value of a static optimal hedge ratio (Ederington 1979). Based on the continuously compounded rates of return of spot and futures price series respectively, we write the following OLS model: S t = α + β · F t + μt

(1)

Where: St and Ft is the continuously compounded rate of return of spot and (S t ,F t ) futures respectively, μt is the error term, β = COV is the minimum V AR(F t ) variance (optimal) hedge ratio. In the above OLS regression model, the arbitrage condition ties the spot and futures prices, so that they cannot drift far apart in the long run. Consequently, the OLS model is inappropriate because it ignores the existence of cointegration relationship between the spot and futures prices. Lien (2009) argues that the estimated hedge ratio will be smaller if the cointegration relationship is not taken into consideration. If spot and futures are co-integrated, an error correction term should be added to the OLS model. Thus, we consider an error correction model. First, the long-run co-integrating equation is specified as follows: St = β 0 + β 1 · Ft + εt where β1 is the co-integration vector, β0 is the constant term. Inserting the lagged regression residual from the cointegration equation into the VECM, we obtain: S t = δ10 + β11 · εˆ t−1 +

F t = δ20 + β21 · εˆ t−1 +

n 

γs1i · S t−j +

m 

j =1

i=1

n 

m 

j =1

γf 1i · S t−j +

γs2i · F t−i + μst

f

γf 1i · F t−i + μt

(2a)

(2b)

i=1 f

Where: δ10 and δ20 are intercepts, β11 and β21 are parameters, μst and μt are whitenoise disturbance terms. β•1 · εˆ t−1 , is the error correction term which measures how

17 Since

EUA and CER futures are affected by daily marking-to-market cash requirements, adjustments might be made as “tailing” the hedge. These adjustments reduce the size of hedge ratios especially for longer hedges.

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the dependent variable (in the vector) adjusts to previous long-term disequilibrium. The coefficients δ11 and δ21 is the speed of adjustment parameters. The more negative the δ11 or δ21 , the greater the response of S and F to β•1 · εˆ t−1 , the previous periods disequilibrium.

3.2.2

Dynamic Hedging and Estimation of Time Varying Hedge Ratios

OLS and VECM static hedge ratios assume the error term with a mean of zero and a time-invariant variance. For a sample of limited observations, Lien (2009) demonstrates that a sufficiently large variation in the conditional variance of the futures return favors the time-varying hedge ratio performance against this of static hedge ratio (OLS and VECM). Furthermore, Bangzhu and Chevallier (2017) emphasise on the importance of asymmetric volatility when they find negative leverage effects on the conditional volatility of EUA spot and futures between 2008 and 2009. Therefore, we consider two models which allows the second moment to be time-varying with symmetric effects (VECM GARCH model) and with asymmetric effects (VECM GJR GARCH model) on volatility. These two bivariate models require allowing the conditional variance-covariance matrix of the m-dimensional zero mean random variables εt , to depend on elements of the information set t-1 . Letting Ht , be measurable with respect to t-1 , we allow GARCH effects in the estimation of optimal hedge ratio through the following VECM GARCH (1,1) model as specified below: S t = α0 + β0 (S t−1 − λF t−1 ) + εs,t

(3a)

Ft = α1 + β1 (St−1 − λFt−1 ) + εf,t

(3b)

Where:     εs,t hss,t hsf,t |t−1 ∼ N (0, H t ) and H t = . εf,t hsf,t hff,t Ht is the 2 × 2 variance-covariance matrix, εft and εst are the vector of residuals of Eqs. (3a) and (3b) represent the residuals obtained from the spot and futures mean equations with conditional mean 0. The term (St − 1 − λFt − 1 ) is the error correction term that represents the cointegration between the spot (S) and futures (F) series with λ as the cointegration parameter. Then, we model the conditional covariance matrix Ht by using a BEKK parameterization to ensure a positive semi-definite conditional variance-covariance matrix in the optimisation process: a necessary condition for the estimated variance to be zero or positive. The BEKK parameterization for the VECM GARCH (1,1) model is the following:

Corporate Risk Management and Hedge Accounting Under the Scope of IFRS 9

H t =C  C+A H t−1 A+B  εt εt B

19

(4)

We thus expand Eq. (4) in the following manner:             b b b   h 2  hss,t   Css,t   a11 a12 a13   εs,t−1   11 12 13   ss,t−1          Ht =  hsf,t  =  Csf,t  +  a21 a22 a23  ·  εs,t−1 εf,t−1  +  b21 b22 b23  ·  hsf,t−1    h  C   a a a   ε2  b31 b32 b33   hff,t−1  ff,t ff,t 31 32 33 f,t−1 (5) Here, conditional variance and covariance only depend on their own lagged squared residuals and lagged values. We use the BHHH (Berndt, Hall, Hall, Hausman) algorithm to produce the maximum likelihood parameter estimates and their corresponding asymptotic standard errors. The symmetric VECM GARCH model incorporates a time-varying conditional covariance and variance between spot and futures prices generating more realistic time-varying hedge ratios. The time varying hedge ratio which is optimal at time t hsf,t is then equal to ht = hff,t . To allow for asymmetric effects of negative (εi, t < 0) and positive (εi, t ≥ 0) shocks on conditional variance, Glosten et al. (1993) introduced the asymmetric GJR GARCH presented below: 2 2 ht = ω + α1 εt−1 + β1 ht−1 + γ1 εt−1 I t−1

(6)

Where:

 I t−1 =

1, εi,t ≥ 0 1, εi,t < 0

 (7)

The short-run persistence of positive shocks is given by α1 and short-run persistence of negative shocks is given by α 1 (α 1 + γ 1 ). Further, the VECM GJR GARCH model differs from the VECM GARCH model since the Ht variance-covariance matrix (see Eq. 5) is replaced by: H t = C  C + A H t−1 A + B  εt εt B + G ηt−1  ηt−1

(8)

Where: Ht is a linear function of its own past values and values of squared shocks while ηt accounts for asymmetry in the conditional variances. A, B, and G are matrices of coefficients, ηt is the additional quadratic form of the vector of negative return shock. Parameter estimates of Eq. (8) are obtained by maximizing the below loglikelihood function: Lt ( ) = − log (2 ) −

1 1 log |H t | − et ( ) H t−1 ( ) et ( ) 2 2

(9)

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Y. Rannou and P. Barneto

Where: θ is the vector of all parameters, βij for i = EUA (resp. CER) spot and futures series, j = 1 or 2 whether it is variance or covariance respectively. In order to maximize this log-likelihood function, we use the simplex method and the BHHH algorithm. Then, we compute the optimal time-varying hedge ratio h* as the conditional covariance between spot and futures return divided by the conditional futures return variance. Finally, we calculate the time-varying ratio at hsf as made previously for the symmetric VECM GARCH (1,1) time t: h∗ = hff model.

3.3 Assessment of Hedging Effectiveness We use two risk measures to compare the effectiveness of the four above-mentioned hedge strategies. Since the basic motivation for hedging is to form a portfolio that reduces fluctuations in its value, the hedge is considered as effective as soon as a significant reduction in the portfolio variance is reported. In this respect, the first measure of hedging effectiveness used is based on the reduction in the variance of a hedged portfolio as compared with the variance of an unhedged portfolio (i.e. the unhedged spot return) (Ederington 1979). We begin by calculating the returns of hedged portfolios constructed from the four above mentioned models of hedge ratio estimation. The hedged portfolios are constructed every trading day and their respective returns (RH,t ) are given by: R H ,t = (S t ) − ht × (F t )

(10)

Where: ht denotes the hedge ratio estimated at the (trading) day t according to the four models (OLS, VECM, VECM GARCH, VECM GJR GARCH), Ft and St are the changes of futures and spot series at the day t respectively. We also construct unhedged portfolios every trading day and their respective returns (RU,t ) are therefore based on the daily spot changes. Then, we calculate the variance of the unhedged (RU,t ) and hedged (RH,t ) portfolios as below:  2 V AR R U ,t = σS,t

(11)

 2 2 + ht 2 · σF,t − 2ht · σSF,t V AR RH,t = σS,t

(12)

Where: σs and σF are the standard deviations of spot and futures changes at day t respectively, σ S, F, t the covariance of spot and futures changes at day t, ht is the hedge ratio estimated from the four models (OLS, VECM, VECM GARCH, VECM GJR GARCH) at day t. Intuitively, a smaller variance of the hedged portfolio VAR(RH,t ) indicates that the hedging strategy used is better.

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21

Next, we calculate the degree of hedging effectiveness (HE) as the percentage reduction in variance of the hedged and the unhedged portfolios as Ederington (1979) recommended: H E V AR

   V AR RU,t − V AR RH,t V AR RH,t   = =1− V AR RU,t V AR RU,t

(13)

HEVAR measures the relative reduction in variance gained by taking the optimal combined futures position (ht ) in this case. Put differently, HEVAR estimates the greatest degree of risk reduction attainable if ht is selected. However, it does not reveal the extent to which the user actually reduces risk toward the minimum achievable. The second hedging effectiveness measure that we have used is the Value at Risk (VaR) measure previously applied to the EUA Phase II futures by Philip and Shi (2016). In fact, Harris and Shen (2006) demonstrate that the minimum-variance hedging reduces the standard deviation of portfolio returns but also increases simultaneously the portfolio kurtosis and the effectiveness of hedging compared to VaR. Based on the demonstration made by Harris and Shen (2006), we employ the minimum-VaR measure that minimizes the historical VaR of the hedge portfolio as an alternative to the minimum-variance measure seen before. Assuming the hedged portfolio return is normally distributed, we write the VaR of the hedged portfolio at a confidence level α similar to Philip and Shi (2016) as below:  

  V aR = V0 × E RH,t + zα V AR RH,t (14) Where: V0 is the initial wealth of the portfolio (in Euros), E(RH,t ) is the expected return (or loss) of the hedged portfolio given a (variance) risk: VAR(RH,t ) and zα denotes the quantile of the normal distribution at α. Intuitively, a smaller VaR exposure of the hedge portfolio signals a better hedging strategy. In particular, we consider a portfolio with an initial value of 100 million euros and a 95% confidence level under which a power firm using carbon hedge strategies would expect losses in excess of the VaR to occur. In other words, VaR is the valueat-risk figure estimated with zα equals to the normal distribution 5% quantile value (consistent with a 95% confidence level). After proceeding similarly to calculate the VaR of the unhedged portfolio, we compute the percentage reduction in VaR that serves as a second measure of hedge effectiveness such that:    VaR RU,t − VaR RH,t VaR RH,t   HEVaR = =1− (15) VaR RU,t VaR RU,t

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Y. Rannou and P. Barneto

4 Empirical Results and Impact Assessment 4.1 Values of Hedging Ratios Table 6 presents the optimal hedge ratios that are estimated with the methods discussed above: naïve, OLS, VECM, VECM GARCH and VECM GJR GARCH using the front and the second nearest EUA or CER December futures contract. As can be seen from Panels A and B of Table 6, the estimated hedge ratios differ from year to year and from model to model both for the EUA and the CER markets. First, the value of hedge ratios for the VECM and VECM GARCH are very similar in most cases. This result is not surprising since these models share the same error correction fundamentals. Besides, the difference of values is greater once asymmetries in return distribution are taken into account with the GJR GARCH model. This difference may induce significant impact on hedge ratio performance assessment, as hedge ratios are important inputs for the hedging effectiveness estimation. Second, both time-invariant and time-varying hedge ratios diminish over the period 2013–2015 compared to Phase II (2008–2012). We can explain this result by the higher variance of EUA and CER futures price variations observed in Phase III.18 Interestingly, the significant variance of EUA and CER futures has led to lower the values of hedge ratios, which fall outside the range 80–125% required by IAS 39 from 2012. However, this authorised range does not exist in IFRS 9 and the hedge relationship could be verified provided that the economic justification is provided.

4.2 Results of Hedging Effectiveness Assessment In the view of a wide range of static and dynamic hedge ratios that power companies can apply, it is now important to assess their performance in terms of hedging effectiveness. Table 7 reports how effective Naïve, OLS, VECM, VECM-GARCH and VECM GJR GARCH models are in terms of variance or VaR reduction for EUA and CER front December futures.19 If all models achieve an important level of variance reduction, the VECM GJR GARCH outperforms the other models. Given the reaction of financial markets to news and the corresponding need to adjust offsetting hedges, this result appears to be obvious, consistent with Brooks et al. (2002)

18 Since

the optimal hedge ratio is obtained by dividing the covariance between spot and futures returns by the variance of the futures return, any impact on the variance of the futures returns will affect the value of hedge ratios. 19 The hedge effectiveness percentages estimated from the second nearest EUA and CER December futures are very similar to those estimated from the front EUA and CER December futures both in Phase II and III.

Corporate Risk Management and Hedge Accounting Under the Scope of IFRS 9

23

Table 6 Estimation results of optimal (minimum variance) hedge ratios Hedging VECM VECM GJR Horizon Contract Naïve (%) OLS (%) VECM (%) GARCH (%) GARCH (%) Panel A: Hedge ratios when EUA (resp. EUA futures) is the hedged item (resp. hedging instrument) 2008 Dec-08 100 82.28 82.27 82.18 82.11 Dec-09 100 76.34 77.87 78.18 78.09 2009 Dec-09 100 83.19 83.12 82.93 83.03 Dec-10 100 81.38 78.02 77.48 77.97 2010 Dec-10 100 81.21 81.57 81.54 81.51 Dec-11 100 79.67 79.18 79.59 79.03 2011 Dec-11 100 77.18 76.19 76.35 78.61 Dec-12 100 73.43 72.46 73.01 75.02 2012 Dec-12 100 76.54 75.34 76.88 78.97 Dec-13 100 72.98 72.35 72.76 74.55 2013 Dec-13 100 72.12 71.24 72.01 71.91 Dec-14 100 67.28 66.67 67.42 67.57 2014 Dec-14 100 68.31 66.92 66.95 67.06 Dec-15 100 66.78 66.11 66.78 66.89 2015 Dec-15 100 69.92 68.45 69.98 70.11 Dec-16 100 67.92 67.19 67.74 68.87 Panel B: Hedge ratios when CER (resp. CER futures) is the hedged item (resp. hedging instrument) 2009 Dec-09 100 82.34 82.27 82.25 82.31 Dec-10 100 75.67 75.94 76.02 76.67 2010 Dec-10 100 85.11 84.52 84.54 84.49 Dec-11 100 80.54 79.97 80.02 80.13 2011 Dec-11 100 79.18 79.03 79.01 78.71 Dec-12 100 75.56 75.90 76.28 76.12 2012 Dec-12 100 72.76 72.34 72.20 72.30 Dec-13 100 69.20 69.06 69.18 69.40 2013 Dec-13 100 70.87 70.76 70.83 71.25 Dec-14 100 67.75 67.45 67.58 68.16 2014 Dec-14 100 67.95 67.82 67.88 68.69 Dec-15 100 65.59 65.22 65.79 66.78 2015 Dec-15 100 67.89 67.98 67.69 68.02 Dec-16 100 65.74 66.11 65.90 66.57

who find that GARCH hedge models that consider asymmetries in returns (e.g., GJR GARCH) better perform when applied to commodity derivatives. Quite importantly, the measures of hedging effectiveness based on the reduction of variance (HEVAR ) exhibit a significantly declining trend from 2013 to 2015. For example, applying the VECM GJR GARCH model generates a risk reduction for the EUA portfolio of 94.28% reduction in 2013 compared to a 86.44% reduction in 2015. It is noteworthy that a similar declining trend is observed in CER markets in

OLS

VECM

0.0162

0.0094

0.0094

0.0087 88.68%

HEVAR

0.0041

0.0023

0.0064

0.0063

0.0062

0.0076

0.0074

74.18% 82.74% 82.76% 82.97%

0.0077

76.13% 84.35% 84.37% 84.60%

Dec-15 VAR Unhedged = 0.0435 0.0078

HEVAR

0.0022

77.26% 87.67% 88.08% 90.44%

Dec-14 VAR Unhedged = 0.0398 0.0065

HEVAR

0.003

75.90% 87.56% 90.99% 93.43%

Dec-13 VAR Unhedged = 0.0343 0.00505 0.0042

HEVAR

0.0041

86.44%

0.0079

86.68%

0.0059

92.71%

0.0025

94.28%

0.0021

91.85%

Dec-12 VAR Unhedged = 0.0332 0.004

HEVAR

79.54% 86.41% 86.78% 87.84%

0.0042 92.19%

0.0046 0.00425

0.0045

85.34% 89.40% 89.96% 91.29%

0.0048

0.0091

87.71%

0.0158

Dec-11 VAR Unhedged = 0.0349 0.00515 0.00475 0.00465 0.00467

HEVAR

0.0163

87.48% 88.25% 88.19% 89.07%

Dec-10 VAR Unhedged = 0.0448 0.0066

HEVAR

0.0164

85.91% 87.28% 87.12% 87.59%

Dec-09 VAR Unhedged = 0.0795 0.0104

HEVAR

Dec-08 VAR Unhedged = 0.1285 0.0171

HEVAR

0.0056

0.0059

0.0038

0.0032

0.0065

0.006

0.0056

0.0073

0.0071

0.0072

0.0077

0.0066

0.0061

0.0088

0.0073

70.12% 79.05% 81.33% 86.93%

0.0096

74.69% 83.89% 86.19% 87.24%

Dec-15 VAR Unhedged = 0.0482 0.0104

HEVAR

0.0055

81.65% 85.28% 85.69% 85.48%

Dec-14 VAR Unhedged = 0.0478 0.0081

HEVAR

0.0051

77.22% 82.98% 84.29% 85.34%

Dec-13 VAR Unhedged = 0.0496 0.0081

HEVAR

0.0103

83.02% 84.10% 89.76% 91.37%

Dec-12 VAR Unhedged = 0.0382 0.0067

HEVAR

0.011

83.41% 88.86% 87.99% 87.77%

Dec-11 VAR Unhedged = 0.0371 0.0063

HEVAR

0.0109

85.76% 86.56% 86.44% 87.30%

Dec-10 VAR Unhedged = 0.0458 0.0076

HEVAR

Dec-09 VAR Unhedged = 0.0811 0.0115

88.38%

0.0069

88.49%

0.0057

88.91%

0.0062

84.55%

0.0058

93.80%

0.0029

89.30%

0.0051

86.07%

0.0112

71.34% 77.01% 73.11% 77.98% 74.34% 76.30%

80.35% 73.94% 76.35% 74.40% 68.29% 66.30%

68.28%

897,202A C

69.67%

867,746A C

75.38%

609,995A C

77.24%

538,423A C

74.62%

665,156A C

80.65%

67.99%

905,401A C

69.78%

864,601A C

74.25%

637,988A C

77.67%

528,244A C

75.06%

653,623A C

78.93%

559,662A C

78.63%

516,027A C

81.46%

412,008A C

76.89%

472,886A C

74.63%

525,258A C

78.53%

441,072A C

77.10%

510,263A C

79.15%

492,005A C

71.69%

758,645A C

VECM

67.73%

912,753A C

69.90%

861,169A C

74.53%

631,057A C

78.38%

511,455A C

75.89%

631,871A C

80.19%

526,193A C

78.35%

522,789A C

80.15%

441,119A C

77.15%

467,566A C

81.63%

380,331A C

81.47%

380,678A C

80.93%

424,924A C

79.04%

494,600A C

72.10%

747,650A C

HEVaR

62.20%

65.80%

64.30%

64.03%

67.26%

1,011,072A C

69.38%

866,085A C

70.29%

850,016A C

76.41%

584,475A C

79.33%

488,976A C

77.90%

579,190A C

80.78%

510,520A C

79.33%

499,097A C

82.05%

398,892A C

77.76%

455,080A C

82.02%

372,256A C

83.86%

331,576A C

80.52%

434,057A C

80.66%

456,373A C

76.25%

636,447A C

VECM GARCH VECM GJR GARCH

VaR Unhedged = 3,088,185A C 1,167,338A C 1,056,160A C 1,102,482A C 1,110,827A C

HEVaR

VaR Unhedged = 2,828,496A C 953,209A C

HEVaR

VaR Unhedged = 2,861,010A C 907,237A C

HEVaR

VaR Unhedged = 2,477,611A C 634,279A C

HEVaR

VaR Unhedged = 2,365,625A C 559,475A C

HEVaR

VaR Unhedged = 2,620,772A C 682,972A C

HEVaR

VaR Unhedged = 2,656,190A C 521,945A C

513,974A C

78.74%

76.80%

HEVaR

81.50% 513,368A C

79.55%

411,113A C

76.77%

475,340A C

77.40%

467,905A C

80.47%

401,214A C

73.21%

596,943A C

77.04%

541,792A C

71.37%

767,220A C

VaR Unhedged = 2,414,685A C 560,218A C

HEVaR

VaR Unhedged = 2,222,230A C 454,452A C

HEVaR

VaR Unhedged = 2,046,231A C 484,963A C

HEVaR

VaR Unhedged = 2,070,372A C 531,266A C

HEVaR

VaR Unhedged = 2,054,353A C 452,375A C

HEVaR

VaR Unhedged = 2,228,223A C 599,174A C

HEVaR

VaR Unhedged = 2,359,711A C 542,501A C

HEVaR

OLS

Note: The variance and the VaR of the EUA (resp. CER) hedged or unhedged portfolios are calculated along a 1 year hedge horizon using the EUA (resp. CER) front-end December futures. The variance reduction denoted HEVAR is computed according to the Eq. (13) and given the hedge ratios estimated in Table 6. The reduction of the Value at Risk denoted HEVaR is calculated according to the Eq. (15) and given the hedge ratios estimated in Table 6

2015

2014

2013

2012

2011

2010

2009

Panel B: Variance reduction and VaR measures when CER (resp. CER futures) is the hedged item (resp. hedging instrument)

2015

2014

2013

2012

2011

2010

2009

2008

Naïve

VaR Unhedged = 2,679,760A C 768,021A C

VECM GARCH VECM GJR GARCH Value at Risk (VaR) hedged

Panel A: Variance reduction and VaR measures when EUA (resp. EUA futures) is the hedged item (resp. hedging instrument)

Naïve

Assessment of hedging effectiveness from the hedge ratios estimated in Table 6 with the front-end December futures contract

Hedging Horizon Futures Variance (VAR) Hedged

Table 7

24 Y. Rannou and P. Barneto

Corporate Risk Management and Hedge Accounting Under the Scope of IFRS 9

25

line with Fan et al. (2013) results. Notwithstanding this evolution, this first set of results confirms that the potential of hedging effectiveness remains strong for both EUA and CER hedged portfolio. For a portfolio of carbon assets with an initial value of 100 million euros and assuming a 1-year hedging horizon, the VaR exposure averaged over the period 2008–2015 is 447,972 euros (resp. 698,619 euros) for EUA (resp. CER) markets when the VECM GJR GARCH hedge model is applied, which is a decrease of 73,890 (resp. 36,903) euros as compared to the VaR exposure related to the OLS hedge model. Overall, our results confirm that rebalancing EUA and CER portfolio according to a time varying hedge ratio (VECM GARCH and VECM GJR GARCH) offers more significant risk reductions in terms of VaR exposure. Also, the measures of hedging effectiveness based on the reduction of the Value at risk (HEVaR ) are lower in Phase III for both EUA and CER futures. For instance, applying the VECM GJR GARCH model leads to a risk reduction for the EUA hedged portfolio of 92.02% in 2012 while it offers a risk reduction of 79.33% in 2015.

4.3 Effects of IFRS 9 Hedge Accounting on Financial Statements According to IFRS 7 The disclosure requirements for firms applying hedge accounting under IFRS 9 are detailed in IFRS 7. These requirements imply that firms shall disclose information about: • The risk management strategy and how it is applied to manage risks; • How the risk management activities may affect the amount, timing and uncertainty of future cash flows; • The effect that hedge accounting has had on the statement of financial position, the statement of comprehensive income and the statement of changes in equity. The firm’s hedges qualified under IFRS 9 should be presented either in a note or in a separate section in the financial statements. As shown in Table 8, those disclosures are extensive, but consistent with the objective that hedge accounting reflects the firm’s risk management activities. Specifically, firms are intended to describe every qualified hedge under IFRS 9 by type of managed risks (i.e. interest rate risk, foreign exchange risk, and commodity risk); this description must include how each risk arises, how and to what extent, the risk is managed. To this end, firms should assess the appropriate and sufficient level of detail, the balance between different disclosure requirements, and the need to bring further explanations. For the sake of illustration, we present, in the following paragraphs, a case study describing all reporting implications for a non-financial firm: Alpha that discloses carbon hedges in its financial statements according to the IFRS 7 formatted presentations.

26

Y. Rannou and P. Barneto

Table 8 Disclosure requirements Category The firm’s risk management strategy and how this strategy is applied to manage risk?

How the firm’s hedging activities may affect the amount, timing and uncertainty of its future cash flows?

How does the hedge accounting influence the financial statements including the statement of financial position, the statement of other comprehensive income (OCI) and the statement of changes in equity of the firm?

Comments/Goals Information disclosed about a firm’s risk management strategy should help users of financial instruments to assess: How each risk appears; How the firm manages each risk i.e. whether it fully hedges an item for all risks or hedges a risk component(s) of an item; The extent of risk exposures that the firm manages. Firms must provide a breakdown that discloses the following: The monetary amount or quantity (e.g., tCO2eq emitted for power firms) to which the firm is exposed for each risk; The amount or quantity of the risk exposure being hedged; How firm hedging modifies quantitatively the exposure; For each category of risk, a description of the sources of hedge ineffectiveness needs to be disclosed. Both the carrying and notional amounts related to the hedging instruments, accumulated gains or losses on hedged items, must be disclosed, in a tabular format, by risk category for each type of hedge (i.e. fair value hedge, cash flow hedge, hedge of a net investment in a foreign operation).

Alpha is a power firm that holds a coal-fired and a gas-fired installation to produce electricity. Alpha sells its electricity production through a variety of supply contracts which are priced using two specific formulas: (1) the clean spark spread expressed in A C/MWh, that represents the net revenue a gas-fired installation makes from selling power, having bought gas and the required number of EUAs; (2) the clean dark spread expressed in A C/MWh, that represents the net revenue a coal-fired installation makes from selling power, having bought coal and the required number of EUAs. The market risk for Alpha mainly arises from the fluctuations of commodity prices. Alpha has established guidelines for entering into contractual arrangements (i.e. derivatives that are priced according to pricing benchmarks) in order to manage its commodity price risks on a mid-term basis. Notably, Alpha forecasts its volume of expected carbon emissions for a period of 18 months and manages carbon price risk exposure on a 12-month rolling basis. Alpha’s risk management strategy includes the 100% hedging of its exposure to EUA carbon price risks related to

Corporate Risk Management and Hedge Accounting Under the Scope of IFRS 9

27

its electricity production. Hence, Alpha determines a carbon price exposure that is separately identifiable and reliably measurable. This exposure is an eligible risk component for designation as an hedged item. Put differently, the underlying risk of the EUA futures contracts is here identical to the hedged risk component (i.e. the EUA benchmark price). In January 2013, the treasurer of Alpha anticipates a higher carbon price risk exposure because of the gradual abandonment of free EUAs in Phase III. Therefore, he buys a large amount of 100,000 December 2013 futures contracts valued at 10 euros each to purchase EUA assuming that Alpha hedges a forecasted EUA consumption with a EUA futures. The amount of this hedging instrument is reported in Fig. 2 according to the format of Paragraph 24A of IFRS 7 in the statement of financial position of Alpha as of 31 December 2013. Alpha has previously established a hedge ratio of 0.75:1 for its hedging relationship. Alpha’s exposure to the variability in the purchase price of EUA is integrated into its general risk management and its decision to switch from coal hired installations to gas hired installations (resp. or vice versa) on the basis of clean spark (resp. dark) spread. Next, we look in Fig. 3 at what happens when the correlation between the hedged item (i.e. EUA) and the hedging instrument (i.e. EUA futures) changes from 100% to 95% under IAS 39 vs IFRS 9. Under IAS 39, a hedge relationship has to be discontinued if the hedge ratio falls outside the 80–125% boundaries. Given that 75% is outside these boundaries, the full amount of line 1 IAS 39’s hedging instrument is reported in the P&L account. By contrast, IFRS 9 does not impose such boundaries but allows rebalancing to avoid hedge discontinuation.

EUA December 2013 futures

Notional amount

Carrying Amount of the hedging instrument

100,000 contracts (@10€ per contract)

(1,000,000)

Line item in the statement of financial position Short-term derivative financial liabilities

Change in fair value used for calculating hedge ineffectiveness for the period (250,000)

Fig. 2 Alpha’s disclosed amount of carbon hedging instrument according to Paragraph 24A of IFRS7

IAS 39 IFRS 9 without rebalance IFRS 9 with rebalance

Hedging instrument

Hedged item

Hedge Ratio

OCI

P&L

Comments

-/- 750,000

1,000,000

75%

0

-/- 750,000

Hedge to be discontinued. Prospective test outside the boundaries

-/- 750,000

1,000,000

75%

-/- 1,000,000

-/- 250,000

Hedge can continue. No boundaries under IFRS 9.

-/- 750,000

1,050,000

71.4%

-/- 1,050,000

-/- 300,000

Rebalance with increase 20% hedged item

Fig. 3 Effects of hedge accounting on the Alpha’s financial position and performance under the scope of IAS 39 or IFRS 9

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Cash flow hedge (1)

Y. Rannou and P. Barneto

Hedging gain or loss recognised in OCI

Hedge ineffectiveness in profit and loss

Line item in the statement of comprehensive income (OCI) that includes hedge ineffectiveness

Amount reclassified from the cash flow reserve (OCI) to P&L

Line item affected in profit or loss because of the reclassification

COMMODITY PRICE RISK EUA price risk (With rebalancing) Hedges of forecasted Operating Expenses (750,000) (300,000) Other income 50,000 purchases of (Emission derivatives) EUA auctioned (1) The information presented in the statement of changes in equity (through the cash flow hedge reserve) should have the same level of detail as the proposed disclosure requirements.

Fig. 4 Alpha’s disclosed amount of carbon hedged item according to Paragraph 24B of IFRS7

If Alpha opts for maintaining its hedge ratio constant (see line 2 IFRS 9 without rebalance), 1000,000 euros are recorded in the OCI and 250,000 euros of hedge ineffectiveness are recognized in the P&L account. If Alpha decides to rebalance the hedge relationship by increasing the volume of the hedged item by 5%, the hedge ratio changes from 75% to 75%/ (100 + 5% × 100) = 71.4%. Hence, the over hedge between the hedged item and the hedging instrument is 300,000 reported in the P&L account while the augmented amount 1,050,000 = 1000,000 × (100 + 5% × 100) is recognized in the OCI as shown in the line 3 IFRS 9 with rebalance. As a result, the modified hedging relationship involves reclassification of 50,000 euros from the cash flow hedge reserve of the OCI to the P&L account. As shown in Fig. 4, this change must be reported according to the indications given by the Paragraph 24B of IFRS 7.

5 Conclusion The global quest for reducing carbon emissions has given rise to dedicated risk management programs and has thus become part of strategic operational decisions for firms involved in energy intensive processes. Accordingly, most European power firms use carbon futures to hedge their immediate or potential exposure of risks associated with carbon emission compliance (Schopp and Neuhoff 2013). As the Task Force on Climate-related Financial Disclosures of the Financial Stability Board (FSB) has recently underlined, the impacts of climate change may be not correctly priced without accountability of carbon emissions and related price risks (FSB 2017). Nonetheless, the absence of a commonly accepted accounting standard since the withdrawal of IFRIC 3 and the too restrictive IAS 39 has led to the use of various methods to report carbon derivatives. If it raises doubts about the comparability of their financial statements, the ability to inform on their risk management strategies and their cost of complying with EU ETS obligations is also hindered. To overcome these two issues, two professional organisations, CDSB and

Corporate Risk Management and Hedge Accounting Under the Scope of IFRS 9

29

IETA, have recommended that the IFRS 9 requirements should be applied to account for EUA or CER derivatives (CDSB and IETA 2013). Following this recommendation, our prospective study complements the study of Haupt and Ismer (2013) by showing the relevance of the IFRS 9 hedge accounting requirements for the case of European power firms. By adopting them, they may provide a more relevant balance sheet and P&L information through the OCI when reporting EUA and CER futures position and reduce the volatility in their earnings if they had applied the fair value approach. We contribute to the literature on the risk management techniques related to carbon markets in three directions. First, we compare relevant methods to assess static and time-varying hedge ratios and associated hedging effectiveness. Notably, we find that the estimated hedge ratios sometimes fall outside the range of 80–125% boundaries in Phase III especially for the case of less liquid CER markets confirming the relevance of IFRS 9 abandoning these boundaries. Second, we provide evidence of the superiority of time-varying carbon hedges that may be used in the context of rebalancing. Third, we show that the associated hedging effectiveness measured by variance reduction and VaR are noteworthy and may help companies to monitor continuously their carbon hedging strategies. Taken together, our findings confirm the relevance of the IFRS 9 framework to account for carbon hedges using EUA and CER derivatives, which are increasingly important for power firms since they have received less and less free EUAs since 2013. In this respect, we provide a case study with a given power firm to illustrate how it can use IFRS 7 disclosure requirements to report carbon hedges using EUA derivatives in its financial statements provided that the IFRS 9 requirements have been met. Two avenues for further research may be considered. On the one hand, other energy derivatives could be incorporated into global commodity portfolios including carbon futures (Kleindorfer and Li 2011) to test the appropriateness of the macro hedging accounting that could be proposed under IFRS 9.20 On the other hand, the European Market Infrastructure Regulation (REMIT), a chapter of Mifid that has been recently adopted imposes the centralised settlement and reporting of all traded energy derivatives including carbon derivatives. The analysis of potential synergies between the provision of REMIT and IFRS 9 information, which can reduce the costs of the implementation of IFRS 9 for power firms, is left for future work.

20 The

IASB issued a discussion paper on ‘Accounting for dynamic risk management: a portfolio revaluation approach to macro hedging’ in April 2014 (IASB, 2014). After having received comments of experts, the IASB expects to release the core IFRS 9 model of macro hedging by the second half of the year 2019.

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References Bangzhu Z, Chevallier J (2017) Pricing and forecasting carbon markets: models and empirical analyses, 1st edn. Springer, Cham Berta N, Gautherat E, Gun O (2017) Transactions on the EU ETS: a bubble of compliance in a whirlpool of speculation. Camb J Econ 41:575–593 Brooks C, Henry OT, Persand G (2002) The Effect of Asymmetries on Optimal Hedge Ratios. J Bus 75(2):333–352 CDC Climat (2013) Tendances carbone methodology, January 2013 newsletter. Available online. http://www.cdcclimat.com/IMG/pdf/methodologie_tendances_carbone_en_v8.pdf. Accessed 5 May 2018 Chevallier J (2012) Econometric analysis of carbon markets: the European Union emissions trading scheme and the clean development mechanism, 1st edn. Springer, Dordrecht Climate Disclosure Standard Board (CDSB), International Emissions Trading Association (IETA) (2013) Response to emission trading schemes draft comment paper. International Emissions Trading Association, Geneva Ederington LH (1979) The hedging performance of the new futures markets. J Financ 34:157–170 European Financial Reporting Advisory Group (2005) Final endorsement advice: adoption of IFRIC 3 Emission Rights. European Financial Reporting Advisory Group, Brussels. Available via IASPlus. https://www.iasplus.com/en/binary/efrag/0505ifric3endorsementadvice.pdf. Accessed 4 Feb 2018 Fan JH, Roca E, Akimov A (2013) Dynamic hedge ratio estimations in the European Union Emissions offset credit market. J Clean Prod 42:254–262 Fan JH, Roca E, Akimov A (2014) Estimation and performance evaluation of optimal hedge ratios in the carbon market of the European Union Emissions Trading Scheme. Aust J Manag 39(1):73–91 Feng Z-H, Wei Y, Wang K (2012) Estimating risk for the carbon market via extreme value theory: an empirical analysis of the EU ETS. Appl Energy 99:97–108 Feng Z-H, Yu J, Guo J, Li Z-K (2016) The optimal hedge for carbon market: an empirical analysis of EU ETS. Int J Global Energy Issues 39:129–140 Financial Stability Board (FSB) (2017) Recommendations of the task force on climate-related financial disclosures. Financial Stability Board, Basel Glosten LR, Jagannathan R, Runkle DE (1993) On the relation between the expected value and the volatility of the nominal excess return on stocks. J Financ 48:1779–1801 Harris RDF, Shen J (2006) Hedging and value at risk. J Futur Mark 26:369–390 Haupt M, Ismer R (2013) The EU emissions trading system under IFRS – towards a true and fair view. Account Eur 10(1):71–97 Ibikunle G, Gregoriou A, Hoepner AGF, Rhodes M (2016) Liquidity and market efficiency in the world’s largest carbon market. Br Account Rev 48(4):431–447 International Accounting Standard Board (IASB) (2010) IFRS 9: Hedge accounting, exposure draft (ED/2010/13). IFRS Publications, London International Accounting Standard Board (IASB) (2013) IFRS 9: financial instruments (Hedge accounting and amendments to IFRS 9, IFRS 7 and IAS 39) implementation guidance. IFRS Publications, London International Accounting Standard Board (IASB) (2014) Accounting for dynamic risk management: a portfolio revaluation approach to macro hedging. Discussion paper (DP 2014/1). IFRS Publications, London International Emissions Trading Association (IETA) (2007) Trouble-entry accounting – revisited: uncertainty in accounting for the EU emissions trading scheme & certified emission reductions. International Emissions Trading Association, Geneva Kalaitzoglou IA, Ibrahim BM (2013) Does order flow in the European carbon futures market reveal information? J Financ Mark 16(3):604–635

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Kawaller I (2015) Accounting for commodity hedges: hypothetically speaking. AFP Exch Mag 2015:58–61 Kleindorfer PR, Li L (2011) Portfolio risk management and carbon emissions valuation in electric power. J Regul Econ 40(3):219–236 Lien D (2009) A note on the hedging effectiveness of GARCH models. Int Rev Econ Financ 18:110–112 Lopes PT (2007) Accounting for electricity derivatives under IAS 39. J Deriv Hedge Funds 13(3):233–246 Lovell H, Bebbington J, Larrinaga-Gonzalez C, Sales de Aguiar T (2013) Putting carbon markets into practice: a case study of financial accounting in Europe. Eviron Plann C Gov Policy 31(4):741–757 Lucia J, Mansanet-Bataller M, Pardo Á (2015) Speculative and hedging activities in the European carbon market. Energy Policy 82:342–351 Medina V, Pardo A (2013) Is the EUA a new asset class? Quant Finan 13(4):637–653 Medina V, Pardo A, Pascual R (2013) Carbon credits: who is the leader of the pack? Int J Energy Econ Policy 3:210–222 Onali E, Ginesti G (2014) Pre-adoption market reaction to IFRS 9: a cross-country event-study. J Account Public Policy 33:628–637 Philip D, Shi Y (2016) Optimal hedging in carbon emission markets using Markov regime switching models. J Int Financ Mark Inst Money 43:1–15 Qian W, Schaltegger S (2017) Revisiting carbon disclosure and performance: legitimacy and management views. Br Account Rev 49:365–379 Rannou Y, Barneto P (2016) Futures trading with information asymmetry and OTC predominance: another look at the volume/volatility relations in the European carbon markets. Energy Econ 53:159–174 Schopp A, Neuhoff K (2013) The role of hedging in carbon markets, DIW Berlin discussion papers series no 1271 Trotignon R, Leguet B (2009) How many CERs by 2013? Caisse des Dépôts et Consignations (CDC) working paper no 2009–5 Trück S, Härdle W, Weron R (2016) The relationship between spot and futures CO2 emission allowance prices in the EU-ETS. In: Gronwald M, Hintermann B (eds) Emission trading systems as a climate policy instrument – evaluation & prospects, 1st edn. MIT Press, London, pp 183–212 World Federation of Exchanges (WFE) (2018) WFE IOMA 2017 derivatives report. World Federation of Exchanges, London

Corporate Fraud Risk Management Rasha Kassem

1 The Meaning and Nature of Corporate Fraud The broader definition of fraud encompasses any crime for personal gain that uses deception and trickery to harm victims. In many cases, the victims are unaware they have been defrauded or deceived until after a long time, but fraud criminals will always have the intention to deceive fraud victims for some personal gain. This personal gain could either be financial (e.g. to receive a bonus; or to obtain financing), or non-financial (e.g. Ego, revenge, or pathological desire for crime). There are two main differences between fraud and error. Firstly, fraud involves the “intent to deceive”, while error does not involve any intent to deceive or to cause harm. Intent means willingly and knowingly committing the crime, while realizing the harm that may be caused to the victim(s). Secondly, in the case of fraud, fraud criminals will always conceal their crimes to avoid detection and prosecution. However, in the case of error, although we all make mistakes, an honest person will never try to conceal his/her own mistake. An example of an error is an incorrect entry of a product’s price in a sales invoice made by one of the company’s employees with no intention to deceive the company and no attempt to conceal this mistake. However, if the employee knowingly entered an incorrect product’s price and then concealed it to avoid detection, this is an example of fraud. Therefore, the intent to deceive and the act of concealment play an important role in differentiating between fraud and error. From a legislation perspective, the Fraud Act 2006 in England, Wales, and Northern Ireland gives a statutory definition of the criminal offence of fraud, defining it in three classes: (1) fraud by false representation (e.g. Financial statements fraud);

R. Kassem () Coventry University, Coventry, UK e-mail: [email protected] © Springer Nature Switzerland AG 2021 C. Zopounidis et al. (eds.), Financial Risk Management and Modeling, Risk, Systems and Decisions, https://doi.org/10.1007/978-3-030-66691-0_2

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(2) fraud by failing to disclose information (e.g. Improper disclosure cases in the financial statements), and (3) fraud by abuse of position (e.g. Bribery and corruption or assets misappropriation). The Fraud Act 2006 has enabled the investigator to concentrate on gathering evidence in a way that focuses on the suspect’s intentions and actions rather than evidencing that a victim has been deceived.1 The fraud Act 2006 does not apply in Scotland though. In Scotland, criminal fraud is mainly dealt with under the common law and a number of statutory offences including: (i) common law fraud; (ii) uttering; (iii) embezzlement; and (iv) statutory frauds. In Scotland, the term ‘fraud’ refers to the deliberate use of deception or dishonesty to disadvantage or cause loss to another person or party.2 Under common law in the United States (US), four general elements must be present for a fraud to exist: (i) a material false statement; (ii) knowledge that the statement was false when it was uttered; (iii) reliance on the false statement by the victim; and (iv) damages as a result (See Wells 2011).

2 The Types of Corporate Fraud Fraud against an organization can either be committed internally by employees, managers, owners, and directors of the entity, or externally by customers, vendors, and other parties. Fraud committed internally against the organization is called internal fraud; insider fraud or threat; corporate fraud; or occupational fraud. Fraud committed externally against the organization is called external fraud. Other schemes defraud individuals, rather than organizations such as in the case of identity theft, Ponzi schemes, or pension fraud. External fraud is a type of fraud where external third parties, such as businesses, individuals or organized crime groups, steal money from a department or agency, either by obtaining payments to which they are not entitled or keeping monies they should pay over to the department. Examples of external fraud include but are not limited to customer fraud, supplier fraud, and cyber-crimes. Internal fraud, on the other hand, can be defined as “the use of one’s occupation for personal enrichment through the deliberate misuse or misapplication of the employing organisation’s resources or assets” (Wells 2005). Internal fraud includes three main types of fraud: (1) Asset misappropriation, (2) Financial statements fraud, and (3) Corruption (See ACFE 2018). The Association of Certified Fraud Examiners (ACFE) noted in its 2018 Report to the Nations on Occupational Fraud and Abuse that internal fraud is the costliest type of fraud. Hence the focus of this chapter will only be on “internal fraud”. As mentioned earlier, internal fraud could also be referred to as “insider fraud or threat”,

1 https://www.legislation.gov.uk 2 https://www.fraudadvisorypanel.org/wp-content/uploads/2015/12/Criminal-fraud-in-Scotland-

4th-edition-December2015.pdf

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“occupational fraud”; or “corporate fraud”. But, for the purpose of this chapter, internal fraud will be referred to as “corporate fraud”.

2.1 Assets Misappropriation The first type of corporate fraud is “Asset misappropriation” which involves stealing an asset of a company for personal use at the company’s expense or misuse of a company’s resources (Wells 2011). Asset misappropriation is often accompanied by false or misleading records or documents to conceal the theft (Soltani 2007). Assets are resources owned and controlled by an entity which are expected to derive future benefits (Weygandt et al. 2015). Some examples of assets include cash, cheques, stock or inventory, receivables, land, building, vehicles, and machinery. Assets misappropriation is usually perpetrated by employees in relatively small and immaterial amounts. However, it can also involve management, who are usually more able to disguise or conceal misappropriations in ways that are difficult to detect (Jones 2011). For example, Walt Pavlo a Senior Manager in Billing Collections at MCI/WorldCom embezzled around $800,000 from his company by creating a shell company (i.e. fictitious company) and writing off customers’ debts in return for a fee. In a global study by the ACFE, asset misappropriation was found the most common types of corporate fraud (ACFE 2018). Asset misappropriation does not only include the theft of cash but also payroll fraud, cheque tampering, and expense disbursements schemes. Examples of asset misappropriation include: Purchasing fictitious services rather than goods such as consulting services which is difficult to be traced; stealing and forging a company’s cheques; an employee causes his employer to issue a payment by making false claims for compensation; and adding a fictitious person or failing to remove the name of a retired employee who used to work for the company which is called a “ghost employee” (See Wells 2005 for more examples).

2.2 Financial Statements Fraud The second type of corporate fraud is “Financial statements fraud (also called fraudulent financial reporting)”. It can be defined as a deliberate attempt by corporations to deceive users of the financial statements by preparing materially misstated financial statements (Rezaee 2005). Financial statements fraud could be committed through misstating a company’s revenues and/or assets, concealing expenses and/or liabilities, and through improper disclosure. According to the findings of the ACFE global fraud study (2018), financial statements fraud is the costliest type of corporate fraud causing a median loss of $850,000 and that it is more likely to be committed by management and executives.

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Recent corporate fraud cases such as what happened in Tesco, Carillion, and Patisserie Valerie in the UK are good examples of financial statements fraud. In the cases of Tesco and Patisserie Valerie for instance, the company’s revenues were overstated so that some corrupt management could receive their bonuses. In the case of Carillion, the goodwill (which is an intangible asset) was overstated resulting in the company’s collapse.

2.3 Corruption The third type of corporate fraud is “Corruption”. Most people think that corruption can only be in the form of bribery, however in fact corruption is not just about bribery, it also involves conflicts of interest, economic extortion, and illegal gratuities. Corruption is the hardest type of fraud to detect due to the absence of audit trail. As defined by business dictionary, corruption is “Wrongdoing on the part of an authority or powerful party through means that are illegitimate, immoral, or incompatible with ethical standards”. Bribery can be defined as the offering, giving, receiving, or soliciting anything of value to influence the decision of a government agent or official or anyone with power within the organization (Wells 2011). Put simply, it is giving or taking a reward in return for acting dishonestly or in breach of the law. The Bribery Act 2010 in the UK makes bribery for businesses for commercial benefit a criminal offence and it applies to UK businesses regardless of whether the act of bribery occurs inside or outside the UK. For instance, Rolls Royce has been investigated by the Serious Fraud Office (SFO) in 2013 for committing corruption and bribery. The charges against the company included falsifying accounts to hide the illegal use of local middlemen, and paying tens of millions in bribes to win engine and other contracts in Indonesia, Thailand, China and Russia. Conflict of interest is another type of corruption. Conflict of interest is a situation in which an individual has competing interests or loyalties. It occurs when an employee, manager, or executive has an undisclosed economic or personal interest in a transaction that adversely affects the organization. This means in order to be classified as a conflict of interest, the individual’s interest in the transaction must be undisclosed. To clarify this more, consider the following example: If a company’s director is taking a decision about which supplier to consider in the market and found that one of these suppliers is a close friend. To avoid being in a conflict of interest situation, the director should disclose to the rest of the board of directors the fact that one of the suppliers that will be considered is a friend. The entire board should then conduct a fair assessment of the quality and price of the goods offered by each supplier. The decision about which supplier to go for should be based on what is best for the company’s interest and not on the director’s best interest.

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In the case of extortion, however, threats of damage to the victim’s reputation, or to his/her financial well-being may be involved. In extortion, a fraud criminal demands a sum of money or something of value with a threat of harm if the demands are not met. The harm could include physical harm, but could easily be the denial of a business contract or opportunity or the threat of actions to damage the reputation of a person or the company (Coenen 2008). According to the legal dictionary, extortion refers to “the crime of obtaining money or property by using threats of harm against the victim, or against his property or family”. Therefore, anything obtained by the use of extortion, including consent, has been illegally obtained, and the perpetrator has committed a felony. The last type of corruption is illegal gratuities. In illegal gratuities, a decision is made and benefits a certain person or company who lately rewards the decision maker while this decision is not initially influenced by any sort of payment. However, it is called illegal because there might be an understanding that future decisions beneficial to that certain person will also be rewarded (Wells 2005). For example, imagine a case where a teacher gave a student an “A” for his/her good performance in an assessment without prior knowledge of the student. The student then decided to buy an expensive gift for the teacher as a way of showing appreciation. If the teacher lacks integrity, s/he might be tempted to give the student another high grade in the future in order to be rewarded. In this case, the gratuity might turn into a bribe or an extortion in case the student refused to buy another gift for the teacher. That is why in most Universities, companies, and organizations, particularly in the UK, employees are required to report any gifts received to their employers in order to reduce the risk of corruption.

3 The Impact of Corporate Fraud Fraud is, in many ways, a unique type of crime. Fraud overlaps with many other types of crimes and there is no one body or organization that can deal with it in its entirety. Fraud could take place in different contexts and fraud criminals could use different methods to commit fraud. Although fraud is not a new crime, it has evolved recently with the advancements in technology and the use of the internet (UK Home Office 2018). Fraud risk is a universal concern for all business and government entities regardless of the size, type of industry, and context. Any entity with assets is in danger of those resources being targeted by fraud criminals. This includes companies, banks, charities, Universities, and government institutions. Among the various kinds of fraud that organizations might be faced with, corporate fraud is likely the largest and most prevalent threat. Corporate fraud can cost an organization huge amount of losses. According to the findings of the ACFE global fraud study in 2018 which was based on an analysis of 2690 cases of corporate fraud that were investigated between January 2016 and October 2017 in 125 countries around the world, the total loss caused by corporate

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fraud exceeded USD 7.1 billion. The mean, or average, loss due to the frauds in the ACFE study was USD 2.75 million. The value of fraud cases reaching courts in the UK for 2019 has increased to over £1 billion. The cost of corporate fraud has more than doubled to £46 million in the UK (KPMG 2020). Assets misappropriation are by far the most common, occurring in 89% of the cases. However, they are also the least costly, causing a median loss of $114,000. Corruption schemes are the next most common form of occupational fraud; 38% of the cases involved some form of corrupt act. These fraud schemes resulted in a median loss to the victim organizations of $250,000. The least common and most costly form of occupational fraud is financial statement fraud, which occurred in 10% of the cases and caused a median loss of $800,000 (ACFE 2018). However, the cost of corporate fraud goes beyond financial losses. Corruption is likely to reduce investments that will also bring about a lower GDP (Lambsdorff 2003), undermine firm growth and reduces the propensity to export (Kimuyu 2007). The impact of corruption on reputational risk may be severe even when financial impact is minimal (IIA 2014). For example, the FIFA corruption scandal did not only involve charges that at least $150 million in corrupt payments were made to FIFA officials, but is also centred on a sport that is followed by more than two billion fans around the world and therefore this collapse has led to feelings of anger and betrayal as well as unwelcome media attention and scrutiny. The cost of asset misappropriation and financial statements fraud also goes beyond financial losses as it damages an organization’s public image and reputation, and investors’ confidence in the capital market. Financial statements fraud leads to loss of productivity from hiring and firing employees who have committed fraud as well as the time needed to sort out the situation (Rezaee 2005). For example, many investors were hit by the bad news about the collapse of BHS and Carillion in the UK. Customers were unhappy after the fraud scandal of overstatement of revenue by Tesco in the UK, and the company has witnessed a decline in sales as a result. Reported losses for all fraud types in 2016 in the UK totalled around £769 million (UK Home office 2018). The cost of fraud, whether financial or non-financial, could be massive as explained earlier. Therefore, one way to reduce the cost of fraud is to reduce its risk by investing in effective fraud prevention strategies. As they say in the world of medical science “when it comes to disease, prevention is better than cure”, fraud prevention is also better than fraud detection. That is because in most cases, fraud detection could be difficult and time consuming. Also, it is difficult to stop harm once fraud has been committed. Therefore, it is better to prevent fraud from happening in order to reduce its risk and the harm it causes to victims. Designing effective fraud prevention strategies require effective fraud risk assessment and fraud risk management plans. However, before discussing how organizations could design effective fraud prevention strategies, it is important to first understand what is meant by risk, and what is the difference between risk assessment and risk management.

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4 The Meaning of Risk It is important to clarify that there is no single definition of risk. The meaning of risk depends on and varies based on the type of risk; objectives and targets that need to be achieved; the context in which risk is defined; and whether risk is favourable or unfavourable. However, a general definition of risk views risk as the variation from the expected outcome over time (Kallman 2005). Favourable or positive risk could be seen as an opportunity while unfavourable or negative risk could be seen as a probability or threat of damage or harm. According to the business dictionary, negative risk can be defined as “a probability or threat of damage, injury, liability, loss, or any other negative occurrence that is caused by external or internal vulnerabilities, and that may be avoided through pre-emptive action”. To put it simply, positive risk could be referred to as an “opportunity” while negative risk could be referred to as a “threat”. Examples of opportunity or positive risk include: A new business venture; favourable acquisition or merger. While negative risk include: Fraud risk; business risk; control risk; liquidity risk; economic risk; political risk; risk of losing customers; and risk of losing qualified staff. Negative risks can be dangerous and expensive. However, an integrated approach to management of both threats and opportunities can ensure that unwelcome negative effects are minimized while at the same time maximizing the chances of exploiting unexpected positive effects (Hillson 2001).

5 Risk Assessment Versus Risk Management Despite the fact that risk assessment goes hand in hand with risk management, both terms are different. Risk assessment is a systematic process of evaluating the potential risks that a business might face. However, risk management is about dealing with potential risks and involves the plan that businesses devise to either mitigate, reduce, or avoid potential risks. To clarify, risk assessment is the information about the risk, while risk management is the plan for dealing with the information about risk. Risk assessment involves three steps: (1) risk identification, (2) risk analysis, and (3) risk evaluation. Risk Identification involves identifying what could go wrong and potential risks that exist within a business environment. This requires a good understanding of the nature of business and industry. Risk analysis requires assessing the probability or the likelihood of the risk and the potential impact of that risk (i.e. who or what could be hurt by the risk). Risk evaluation requires an assessment of the severity of the risk or how bad risk could be if it happens. This requires categorizing the risk into high risks, medium risks, and low risks that can be tolerated. When evaluating risks, companies should also consider how soon these

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risks could happen, what are the losses and costs that might be incurred, and whether the risks will impact daily operations. It is not enough for companies to assess risks but they also have to manage risks, should they want to survive and operate successfully. Risk assessment and risk management are like partners. Without a risk assessment, businesses will not know what risks to put in their risk management plans. Although companies might not be able to stop or avoid all risks, with a sound risk assessment and risk management plan companies could at least be prepared to deal with the impact of unavoidable risks. Risk management helps organizations prepare for the unexpected. How companies deal with risks impact their success and survival in the market.

6 Designing Effective Fraud Prevention Strategies Fraud risk is one of the types of negative risks that are common to any organization regardless of its type, size, purpose, or industry. Any entity with assets is vulnerable to fraud. Therefore, it is important that organizations learn how to design effective fraud prevention strategies in order to manage fraud risks. In order to design effective fraud prevention strategies, organization. Should effectively assess and manage fraud risks. This chapter suggests considering the following framework to effectively assess and manage fraud risk (see Fig. 1):

Step 1: Fraud Risk identification: -Understand the psychology of fraud criminals -Identify fraud risk factors in the organization Step 2: Fraud Risk analysis: -What is the likelihood of fraud risk? -What is the cost of fraud risk? -What is the impact of fraud risk? Step 3: Fraud Risk evaluation: -What is the severity of the risk? Is it high risks, medium risks, or low risks? Step 4: Design effective anti-fraud controls that reduce or eliminate fraud risk factors

Fraud Risk Assessment

Effective Fraud Prevention Strategies Fraud Risk Management

Step 5: Maintain sound corporate governance system to ensure fraud risk is reduced throughout the organization

Fig. 1 Framework for designing effective fraud prevention strategies

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Figure 1 shows that in order to design effective fraud prevention strategies, organizations should consider five main steps: (i) Fraud Risk identification; (ii) fraud risk analysis; (iii) fraud risk evaluation; (iv) designing effective anti-fraud controls that could reduce or eliminate fraud risk factors; (v) maintaining a sound corporate governance system to ensure fraud risk is reduced throughout the organization. The first three steps are part of effective fraud risk assessment and the last two steps are related to fraud risk management. In fraud risk identification, organizations need to first understand the psychology of fraud criminals or in other words: Why people commit fraud?. Based on their understanding of the psychology of fraud criminals, organizations can then identify which fraud risk factors exist in their organizations and why. Understanding why fraud is committed is important in order to design procedures that could reduce fraud risk factors (Wells 2011). The factors that increase the risk of fraud are further discussed under the sub-section: “Understanding the psychology of fraud criminals”. Fraud risk analysis requires organizations to determine (a) the likelihood of fraud risk (i.e. is it likely or unlikely?); (b) the cost of fraud risk? (i.e. how much could fraud cost us? do we have enough resources to cover the cost of fraud?); and (c) the impact of fraud risk (i.e. can it impact daily operations? how much disruption can be caused?). In evaluating fraud risk, organizations need to consider the severity of fraud risk. For example, is it high risk, medium risk, or low risk?. The following sub-sections discuss how organizations could use anti-fraud controls and sound corporate governance in order to manage fraud risks.

6.1 Understanding the Psychology of Fraud Criminals Fraud can be committed when individuals have strong motives to commit fraud; have low integrity; are able to rationalize or justify their fraudulent behavior; have existing opportunities that enable the fraud to be committed without being caught; and have traits that enhance their capabilities to commit fraud (Cressey 1950; Albrecht et al. 1984; Wolfe and Hermanson 2004; Kassem and Higson 2012). One of the factors that increase the risk of fraud is the “motive”. The motive to commit fraud is like “the source of heat for the fire” (Lister 2007). Motives could either be financial like greed; the desire to receive bonuses or remunerations; and the need to get financing, or non-financial such as to save ones ego; pressure from investors or analysts; coercion; or revenge (Kassem 2017). The motives to commit fraud are key antecedents to fraud. This is evident in many past and recent fraud cases. For example, in the case of Enron in 2002, the executives were motivated by greed and their desire to receive excessive remunerations. Also, Nissan’s CEO’s desire to escape shareholders’ criticism over his remuneration motivated him to manipulate the financial statement numbers and disclosure in 2019. Organizations should, therefore, identify and eliminate, or at least reduce any factors that may increase the motivations risk. Examples of fraud risk factors that

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may increase the motivation risk include: treating employees with no fairness and respect; unfair promotion and payment system; putting undue pressure on employees to achieve unrealistic targets; leaders who have no ethical values and lack integrity. Another key factor in increasing the risk of fraud is “integrity”. Individuals who have the motive(s) to commit fraud and also lack integrity, are more likely to commit fraud. An individual’s degree of honesty and integrity could determine whether or not this person is likely to commit fraud (Albrecht 2014). Integrity goes hand in hand with motives. Therefore, organization should be committed to high levels of ethical values and integrity in order to reduce the risk of fraud. This requires them to invest in antifraud education and fraud awareness campaigns; appoint staff who are committed to high ethical values and integrity; design code of ethics and monitor staff compliance with the code; conduct background checks before employing their staff; and reward good behavior and integrity. The opportunity to commit fraud is like the “the fuel that keeps the fire going” (Lister 2007). Opportunity comes about when there is a weakness in a company’s or organization’s internal control system and poor corporate governance mechanisms. An internal control system is a system that provides reasonable assurance that three main objectives are met: (1) financial objective – the financial statements are true and fair, and are prepared in accordance with the required accounting standards, (2) operational objective – the business operations are run as effectively and efficiently as planned, (3) compliance objective – the business is complying with laws and regulations. Corporate governance is a system by which companies are directed and controlled. Effective corporate governance system will focus on designing and implementing a sound internal control and monitoring system. Examples of opportunities that can increase the risk of fraud include: lack of segregation of duties; concentration of power in the hand of one or few individuals; weak or ineffective board of directors; lack of physical safeguard over assets and records; lack of monitoring; no commitment to competence; weak or ineffective audit committee; dishonest or unqualified external auditors; lack of or ineffective internal audit function; and lack of penalty system (Dunn 2004; Albrecht et al. 2008, 2010; Wells 2011). In order to reduce the risk of opportunities to commit fraud, organizations need to design and implement an effective internal control system with more focus on anti-fraud controls and continuous monitoring. Organizations also need to maintain sound corporate governance systems that ensure that their board of directors are committed to high ethical values and integrity; competent and qualified; properly discharging their governance responsibilities; employing staff that have integrity; conducting continuous monitoring; and are holding individuals accountable for their actions. Fraud perpetrators’ capabilities should also be considered at the same time the company is assessing the opportunity risk. That is because not all individuals are capable of exploiting existing internal control weaknesses. Some of the traits that could make some individuals more capable to commit fraud than others include:

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(1) their ability to overcome stress, (2) confidence of the ability to escape penalty if caught, (3) power within the organization, (4) knowledge of accounting and internal control weaknesses (Wolfe and Hermanson 2004). Another factor that may increase the risk of fraud is rationalization. Rationalization is a justification of fraudulent behavior due to an individual’s lack of personal integrity (Rae and Subramaniam 2008). Examples of rationalization include: “I am only helping a friend”, “I am just borrowing the money, not stealing it”, “we need to keep the stock price high”, “all companies use aggressive accounting practices so why cannot we”, or “I only wanted to save the company”. Rationalization could be viewed as “the oxygen that keeps the fire burning” (Lister 2007) for some fraud criminals but it is not an essential fraud risk factor for all types of fraud criminals. For instance, first time offenders may need to rationalize fraud in order to escape the feeling of guilt. However, other fraud criminals will not need to rationalize their fraudulent behavior because they have pathological desire for crimes, and lack integrity. This type of fraud criminals will deliberately defraud organizations through looking for an existing opportunity to commit fraud without being caught. We could therefore say that rationalization is closely linked to an individual’s level of integrity because individuals with high integrity will not rationalize fraud. Rationalization could also be linked to the motivation to commit fraud given that fraud criminals could use their motivations to justify the perpetration of fraud. For example, “they are not treating me well” could be a justification for a fraud perpetrator that seeks revenge. “they are not paying me enough” could be a justification for employees suffering low payments or those having financial need. Organizations should be aware of the factors that could increase the motivations risk and therefore, rationalization for fraud. Simple procedures like treating employees fairly and with respect, and/or designing fair remuneration packages could help in reducing the motivations risk as well as the risk of rationalizing fraudulent acts. More examples of fraud risk factors are available in Toolkit #1 and Toolkit #2.

6.2 Designing Effective Anti-fraud Controls An internal control system is a system that provides reasonable assurance that three main objectives are met: (1) financial objective – the financial statements are true and fair, and are prepared in accordance with the required accounting standards, (2) operational objective – the business operations are run as effectively and efficiently as planned, (3) compliance objective – the business is complying with laws and regulations. Any weaknesses in an organization’s internal control system, increase the opportunity for fraud. Weaknesses in internal controls could also increase the risk of other fraud factors such as the motives to commit fraud and the ability of individuals to rationalize their fraudulent acts.

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Monitoring Information & communication Control Activities Risk Assessment Control Environment

Fig. 2 COSO internal control components illustrated

Based on the recommendations of the Committee of Sponsoring Organizations of the Treadway Commission (COSO 2013), any effective internal control system should include all the following five main control components: (i) control environment; (ii) risk assessment; (iii) control activities; (iv) information and communication; and (v) monitoring. COSO was organized in 1985 to sponsor the National Commission on Fraudulent Financial Reporting (FRF). The National Commission on FRF is an independent private-sector initiative that studied the causal factors that can lead to fraudulent financial reporting. COSO is dedicated to the development of frameworks and guidance on enterprise risk management, internal control, and fraud deterrence. According to COSO, the effectiveness of the internal control system is assessed based on these five components of internal control. All five components MUST be present, functioning, and operating together in order to conclude that internal control is effective. Figure 2 illustrates the five main control components suggested by COSO. As shown in Fig. 2, the first control component is the control environment which is the core of any effective internal control system. The control environment consists of the actions, policies, and procedures that reflect the overall attitudes of top management, directors, and owners of an entity about internal control and its importance to the entity (Elder et al. 2010). Tone at the top or the control environment in an organization reflects top management’s attitude and commitment to ethical values and culture of effective fraud risk management. The underpinning of this culture must be derived from the top through a comprehensive risk appetite framework that considers aligning strategy with risk appetite, reflects the entity’s risk management philosophy, influences the culture and operating style, guides resource allocation, and aligns the organization, people, process and infrastructure.

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According to COSO (2013), any effective control environment should include the following sub-components: (a) the board’s commitment of integrity and high ethical values; (b) the organization’s commitment to competence; (c) having effective human resources policies and practices; (d) having a clear organizational structure; management’s philosophy and operating style; (e) the board of directors and audit committee effective participation in the organization’s affairs; (f) and the extent by the organization are holding individuals accountable for their responsibilities. If the tone set by managers upholds ethics and integrity, employees will be more inclined to uphold those same values. However, if upper management appears unconcerned with ethics and focuses solely on the bottom line, employees will be more prone to commit fraud because they feel that ethical conduct is not a focus or priority within the organization. Employees pay close attention to the behavior and actions of their bosses, and they follow their lead. In short, employees will do what they witness their bosses doing.3 Corporate greed at the executive level has destroyed hundreds of companies, drained stockholders of their investments, and left innocent employees without work. Ken Lay, Jeffrey Skilling, and Andrew Fastow from Enron; Bernie Ebbers from MCI/WorldCom; and Dennis Kozlowski at Tyco have become household names, and to many are synonymous with what is wrong with our corporate system. These CEO criminals were sending a clear (though perhaps unintentional) message to their employees that committing fraud is acceptable as long as it makes the company seem profitable. They were obviously not setting an ethical tone at the top for their employees. It is crucial to a company’s success for executives and management to set an ethical example (or tone) of how their employees should behave in the workplace. When those in top positions set the wrong, unethical example by committing fraud, their employees will take heed and follow in their bosses’ fraudulent footsteps, creating an entire culture of workplace fraud. When executives put pressure on their employees to meet unrealistic goals to yield profits for the company, they are essentially forcing employees to do whatever it takes to achieve those goals, whether they achieve those goals improperly or not. To reflect its importance, Fig. 2 shows that the second internal control component is risk assessment. The organization should specify objectives with sufficient clarity to enable the identification and assessment of risks relating to objectives. Organizations should consider the potential for fraud by assessing all the fraud risk factors we have discussed in this chapter (motives for fraud; opportunities that enable fraud perpetration; rationalization of fraud; integrity; and fraud perpetrators’ capabilities). Organizations should also understand the inherent risk of their company, and assess changes that could have significant impact on the internal control system such as changes in the external environment, changes in the business model, changes in leadership.

3 ACFE.

Tone at the top. Available at www.acfe.com

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Management has primary responsibility for establishing and monitoring all aspects of the agency’s fraud risk-assessment and prevention activities. Fraud risks are often considered as part of an enterprise-wide risk management program, though they may be addressed separately as well. The fraud risk-assessment process should consider agency vulnerabilities and its exposure to material losses, taking into account the agency’s size and the complexity of its operations. To mitigate fraud risk, management should conduct an internal risk assessment to identify and prioritize the different types of fraud risks and apply appropriate fraud mitigation strategies. This process is an essential component of a healthy control environment and can reduce certain fraud risks. Most fraud risks can be mitigated with an appropriate system of internal control. Once a fraud risk assessment has been performed, the agency must identify the ongoing processes, controls, and other monitoring procedures that are needed to identify and/or mitigate those risks. The third internal control component is control activities and it involves the policies and procedures that help ensure that management’s instructions and guidelines are carried out, necessary actions are taken to address the risks faced by the organization, and that company’s objectives are achieved. The control activities control component includes other specific sub-components that could help organizations reduce fraud risk such as adequate segregation of duties; proper authorization of transactions and activities; adequate documents and records; physical control over assets and records; and independent checks on performance. The fourth control component is information and communication. This component refers to the methods used to initiate, record, process, and report an entity’s transactions and to maintain accountability for related assets. Required information has to be identified and communicated in a suitable format and time to employees and management at all levels to enable individuals to carry out their responsibilities. Effective communication with external parties such as customers, suppliers, and shareholders is also needed. The fifth internal control component is monitoring which overshadows all other four internal control components. Monitoring is a process that assesses the quality of the internal control system’s performance over time. It includes regular management and supervisory activities. Internal control deficiencies should be reported to upper level management and serious matters should be reported to the board of directors (BOD). Monitoring is important because it ensures the other components of COSO internal control framework are running as effectively as planned and it helps to reduce fraud risk. Effective board of directors should provide oversight on all five components of the internal control system; stay involved in the company’s affairs; continually assesses and monitors management’s activities; and reduce the risk of management’s override of internal control system. The board should also create an audit committee that is charged with oversight responsibility for financial reporting. Effective audit committees should monitor the work of both internal and external auditors. Examples of effective anti-fraud controls include: ensuring that top management and the board of directors are committed to integrity and ethical values; top

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management should lead by example; the organization should establish a code of ethics and evaluate the adherence of staff at all levels to ethical values; raising fraud awareness through education and training; top management should treat employees with fairness and respect; ensuring that there is adequate segregation of duties at all levels within the organization; maintaining proper safeguards over assets and records to reduce the risk of theft and abuse; continuous monitoring; and prosecuting fraud criminals rather than dismissing them. More examples of anti-fraud controls are provided in Toolkit #3.

6.3 Maintaining a Sound Corporate Governance System Corporate governance is broadly defined as a system by which companies are directed and controlled. Effective corporate governance system will focus on designing and implementing a sound internal control and monitoring system. A company’s culture should promote integrity and openness, value diversity and be responsive to the views of shareholders and wider stakeholders (Financial Reporting Council (FRC) 2018). Sound fraud risk management is in the heart of any effective corporate governance system. The FRC in the UK is responsible for monitoring the quality of corporate governance in the UK and issues an updated code of corporate governance every year. The code of corporate governance in the UK is a code of good governance practices that applies the market-based approach “comply or explain”. The “comply or explain” approach requires companies to apply the main principles of the UK code of corporate governance and the related provisions or to explain the rationale behind any deviations from the code. Shareholders are given the right to either approve or disapprove the board of directors’ rationale for any deviation from the code. According to the 2018 UK code of corporate governance, boards of directors are responsible for the governance of their companies through establishing formal and transparent procedures for maintaining fair financial reporting, effective risk management and internal control system, and for keeping good relationship with the company’s auditors and shareholders (FRC 2018). Good corporate governance requires the efforts and dedication of the entity’s board of directors; management and employees at all levels; the audit committee; internal auditors; and external auditors. Some examples of good corporate governance practices include: Having effective board of directors; having effective internal control system; having adequate risk assessment and risk management; top management and board of directors promoting integrity and ethical values throughout the organization; continuous monitoring; regular evaluation of employees and management performance; setting realistic targets; and maintaining good communication and relationship with employees, suppliers, customers, and shareholders. More examples of good corporate governance practices are listed in Toolkit #4.

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Managing fraud risk requires individuals and organizations with integrity and commitment to the success of the business. We mentioned earlier that sound risk management is in the heart of an effective corporate governance system. This section will explain the role of board of directors, external auditors, internal auditors, and the audit committee in maintaining good governance practices, and managing corporate fraud risk.

6.3.1

Board of Directors and Corporate Fraud Risk Management

Any corporation is headed by the board of directors who sets the strategic direction for the business and is responsible for monitoring management performance. One of the important principles in corporate governance is “Accountability”. Accountability entails that the board of directors of a company confirm in the annual report that they have carried out a robust risk assessment and describe how those risks are being managed or mitigated. Board of directors are also expected to monitor the company’s risk management and internal control systems. Weak internal control system and poor corporate governance could increase the risk of fraud. The most prominent organizational weakness that contributed to corporate fraud according to the ACFE global fraud study in 2018 was a lack of internal controls followed by an override of existing internal controls by management and those charged with governance. Ineffective board leadership could increase fraud risks. Research indicates that the opportunity to commit fraudulent financial reporting increases when the firm does not have strong corporate governance mechanisms (Hasnan et al. 2013). Dunn (2004) found that financial reporting fraud is more likely to occur when there is a concentration of power in the hands of insiders where they regulate the flow of information needed to make decisions and also control the board through ownership interest. A strong risk culture has a strong effective governance structure which is fit for the needs of the organization. It will be featured in many of the organizations business functions and be an integral part of the decision-making process. The structure will have a clear pathway which shows the hierarchy of this decision making by dedicated risk teams and committees. The organization should raise fraud awareness through education and training; establish a whistle-blower programme; and distribute anonymous surveys to gauge employee views on the risk culture of the firm (Thackeray 2018b). The board of directors should ensure that the organizational culture and structure is conducive and open to fraud risk management. The board should also create a structure with a dedicated entity, department or person to lead all fraud risk management activities; plan regular fraud risk assessments and assess risks to determine a fraud risk profile; and design and implement a fraud hotline or reporting system. As part of managing the hotline, a dedicated team appointed by the board of directors should determine risk responses and document an anti-fraud strategy based

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on your fraud risk profile and develop a plan outlining how you will respond to identified instances of fraud. The board of directors should then conduct risk-based monitoring, and evaluate all components of the fraud risk management framework (Thackeray 2018a). The toolkit provided in this chapter include examples of antifraud controls that management and the board of directors need to implement in order to manage the risk of fraud (see Toolkit #3).

6.3.2

External Auditors and Corporate Fraud Risk Management

External auditors have an important role to play in corporate fraud risk assessment and management. External auditors serve as one of the few credible sources of external governance mechanisms capable of discouraging opportunistic behavior of managers (Chen et al. 2013; ICAEW 2005). External auditors could act as an effective fraud deterrent mechanism because most fraud perpetrators fear getting caught and the associated consequences (Rezaee and Riley 2010; Dorminey et al. 2012). External audit is an effective corporate governance mechanism because it provides those charged with governance with timely observations arising from the audit that are significant and relevant to their responsibility to oversee the financial reporting process (ISA 260).4 External audit can act as a fraud deterrent mechanism. According to a global study by the ACFE (2016), fraud perpetrators are less likely to commit fraud if they know someone is watching. The international audit standards (e.g. ISA 200; ISA 2405 ) as well as American standards on auditing (e.g. SAS 996 ) require external auditors to provide reasonable assurance that the financial statements are free from material misstatements whether due to errors or fraud. Therefore, external auditors are responsible for assessing and responding to fraud risk arising from assets misappropriation and financial statements fraud. They are also required to assess the risks arising from illegal acts such as bribery and corruption (ISA 2507 ). The word “materiality” refers to the threshold or cut-off point after which financial information becomes relevant to the decision making needs of the users. Information contained in the financial statements must therefore be complete in all material respects in order for them to present a true and fair view of the affairs of the entity. If fraud is committed and impacted on the financial statements, the financial 4 International

Standard on Auditing (ISA 260): Communication with those charged with governance. Available at http://www.iasb.org 5 ISA 200: Overall objectives of the independent auditor. Available at http://www.iasb.org; ISA 240: The auditor’s responsibilities related to fraud in an audit of financial statements. Available at http://www.iasb.org 6 SAS 99: Statement on Auditing Standards No. 99: Consideration of Fraud in a Financial Statement Audit. Available at http://www.aicpa.org 7 ISA 250: Consideration of laws and regulations in an audit of financial statements. Available at http://www.iasb.org

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statements cannot be true or fair. The word materiality also means that auditors are not responsible for detecting every type of fraud but only fraud that has material (i.e. Significant) impact on the financial statements. In their assessment of fraud risk, external auditors need to consider fraud risk factors that may help to increase the risk of motivations to commit fraud, the risk of opportunity to commit fraud, and the risk of rationalization of fraud. The toolkits provided in this chapter include examples of risk factors that external auditors need to consider while assessing the risk of fraud (see Toolkit #1 and Toolkit #2).

6.3.3

The Role of Internal Auditors and the Audit Committee in Fraud Risk Management

Internal auditors are appointed by companies in order to evaluate and report on the effectiveness of their internal control and risk management systems; identify indicators or red flags for fraud; identify control weaknesses which may allow fraud to occur; and to recommend fraud investigations where appropriate. In an effective corporate governance system, internal auditors are also expected to communicate with management regarding fraud occurrences, and assist in the prosecution of fraud criminals. The audit committee is normally established by the board but should maintain independence from the board. The audit committee should include independent non-executives directors that have sufficient financial expertise including a good understanding of the role of external and internal auditors. The role of the audit committee involves monitoring the integrity of the financial statements of the company; reviewing the company’s internal control and risk management systems; monitoring and reviewing the effectiveness of the company’s internal audit function; and making recommendations to the board in relation to the remuneration, appointment, re-appointment and removal of the external auditor. The audit committee is expected to review and monitor the external auditor’s independence and objectivity, and the effectiveness of the audit process. It should also develop and implement policy on the engagement of the external auditor to supply non-audit services, taking into account relevant ethical guidance regarding the provision of non-audit services by the external audit firm. The audit committee (or the board of directors where no audit committee exists) must systematically and periodically evaluate management’s identification of fraud risks, the implementation of antifraud prevention and detection measures, and the creation of the appropriate “tone at the top.” Active oversight by the audit committee serves as a deterrent to management and employees engaging in fraudulent activity and helps management fulfil its responsibility. Active oversight by the audit committee helps to reinforce management’s commitment to creating a culture with “zero tolerance” for fraud.

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7 Chapter Summary This chapter explains and describes the meaning, nature, and impact of corporate fraud; discusses the types of corporate fraud; highlights the difference between risk assessment and risk management, and discusses how organizations could effectively assess and manage fraud risk. The chapter proposes a framework including five important steps that could help organizations design effective fraud prevention strategies. The chapter emphasizes the importance of understanding the psychology of fraud criminals; identifying fraud risk factors; designing effective anti-fraud controls; and maintaining corporate governance system in order to effectively manage the risk of corporate fraud. Sound fraud risk management is in the heart of any effective corporate governance system. The board of directors, staff at all levels, internal and external auditors, and the audit committee all have a role to play in corporate fraud risk management which has been outlined in this chapter. This chapter also provides various examples of good governance practices, and the fraud risk factors that could help organizations and auditors assess the risk of corporate fraud. It also provides examples of anti-fraud controls that could help businesses manage the risk of fraud (See toolkits 1 to 4). Toolkit #1 Factors that may increase the risk of motive/rationalization to commit fraud • New regulations or laws that might impact the company’s profitability or ability to continue in the market • Pressure from family to earn more • Pressure from investors to pay dividends or to achieve certain targets • Pressure to meet or beat analysts’ forecasts • High competition in the market • Deteriorating financial position in the market • Bonuses or remuneration that are linked to financial performance • High budget variances • Large amount of debt • Treating employees unfairly and disrespectfully • Putting too much pressure on employees to achieve unrealistic targets • Paying less than average industry salaries • Unfair or vague criteria for promotion and pay rise • Excessive workloads with unrealistic deadlines • Leading by fear • No commitment to integrity and ethical values within the organization Toolkit #2 Factors that may increase the risk of opportunity to commit fraud • Lack or inadequate segregation of duties • Concentration of power in the hand of one or few individuals • Weak or ineffective audit committees

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• • • • • • • • • • • •

Weak or ineffective board of directors Lack of independent non-executive directors on board Lack of monitoring and independent checks on performance Dishonest external auditors that do not care about fraud risk or investors’ interests External auditors that are lacking knowledge of fraud risk Lack of internal or external audit function Ineffective, dishonest, or inexperienced internal auditors Unqualified staff especially in the finance department Lack of or inadequate safeguard over assets and records Inadequate documents and records (i.e. lack or insufficient audit trail) Lack of job rotation Not taking corrective actions when needed and lack of or ineffective penalty system • Lack of proper fraud risk assessment and management Toolkit #3 Examples of anti-fraud controls for managing corporate fraud risk • Fraud and ethics periodic training to all staff including management and directors • The design and implementation of an effective code of ethics • Tone at the top or leading by example • Appointing staff that are committed to integrity and ethical values, and are qualified to do the job • Establishing an effective internal audit department to assess control risks and fraud risks • Appoint external auditors that have experience in fraud risk assessment • Separating the duties of the chairman and CEO at the board level • Setting up CCTV cameras • Appointing someone or a team that could actively look for fraud risk factors and provide recommendations on managing fraud risk • Design fair remuneration packages to staff at all levels • Establish an anonymous whistle-blower line • Encourage staff to report fraud and unethical behavior • Introduce a zero-tolerance to fraud and unethical behavior policy • Conduct continuous monitoring and evaluation of staff performance and behavior • Use anonymous staff surveys to learn more about staff issues or concerns • Use anonymous staff surveys to learn about their perception of management integrity Toolkit #4 Examples of good corporate governance practices • Setting clear objectives, mission, vision, and a sound strategy • Investing in staff development and training • Promoting diversity, fairness, and transparency • Following rules and regulations • Giving back to the community

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• Having independent and qualified external auditors to audit the company’s financial statements • Having an effective audit committee to monitor the performance of external auditors and the quality of the company’s financial reporting • Having a qualified internal auditor to evaluate the effectiveness of the company’s internal control system and to detect/prevent fraud • Carefully designing directors’ remuneration • Firing ineffective board members, management, or employees • Prosecuting fraud perpetrators instead of firing them • Designing a fair reward system that is based on performance

References Albrecht S (2014) Iconic fraud triangle endures. Fraud Magazine. Available at https://www.fraudmagazine.com/article.aspx?id=4294983342 Albrecht S, Howe K, Romney M (1984) Deterring fraud: the internal auditor’s perspective. Institute of Internal Auditors Research Foundation. Available at https://na.theiia.org/iiarf/pages/the-iiaresearch-foundation.aspx Albrecht WS, Albrecht C, Albrecht CC (2008) Current trends in fraud and its detection. Inf Secur J 17:17–25 Albrecht C, Turnbull C, Zhang Y, Skousen CJ (2010) The relationship between South Korean chaebols and fraud. Manag Audit J 33(3):20–32 Association of Certified Fraud Examiners (ACFE) (2016) Report to the nation on occupational fraud and abuse. Available at http://www.acfe.com Association of Certified Fraud Examiners (ACFE) (2018) Report to the nation on occupational fraud and abuse. Available at http://www.acfe.com Chen J, Cumming D, Hou W, Lee E (2013) Executive integrity, audit opinion, and fraud in Chinese listed firms. Emerg Mark Rev 15:72–91 Coenen T (2008) Essentials of corporate fraud. Wiley, Hoboken COSO (2013) COSO framework and sox compliance. Available at https://www.coso.org/documents/COSO%20McNallyTransition%20ArticleFinal%20COSO%20Version%20Proof_5-31-13.pdf Cressey DR (1950) Management fraud, accounting controls, and criminal logical theory. In: Elliot RK, Willingham JJ (eds) Management fraud: detection and deterrence. Petrocelli Books, Princeton Dorminey J, Fleming A, Kranacher M, Riley R (2012) The evolution of fraud theory. Issues Account Educ 27(2):555–579 Dunn P (2004) The impact of insider power on fraudulent financial reporting. J Manag 30(3):397– 412 Elder RJ, Beasley MS, Arens AA (2010) Fraud auditing. In: Auditing and assurance services: an integrated approach, 13th edn. Pearson, Upper Saddle River Financial Reporting Council (FRC) (2018) The UK code of corporate governance. Available at https://www.frc.org.uk Hasnan S, Abdul RR, Mahenthiran S (2013) Management motive, weak governance, earnings management, and fraudulent financial reporting: Malaysian evidence. J Int Account Res 12(1):1–27 Hillson D (2001) Extending the risk process to manage opportunities. In: Fourth European Project Management Conference, PMI Europe, London UK, 6–7 June. Available at: http:// citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.564.8597&rep=rep1&type=pdf

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Institute of Chartered Accountants in England and Wales (ICAEW) (2005) The audit quality forum. Agency theory and the role of the audit. Available at http://www.icaew.com Institute of Internal Auditors (IIA) (2014) Auditing anti-bribery and anti-corruption programs. Available at: https://global.theiia.org Jones M (2011) Creative accounting, fraud, and international accounting scandals. Wiley, Chichester Kallman J (2005) What is risk? Risk Manage 52(10):57–65 Kassem R (2017) Exploring external auditors’ perceptions of the motivations behind management Fraud in Egypt – a mixed method approach. Manag Audit J 33(1):16–34 Kassem R, Higson AW (2012) The new fraud triangle model. J Emerg Trends Econ Manag Sci 3(3):191–195 Kimuyu P (2007) Corruption, firm growth and export propensity in Kenya. Int J Soc Econ 34(3):197–217 KPMG (2020) Fraud barometer 2019. Available at www.kpmg.com/uk Lambsdorff J (2003) How corruption affects persistent capital flows. Econ Gov 4:229–243 Lister LM (2007) A practical approach to fraud risk, Internal Auditor Rae K, Subramaniam N (2008) Quality of internal control procedures: antecedents and moderating effect on organisational justice and employee fraud. Manag Audit J 23(2):104 Rezaee Z (2005) Causes, consequences, and deterrence of financial statement fraud. Crit Perspect Account 16(1):20–54 Rezaee Z, Riley R (2010) Financial statement fraud: prevention and detection, 2nd edn. Wiley, Hoboken Soltani B (2007) Corporate fraud, corporate scandals, and external auditing. In: Auditing: an international approach. Pearson Education Limited, Edinburgh Thackeray J (2018a) A framework for effective fraud risk management. Available at http:// www.acfeinsights.com Thackeray J (2018b) Three ingredients of a strong risk management culture. Available at http:// www.acfeinsights.com UK Bribery Act (2010). Available at http://www.legislation.gov.uk/ukpga/2010/23/contents UK Fraud Act (2006). Available at http://www.legislation.gov.uk/ukpga/2006/35/contents UK Home Office (2018) The nature and scale of fraud: a review of the evidence. Available at https://www.gov.uk/government/publications/the-scale-and-nature-of-fraud-a-reviewof-the-evidence Wells JT (2005) Principles of fraud examination. Wiley, Hoboken/New York Wells JT (2011) Corporate fraud handbook: prevention and detection, 3rd edn. Wiley, Hoboken Weygandt J, Kimmel P, Kieso D (2015) Financial accounting, 3rd edn. Wiley, Hoboken Wolfe DT, Hermanson DR (2004) The fraud diamond: considering the four elements of fraud. CPA J 74:38

Leverage Financing and the Risk-Taking Behavior of Small Business Managers: What Happened After the Crisis? Nour Khairallah, Ramzi Benkraiem, and Catherine Deffains-Crapsky

1 Introduction Throughout the years, SMEs have received significant attention from economists. These firms are considered as a source of dynamism for the economy as they promote competitiveness, stimulate innovation, and generate employment opportunities. According to the OECD’s report in 2018, they account for almost the totality of the firms, ensure 60% of the jobs and generate 50% to 60% of the added value on average.1 SMEs are engaged in more growth opportunities when compared to larger firms (Kirschenmann 2016), yet they lack sufficient resources to self-finance their projects. In addition, they suffer from heavy transaction costs and a restrained entrance to financial markets. Thus, the vast majority of these firms rely on bank financing (Berger et al. 2001b). On the other hand, managers of SMEs are prone to engage in high levels of risk as they are captivated by expanding their firms. The risk-taking behavior of managers

1 Information

retrieved from: OECD (2018), Financing SMEs and Entrepreneurs 2018: An OECD Scoreboard, OECD publishing, Paris. https://doi.org/10.1787/fin_sme_ent-2018-en

N. Khairallah () Granem, Université d’Angers, Angers, France Audencia Business School, Rn’B Lab, Nantes, France e-mail: [email protected] R. Benkraiem () Audencia Nantes School of Management, Nantes Cedex 3, France e-mail: [email protected] C. Deffains-Crapsky () Granem, Université d’Angers, Angers, France e-mail: [email protected] © Springer Nature Switzerland AG 2021 C. Zopounidis et al. (eds.), Financial Risk Management and Modeling, Risk, Systems and Decisions, https://doi.org/10.1007/978-3-030-66691-0_3

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derives from the ‘empire building’ strategy (Jensen 1986). In fact, it has been shown that managers seek excessive growth and investment to boost their power in the firm, enhance their reputation on the market and raise their compensation (Hope and Thomas 2008; Jensen 1986). Despite the importance of the corporate leverage and the risk-taking behavior of managers for the survival and the growth of SMEs, there is surprisingly little empirical proof on the relationship between these two components. An existing body of literature provided theoretical evidence on the extent to which corporate leverage has an influence on the risk-taking behavior of managers. This paper is motivated by three of these theories: the Free Cash Flow Theory by (Jensen 1986), the debt and optimal capital structure by (Myers 1977), the capital structure theory by (Maksimovic and Titman 1991). Jensen (1986) and Myers (1977) presented theoretical models that emphasize the conflict of interests between managers and shareholders and the role of debt when it comes to influencing the manager’s risk-taking behavior. They show that leverage plays a disciplining role preventing the manager from increasing his risk-taking behavior. Meanwhile, Maksimovic and Titman (1991) provided evidence that corporate leverage enhances the managerial risk-taking behavior. Nevertheless, the empirical evidence on this relationship remains scarce. Previous studies provided mixed results. Some authors claimed that leverage attenuates the risk-taking behavior of managers (Adams et al. 2005; Faccio et al. 2016; Nguyen 2012), whilst others stated that leverage amplifiess it (Boubakri et al. 2013; Faccio and Mura 2011; Vo 2016). Nonetheless, Cheng (2008) and Nguyen (2011 reported that there is no significant influence of leverage on managerial risk-taking. Yet, to the best of our knowledge, there is no empirical study entirely dedicated to the examination of this relationship. Thus, this paper tries to fill this gap in the literature by empirically investigating the impact of firm leverage on the risk-taking behavior of managers in SMEs during and after the financial crisis of 2008. To address this problem, we consider a sample composed of 1403 French small and medium-sized firm observations listed on the Euronext Paris stock exchange over the period 2008 to 2016. This paper highlights the impact of the financial crisis of 2008 on the risk-taking behavior of corporate managers. Thus, the regressions will be run over the entire period and over the two sub-periods (i.e. during 2008 and from 2009 to 2016). Following Adams et al., (2005), we measure the manager’s risk-taking behavior using the absolute deviation from the firm’s expected earnings. The regressions also include other control variables such as the size, sales growth, tangibility, liquidity and interest coverage ratio. In addition, we examine the robustness of our results using the instrumental variable approach that controls for endogeneity. The results indicate that over the whole period corporate leverage significantly serves as an enhancement tool for the risk-taking behavior of managers in SMEs. This role is more important after than during the crisis. The intuition is that, credit rationing generated by the financial crisis of 2008 reduced the monitoring activities of banks which has increased the risk-taking behavior of corporate managers. In other words, the financial crisis of 2008 has had many repercussions on the banking

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sector which mostly affected the small vulnerable businesses. In order to enhance the financial stability, several governments discussed and imposed norms on banks such as the Basel II and III reforms. They were demonstrated in a higher level of restrictions and credit rationing, especially applied on the lending to small risky firms. As banks amplified the credit rationing on SMEs’ financing during the crisis, they reduced their monitoring activities after it. Following Williamson (1987) and in contrast to Diamond (1984), this paper considers that bank monitoring takes place after rather than before the allocation of funds. Thus, by increasing the restrictions set on small businesses’ bank financing and reducing credit availability at the expense of higher monitoring activities, managers tend to engage in higher risk activities. The contribution of this paper is threefold. To the best of our knowledge, this article represents a first empirical attempt that directly links the leverage with the manager’s risk-taking behavior. Second, this relationship takes place in a small and medium-sized enterprises framework which has been long ignored since most of the research has been conducted on larger firms. Third, this paper investigates the impact of the global crisis of 2008 on the relationship between managerial risktaking and leverage in France. The remainder of this paper is organized as follows: Section II develops the theoretical framework and the hypotheses. Section III presents the sample and the empirical methods adopted in this paper. Section IV describes the empirical findings and the robustness test. Finally, section V concludes the article.

2 Literature Review This chapter reviews the previous literature that discussed the relationship between long-term debt and the managerial behavior. The first section presents a survey on the bank financing of SMEs during and after the financial crisis of 2008. Then, the second section explains the capital structure theories and presents theoretical and empirical evidence regarding the relationship between leverage and managerial risk-taking behavior.

2.1 SMEs Bank Financing In a normal economy, SMEs struggle to survive, grow and expand as they encounter many obstacles when it comes to financing their projects. Due to their small structure, SMEs lack sufficient resources to self-finance their projects which induces them to become bank dependent. However, banks find difficulty to assess the risk of these firms (Danielson and Scott 2007) for several reasons; the presence of a high level of informational asymmetry in their opaque structure, the low level of collateral they are capable of offering and the lack of financial history (Beck and

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Demirguc-Kunt 2006; Beck et al. 2008, 2011; Danielson and Scott 2007) which make them suffer from heavier transaction costs and greater risk premiums in comparison to larger firms (Beck et al. 2008). Thus, previous literature showed that small banks tend to develop a long-term relationship lending based on soft information with their small scaled customers (Berger et al. 2001a; Berger and Udell 1996; Boot 2000; Elyasiani and Goldberg 2004). Whilst others stated that banks prefer to impose stringent covenants, larger collaterals, and a stricter monitoring (Blazy and Weill 2013; Chava and Roberts 2008; Chen and Wei 1993; Cole et al. 2004; Diamond 1984; Rajan and Winton 1995). More recently, other lending alternatives based on a transactional relationship that uses hard information– the assets-based lending and the leasing technique – have seen the light, which allowed large banks to start providing funds to SMEs (Beck and Demirguc-Kunt 2006). During the financial crisis of 2008, the SMEs’ financial situation got more fragile due to various reasons. Among these, we highlight their inability to reduce their size already small, they are less diversified when compared to larger firms, their financial structure becomes more vulnerable, and they have less financing alternatives as they depend mostly on bank financing (OCDE 2009). Furthermore, it has been shown that during the financial crisis, corporate insolvencies in Europe marked on average an increase of 10.9% from 2007 to 2008. More particularly, in France, the insolvencies exceeded the European average by reaching 49,100 corporate insolvencies in 20082 and an increase of 15.4% from 2007 to 2008 (Insolvencies in Europe 2008–2009 report, credit reform). Consequently, in order to assist SMEs survival during and most importantly after the crisis and to boost their access to bank financing, governments injected funds to ensure the recapitalization of banks and improved their previous programs by implementing new tools such as the execution of a “credit mediator” and the application of the revised versions of the Basel Accords. The “credit mediators” are characterized by an intermediation role between banks and firms facing difficulties or a rejection of bank financing. They aim to assist these firms by re-submitting their demand of bank financing and by asking the banks to re-examine them which facilitates the SMEs’ access to loans. Furthermore, during the crisis, the European committee detected the necessity to apply the reform of Basel II. The Basel Accords’ objective relies on enhancing the stability of the banking system through the recognition of several types of risk (Aubier 2007). Basel II was first originated and signed in 2004 by the Basel committee on Banking Supervisions (BCBS), and was later effective in January 2008. It aims on extending the Basel I principles3 by including a more elaborated risk framework and on reforming the banking system. The banks’ capital requirements were, henceforth, measured through the assessment of three types of risk: credit risk, 2 Corporate insolvencies in European countries reached 150,240 in total which places France as the

highest country with 49,100 corporate insolvencies (32.68% of the total corporate insolvencies). I reform also known as the Basel Capital Accord was signed by the Basel committee and published in July 1988. Its objective was to enhance the stability of the international banking system by imposing a ratio of capital to risk-weighted assets equal to a minimum of 8% on banks of the member countries.

3 Basel

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operational risk and market risk. They were provided with several risk measurement approaches. When using for example, an internal rating-based (IRB) approach to assess the credit risk of an SME financing, banks would be charged with less capital requirement than with the employment of the regulatory ratio (Dietsch 2016). Therefore, it was expected that these new capital recommendations will not imply an increase of the restrictions set on SMEs, rather they will facilitate their access to bank financing as long as the risk encountered by these firms is controlled (Golitin 2007). Nevertheless, after the financial crisis of 2008, banks were still forced to impose severer constraints on SMEs financing and to reduce their access to shortterm funds as banks themselves suffered from illiquidity problems, restricted access to funds, and higher exposure to risks (OCDE 2009). In response to the deficiencies in the financial system that were exposed by the financial crisis of 2008, reinforcing Basel II three pillars was assumed to be compulsory. Hence, the BCBS agreed in 2010 to update the second version of the Basel Accords. The new Basel Accord, known as Basel III, was published in 2013 and introduced two new requirements. Under the first condition, banks are supposed to maintain a leverage ratio, measured by dividing tier 1 capital over the bank’s average total consolidated assets, in excess of 3%. Following the second condition, banks are expected to maintain two liquidity ratios that ensure their survival in case of the occurrence of another banking crisis. The “liquidity cover ratio” (LCR) requires from banks to hold a sufficient amount of high-quality liquid assets in order to meet their engagements over 30 days during a period of severe stress. The “Net stable funding ratio” (NSFR) encourages banks to finance their activities with long-term stable funds by holding a sufficient amount of long-term assets that covers their engagements for a period of 1 year of stress. These two reforms have certainly reinforced the banking system by imposing stricter conditions on banks in order to prevent the event of the financial crisis from occurring again. Nevertheless, they have clearly urged banks to reduce the availability of funds and to impose a more stringent credit rationing especially on SMEs due to their high level of opacity and informational asymmetries. The phenomenon of credit rationing has been present for several years and has been the subject of previous literature, yet became more intense since the crisis (Lee et al. 2015). In fact, prior authors showed that this issue is not only triggered by components of the microeconomic level, yet is also associated to the macroeconomic approach in which this paper is concerned. Jaffee and Russell (1976) and Stiglitz and Weiss (1981) were the first authors to address this problem. The former authors stated that “credit rationing occurs when lenders quote an interest rate on loans and then proceed to supply a smaller loan size than that demanded by the borrowers.” (p.651). While the latter authors defined credit rationing as “( . . . ) circumstances in which either (a) among loan applicants who appear to be identical some receive a loan and others do not, and the rejected applicants would not receive a loan even if they offered to pay a higher interest rate; or (b) there are identifiable groups of individuals in the population who, with a given supply of credit, are unable to obtain loans at any interest rate, even though with a larger supply of credit, they would.”

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(p.394–395). In this paper, we do not differentiate between the credit rationing types, rather we are interested by the reasons behind the occurrence of this problem. The credit rationing deriving from the macroeconomic level is associated to a “credit crunch” situation mostly present during and after a crisis. Characterized by a shrinkage in the availability of loans in addition to a tightening of loan access conditions (Nguyen and Qian 2014), credit crunch following a financial crisis affects a large number of firms especially small ones since they are the most likely to be risky and vulnerable. Many empirical studies confirmed that this cyclical problem marked its presence across SMEs in several countries after the financial crisis of 2008. Lee et al. (2015) showed that the access to bank financing for UK firms became harder after the crisis than during it. Koráb & Pomˇenková (2017) revealed the existence of a credit crunch between the fourth quarter of 2008 and the fourth quarter of 2012 in Greece. As a result, Greek SMEs suffered from a restrained access to bank financing. In addition, Iyer et al. (2014) detected a reduced credit availability among Portuguese SMEs during the crisis of 2008. In addition, given the fact that France was among the largest European countries that endured from a bank financing gap above the euro area average (Wehinger 2014), French SMEs suffered from the restrained access to bank financing and a reduced credit availability during and after the financial crisis of 2008. It has been shown that, since 2009, banks enlarged their assessment of the risk determined by firms, especially for SMEs (Wehinger 2014).

2.2 Related Theories and Hypothesis Development Capital structure has always been a subject of interest in most of the studies. It has been defined as the mixture of long-term sources that the firm uses as funds. These sources are composed of debt instruments as well as preferred and common stocks. The objective is to choose the combination of these sources that maximizes the firm’s market value and reduces its cost of capital. This problem has been discussed for a longtime, yet remains unresolved. The first authors to initiate these discussions were Modigliani and Miller in 1958. In their paper, the authors considered the existence of a perfect capital market in which agency costs, asymmetric information, transaction costs and bankruptcy costs do not apply. Under these strict assumptions, they found that the market value of any firm is not affected by the choice of its capital structure, its level of leverage especially. Rather, they argued that the value of the firm is estimated by the expected earnings scaled by the average cost of capital of the class4 to which it belongs. In addition, they found that the average cost of capital of the business is

4 Modigliani and Miller (1958) divided the firms in their study into classes according to their returns

such that “( . . . ) the return on the shares issued by any firm in any given class is proportional to the return on the shares issued by any other firm in the same class” (p.266).

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also independent from its capital structure. Their proposition was referred to as the capital structure irrelevance theorem. Meanwhile, since the existence of informational asymmetries, transaction costs, bankruptcy costs and taxes in the real world make the assumption of a perfect capital market seems quiet unrealistic, several authors challenged Modigliani and Miller’s (1958) suggestions and claimed that their theorem is only valid under perfect capital market assumptions. In fact, Modigliani and Miller (1963) started themselves to alter their initial propositions. They corrected their original statement “( . . . ) the market values of firms in each class must be proportional in equilibrium to their expected returns net of taxes (that is, to the sum of the interest paid and expected net stockholder income)” (p.272) by arguing that the actual return after tax of two firms in the same risk-class can be different if the level of leverage is not the same in these firms. They assumed that, the choice of capital structure does not only depend on the expected returns but also on the tax rate and the amount of leverage. In addition, they proved that the benefits of tax on debt financing are greater than what was formerly shown in their first work. Thus, the use of debt expands the value of the firm of a volume equal to the marginal tax rate times the debt market value. Ever since, many theories concerning the firm’s capital structure were established. Of these, we develop (i) the debt and optimal capital structure theory of Myers (1977), (ii) the cash flow theory of Jensen (1986), and (iii) the capital structure choice theory by Maksimovic and Titman (1991). In his paper, Myers (1977) found that even with the existence of a perfect capital market with symmetric information between the agents, firms will find it rational to limit the amounts of their borrowings. He showed that, the leverage of the firm influences the investment decision-making of its management. In fact, when a firm is debt financed, the manager will be preoccupied by meeting all the interest and principal payments that he will forego positive investment opportunities. As a result of debt overhang, less positive net present value projects will be taken into consideration which leads to the under-investment phenomena. Consistent with the findings of Myers (1977), Jensen (1986) showed that leverage reduces the over-investment problem. In fact, managers are usually captivated by an empire building strategy. Therefore, they have incentives to expand the size of their firms by investing in projects. The author showed that the manager of a firm with a surplus of cash flow and low investment opportunities is more likely to engage in negative net present value projects. He defined the free cash flow as the excess of cash required to invest in positive net present value projects. Thus, investing in value destroying projects is not in the interest of the shareholders of the firm who prefer to receive the excess of cash flow in form of dividends. Consequently, they will use debt as a tool to reduce the risk-taking issue. By doing so, managers will be monitored by creditors. As a result, they will be forced to lower their overinvestment strategy in order to meet all of the interest and principal payments and to avoid going bankrupt. Therefore, leverage has an attenuating role on managerial risk-taking.

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In contrast, Maksimovic and Titman (1991) documented in their paper the incentives that a highly leveraged firm should have in order to maintain its reputation and to continue offering high-quality products. Furthermore, they reported that, generally, individuals are reluctant to do business with a highly leveraged firm due to the costs they will incur if it goes bankrupt. The employees, customers and stakeholders are usually cautious when dealing with a leveraged firm because they are more likely to suffer from the costs in the event of a financial distress than other agents. Consequently, a manager agreeing to engage in a highly leveraged firm, has to tolerate the severe bankruptcy costs resulting from the firm’s probability of default. His willingness to engage in such situation makes him risk-taking. Thus, leverage is positively associated to the risk-taking behavior of managers. In a recent study, Faccio et al. (2016) employed leverage as a proxy for corporate risktaking. They suggested that “given a (negative) shock to firm’s underlying business conditions, the higher the leverage, the greater the (negative) impact of the shock on the firm’s net profitability (including a higher probability of default)” (p.196). Hence, leverage positively influences the corporate risk-taking. Nevertheless, there is little empirical evidence on how firm leverage influences the managerial risk-taking. More precisely, prior empirical studies provided mixed results regarding this relationship. Adams et al. (2005) employed three measures for corporate performance and found that leverage is positively correlated to the standard deviation of stock returns, while it is negatively correlated to the standard deviation of Tobin’s Q and not significantly correlated to the standard deviation of ROA over the period 1992 to 1999. Nguyen (2012) reported a strong positive association between leverage and the volatility of ROA and stock returns, and a negative association with the volatility of the market to book value of assets. On another hand, Cheng (2008) documented that there is no significant impact of leverage on the volatility of earnings measured by ROA, Tobin’s Q and monthly stock returns in US firms over the period 1996 to 2004. In consistence with these findings, Nguyen (2011) defined managerial risk-taking as the absolute deviation from the firm’s expected earnings (i.e. expected ROA and Tobin’s Q). The author found that there is no significant impact of leverage on corporate risk-taking among Japanese firms over the period 1998 to 2007. Meanwhile, when employing other measures for corporate risk-taking, Nguyen (2011) reported a strong positive relationship between leverage and the standard deviation of ROA and stock return, and a negative association with the standard deviation of the market to book ratio. Nonetheless, Faccio et al. (2016) stated a strong negative relationship between leverage and corporate risk-taking measured by the volatility of ROA and the likelihood of survival of firms across 18 countries during the period 1999 to 2009. In consistence with these findings, Firth et al. (2008) reported a significant negative association between leverage and firm’s investments in China. In contrast, several recent papers claimed that a leveraged firm is associated with higher earnings volatility and more risk-taking activities (Faccio and Mura 2011; Boubakri et al. 2013; Vo 2016). More precisely, after employing the volatility of ROA as a measure

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for corporate risk-taking, Faccio and Mura (2011) found a positive impact of leverage on the volatility of earnings over the period 1999 to 2007. Their findings hold when they use the standard deviation of ROE and the difference between the maximum and minimum ROA as alternative measures for firm risk-taking. Boubakri et al. (2013) considered the volatility of ROA as a measure for corporate risk-taking and reported a strong positive relationship with firm leverage. Further, Vo (2016) measured corporate risk-taking as the ratio of volatility of earnings (ROA and ROE) over firm earnings in Vietnamese firms over the period 2007 to 2014. The author documented leverage as a tool that stimulates earnings volatility.

3 Sample and Methodology This chapter describes the sample and methodology employed in this article. The first section presents the sample selection procedure. The second section reports the measurements of the risk-taking behavior, leverage and other control variables.

3.1 Sample In this article, the financial information is gathered from Amadeus. This database provided by the Bureau Van Dijk Electronic Publishing office, contains information on privately and publicly held firms. It covers around 21 million firms across Europe. The sample includes all non-financial SMEs listed on the Euronext Paris stock exchange over the period 2008 to 2016. Financial institutions represented by banks, securities and insurance companies as well as holdings (64–66, 69, 70 and 99 NACE Rev. 2 codes5 )are excluded from the sample due to their different business nature and risk-taking metrics. The chosen period of study allows us to compare the results obtained during and after the financial crisis of 2008 and to highlight the impact of the crisis on the risk-taking behavior of corporate managers. The sample is, thus, divided into two sub-periods during 2008 and from 2009 to 2016. Hence, the regressions will be run over the whole sample and the two sub-periods. First, we begin by identifying publicly held firms that have less than 250 employees, a turnover lower than A C50 million or a balance sheet not exceeding A C43 million6 over the period 2008 to 2016. This step yields an initial sample composed of 1578 SMEs. Next, we eliminate 175 firm-observations from the sample due to the missing data of dependent and independent variables. This procedure generates a final sample composed of 1403 firm-observations over an 8-year period.

5 NACE

codes serve as an industry classification code for European firms. (Source: Eurostat). Commission definition of SMEs.

6 European

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Table 1 Sample

Panel A: Sample selection Non-financial SMEs from 2008 to 2016 SMEs with missing data Final sample Panel B: Time distribution 2016 2015 2014 2013 2012 2011 2010 2009 2008 Final sample

1578 −175 1403 168 164 185 169 150 146 138 147 136 1403

Table 1 summarizes the sample selection process and reports the time distribution of firm observations over the entire period. Panel B indicates that the number of SMEs has been rising over the past eight years in France, especially after the financial crisis of 2008.

3.2 Methodology 3.2.1

Model

To investigate the impact of leverage on the risk-taking behavior of corporate managers in SMEs, we employ the following model: a Risk i,t = ∝0 + ∝1 Lev i,t + ∝2 Yi,t + ∝3 Xi + εi,t

(1)

Where (i) Riski,t is defined as the risk-taking behavior of the manager represented by the corporate risk-taking of firm i at time t; (ii) Levi,t is represented by the level of leverage of firm i at time t; (iii) Ya i,t is a vector of firm characteristics that is associated to the managerial risk-taking, it includes: Si,t (Firm Size) is measured by the logarithm of total assets of firm i at time t; Ghi,t (Sales Growth) is computed by the difference between the net sales of two consecutive years divided by net sales of the earlier year of firm i; Pr j,t (Profitability) is defined as the Tobin’s Q ratio of firm i at time t; Chi,t (Cash holdings) is determined as the ratio of cash and cash equivalents over the total assets of firm i at time t; Tgj,t (Tangibility) is estimated by the fixed assets divided by the total assets of firm i at time t and Lqi,t (Liquidity) is measured by the current ratio equal to current assets divided by current liabilities. Ic i,t (Interest coverage ratio) is equal to the ratio of paid interest scaled by EBITDA.

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(iv) Xi is determined as the set of dummy variables that controls for year and firm effects. (v) εi,t is defined as the error term.

3.2.2

Measuring Risk-Taking Behavior

Following Adams et al. (2005) and Nguyen (2012), managerial risk-taking is estimated by the absolute deviation from the firm’s expected earnings. In this paper, we consider two proxies for the firm’s earnings: the return on assets ratio (ROA) and the return on equity ratio (ROE). ROA is defined as the ratio of earnings before interest, taxes, depreciation and amortization (EBITDA) divided by total assets. This ratio reflects the profitability of the firm’s decisions. ROE is measured by the ratio of net income over shareholder’s equity. This ratio explains whether the company’s operations are efficient. Both ratios are considered as the dependent variables in Eqs. (2) and (3), respectively. In addition, both equations employ leverage and other control variables that have an impact on the firm’s expected performance. The firm’s expected ROA and ROE are estimated as follows: ROAi,t = γ0 + γ1 Leveragei,t + γ2 Control variables i,t + εi,t

(2)

ROE i,t = γ0 + γ1 Leveragei,t + γ2 Control variables i,t + εi,t

(3)

The residuals are statistically defined as the deviation between the results of the model and the actual results. In our model, they are referred to as the deviation between the firm’s earnings and the expected ones. Thus, the absolute value of the residuals obtained from Eqs. (2) and (3) can be employed as proxies for managerial risk-taking. |εi,t | are, thus, regressed on leverage and other control variables in eq. (4), as follows:   εi,t  = ρ0 + ρ1 Leveragei,t + ρ2 Control variables i,t + i,t

(4)

A positive (negative) ρ1 indicates that leverage can be considered as an enhancement (disciplining) tool for managerial risk-taking behavior.

3.2.3

Leverage

Leverage is our second main variable. To estimate it, we use two proxies. The first one is measured by the ratio of total financial debt7 to total assets. The second one is computed using the ratio of total long-term debt divided by total assets. The firm’s relative level of debt indicates the managerial acceptance for riskiness since the

7 Financial

debt is measured by long-term debt plus short-term loans of each firm in the sample.

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higher is the amount of debt the higher is the risk of bankruptcy. This implies that α1 in Eq. (1) above is expected to be positive and statistically significant.

3.2.4

Control Variables

Previous studies stated that, several firm-control variables (besides leverage) are associated to managerial risk-taking. Among them, our model includes: (1) Firm Size is defined as the natural logarithm of total assets. In general, smaller firms are more likely to be risky when compared to larger firms known for their greater risk management skills (Choy et al. 2014; John et al. 2008; Langenmayr and Lester 2015; Vo 2016). Hence, this paper predicts a negative relationship between the firm’s size and managerial risk-taking. (2) Sales Growth is measured by the difference between the net sales of two consecutive years divided by net sales of the earlier year. This variable captures the firm’s investment opportunities. The higher is the value of the sales growth, the more likely is the firm to engage in risky projects (Core and Guay 1999; Langenmayr and Lester 2015; Rajgopal and Shevlin 2002). In this case, we suppose a positive relationship between sales growth and corporate risk-taking. (3) Firm Profitability is estimated by the Tobin’s Q ratio (Firth et al. 2008). Actually, this ratio is defined by the market capitalization of the firm scaled by the book value of its total assets. Thus, the higher is the profitability the more risk-taking is the firm. In fact, this paper assumes a positive relationship between the firm’s profitability and the managerial risk-taking. (4) Cash holdings is defined by the firm’s cash and cash equivalents scaled by its total assets. The higher is the level of cash available in the firm, the more likely is the manager engaged in higher risk levels. Therefore, we predict a positive relationship between cash holdings and managerial risk-taking. (5) Tangibility is defined as the firm’s fixed assets scaled by its total assets (Faccio et al. 2016). In fact, fixed assets include all the long-term tangibles that a company acquires (i.e. machinery, buildings, trucks, etc.). Mostly, the higher are these acquisitions the more risk-averse is the firm. Consequently, we expect a negative relationship between the tangibility and the variability of the firm’s performance. (6) Liquidity is represented as the firm’s current assets divided by its current liabilities. This ratio points at the firm’s ability to repay its short-term debt with its current assets. In general, the higher is the liquidity ratio the more risk-averse is the firm. Thus, this paper predicts a negative relationship between the liquidity and the corporate risk. (7) Interest coverage ratio is equal to the ratio of paid interest over EBITDA. This ratio assesses the company’s ability to pay the interest expenses of its loans. A high interest coverage ratio indicates that the interest expenses exceed the firm’s earnings, which implies that the corporate manager has a risk-taking behavior. Thus, we expect a positive association between the interest coverage ratio and the managerial risk-taking.

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Growth Opportunities

Jensen (1986) specified that managers of firms with free cash flow and low growth opportunities tend to invest in negative net present value projects. In addition, Lang et al. (1996) mentioned in their paper that “managers of firms with valuable growth opportunities should choose lower leverage because these firms might not be able to take advantage of their investment opportunities if they have to raise outside funds” (p.4). Following (Aivazian et al. 2005; Benkraiem et al. 2017; Firth et al. 2008; Lang et al. 1996), we underline the necessity to distinguish firms with high growth opportunities from those with low growth opportunities. The differentiation is run according to the firm’s sales growth. For instance, a (high) low growth firm is associated to a sales growth (higher) lower or equal to 0. Equation (5) examines the differences in the impact of leverage on managerial risk-taking for high versus low growth firms, as follows:  a Risk i,t = ∝0 + ∝1 Lev i,t + ∝2 Lev × Gh i, t + ∝3 Yi,t + ∝4 Xi + εi,t

(5)

Where (i) Riski,t is defined as the risk-taking behavior of the manager represented by the corporate risk-taking of firm i at time t; (ii) Levi,t is represented by the level of leverage of firm i at time t; (iii) Gh’ is a dummy variable equal to 1 if sales growth is higher than 0 and equal to 0 otherwise; (iv) Lev x Gh’ is the interaction term between leverage and growth dummy variable of firm i at time t; (v) Ya i,t is described as a vector of firm characteristics that is associated to the managerial risktaking, it includes: Si,t (Firm Size) is measured by the logarithm of total assets of firm i at time t; Ghi,t (Sales Growth) is computed by the difference between the net sales of two consecutive years divided by net sales of the earlier year of firm i; Pr j,t (Profitability) is defined as the Tobin’s Q ratio of firm i at time t; Chi,t (Cash holdings) is determined as the ratio of cash and cash equivalents over the total assets of firm i at time t; Tgj,t (Tangibility) is estimated by the fixed assets divided by the total assets of firm i at time t and Lqi,t (Liquidity) is measured by the current ratio equal to current assets divided by current liabilities. Ic i,t (Interest coverage ratio) is equal to the ratio of paid interest scaled by EBITDA. (vi) Xi is determined as the set of dummy variables that controls for year and firm effects. (vii) εi,t is defined as the error term.

4 Summary Statistics and Results This chapter presents the empirical findings obtained from the regressions. The first section displays the descriptive statistics of the sample and the two sub-periods. The second section reports the results of the Ordinary Least Square and Fixed Effects panel regression estimation that controls for all the unobserved year and firm effects. The third section describes the sensitivity analysis results.

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4.1 Summary Statistics Table 2 reports the summary statistics of the dependent and independent variables for the entire sample and the two sub-periods (i.e. during 2008 and from 2009 to 2016). The absolute deviation of the firm’s performance ranges from 8.5% to 25.5% on average, which indicates that managers of French listed SMEs tend to have a risk-taking behavior from 2008 to 2016. More precisely, their risk-taking behavior is more likely to increase after than during the financial crisis. At the same time, corporate leverage proxies report lower averages after than during the crisis. This implies that the access to bank financing for small businesses became more restrictive after the crisis. However, we must precise that the small business credit application increased after the financial crisis (OCDE report, 2013). For instance, French SMEs remain as highly bank dependent since they report an average of 11% and 10.2% of total long-term debt to total assets during and after the crisis, respectively. Firm size is slightly lower after than during the crisis with averages equal to 9.65 and 9.71, respectively. On the contrary, sales growth increased after the crisis as it marked 18.9% and 89.6% during and after the crisis, respectively. Profitability measured by Tobin’s Q displays averages of 0.93 and 1.64 during and after the crisis, respectively. The performance of French SMEs is better after than during the crisis. In addition, these firms maintained approximatively the same level of cash holdings over the entire period as they reported an average of 24.2% and 24.5% during and after the crisis, respectively. Further, tangibility remained on average at the same level during the entire period. On the other hand, liquidity decreased after the crisis as it reported an average of 3.4 and 3 during and after the crisis, respectively. Small firms were not able to maintain their liquidity stable during the whole period. Simultaneously, the interest coverage ratio highly increased after the financial crisis. Table 3 reports the Pearson’s correlation matrix that measures the association between the different independent variables employed in our model. Most of the coefficients generated from the matrix are statistically significant and report low correlations. For instance, these correlations are not strong enough to report serious multicollinearity problems among our independent variables. Yet, as expected, the two proxies of corporate leverage report the highest correlation. On the other hand, the results show that larger firms among SMEs tend to more leveraged. Tobin’s Q and cash holdings are negatively associated to corporate leverage. The higher are the profitability and cash holdings in the firm, the lower is the level of leverage that the firm needs. In addition, liquidity is negatively related to the leverage ratios. While, it is positively correlated to firm size, Tobin’s Q and cash holdings. Further, sales growth is positively associated to the profitability of the firm.

Risk 1 Risk 2 Risk 3 Risk 4 Risk 5 Risk 6 Risk 7 Risk 8 ROE ROA Leverage 1 Leverage 2 Firm size Sales growth

9.705 1.236 0.832 10.29

0.103 0.133

P50 0.053 0.05 0.134 0.136 0.048 0.05 0.140 0.139 0.010 0.010 0.109

P75 0.121 0.120 0.338 0.324 0.120 0.120 0.330 0.325 0.100 0.050 0.221

8.964 9.703 10.43 −0.078 0.048 0.214

9.648 1.428 0.189 0.562

0.165

P50 0.035 0.029 0.103 0.099 0.036 0.035 0.103 0.110 0.045 0.020 0.108

P75 0.107 0.108 0.271 0.295 0.113 0.108 0.272 0.291 0.155 0.070 0.255

8.927 9.783 10.50 −0.06 0.06 0.236

0.002 0.039 0.114

During the crisis (2008) Standard deviation P25 Mean 0.075 0.110 0 0.074 0.111 0 0.208 0.312 0 0.209 0.322 0 0.074 0.108 0 0.074 0.108 0 0.208 0.313 0 0.208 0.323 0 −0.105 0.491 −0.22 −0.044 0.201 −0.09 0.167 0.183 0.019

0.005 0.056 0.138 0.110

Entire period (2008 to 2016) Standard deviation P25 Mean 0.087 0.114 0 0.088 0.116 0 0.275 0.585 0 0.272 0.602 0 0.085 0.110 0 0.085 0.111 0 0.273 0.578 0 0.271 0.592 0 −0.169 0.748 −0.220 −0.058 0.193 −0.120 0.149 0.151 0.028

Table 2 Descriptive Statistics

9.711 1.214 0.896 10.79

0.102 0.129

P50 0.053 0.05 0.134 0.137 0.050 0.051 0.144 0.144 0.010 0 0.11

P75 0.122 0.123 0.342 0.325 0.122 0.122 0.334 0.331 0.100 0.05 0.217

(continued)

8.965 9.695 10.42 −0.08 0.045 0.209

0.006 0.059 0.140

After the crisis (2009 to 2016) Standard deviation P25 Mean 0.088 0.115 0 0.089 0.116 0 0.283 0.605 0 0.277 0.623 0 0.086 0.110 0 0.086 0.111 0 0.281 0.596 0 0.278 0.611 0 −0.176 0.771 −0.22 −0.06 0.192 −0.12 0.147 0.147 0.029

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0.115 0.179 3.040 6.985 0.054 5.289

0.244 0.233

0.242 0.240

0.015 0.038 0.129 0.115 0.183 1.255 1.817 2.934 3.385 8.801 −0.025 0.016 0.123 −0.290 5.187

0.057 0.178 0.365

0.389 0.245

0.016 0.0443 0.129 0.115 1.131 1.798 2.934 3.002 −0.01 0.040 0.179 0.091

0.038 0.172 0.179 6.759 5.301

0.232

0.178 0.362 0.015 0.038 0.129 1.260 1.819 2.934 −0.03 0.015 0.119

0.059

After the crisis (2009 to 2016) Standard P75 Mean deviation P25 P50 P75 1.146 1.640 2.507 0.430 0.875 1.871

Where Risk 1 represents the absolute value of the residuals retrieved from the OLS regression of ROA on Leverage 1 and control variables. Risk 2 represents the absolute value of the residuals retrieved from the OLS regression of ROA on leverage 2 and control variables. Risk 3 represents the absolute value of the residuals retrieved from the OLS regression of ROE on Leverage 1 and control variables. Risk 4 represents the absolute value of the residuals retrieved from the OLS regression of ROE on leverage 2 and control variables. Risk 5 represents the absolute value of the residuals retrieved from the FE regression of ROA on Leverage 1 and control variables. Risk 6 represents the absolute value of the residuals retrieved from the FE regression of ROA on leverage 2 and control variables. Risk 7 represents the absolute value of the residuals retrieved from the FE regression of ROE on Leverage 1 and control variables. Risk 8 represents the absolute value of the residuals retrieved from the FE regression of ROE on leverage 2 and control variables. Leverage 1 is the ratio of financial debt to total assets. Leverage 2 is defined as the long-term debt divided by total assets. Firm Size is measured by the logarithm of total assets. Sales growth is measured by the difference between the net sales of two consecutive years divided by net sales of the earlier year. Tobin’s Q ratio is equal to the market capitalization of the firm divided by the book value of its total assets. Cash holdings is defined as the ratio of cash and cash equivalents over the total assets. Tangibility is measured by the ratio of fixed assets over the firm’s total assets. Liquidity is estimated by current assets divided by current liabilities. Interest coverage ratio is equal to the ratio of paid interest over EBITDA. *, **, *** indicate significance at the 10%, 5% and 1% level, respectively

Tobin’s Q Cash holdings Tangibility Liquidity Interest coverage ratio

Entire period (2008 to 2016) During the crisis (2008) Standard Standard deviation P25 deviation P25 Mean P50 P75 Mean P50 1.579 2.428 0.419 0.853 1.791 0.938 1.184 0.301 0.609

Table 2 (continued)

70 N. Khairallah et al.

1 0.370*** 0.033 −0.076* −0.223*** 0.178*** −0.085** −0.001

Leverage 2

1 0.009 −0.175*** 0.050 0.148*** 0.112*** 0.030

Firm Size

1 0.242*** 0.015 −0.034 0.0003 0.0004

Sales Growth

1 0.272*** −0.079* 0.154*** −0.021

Tobin’s Q

1 −0.203*** 0.555*** 0.047

Cash holdings

1 −0.087** −0.007

Tangibility

1 0.020

Liquidity

1

Interest coverage ratio

Where Leverage 1 is the ratio of financial debt to total assets. Leverage 2 is defined as the long-term debt divided by total assets. Sales growth is measured by the difference between the net sales of two consecutive years divided by net sales of the earlier year. Tobin’s Q ratio is equal to the market capitalization of the firm divided by the book value of its total assets. Cash holdings is defined as the ratio of cash and cash equivalents over the total assets. Tangibility is measured by the ratio of fixed assets over the firm’s total assets. Liquidity is estimated by current assets divided by current liabilities. Interest coverage ratio is equal to the ratio of paid interest over EBITDA. *, **, *** indicate significance at the 10%, 5% and 1% level, respectively

Leverage 1 Leverage 2 Firm size Sales growth Tobin’s Q Cash holdings Tangibility Liquidity Interest coverage ratio

Leverage 1 1 0.850*** 0.371*** 0.019 −0.143*** −0.343*** 0.165*** −0.197*** 0.001

Table 3 Pearson correlation matrix between independent variables

Leverage Financing and the Risk-Taking Behavior of Small Business. . . 71

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4.2 Empirical Results Table 4 presents the findings of our model. As stretched above, each regression is run over the entire period and the two sub-periods (i.e. 2008 and from 2009 to 2016). The impact of leverage on the absolute deviation of the firm’s performance is measured according to two proxies (ROA and ROE). To provide complete results, we employ ordinary least square (OLS) regression and fixed-effect (FE) panel regression estimation that controls for all the unobserved year and firm effects. According to the first table, results show that the entire leverage coefficients are positive and statistically significant at the 1% level (expect for one coefficient statistically significant at the 5% level). This indicates that, leverage has a positive impact on the risk-taking behavior of managers across French listed SMEs over the period 2008 to 2016. These results strongly hold for the two leverage proxies and the two firm’s performance proxies in OLS and FE regressions. Leverage coefficients vary from 0.076 to 1.410. This implies that, an increase of 0.1 in the ratios of leverage leads to an increase of 0.076 to 1.410 in managerial risk-taking. These findings are in contrast with those of Jensen (1986) and Myers (1977) who highlighted the disciplining role of leverage that attenuates the risk-taking behavior of corporate managers. Consequently, our results report leverage as an enhancement tool that increases managerial risk-taking. Furthermore, leverage variable displays stronger results after than during the crisis. For instance, when using ROA as a proxy for firm’s performance, leverage reports positive and statistically significant coefficients after the global crisis, while insignificant coefficients during it. These results are comparable to those obtained when using ROE as a proxy for firm’s performance. Nonetheless, leverage coefficients are more significant during the crisis when using ROE rather than ROA. Thus, leverage has a higher impact on managerial risk-taking after than during the crisis. Benkraiem et al. (2017) stated that, creditors were highly involved in managers’ monitoring before the crisis. Nevertheless, as the crisis started, they favored an increase of the restrictions set on SMEs’ bank financing and a reduction of credit availability at the expense of the former monitoring. This has motivated corporate managers to enhance their risk-taking behavior as they were not strongly monitored. As expected, firm size variable reports negative and statistically significant coefficients over the entire period for both firm performance proxies. These results are consistent with the coefficients during the crisis for ROE and after the crisis for ROA. Accordingly, a manager is more likely to have a risk-taking behavior in smaller firms. Simultaneously, cash holdings and profitability are positively linked to managerial risk-taking. This implies that, managers of firms with high profitability and cash tend to become more risk-taking. Profitability and managerial risk-taking are more positively correlated after than during the crisis for both firm’s performance proxies. However, cash holdings variable report higher coefficients during than after the crisis, when using ROA as a proxy for firm’s performance. Yet, these coefficients are less significant when using ROE. On the other hand, liquidity

Constant

Interest coverage ratio

Liquidity

Tangibility

Cash holdings

Tobin’s Q

Sales growth

Firm size

−0.006 (0.0044) −0.0004 (0.0003) 0.012*** (0.003) 0.121*** (0.025) −0.045** (0.021) −0.009*** (0.002) 0.00001

(0.0005) 0.093* (0.054)

(0.0006) 0.208*** (0.035)

0.080*** (0.0292)

−0.013*** (0.004) −0.0005 (0.0003) 0.013*** (0.002) 0.139*** (0.02) −0.017 (0.019) −0.008*** (0.002) −0.0003

Entire Period (2008 to 2016) ROA Leverage 1 0.076*** (0.027) Leverage 2

(0.0006) 0.234*** (0.035)

0.102*** (0.029) −0.016*** (0.004) −0.0004 (0.0003) 0.013*** (0.002) 0.144*** (0.02) −0.025 (0.019) −0.008*** (0.002) −0.0003

Table 4 Regressions of risk-taking on leverage for the entire period

(0.0005) 0.116** (0.055)

0.097*** v(0.0323) −0.007* (0.0044) −0.0004 (0.0004) 0.012*** (0.003) 0.119*** (0.024) −0.053** (0.021) −0.0087*** (0.002) 0.00005 (0.003) 1.104*** (0.193)

−0.101*** (0.021) 0.003 (0.002) 0.049*** (0.009) 0.250** (0.113) −0.203* (0.106) −0.020** (0.009) −0.002

ROE 1.410*** (0.150)

(0.003) 0.478 (0.292)

−0.065*** (0.0240) 0.002 (0.002) 0.046** (0.018) 0.198 (0.181) −0.309*** (0.099) −0.020 (0.014) −0.002

1.384*** (0.280)

(0.004) 1.028*** (0.206)

0.909*** (0.175) −0.077*** (0.021) 0.003 (0.002) 0.052*** (0.01) 0.111 (0.117) −0.280** (0.112) −0.025*** (0.009) −0.002

(continued)

(0.002) 0.241 (0.305)

0.853*** (0.253) −0.028 (0.0241) 0.003 (0.002) 0.047*** (0.017) 0.032 (0.179) −0.382*** (0.082) −0.025 (0.016) −0.001

Leverage Financing and the Risk-Taking Behavior of Small Business. . . 73

1028 0.154 Yes Yes

1028 0.148 No No

1028 0.156 Yes Yes

ROE 1028 0.124 No No 1028 0.138 Yes Yes

1028 0.081 No No

1028 0.095 Yes Yes

Where Leverage 1 is the ratio of financial debt to total assets. Leverage 2 is defined as the long-term debt divided by total assets. Firm Size is measured by the logarithm of total assets. Sales growth is measured by the difference between the net sales of two consecutive years divided by net sales of the earlier year. Tobin’s Q ratio is equal to the market capitalization of the firm divided by the book value of its total assets. Cash holdings is defined as the ratio of cash and cash equivalents over the total assets. Tangibility is measured by the ratio of fixed assets over the firm’s total assets. Liquidity is estimated by current assets divided by current liabilities. Interest coverage ratio is equal to the ratio of paid interest over EBITDA. Standard errors clustered at the firm level are in parentheses. *, **, *** indicate significance at the 10%, 5% and 1% level, respectively

Entire Period (2008 to 2016) ROA Observations 1028 R-squared 0.136 Year No Firm No

Table 4 (continued)

74 N. Khairallah et al.

Leverage Financing and the Risk-Taking Behavior of Small Business. . .

75

and tangibility are negatively correlated to the risk-taking behavior of managers. This indicates that managers tend to be less risk-taking when their firm has more fixed assets and is able to cover its current liabilities by its current assets. These negative correlations between these two variables (i.e. tangibility and liquidity) and managerial risk-taking are higher during than after the global crisis. Table 5 provides the results of our second model that underlines the interaction between leverage and growth dummy variable. Leverage has a strong and robust positive impact on managerial risk-taking over the period 2008 to 2016. The findings hold for all the leverage and corporate risk-taking proxies. The leverage coefficients range from 0.108 to 2.043 for OLS estimations and from 0.097 to 1.982 for FE estimations. The ratio of total financial debt to total assets reports the highest coefficients for OLS and FE regressions when using ROE as a proxy for firm’s performance, while the ratio of long-term debt to total assets has the highest coefficients for OLS and FE regressions when using ROA as a proxy for firm’s performance. The interaction of the two leverage proxies with the growth dummy variable displays negative coefficients for all the regressions of the model. Note that the growth dummy variable is equal to 1 if sales growth is positive and is equal to 0 otherwise. The coefficients of this interaction vary −0.054 to −1.09 for OLS estimations and from −0.029 to −1.022 for FE estimations over the entire period. Simultaneously, this relationship holds and remains statistically significant after the crisis for both proxies of firm’s performance. Yet, the interaction between leverage and growth dummy variable displays insignificant coefficients during the crisis when using ROA as a proxy for firm’s performance, but negative and significant coefficients when using ROE as a proxy for firm’ performance. This implies that, leverage has a negative impact on the risk-taking behavior of corporate managers for firms with high growth opportunities, especially after the global crisis. SMEs with high growth opportunities suffer from a higher level of monitoring when compared to those with low growth opportunities. For instance, the shareholders of a firm with high growth perspectives are more likely to expropriate its profits. This implies that, creditors will increase their monitoring activities on the borrowers in order to preserve their loans repayments (Jensen 1986). Consequently, managers of these firms reduce their risk-taking behavior as they are being exposed to an increased level of monitoring by creditors. As for the other explanatory variables, the second model provides comparable evidence to the first model. For instance, the results show that firm size, liquidity and tangibility are negatively associated to managerial risk-taking. On the other hand, profitability and cash holdings display positive and statistically significant coefficients.

4.3 Sensitivity Analysis The above regressions control for the unobserved characteristics related to firm and time effects. The variables employed in these regressions are considered as

Constant

Interest coverage ratio

Liquidity

Tangibility

Cash holdings

Tobin’s Q

Sales growth

Firm size

Leverage 2

Leverage 1

−0.006 (0.015) −0.019 (0.024) 0.009 (0.021) 0.182** (0.085) −0.051 (0.067) −0.011* (0.006) 0.001 (0.002) 0.168 (0.137)

−0.002 (0.015) −0.009 (0.017) 0.008 (0.017) 0.179*** (0.063) −0.075** (0.032) −0.010*** (0.003) 0.001 (0.001) 0.093 (0.184)

During the Crisis (2008) −0.039 −0.024 (0.090) (0.064) −0.012 (0.102) −0.010 (0.016) −0.014 (0.024) 0.019 (0.021) 0.180** (0.084) −0.062 (0.067) −0.011* (0.006) 0.001 (0.002) 0.201 (0.147)

−0.010 (0.067) −0.006 (0.014) −0.0001 (0.017) 0.018 (0.016) 0.175*** (0.061) −0.080** (0.032) −0.010*** (0.003) 0.001 (0.001) 0.124 (0.175)

Table 5 Regressions of risk-taking (using ROA) on leverage during vs. after the crisis

−0.014*** (0.004) −0.0005 (0.0003) 0.013*** (0.002) 0.140*** (0.021) −0.016 (0.020) −0.008*** (0.002) −0.0002 (0.001) 0.211*** (0.036)

−0.007 (0.004) −0.0005 (0.0003) 0.012*** (0.003) 0.120*** (0.024) −0.044** (0.022) −0.008*** (0.002) 0.0001 (0.001) 0.099* (0.054)

After the Crisis (2009 to 2016) 0.100*** 0.103*** (0.028) (0.030) 0.136*** (0.0316) −0.016*** (0.004) −0.0004 (0.0003) 0.013*** (0.002) 0.146*** (0.021) −0.023 (0.020) −0.008*** (0.002) −0.0002 (0.001) 0.235*** (0.036)

0.126*** (0.034) −0.008* (0.005) −0.0004 (0.0004) 0.012*** (0.003) v0.118*** (0.024) −0.052** (0.021) −0.009*** (0.002) 0.0001 (0.001) 0.121** (0.056)

76 N. Khairallah et al.

90 0.135 No No

90 0.138 Yes Yes

90 0.144 No No

90 0.152 Yes Yes

938 0.146 No No

938 0.163 Yes Yes

938 0.161 No No

938 0.166 Yes Yes

Where Leverage 1 is the ratio of financial debt to total assets. Leverage 2 is defined as the long-term debt divided by total assets. Firm Size is measured by the logarithm of total assets. Sales growth is measured by the difference between the net sales of two consecutive years divided by net sales of the earlier year. Tobin’s Q ratio is equal to the market capitalization of the firm divided by the book value of its total assets. Cash holdings is defined as the ratio of cash and cash equivalents over the total assets. Tangibility is measured by the ratio of fixed assets over the firm’s total assets. Liquidity is estimated by current assets divided by current liabilities. Interest coverage ratio is equal to the ratio of paid interest over EBITDA. Standard errors clustered at the firm level are in parentheses. *, **, *** indicate significance at the 10%, 5% and 1% level, respectively

Observations R-squared Year Firm

Leverage Financing and the Risk-Taking Behavior of Small Business. . . 77

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N. Khairallah et al.

exogenous. Due to the fact that the conditions set on bank financing have led creditors to ration the number and size of loans attributed to borrowers, one can assume that borrowers have anticipated the banks’ behavior and have auto-censored themselves from accessing to bank financing. This arises the endogeneity problem between leverage and managerial risk-taking. To address this issue, we employ the two-stages least square instrumental variable approach (Tables 6, 7, 8 and 9). Cash reserves are considered as the instrumental variable. It is defined as the natural logarithm of cash flow. The reasoning is motivated by Jensen (1986) who stated that leverage and cash flow are positively correlated. Thus, in the first stage we regress leverage on cash reserves. Table 10 shows that the two leverage proxies report strongly positive coefficients. In the second stage, we employ the predicted values in our model and rerun the regressions. Table 11 displays the findings obtained over the entire period. As expected, the leverage proxies (financial debt ratio and long-term debt ratio) display positive and statistically significant coefficients at the 1% level when using ROA and ROE as measures for firm performance. Furthermore, the interaction term between leverage and the sales growth dummy variable reports negative and statistically significant coefficients at the 1% level (Table 12). On another hand, Tables 13 and 14 report the results obtained during and after the financial crisis of 2008, respectively. They show that the robustness of the leverage coefficients is more important after than during the crisis. Meanwhile, the coefficients of the interaction term between leverage and the sales growth dummy variable are negative and statistically significant at the 1% level after the financial crisis only.

5 Conclusion Small and medium-sized enterprises are gaining higher importance nowadays as they highly contribute in the economic and financial stability of the countries. Although corporate leverage has a significant weight in the capital structure of these firms, there is little evidence on its impact on the risk-taking behavior of their corporate managers. Thus, this paper tries to fill this gap by empirically investigating the relationship between corporate leverage and managerial risk-taking. To address this problem, the study is motivated by three of the capital structure theories that highlight the role of leverage in firms. In the first theory, Myers (1977) stated that managers are less likely to invest in positive net present value projects as a result of debt overhang. In the second theory, Jensen (1986) showed that leverage is considered as a disciplining tool that reduces the over-investment problem of corporate managers. In contrast, Maksimovic and Titman (1991) documented in their paper that, individuals are generally reluctant to do business with a highly leveraged firm. Thus, managers engaging in a highly leveraged firm are considered to be risk-taking.

Constant

Interest coverage ratio

Liquidity

Tangibility

Cash holdings

Tobin’s Q

Sales growth

Firm size

Leverage 2

Leverage 1

−0.104** (0.042) −0.087 (0.067) −0.057 (0.059) 0.277 (0.240) −0.206 (0.188) −0.017 (0.017) 0.007 (0.006) 1.361*** (0.387)

−0.121** (0.051) −0.085 (0.051) −0.060 (0.042) 0.296* (0.162) −0.200* (0.101) −0.018 (0.011) 0.007** (0.003) 1.624*** (0.566)

During the Crisis (2008) 0.428* 0.460* (0.254) (0.262) 0.264 (0.302) −0.0952** (0.046) −0.075 (0.072) −0.015 (0.062) 0.162 (0.250) −0.256 (0.200) −0.020 (0.018) 0.006 (0.006) 1.320*** (0.437)

0.320 (0.289) −0.120** (0.052) −0.068 (0.050) −0.022 (0.051) 0.182 (0.177) −0.262** (0.102) −0.021* (0.012) 0.006** (0.003) 1.705*** (0.564)

Table 6 Regressions of risk-taking (using ROE) on leverage during vs. after the crisis

−0.101*** (0.022) 0.002 (0.002) 0.050*** (0.010) 0.268** (0.121) −0.208* (0.114) −0.019** (0.009) −0.003 (0.004) 1.071*** (0.206)

−0.059** (0.025) 0.002 (0.002) 0.046** (0.018) 0.217 (0.195) −0.325*** (0.103) −0.020 (0.016) −0.003 (0.003) 0.369 (0.321)

After the Crisis (2009 to 2016) 1.560*** 1.523*** (0.164) (0.313) 1.056*** (0.192) −0.076*** (0.023) 0.003 (0.002) 0.052*** (0.011) 0.135 (0.125) −0.272** (0.122) −0.025** (0.010) −0.002 (0.004) 0.991*** (0.220)

(continued)

0.968*** (0.280) −0.021 (0.026) 0.002 (0.002) 0.046*** (0.017) 0.0438 (0.194) −0.385*** (0.087) −0.025 (0.018) −0.002 (0.003) 0.121 (0.341)

Leverage Financing and the Risk-Taking Behavior of Small Business. . . 79

During the Crisis (2008) 90 90 0.154 0.161 No Yes No Yes 90 0.125 No No

90 0.137 Yes Yes

After the Crisis (2009 to 2016) 938 938 938 0.133 0.148 0.085 No Yes No No Yes No

938 0.098 Yes Yes

Where Leverage 1 is the ratio of financial debt to total assets. Leverage 2 is defined as the long-term debt divided by total assets. Firm Size is measured by the logarithm of total assets. Sales growth is measured by the difference between the net sales of two consecutive years divided by net sales of the earlier year. Tobin’s Q ratio is equal to the market capitalization of the firm divided by the book value of its total assets. Cash holdings is defined as the ratio of cash and cash equivalents over the total assets. Tangibility is measured by the ratio of fixed assets over the firm’s total assets. Liquidity is estimated by current assets divided by current liabilities. Interest coverage ratio is equal to the ratio of paid interest over EBITDA. Standard errors clustered at the firm level are in parentheses. *, **, *** indicate significance at the 10%, 5% and 1% level, respectively

Observations R-squared Year Firm

Table 6 (continued)

80 N. Khairallah et al.

Interest coverage ratio

Liquidity

Tangibility

Cash holdings

Tobin’s Q

Sales growth

Firm size

Lev2 x Gh’

−0.013*** (0.004) −0.0005 (0.0003) 0.013*** (0.002) 0.140*** (0.020) −0.018 (0.019) −0.008*** (0.002) −0.0003 (0.0006)

Entire Period (2008 to 2016) ROA Leverage 1 0.108*** (0.034) Lev1 x Gh’ −0.054 (0.033) Leverage 2

−0.006 (0.004) −0.0004 (0.0003) 0.012*** (0.003) 0.121*** (0.025) −0.044** (0.021) −0.006*** (0.002) −0.00001 (0.001)

0.097*** (0.035) −0.029 (0.028) 0.159*** (0.0419) −0.079* (0.044) −0.016*** (0.004) −0.0004 (0.0003) 0.012*** (0.002) 0.143*** (0.020) −0.028 (0.019) −0.008*** (0.002) −0.0003 (0.0006)

0.136*** (0.042) −0.052 (0.035) −0.008* (0.005) −0.0004 (0.0004) 0.012*** (0.002) 0.119*** (0.024) −0.053** (0.021) −0.006*** (0.002) 0.0001 (0.001) −0.094*** (0.020) 0.003* (0.002) 0.055*** (0.009) 0.270** (0.110) −0.192* (0.103) −0.020** (0.009) −0.002 (0.003)

ROE 2.043*** (0.182) −1.090*** (0.178)

Table 7 Regressions of risk-taking on leverage and growth opportunities for the entire period

−0.069*** (0.023) 0.003 (0.002) 0.051*** (0.017) 0.213 (0.180) −0.281*** (0.094) −0.020 (0.014) −0.002 (0.003)

1.982*** (0.332) −1.022*** (0.300) 1.403*** (0.245) −0.706*** (0.255) −0.078*** (0.021) 0.003 (0.002) 0.053*** (0.010) 0.119 (0.116) −0.283** (0.112) −0.025*** (0.009) −0.002 (0.004)

(continued)

1.262*** (0.277) −0.586* (0.313) −0.032 (0.024) 0.003 (0.002) 0.048*** (0.016) 0.039 (0.179) −0.378*** (0.083) −0.025 (0.016) −0.002 (0.003)

Leverage Financing and the Risk-Taking Behavior of Small Business. . . 81

0.098* (0.054) 1028 0.155 Yes Yes

0.236*** (0.035) 1028 0.151 No No

0.123** (0.055) 1028 0.159 Yes Yes

ROE 1.010*** (0.188) 1028 0.157 No No 0.586** (0.276) 1028 0.165 Yes Yes

1.024*** (0.204) 1028 0.090 No No

0.300 (0.298) 1028 0.101 Yes Yes

Where Leverage 1 is the ratio of financial debt to total assets. Leverage 2 is defined as the long-term debt divided by total assets. Gh’ is a dummy variable equal to 1 if Sales Growth > 0 and 0 otherwise. Leverage x Gh’ is the interaction term between leverage ratio and growth dummy variable. Firm Size is measured by the logarithm of total assets. Sales growth is measured by the difference between the net sales of two consecutive years divided by net sales of the earlier year. Tobin’s Q ratio is equal to the market capitalization of the firm divided by the book value of its total assets. Cash holdings is defined as the ratio of cash and cash equivalents over the total assets. Tangibility is measured by the ratio of fixed assets over the firm’s total assets. Liquidity is estimated by current assets divided by current liabilities. Interest coverage ratio is equal to the ratio of paid interest over EBITDA. Standard errors clustered at the firm level are in parentheses.*, **, *** indicate significance at the 10%, 5% and 1% level, respectively

Entire Period (2008 to 2016) ROA Constant 0.206*** (0.035) Observations 1028 R-squared 0.140 Year No Firm No

Table 7 (continued)

82 N. Khairallah et al.

Interest coverage ratio

Liquidity

Tangibility

Cash holdings

Tobin’s Q

Sales growth

Firm size

Lev2 x Gh’

Leverage 2

Lev1 x Gh’

Leverage 1

−0.0004 (0.016) −0.021 (0.026) 0.004 (0.021) 0.166* (0.087) −0.043 (0.068) −0.011* (0.006) 0.002 (0.002)

0.005 (0.015) −0.012 (0.018) 0.005 (0.018) 0.164** (0.065) −0.070* (0.035) −0.010*** (0.003) 0.001 (0.001)

During the Crisis (2008) −0.040 −0.040 (0.112) (0.090) −0.047 −0.029 (0.119) (0.084) −0.005 (0.162) −0.049 (0.166) −0.007 (0.016) −0.014 (0.026) 0.010 (0.022) 0.171** (0.086) −0.051 (0.069) −0.010 (0.006) 0.001 (0.002) 0.019 (0.118) −0.072 (0.110) −0.001 (0.015) 0.0001 (0.018) 0.012 (0.018) 0.164** (0.063) −0.069* (0.035) −0.010*** (0.003) 0.001 (0.001) −0.014*** (0.004) −0.0005 (0.0003) 0.013*** (0.002) 0.141*** (0.021) −0.016 (0.020) −0.008*** (0.002) −0.0002 (0.001)

−0.008* (0.004) −0.0004 (0.0003) 0.012*** (0.003) 0.121*** (0.025) −0.043** (0.021) −0.008*** (0.002) 0.0001 (0.001)

After the Crisis (2009 to 2016) 0.138*** 0.127*** (0.035) (0.035) −0.060* −0.037 (0.035) (0.028)

Table 8 Regressions of risk-taking (using ROA) on leverage and growth opportunities during vs. after the crisis

0.201*** (0.043) −0.087* (0.046) −0.017*** (0.004) −0.0004 (0.0003) 0.013*** (0.002) 0.146*** (0.021) −0.025 (0.020) −0.008*** (0.002) −0.0002 (0.001)

(continued)

0.167*** (0.043) −0.055 (0.037) −0.009* (0.005) −0.0004 (0.0003) 0.012*** (0.003) 0.120*** (0.024) −0.051** (0.021) −0.009*** (0.002) 0.0001 (0.001)

Leverage Financing and the Risk-Taking Behavior of Small Business. . . 83

During the Crisis (2008) 0.122 0.038 (0.144) (0.184) 90 90 0.130 0.135 No Yes No Yes 0.172 (0.150) 90 0.129 No No

0.085 (0.187) 90 0.141 Yes Yes

After the Crisis (2009 to 2016) 0.210*** 0.107* (0.036) (0.055) 938 938 0.151 0.166 No Yes No Yes

0.238*** (0.036) 938 0.166 No No

0.128** (0.056) 938 0.169 Yes Yes

Where Leverage 1 is the ratio of financial debt to total assets. Leverage 2 is defined as the long-term debt divided by total assets. Gh’ is a dummy variable equal to 1 if Sales Growth > 0 and 0 otherwise. Leverage x Gh’ is the interaction term between leverage ratio and growth dummy variable. Firm Size is measured by the logarithm of total assets. Sales growth is measured by the difference between the net sales of two consecutive years divided by net sales of the earlier year. Tobin’s Q ratio is equal to the market capitalization of the firm divided by the book value of its total assets. Cash holdings is defined as the ratio of cash and cash equivalents over the total assets. Tangibility is measured by the ratio of fixed assets over the firm’s total assets. Liquidity is estimated by current assets divided by current liabilities. Interest coverage ratio is equal to the ratio of paid interest over EBITDA. Standard errors clustered at the firm level are in parentheses. *, **, *** indicate significance at the 10%, 5% and 1% level, respectively

Observations R-squared Year Firm

Constant

Table 8 (continued)

84 N. Khairallah et al.

Interest coverage ratio

Liquidity

Tangibility

Cash holdings

Tobin’s Q

Sales growth

Firm size

Lev2 x Gh’

Leverage 2

Lev1 x Gh’

Leverage 1

−0.053 (0.043) −0.072 (0.072) −0.072 (0.058) 0.169 (0.241) −0.148 (0.189) −0.019 (0.017) 0.007 (0.006)

−0.065 (0.05) −0.066 (0.048) −0.069 (0.045) 0.168 (0.160) −0.127 (0.085) −0.020* (0.011) 0.007*** (0.002)

During the Crisis (2008) 0.498 0.517 (0.310) (0.368) −0.552* −0.588* (0.329) (0.298) 0.741 (0.469) −0.711 (0.480) −0.079* (0.046) −0.056 (0.074) −0.052 (0.062) 0.112 (0.248) −0.207 (0.199) −0.018 (0.017) 0.007 (0.006)

0.847** (0.411) −0.809** (0.323) −0.102* (0.053) −0.047 (0.052) −0.057 (0.047) 0.125 (0.178) −0.196* (0.108) −0.019 (0.013) 0.007** (0.003) −0.096*** (0.021) 0.003 (0.002) 0.055*** (0.010) 0.290** (0.117) −0.198* (0.111) −0.019** (0.009) −0.003 (0.004)

−0.067*** (0.024) 0.003 (0.002) 0.051*** (0.018) 0.232 (0.195) −0.300*** (0.099) −0.019 (0.015) −0.003 (0.003)

After the Crisis (2009 to 2016) 2.236*** 2.162*** (0.198) (0.383) −1.165*** −1.084*** (0.194) (0.344)

Table 9 Regressions of risk-taking (using ROE) on leverage and growth opportunities during vs. after the crisis

1.566*** (0.263) −0.733*** (0.278) −0.077*** (0.023) 0.003 (0.002) 0.054*** (0.011) 0.150 (0.125) −0.276** (0.121) −0.025** (0.010) −0.002 (0.004)

(continued)

1.381*** (0.304) −0.594* (0.350) −0.026 (0.025) 0.003 (0.002) 0.048*** (0.017) 0.056 (0.193) −0.382*** (0.088) −0.025 (0.018) −0.002 (0.003)

Leverage Financing and the Risk-Taking Behavior of Small Business. . . 85

During the Crisis (2008) 0.893** 1.100* (0.401) (0.565) 90 90 0.170 0.170 No Yes No Yes 1.183*** (0.433) 90 0.148 No No

1.552** (0.605) 90 0.159 Yes Yes

After the Crisis (2009 to 2016) 1.010*** 0.511* (0.200) (0.302) 938 938 0.166 0.176 No Yes No Yes

0.996*** (0.218) 938 0.094 No No

0.189 (0.333) 938 0.105 Yes Yes

Where Leverage 1 is the ratio of financial debt to total assets. Leverage 2 is defined as the long-term debt divided by total assets. Gh’ is a dummy variable equal to 1 if Sales Growth > 0 and 0 otherwise. Leverage x Gh’ is the interaction term between leverage ratio and growth dummy variable. Firm Size is measured by the logarithm of total assets. Sales growth is measured by the difference between the net sales of two consecutive years divided by net sales of the earlier year. Tobin’s Q ratio is equal to the market capitalization of the firm divided by the book value of its total assets. Cash holdings is defined as the ratio of cash and cash equivalents over the total assets. Tangibility is measured by the ratio of fixed assets over the firm’s total assets. Liquidity is estimated by current assets divided by current liabilities. Interest coverage ratio is equal to the ratio of paid interest over EBITDA. Standard errors clustered at the firm level are in parentheses.*, **, *** indicate significance at the 10%, 5% and 1% level, respectively

Observations R-squared Year Firm

Constant

Table 9 (continued)

86 N. Khairallah et al.

Leverage Financing and the Risk-Taking Behavior of Small Business. . .

87

Table 10 First stage OLS regression of leverage on cash reserves (IV) and the control variables over the entire period (2008 to 2016) Cash reserves Constant Observations R-squared Year Firm

Leverage1 0.026*** (0.004) −0.039 (0.026) 773 0.067 No No

0.026*** (0.008) −0.031 (0.085) 773 0.074 Yes Yes

Leverage2 0.023*** (0.003) −0.065*** (0.022) 773 0.069 No No

0.022*** (0.008) −0.037 (0.075) 773 0.077 Yes Yes

Where Leverage 1 is the ratio of financial debt to total assets. Leverage 2 is defined as the longterm debt divided by total assets. Cash reserves is the natural logarithm of cash flow. Standard errors clustered at the firm level are in parentheses. *, **, *** indicate significance at the 10%, 5% and 1% level, respectively

This paper uses a sample composed of 1403 French small and medium-sized firm observations listed on the Euronext Paris stock exchange over the period 2008 to 2016. In order to highlight the impact of the global crisis on managerial risktaking, the regressions are run over the entire period and, during and after the crisis (i.e. during 2008 and from 2009 to 2016). The empirical findings show that corporate leverage significantly amplifies the risk-taking behavior of corporate managers in French SMEs over the entire period. Nevertheless, this relationship is more robust after than during the crisis. Due to the financial crisis of 2008, banks enhanced credit rationing on SMEs’ lending at the expense of a higher monitoring, which has increased managerial risk-taking. This impact is significantly present in low growth firms. Furthermore, the positive correlation between the risk-taking behavior of managers and the corporate leverage is expected to mark some implications on the shareholders’ and creditors’ decision making process. On the one hand, as shareholders are expected to use debt as a disciplining tool to prevent managers from investing in negative net present value projects, they will have incentives to implement new disciplining tools since debt enhances the risk-taking behavior of managers after the financial crisis of 2008, which is not in their interest. On the other hand, since banks reduced their monitoring scope after crisis, they are expected to use very reliable and accurate tools in order to reduce the adverse selection problem when allocating debt to firms, especially to SMEs. Therefore, we address future researches to investigate the implementation of new disciplining tools applied by investors and new selection tools employed by creditors that manage the risk-taking behavior of managers in small businesses, especially after the financial crisis of 2008. In addition, one can assume that the increase in managerial risktaking will definitely have an important impact on the firm itself (i.e. turnover,

Interest coverage ratio

Liquidity

Tangibility

Cash holdings

Tobin’s Q

Growth

Size

FIT Lev2 x Gh’

FIT Lev2

FIT Lev1 x Gh’

FIT Lev1

−0.031*** (0.002) 0.001*** (0.0003) 0.024*** (0.001) 0.212*** (0.012) −0.045*** (0.009) −0.005*** (0.001) −0.003*** (0.001)

−0.009** (0.004) 0.001*** (0.0003) 0.020*** (0.002) 0.195*** (0.014) −0.057*** (0.014) −0.007*** (0.001) −0.002*** (0.001)

Entire Period (2008 to 2016) ROA 1.603*** 1.538*** (0.074) (0.126) −0.180*** −0.097*** (0.024) (0.025) 1.854*** (0.086) −0.236*** (0.035) −0.031*** (0.002) 0.001*** (0.0004) 0.024*** (0.001) 0.212*** (0.012) −0.045*** (0.009) −0.005*** (0.001) −0.003*** (0.001)

1.836*** (0.149) −0.124*** (0.036) −0.009** (0.004) 0.001*** (0.0003) 0.020*** (0.002) 0.196*** (0.014) −0.058*** (0.014) −0.007*** (0.001) −0.002*** (0.001) −0.084*** (0.011) 0.017*** (0.002) 0.080*** (0.005) 0.170*** (0.054) −0.212*** (0.041) −0.004 (0.004) −0.007** (0.003)

ROE 3.877*** (0.346) −1.020*** (0.113)

−0.021 (0.016) 0.016*** (0.001) 0.070*** (0.008) 0.135** (0.064) −0.270*** (0.038) −0.004 (0.007) −0.006 (0.005)

3.639*** (0.336) −0.757*** (0.092)

Table 11 Second stage regressions of Risk-taking on the predicted values of leverage (FIT Lev) and the control variables

4.549*** (0.400) −1.343*** (0.165) −0.084*** (0.011) 0.017*** (0.002) 0.081*** (0.005) 0.176*** (0.054) −0.212*** (0.041) −0.005 (0.004) −0.007** (0.003)

4.394*** (0.401) −0.955*** (0.134) −0.020 (0.016) 0.016*** (0.001) 0.070*** (0.008) 0.139** (0.064) −0.273*** (0.038) −0.004 (0.007) −0.006 (0.005)

88 N. Khairallah et al.

0.128*** (0.018) 621 0.718 No No

−0.222*** (0.032) 621 0.708 Yes Yes 0.180*** (0.019) 621 0.719 No No

−0.204*** (0.033) 621 0.709 Yes Yes 0.532*** (0.085) 621 0.503 No No

−0.501*** (0.135) 621 0.502 Yes Yes 0.643*** (0.089) 621 0.500 No No

−0.480*** (0.138) 621 0.501 Yes Yes

Where Leverage 1 is the ratio of financial debt to total assets. Leverage 2 is defined as the long-term debt divided by total assets. FIT Lev is a prediction of the leverage. Gh’ is a dummy variable equal to 1 if sales growth is >0 and 0 otherwise. FIT Lev x Gh’ is the interaction term between the prediction of the leverage and the growth dummy variable. Firm Size is measured by the logarithm of total assets. Sales growth is measured by the difference between the net sales of two consecutive years divided by net sales of the earlier year. Tobin’s Q ratio is equal to the market capitalization of the firm divided by the book value of its total assets. Cash holdings is defined as the ratio of cash and cash equivalents over the total assets. Tangibility is measured by the ratio of fixed assets over the firm’s total assets. Liquidity is estimated by current assets divided by current liabilities. Interest coverage ratio is equal to the ratio of paid interest over EBITDA. Standard errors clustered at the firm level are in parentheses. *, **, *** indicate significance at the 10%, 5% and 1% level, respectively

Observations R-squared Year Firm

Constant

Leverage Financing and the Risk-Taking Behavior of Small Business. . . 89

Leverage2 0.040*** (0.012) −0.178** (0.083) 80 0.132 No No 0.036** (0.015) −0.125 (0.147) 80 0.135 Yes Yes

After the Crisis (2009 to 2016) Leverage1 0.026*** 0.025*** (0.004) (0.008) −0.034 −0.024 (0.026) (0.085) 693 693 0.066 0.074 No Yes No Yes

Leverage2 0.021*** (0.003) −0.052** (0.023) 693 0.063 No No

0.020** (0.008) −0.030 (0.075) 693 0.071 Yes Yes

Where Leverage 1 is the ratio of financial debt to total assets. Leverage 2 is defined as the long-term debt divided by total assets. Cash reserves is the natural logarithm of cash flow. Standard errors clustered at the firm level are in parentheses. *, **, *** indicate significance at the 10%, 5% and 1% level, respectively

Observations R-squared Year Firm

Constant

Cash reserves

During the Crisis (2008) Leverage1 0.033** 0.033* (0.014) (0.018) −0.085 −0.075 (0.097) (0.181) 80 80 0.073 0.073 No Yes No Yes

Table 12 First stage OLS regression of leverage on cash reserves (IV) and the control variables during versus after the crisis

90 N. Khairallah et al.

Interest coverage ratio

Liquidity

Tangibility

Cash holdings

Tobin’s Q

Growth

Size

FIT Lev2 x Gh’

FIT Lev2

FIT Lev1 x Gh’

FIT Lev1

−0.010 (0.010) −0.006 (0.016) 0.009 (0.012) 0.270*** (0.043) −0.053* (0.029) −0.010*** (0.003) −0.0003 (0.001)

ROA 0.670** (0.270) 0.007 (0.092)

0.001 (0.010) −0.014 (0.024) 0.011 (0.012) 0.260*** (0.034) −0.074** (0.030) −0.008*** (0.002) −0.001 (0.0004)

0.806** (0.347) 0.003 (0.061) 0.820*** (0.246) −0.137 (0.125) −0.014 (0.010) 0.007 (0.016) 0.015 (0.012) 0.263*** (0.043) −0.066** (0.029) −0.009*** (0.003) −0.001 (0.001)

0.866*** (0.297) −0.103 (0.074) −0.002 (0.093) 0.004 (0.028) 0.018 (0.012) 0.255*** (0.029) −0.082*** (0.030) −0.009*** (0.002) −0.001** (0.0004) −0.052 (0.043) −0.102 (0.067) −0.082 (0.050) 0.196 (0.183) −0.111 (0.122) −0.012 (0.012) 0.004 (0.004)

ROE 0.143 (1.158) 0.428 (0.396)

−0.037 (0.0368) −0.122 (0.077) −0.076** (0.037) 0.198 (0.137) −0.126 (0.094) −0.012 (0.009) 0.003** (0.002)

0.413 (1.113) 0.399 (0.248) 1.144 (1.018) −0.107 (0.515) −0.068 (0.0413) −0.049 (0.065) −0.052 (0.049) 0.226 (0.177) −0.170 (0.118) −0.014 (0.011) 0.002 (0.004)

(continued)

1.352 (0.850) −0.132 (0.246) −0.065** (0.0301) −0.053 (0.089) −0.055 (0.034) 0.225* (0.116) −0.181* (0.106) −0.013 (0.008) 0.002 (0.001)

Table 13 Second stage regressions of Risk-taking on the predicted values of leverage (FIT Lev) and the control variables during the financial crisis

Leverage Financing and the Risk-Taking Behavior of Small Business. . . 91

ROA 0.062 (0.078) 55 0.623 No No

−0.168 (0.101) 55 0.641 Yes Yes 0.120 (0.085) 55 0.643 No No

−0.124 (0.091) 55 0.656 Yes Yes

ROE 0.797** (0.333) 55 0.267 No No 0.488 (0.338) 55 0.280 Yes Yes

0.884** (0.352) 55 0.256 No No

0.762*** (0.271) 55 0.259 Yes Yes

Where Leverage 1 is the ratio of financial debt to total assets. Leverage 2 is defined as the long-term debt divided by total assets. FIT Lev is a prediction of the leverage. Gh’ is a dummy variable equal to 1 if sales growth is >0 and 0 otherwise. FIT Lev x Gh’ is the interaction term between the prediction of the leverage and the growth dummy variable. Firm Size is measured by the logarithm of total assets. Sales growth is measured by the difference between the net sales of two consecutive years divided by net sales of the earlier year. Tobin’s Q ratio is equal to the market capitalization of the firm divided by the book value of its total assets. Cash holdings is defined as the ratio of cash and cash equivalents over the total assets. Tangibility is measured by the ratio of fixed assets over the firm’s total assets. Liquidity is estimated by current assets divided by current liabilities. Interest coverage ratio is equal to the ratio of paid interest over EBITDA. Standard errors clustered at the firm level are in parentheses. *, **, *** indicate significance at the 10%, 5% and 1% level, respectively

Observations R-squared Year Firm

Constant

Table 13 (continued)

92 N. Khairallah et al.

Interest coverage ratio

Liquidity

Tangibility

Cash holdings

Tobin’s Q

Growth

Size

FIT Lev2 x Gh’

FIT Lev2

FIT Lev1 x Gh’

FIT Lev1

−0.032*** (0.003) 0.001*** (0.0004) 0.024*** (0.001) 0.214*** (0.012) −0.045*** (0.009) −0.005*** (0.001) −0.004*** (0.002)

ROA 1.665*** (0.08) −0.182*** (0.025)

−0.009** (0.004) 0.001*** (0.0003) 0.020*** (0.001) 0.196*** (0.014) −0.053*** (0.014) −0.007*** (0.001) −0.004*** (0.001)

1.563*** (0.137) −0.090*** (0.027) 2.021*** (0.097) −0.242*** (0.037) −0.033*** (0.003) 0.001*** (0.0004) 0.024*** (0.001) 0.215*** (0.012 −0.046*** (0.009) −0.005*** (0.001) −0.004*** (0.002)

1.939*** (0.169) −0.119*** (0.039) −0.009** (0.004) 0.001*** (0.0003) 0.020*** (0.001) 0.196*** (0.014) −0.053*** (0.014) −0.007*** (0.0005) −0.004*** (0.001) −0.085*** (0.012) 0.017*** (0.002) 0.081*** (0.005) 0.186*** (0.056) −0.217*** (0.044) −0.003 (0.004) −0.022*** (0.007)

ROE 4.060*** (0.377) −1.031*** (0.120)

−0.016 (0.016) 0.016*** (0.0009) 0.069*** (0.008) 0.144** (0.064) −0.268*** (0.038) −0.002 (0.008) −0.017 (0.016)

3.757*** (0.345) −0.725*** (0.114) 4.983*** (0.458) −1.392*** (0.176) −0.084*** (0.012) 0.017*** (0.002) 0.082*** (0.005) 0.194*** (0.056) −0.216*** (0.044) −0.004 (0.004) −0.022*** (0.007)

(continued)

4.705*** (0.427) −0.938*** (0.166) −0.015 (0.016) 0.016*** (0.001) 0.069*** (0.008) 0.149** (0.064) −0.270*** (0.038) −0.003 (0.008) −0.017 (0.016)

Table 14 Second stage regressions of Risk-taking on the predicted values of leverage (FIT Lev) and the control variables after the financial crisis

Leverage Financing and the Risk-Taking Behavior of Small Business. . . 93

ROA 0.130*** (0.019) 566 0.729 No No

−0.235*** (0.032) 566 0.707 Yes Yes 0.174*** (0.020) 566 0.730 No No

−0.218*** (0.032) 566 0.707 Yes Yes

ROE 0.511*** (0.089) 566 0.522 No No −0.619*** (0.141) 566 0.511 Yes Yes

0.607*** (0.093) 566 0.520 No No

−0.599*** (0.143) 566 0.509 Yes Yes

Where Leverage 1 is the ratio of financial debt to total assets. Leverage 2 is defined as the long-term debt divided by total assets. FIT Lev is a prediction of the leverage. Gh’ is a dummy variable equal to 1 if sales growth is >0 and 0 otherwise. FIT Lev x Gh’ is the interaction term between the prediction of the leverage and the growth dummy variable. Firm Size is measured by the logarithm of total assets. Sales growth is measured by the difference between the net sales of two consecutive years divided by net sales of the earlier year. Tobin’s Q ratio is equal to the market capitalization of the firm divided by the book value of its total assets. Cash holdings is defined as the ratio of cash and cash equivalents over the total assets. Tangibility is measured by the ratio of fixed assets over the firm’s total assets. Liquidity is estimated by current assets divided by current liabilities. Interest coverage ratio is equal to the ratio of paid interest over EBITDA. Standard errors clustered at the firm level are in parentheses. *, **, *** indicate significance at the 10%, 5% and 1% level, respectively

Observations R-squared Year Firm

Constant

Table 14 (continued)

94 N. Khairallah et al.

Leverage Financing and the Risk-Taking Behavior of Small Business. . .

95

employees, etc.). Thus, it would be interesting to discover this path in small businesses by investigating the impact of the risk-taking behavior of managers on the firm characteristics.

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Credit Contagion Between Greece and Systemically Important Banks: Lessons for the Euro Area Dimitrios Koutmos

1 Introduction Both the 2008–09 financial crisis and 2011–13 euro-area debt crisis reveal the fundamental importance in understanding the nexus between sovereign governments and financial institutions. In the last few decades, international banks have morphed into significantly larger institutions than they once used to be and are now more vulnerable to global systemic risks.1 The rapid rate of globalization we will continue to experience in the future will serve to further augment the exposures banks have to global risk shocks and their interconnectedness with the various economic and geopolitical risk qualities of sovereign governments. The Financial Stability Board (FSB), an international body tasked with monitoring and making recommendations about the global financial system, recognizes that the sheer size of some of our financial institutions may pose a central hazard to our

1 The

rate of ‘mega’ bank mergers since the 1990s to today is staggering. Laurence H. Meyer, an economist and former governor for the Federal Reserve System, submitted testimony before the House of Representatives Judiciary Committee on June 3, 1998 explaining how mega mergers have made financial products more homogeneous than what they used to be in the past: https:// www.federalreserve.gov/boarddocs/testimony/1998/19980603.htm. If banks are becoming larger and more homogeneous, it is plausible that their exposure to global systemic risks will amplify. Boyd and De Nicoló (2005) present evidence in favor of the ‘concentration-fragility’ hypothesis – the notion that higher concentration in the banking industry can make our financial system more fragile. Other studies also argue that implicit too-big-to-fail government backings, which favors big banks and not small banks, can serve as a catalyst for excessive risk-taking and instead make GSIBs ‘too-big-to-discipline’ or ‘too-big-to-save’ (Bertay et al. 2013; Boyd and Heitz 2016; Bozos et al. 2013; Christophers 2013; Demirgüç-Kunt and Huizinga 2013; Lavelle 2013).

D. Koutmos () Texas A&M University – Corpus Christi, Corpus Christi, TX, USA e-mail: [email protected] © Springer Nature Switzerland AG 2021 C. Zopounidis et al. (eds.), Financial Risk Management and Modeling, Risk, Systems and Decisions, https://doi.org/10.1007/978-3-030-66691-0_4

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global economy. They proceed to construct a list of global systemically important banks (G-SIBs) which, given their sheer size, complexity and degree of systemic interconnectedness with the global economy, can cause major disruptions to our international financial system in the event of a failure.2 To add to the complexity of the too-big-to-fail conundrum in uncovering the potential risk transmission channels between sovereigns and banks, it is important to understand that international banks headquartered in different countries may model their sovereign risk exposures in different ways. In accordance with the Basel capital framework, and in most jurisdictions, banks may adopt one of two methodologies (and sometimes both concurrently): they may use either the “standardized approach,” which is based on external credit ratings, or the “internal ratings-based” approach, which relies on banks’ individual internal assessment procedures and models (BIS 2013).3 When exploring interconnectedness in financial markets, research thus far appears to predominantly focus on identifying the risk transmission channels, or “spillover” effects, between sovereign nations or their equity markets (Diebold and Yilmaz 2009). For example, beginning in 2011 until today, the International Monetary Fund (IMF) has published a series of spillover reports which seek to map risk channels between sovereign nations and their capital markets. For instance, in their 2015 report, the IMF warned of impending spillover effects from euro-area nations and cited, among other reasons, the large size of their output gaps in relation to the output gaps of other advanced economies (IMF 2015). More empirical research is needed in understanding the financial-sovereign nexus. Gray (2009, p.128) argues that “ . . . regulators, governments, and central banks have not focused enough on the interconnectedness between financial sector risk exposures and sovereign risk exposures . . . ” Alter and Schüler (2012) examine the interdependencies between Eurozone countries and their domestic banks before and after bank bailouts and argue that the “lack of theoretical macroeconomic models that are able to incorporate contagion mechanisms between government and financial sectors have amplified the uncertainty related to the implications of

2 This

list is publicly available: http://www.fsb.org/wp-content/uploads/2016-list-of-globalsystemically-important-banks-G-SIBs.pdf. In an effort to address the ‘too-big-to-fail’ conundrum, the FSB proposes various supervisory recommendations and requirements for GSIBs in order to reduce their default probabilities and the need for direct government and central bank interventions: http://www.fsb.org/what-we-do/policy-development/systematicallyimportant-financial-institutions-sifis/. The Federal Reserve Bank of Richmond has also discussed how too-big-to-fail banks can distort investors’ appreciation for risk and can create moral hazards in our economy: https://www.richmondfed.org/research/our_perspective/toobigtofail#tab-2. They construct a “bailout barometer” that measures the degree of explicit and implicit federal government protection for too-big-to-fail banks: https://www.richmondfed.org/publications/research/ special_reports/safety_net/bailout_barometer_previous_estimates 3 To further add to the complexity of deciphering a bank’s sovereign risk exposure, according to the Basel capital framework, while positive risk weights can be assigned to all but the highest of quality credit ratings (AAA to AA), bank supervisors are given some discretion at setting lower risk weights to sub-AA sovereign credit risks provided that the exposure is denominated and funded in the currency of the corresponding country. This is discussed further in BIS (2013) while a brief summary of this is available at http://www.bis.org/publ/qtrpdf/r_qt1312v.htm#in-4

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government interventions” (p. 3444). Gray et al. (2008) argue, using contingent claims analysis, that there are several possible channels interconnecting financials with sovereign countries. Acharya et al. (2014) explain how a “two-way feedback” mechanism may be at play between financials and sovereigns; specifically, banking crises can weaken the broad economy and transmit distress to government. This risk is then transmitted to holders of sovereign debt and results in a devaluation in government debt (since the cost of sovereign debt and the required rate of return debt holders demand rises commensurate to risk). When government debt experiences a devaluation, the balance sheets of banks holding such debt further deteriorates and leads to further increases in their credit risk. The 2008–09 financial crisis and the 2011–13 euro-area debt crisis both highlight the importance of understanding the financial-sovereign nexus. Headline news seems to brand Greece as the instigator for the euro-area debt crisis. In relation to its European counterparts, Greece has, for better or worse, received numerous bailout packages and has implemented laborious austerity measures to avert exiting the Eurozone. The IMF and European Central Bank (ECB) both contend that if Greece leaves the Eurozone, it may trigger an irreversible “domino effect” for the rest of Europe and potentially other international markets outside of Europe. From a political viewpoint, if Greece leaves, other struggling EU members may also entertain the possibility of exiting – a move that will seal the disintegration of the EU and the multiple layers of complex economic and legal agreements that presently bind all members. Greece’s systematic mismanagement of its domestic and fiscal affairs has done little to quell negativity in news headlines which portray it as the “catalyst” (i.e. the “first domino” to fall) which resulted in the euro-area crisis (CNBC 2015a, b, c; Wall Street Wall Street Journal 2015a, b, c, d; The Guardian 2016). These headlines are important to consider because they influence investors’ attention and moods. These behavioral forces can subsequently lead to shifts in risk tolerances and asset pricing behaviors (Boudoukh et al. 2013; Da et al. 2015; Sicherman et al. 2016). Clark et al. (2004) show the extent to which finance, trading and investing has become intrinsically intertwined with reports and news feeds generated by media companies, such as Bloomberg and CNBC. They show that these media companies, with all their embellishments and hype, impart news on viewers as being urgently needed and momentous: “Breathless excitement characterizes such commentary, being associated with ‘breaking news,’ ‘new information,’ and ‘unexpected events.’ Talk is fast and furious. Talk is also often interrupted by some sudden happening. Talk moves at a breakneck pace covering topic after topic though interrupted, of course, by commercial breaks . . . ” (p. 299). Similarly, Thrift (2001) discusses how a new market culture has formed as a result of the media and that asset price buying and selling decisions can be more prone to irrationality and manipulation.4 A quick

4 Shiller

(2000) explains how business news feeds from the media has become so pervasive in the US that “...traditional brokerage firms found it necessary to keep CNBC running in the lower corner of their brokers’ computer screens. So many clients would call to ask about something they

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and naive Google search of news headlines pertaining to “Greece” along with references to “spillovers,” “contagion,” “domino effects,” and the like yields a vast quantity of news articles implicating Greece as the catalyst for the euro-area debt crisis. In light of the aforementioned, this paper combines two budding trends in academic and policy-related banking research and investor attention; the first trend is the increasing demand by academics and regulators for research that can map the risk transmission channels between financials and sovereigns. The financialsovereign nexus has received little attention relative to research which focuses on spillovers between sovereign nations and their equity markets. The second trend is the pervasive number of news headlines that have spurred from the euro-area debt crisis implicating Greece as the catalyst for credit risk transmissions. Whether these media reports are right or wrong, it is important to understand that the sheer volume and forcefulness of these reports can play a large role in shaping aggregate beliefs. In the words of Shiller (2000), the media can create “self-fulfilling prophecies” whereby Greece may end up being the dominant credit risk transmission channel for the financial system given all the hype in the media implicating it as the instigator for the euro-area debt crisis. When we intersect these two trends, both the growing need for research exploring the financial-sovereign nexus and the volume of news reports implicating Greece as the “first domino” to begin the euro-area crisis, respectively, several unique and deep questions arise. The questions I empirically dissect in this paper are as follows: (a) Is there a long-run equilibrium relation between the CDS spreads of G-SIBs and the sovereign CDS spreads of Greece? As mentioned, G-SIBs are becoming an increasingly powerful force in our financial system. Their sheer size, complexity and concentration can augment their exposure to systemic risks and can produce, as Acharya et al. (2014) describe, “two-way feedback” effects with sovereign nations. Since Greece is implicated for the euroarea crisis, it is interesting to see whether the credit risks of these large too-big-tofail banks, some of which have received government bailouts in the past, share a long-run equilibrium relation with the sovereign credit risk of Greece. It may be the case that a particular group of banks based on their headquarter locations (European banks are in closer geographic proximity to Greece than, say, American banks) or based on a particular adopted methodology for modelling sovereign risk exposure (“standardized approach” versus the “internal ratings-based” approach) can exhibit a higher or lower degree of cointegration. Finally, it may be the case that none of the banks share a long-run equilibrium relation to Greece’s CDS spreads. (b) Was there one-way or two-way feedback effects between the credit risks of Greece and G-SIBs during the 2008–09 financial crisis?

had just heard on the networks that brokers (who were supposed to be too busy working to watch television!) began to seem behind the chase...” (p. 29).

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In the early 2000s, Greece along with other European countries enjoyed abundant access to cheap capital. Investor confidence in Greece’s economy rose further after it replaced its drachma and adopted the euro in 2001. In the mid 2000s, suspicion was growing over whether Greece intentionally misrepresented its finances in order to gain acceptance into the European Monetary Union. In March of 2002 and 2004, respectively, Eurostat refused to endorse and publish the economic reports Greece’s government submitted, thus compelling Greece to revise its figures. In 2004 and in the years following, Greece’s government launched a series of inquiries to determine whether the alleged misreporting was the result of fraud or “irregularities” – as they are often referred to – in accounting treatments (European Commission 2010). The 2008–09 financial crisis, which effectively more than halved the market values of some of the major stock indexes around the world, placed acute strain on Greek public finances and drove up Greece’s borrowing costs. During this time, when accusations of misconduct festered and Greece’s borrowing costs rose sharply, Greece also experienced sharp rises in its CDS spreads. Thus, it is of interest to determine whether G-SIBs were exposed to Greece’s credit risk at the time of the financial crisis. Likewise, it is also of interest to determine whether G-SIBs transmitted credit risk to Greece as well. It is important to understand that a G-SIB can be interlinked with a sovereign entity’s credit risks even though it does not physically hold any of its debt securities. It can instead still experience exposure through derivatives contracts or credit commitments made either directly with the entity in question or with other entities that are directly exposed to the entity in question. In its report, the Bank of International Settlements found that US banks may have more exposure to Greece as a result of derivatives contracts rather than actual Greek debt (BIS 2011). In fact, in their report, they recently began to publish a new table in their Statistical Annex which seeks to highlight “ . . . other potential exposures (on an ultimate risk basis) of reporting banking systems . . . ” (p. 17). The “other potential exposures” which the BIS is referring to are derivatives contracts that can exhibit interlinkages with a sovereign entity. One of the more recent and prominent examples of a G-SIB creating a strong channel between itself and a sovereign through derivatives agreements is the case of Goldman Sachs and Greece. In an effort to disguise its debt and appease Maastricht Treaty conventions which required all Eurozone members to show evidence of improvements in their public finances, Goldman Sachs and Greece engaged in a scheme in which Goldman lent Greece A C2.8 billion that was disguised off-thebooks as a cross-currency swap. Christoforos Sardelis, then head of Greece’s Public Debt Management Agency, referred later to the deal publicly as “a very sexy story between two sinners.” Although this case is rather extraordinary in various dimensions, it does illustrate how a G-SIB can have a “two-way feedback” credit risk transmission with a sovereign even if it may not hold any its debt instruments. (c) Was there one-way or two-way feedback effects between the credit risks of Greece and G-SIBs during the 2011–13 euro-area debt crisis?

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During the 2011–13 euro-area debt crisis, Greece was disproportionately implicated for the crisis at large. Although Greece’s mismanagement of its public fiscal affairs and its suspicious deals with Goldman Sachs only served to fuel salacious news headlines, can it be shown empirically that Greece is the dominant credit risk transmission channel to G-SIBs? Put another way, is Greece the instigator for credit risk shocks in G-SIBs during the euro-area debt crisis? If we answer this, we can assess the extent of Greece’s threat for too-big-to-fail banks. This is an empirical question that has not received attention in the literature. Thus far, Cornett et al. (2016) show that changes in Greek CDS spreads have an insignificant impact on the abnormal returns of international US banks. When attempting to measure banks’ exposures to Greece’s credit risk, they report that Greek CDS spreads provide no explanatory power for rates of return on banks beyond what the US market index provides. Mink and De Haan (2013) show qualitatively similar findings and also show that, although banks’ returns do not react to Greece, they do react positively to news about bank bailouts – even for banks that are not exposed to either Greece or other indebted euro-area countries. From a sovereign-to-sovereign contagion perspective, Koutmos (2018) shows that Greece may not be the instigator, or, catalyst, for Europe’s growing credit risks. According to the Bank of International Settlements, many G-SIBs significantly reduced their exposures to Greece before the 2011–13 euro-area crisis began to swell (BIS 2011).5 Thus, if this is the case, we ought to see minimal credit risk transmissions going from Greece to G-SIBs. In addition, if we can answer (c) above, we can also compare our findings with our findings for (b) above in order to gauge the extent to which transmission channels shifted. This paper seeks to answer the aforementioned questions by dissecting, across various economic credit regimes, the dynamic interdependencies between CDS spreads of Greece and a sample of G-SIBs headquartered in France, Germany, Italy, Spain, Switzerland, the United Kingdom and the United States, respectively. Using a bivariate vector autoregression (VAR) for this purpose, I seek to map credit risk transmission channels and ascertain whether there is one- or two-way feedback between Greece and each of the sampled G-SIBs across credit regimes. If Greece is found to be the dominant credit risk transmission channel, then news headlines which brand it as the “catalyst” for the euro-area debt crisis are well-grounded. If empirical evidence from the VAR does not support this, then it is possible that Greece has merely become a scapegoat for the international banking system’s problems at large, which the media can facilely target given the mismanagement of its domestic affairs. Sovereign as well as firm-specific CDS securities are essentially credit protection contracts whereby protection sellers compensate protection buyers in the event of a predefined credit event. For this insurance protection, the protection buyers pay a fixed fee, which is the CDS spread. As has been shown in the literature, the time-series behavior of CDS spreads provide a unique window for viewing the risk-

5 See

graph 4 on page 18 of BIS (2011). See also figure 6 on page 17 of Nelson et al. (2011).

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neutral probabilities of major credit events as investors see them (Pan and Singleton 2008). In terms of price discovery for sovereign CDS spreads, Blanco et al. (2005) find that the CDS market leads bond prices. As a result, it is not surprising that Acharya and Johnson (2007) suggest that insider trading first takes place in the CDS market – especially in the presence of negative market news. Similarly, Hull et al. (2004) show that CDS spreads can be used to predict rating changes. As mentioned, the motivation for this paper stems from the need to understand the nexus between too-big-to-fail banks and sovereigns. In addition, the pervasive number of news headlines branding Greece as the catalyst for the euro-area crisis may be misplaced if it cannot be shown empirically that Greece serves as the dominant transmission channel. This paper thus contributes to academic and policy discussions and advances literature which focuses on mapping contagion effects in financial markets. The remainder of this paper is structured as follows. The second section describes the sample data and G-SIBs as well as explains the various economic credit regimes that serve as sub-samples. It also seeks to answer empirical question (a). The third section describes the VAR framework for modelling credit risk transmissions in order to answer empirical questions (b) and (c), respectively. The fourth section discusses the results. The fifth section entertains various alternative approaches used as robustness and, finally, the sixth section concludes.

2 Sample Data Characteristics and Credit Risk Regimes 2.1 CDS Data and Sub-Sampled Credit Regimes To examine the extent of the contagion effects between Greece and G-SIBs across credit risk regimes, weekly CDS spreads are collected for Greece and twenty GSIBs, respectively, from Bloomberg starting from October 1, 2004 until July 15, 2016 – a sample period that encompasses the 2008–09 financial crisis as well as the 2011–13 euro-area debt crisis. Figure 1 lists all the twenty sampled G-SIBs considered here along with their Bloomberg ticker codes, the exchange where their equity securities trade and which country they are headquartered in. These G-SIBs are among the largest in the world and are a major influence in international banking (Koutmos 2019). As mentioned earlier, in the sovereign CDS market, protection buyers purchase insurance from protection sellers in the event of some prespecified credit event. For example, in reference to the Greek CDS market, the Greek CDS seller compensates the Greek CDS buyer for prespecified losses on a given face value amount of Greek debt. Thus, the Greek CDS buyer is insuring themselves against Greece’s credit risk by transferring such risk onto the Greek CDS seller. The CDS spread represents the price (fee) that the CDS buyer pays the seller in order to have this insurance. During periods when the probability of a Greek debt default rises there is a commensurate

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D. Koutmos Sample of global systemically important banks (G-SIBs) Bank

1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20.

BNP Paribas SA Crédit Agricole SA Société Générale SA Commerzbank AG Deutsche Bank AG UniCredit Group SpA Banco Bilbao Vizcaya Argentaria SA Banco Santander SA Credit Suisse Group AG UBS Group AG Barclays Bank PLC HSBC Bank PLC Lloyds Bank PLC Royal Bank of Scotland Group PLC Citigroup Goldman Sachs Group JPMorgan Chase & Co. Morgan Stanley Wells Fargo & Co. Bank of America Corp

Bloomberg ticker code BNP FP ACA FP GLE FP CBK GY DBK GY UCG IM BBVA SM SAN SM CSGN VX UBSG VX BARC LN HSBA LN LLOY LN RBS LN C US GS US JPM US MS US WFC US BAC US

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Euronext Euronext Euronext Xetra Xetra Borsa Italiana Bolsa de Madrid Bolsa de Madrid SIX Swiss Exchange SIX Swiss Exchange London Stock Exchange London Stock Exchange London Stock Exchange London Stock Exchange New York Stock Exchange New York Stock Exchange New York Stock Exchange New York Stock Exchange New York Stock Exchange New York Stock Exchange

France France France Germany Germany Italy Spain Spain Switzerland Switzerland United Kingdom United Kingdom United Kingdom United Kingdom United States United States United States United States United States United States

Fig. 1 Sample of global systemically important banks (G-SIBs) This table lists the twenty sampled global systemically important banks (G-SIBs). CDS spread data is gathered from Bloomberg. The ticker code for accessing bank-specific data is indicated. The stock exchange where each bank’s equity shares trade and the country where each bank’s headquarters are domiciled, respectively, are also indicated in the last two columns. CDS pricing data is denominated in Euros for all the European-headquartered banks that trade on the Euronext, Xetra, Borsa Italiana, Bolsa de Madrid, SIX Swiss Exchange and London Stock Exchange. CDS spreads for banks headquartered in the United States and which trade on the New York Stock Exchange are U.S. dollar-denominated

rise in Greek CDS spreads, and vice versa. With reference to G-SIBs, protection buyers purchase insurance from protection sellers in the event of a prespecified credit event pertaining to the underlying G-SIB. During times of upheaval in the financial industry, we experience rising CDS spreads across banks as protection sellers are exposed to a higher probability of bank defaults. After checking the various CDS tenors (maturities) for all the CDS markets for Greece and for each of the sampled G-SIBs, this paper will focus exclusively on 5-year CDS spreads. For Greece and for all twenty G-SIBs, the 5-year CDS tenor is the most liquid and complete in terms of data continuity – a finding that is, by now, standard in credit risk literature. Time-series plots of CDS spreads (in basis points) for Greece and each of the respective G-SIBs are shown in Figs. 2 and 3, respectively. The starting date for all the plots is October 1, 2004 and the end date is until July 15, 2016. The shaded regions represent OECD recession periods for the euro area at large and mark the 2008–09 financial crisis and 2011–13 euro-area debt crisis, respectively.6 Consistent

6 Information

and data (the dummy variables) on the OECD recession indicators for the Euro area can be accessed online: https://fred.stlouisfed.org/series/EUROREC

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Fig. 2 Time series plot of Greece’s sovereign CDS spreads (in basis points) This figure shows the time series plot for Greece’s weekly sovereign CDS spread (in basis points) for the full sample period (October 1, 2004 until July 15, 2016). The shaded regions are OECD recession periods and represent the 2008–09 financial crisis and 2011–13 European debt crisis, respectively. The vertical dotted redlines labeled (a) through (h) denote but a sample of important economic and political events that transpired in Greece as well as internationally. Their dates and the nature of the events are as follows: (a) September 15, 2008: Lehman Brothers files for Chapter 11 bankruptcy protection (b) October 4, 2009: Led by George Papandreou, the center-left party, PASOK, wins in Greece’s election. Following these election results, and from late October until December of 2009, Greece’s credit rating is downgraded by all the ‘big three’ credit agencies. By the end of December of 2009, it is rated as BBB+ by Fitch and A2 by Moody’s (c) February 9, 2010: The first austerity package, which presages a series of future austerity packages, is passed by Greek parliament. This package froze government salaries and instituted a 10% cut in wages and spending in the public sector. It also raised the retirement age and increased fuel prices. Approximately 2 months following this date, on April 23, 2010, George Papandreou formally requests an international effort to bailout Greece, which the European Union, European Central Bank and International Monetary Fund agree to participate in (d) May 25, 2011: The Greek ‘Indignant’ movement, an anti-austerity movement inspired by similar such protests in Spain, begins and executes a series of protests. By late summer of 2011, many of these protests turn violent as Greece passes further austerity packages (e) May 25, 2012: The Athens Stock Exchange (ATHEX) falls below 500 points – an unprecedented low which the market had not seen since the 1980s (f) April 28, 2013: Greece’s parliament approved a plan to abolish 15,000 civil servant jobs as part of a broader economic reform initiative. It also approved the hiring of young Greeks for less than the minimum wage of 586 Euros per month. In an effort to reduce tax burdens on its citizens, it also passed a 15% reduction in property taxes. (g) May 25, 2014: Left-wing party Syriza wins election in Greece (h) August 3, 2015: The Greek Stock Exchange reopens after being closed since June 25, 2015. Upon opening, it fell more than 16%

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Fig. 3 Time series plots of bank CDS spreads (in basis points) This figure shows the time series plots for all sampled banks’ CDS spreads (in basis points) for the full sample period (October 1, 2004 until July 15, 2016). Each bank is abbreviated on the basis of its Bloomberg ticker symbol listed in Fig. (1). The shaded regions (which denote sample regimes (2) and (4), respectively) are OECD recession periods and represent the 2008–09 financial crisis and 2011–13 European debt crisis, respectively. Sample regime (1) embodies a period of normal global economic growth and begins on October 1, 2004 and ends February 29, 2008. Sample regime (2) begins on March 7, 2008 and ends June 26, 2009. Sample regime (3) begins on July 3, 2009 and ends June 24, 2011. Sample regime (4) begins on July 1, 2011 and ends February 22, 2013. Finally, sample regime (5) begins on March 1, 2013 and ends July 15, 2016. The frequency for all CDS spread data is weekly

Credit Contagion Between Greece and Systemically Important Banks: Lessons. . . JPM (2)

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Fig. 3 (continued)

with these OECD recession periods, this paper forms subsamples which reflect distinct economic credit risk regimes. Credit regime 1 (labeled as “(1)” in Fig. 3), represents a period of steady global economic growth and tranquility. The start date for this regime is October 1, 2004 and ends February 29, 2008. During this period, Greece experienced strong growth in its GDP per capita.7 Its CDS spreads also remained relatively flat and low throughout this regime. All sampled G-SIBs also yielded strong equity returns during this period while their CDS spreads remained relatively low and stable. Toward the end of this regime, however, G-SIBs began to show increases and volatility in their CDS spreads. Credit regime 2 (labeled as “(2)” in Fig. 3), represents the 2008–09 financial crisis that marred financial markets around the world. It encapsulates the period when Lehman Brothers filed for bankruptcy. This regime is one of the two sampled OECD recession shaded periods and its starting date is March 7, 2008 and ends June 26, 2009. From Figs. 2 and 3, we can see CDS spreads increase for Greece and each of the G-SIBs (although for Greece it visually appears less noticeable given

7 GDP per capita data is publicly available at http://data.worldbank.org/indicator/NY.GDP.PCAP. CD?locations=GR

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the figure’s scaling in basis points and whereby it experienced astronomical growth in its CDS spreads during 2011–13). Credit regime 3 (labeled as “(3)” in Fig. 3), begins from July 3, 2009 and ends June 24, 2011. This regime can be thought of as an artificial ‘calm before the storm’ period. The reason why it may have been artificial is because monetary authorities went through unprecedented lengths to subdue the mayhem that rocked financial markets during credit regime 2.8 During this regime, Greece’s credit rating was downgraded by all three of the ‘Big Three’ credit rating agencies and, on April 23, 2010, George Papandreou, then prime minister of Greece, formally requested an international bailout of Greece and backed this request by instituting the first in what would be a series of austerity packages for Greek citizens. Although credit regime 3 is not recognized as a recessionary period by the OECD or even the National Bureau of Economic Research (NBER), it is a time when systemic risks were developing in our financial system. The CDS spreads of all the sampled G-SIBs remained elevated or rose even further in this regime and did not fall to regime 1 levels despite central banking efforts. Credit regime 4 (labeled as “(4)” in Fig. 3), is the second sampled OECD recession period. It starts from July 1, 2011 until February 22, 2013 and will go down in history, as did the 2008–09 crisis, as a destructive period for our global financial system. Jean-Claude Pier Trichet publicly stated, before stepping down from his role as president of the ECB in October of 2011, that “ . . . to be in denial of the fact that we have the worst crisis since World War Two would be the most terrible mistake we could make . . . ”. During this regime, Greece experienced significant socioeconomic upheaval. Several anti-austerity movements, such as the Greek Indignant movement, attracted hundreds of thousands of disgruntled Greek citizens who staged a series of protests and strikes against austerity. Many of these protests turned violent and, for several days, shut down parts of Athens, Thessaloniki and other major cities. On May 25, 2012, the ATHEX declined to an unprecedented low which the market had not seen since the 1980s. Sovereign CDS spreads for Greece also reached an astronomical high of over 26,000 basis points during this time period – a level which utterly dwarfed the CDS spreads of other euro-area member states. During regime 4, G-SIBs also experienced significant rises in their CDS spreads. On February 6, 2012, Citigroup economists Ebrahim Rahbari and Willem Buiter coined the term “Grexit” and, in the summer of 2012, Citigroup predicted that there was a 90% probability that Greece would exit the Eurozone – an estimate that raised speculation as to the future of the EU. Finally, credit regime 5, which starts from March 1, 2013 until July 15, 2016, reflects our present-day state of affairs. During this time period, the left-wing party

8 On

November 3, 2010 the Federal Reserve announced it would purchase $600 billion of longerterm treasuries. This program was the second round of quantitative easing (“QE2”) and concluded in June of 2011. The press release for QE2 is available online: https://www.federalreserve.gov/ newsevents/press/monetary/20101103a.htm

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Syriza won the elections on May 25, 2014 with the promise that they would put an end to austerity measures for Greek citizens. On June 25, 2015 Greek monetary authorities halted trading in the ATHEX and, on June 30, 2015, missed an important payment to the IMF (which resulted in a spike in its CDS spread). On August 3, 2015 when the ATHEX opened for trading, it immediately fell more than 16%. In this regime, some G-SIBs such as Crédit Agricole (ACA), Bank of America (BAC), BNP Paribas (BNP), Citigroup (C), Société Générale (GLE), Goldman Sachs (GS), Morgan Stanley (MS), and Wells Fargo (WF), for example, experienced declines in their CDS spreads. Others, such as Barclays (BARC), Credit Suisse (CSGN), Deutsche Bank (DBK) and HSBC (HSBA), for example, experienced sharp rises towards the end of this regime. What all G-SIBs have in common, however, is that their CDS spreads did not converge back to their pre-2008 levels. For all G-SIBs, their CDS spreads remain elevated during the present-day, which may signal fear and uncertainty about the future credit stability of our international financial system. Tables 1a through 1e report summary statistics for the CDS spreads (in basis points) of Greece and each of the sample G-SIBs for each of the aforementioned respective credit regimes. These tables show how benign regime 1 (Table 1a) is relative to the other regimes when events begin to unfold. The levels and volatilities in the CDS spreads grow in regime 2 (Table 1b) and, although they may decrease somewhat in regime 3 (Table 1c), they reach unprecedentedly high levels in regime 4 (Table 1d). Our present-day state of affairs are reflected in regime 5 (Table 1e) and, despite some reduction in CDS levels and their volatilities relative to regimes 2 and 4, they did not reach the docile values we observed during the pre-2008 period.

2.2 Stationarity Tests Stationarity tests are performed and reported in Table 2 for the full sample period (October 1, 2004 until July 15, 2016) for the logarithmic levels (log-levels) and logarithmic first differences (log-changes), respectively for the CDS spreads of Greece and each of the sampled G-SIBs. Justification for expressing CDS spread data in log-levels prior to performing regression-type modelling is provided by Alter and Schüler (2012) and Forte and Pena (2009). Additional justification for log-levels is self-evident when visually examining CDS spread levels in basis points (Figs. 2 and 3); specifically, when we compare the CDS spreads of the G-SIBs with those of Greece, we see that the scales (in basis points) do not compare with one another. Most notably, Greece’s CDS spreads, although more docile and in line with the CDS spreads of other G-SIBs in credit regime 1, become multiplicatively larger during regime 4. Stationarity tests will help us ascertain whether the CDS series contain a unit root in their time-series representations. If log-levels contain a unit root, it is of interest to see whether respective pairs of CDS spreads (between Greece and each Bankj ), whereby j = each sampled G-SIB, are cointegrated. By examining cointegration properties between the CDS spreads of Greece and each bank, we can answer

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Table 1a Summary statistics of CDS spreads (in basis points) CDS spread series Greece ACA BAC BARC BBVA BNP C CBK CSGN DBK GLE GS HSBA JPM LLOY MS RBS SAN UBSG UCG WFC

Mean 13.13 14.90 21.78 16.89 16.80 13.44 23.34 22.56 22.01 20.73 15.00 35.60 15.27 28.01 12.77 38.91 16.65 17.44 15.44 19.59 19.71

Med. 11.35 9.00 16.13 8.94 9.75 8.81 15.11 16.86 15.60 14.73 9.48 27.12 9.91 24.42 8.19 27.10 9.42 10.50 8.54 12.52 13.66

Max. 61.00 109.83 95.79 115.84 101.50 76.73 159.26 113.47 127.09 104.10 100.40 145.47 99.43 97.52 88.53 186.26 132.49 105.00 147.55 94.56 93.36

Min. 3.00 6.00 8.17 5.59 7.86 5.38 7.44 8.13 8.97 10.15 5.97 18.79 4.98 11.54 3.80 17.83 3.96 7.63 4.55 7.48 6.41

Std. dev. 9.08 17.41 17.62 20.34 17.58 13.49 24.73 19.42 18.10 16.75 16.20 22.90 16.80 16.42 14.45 31.26 21.89 17.91 20.91 16.93 18.25

Sample regime 1; October 1, 2004 – February 29, 2008 (N = 179) This table reports summary statistics for the CDS spreads (in basis points) of Greece and each of the sampled banks for sample regime 1 (October 1, 2004 until February 29, 2008). It reports the mean, median (med.), maximum (max.), minimum (min.) and standard deviation (std. dev.). Each sampled bank is abbreviated on the basis of its Bloomberg ticker symbol listed in Fig. (1)

question (a) posed in the introductory section of this paper; namely, is there a longrun equilibrium relation between the CDS spreads of G-SIBs and the sovereign CDS spreads of Greece? If log-levels contain a unit root, then a cointegrating equation in the context of Engle and Granger (1987) may yield stationary residuals – an indication that the CDS spreads of Greece and Bankj are tied together in the long-run and that disequilibria from this relation are transitory and random across various points in time. As we see from Figs. 2 and 3, there appears to be similar time-series comovement between the CDS spreads of Greece with those of each Bankj , however, this is not necessarily proof for cointegration, as is discussed later on. Table 2 reports stationarity tests of log-levels and log-changes using the augmented Dickey-Fuller (ADF) test (Dickey and Fuller 1981), the Phillips-Perron (PP) test (Phillips and Perron 1988), and the Elliott, Rothenberg and Stock point optimal (ERS) test (Elliott et al. 1996), respectively. The purpose of estimating all three tests is to provide confirmatory, rather than competing, evidence that log-levels contain a unit root (i.e. are non-stationary) whereas log-changes do not contain a unit root (i.e. are stationary).

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Table 1b Summary statistics of CDS spreads (in basis points) CDS spread series Greece ACA BAC BARC BBVA BNP C CBK CSGN DBK GLE GS HSBA JPM LLOY MS RBS SAN UBSG UCG WFC

Mean 131.15 92.06 161.98 142.77 98.10 70.73 272.87 91.90 128.29 106.17 96.42 219.88 91.96 122.96 115.42 332.11 139.32 99.84 164.35 109.79 139.76

Med. 132.70 90.50 136.38 140.85 92.76 68.83 209.73 84.81 120.69 106.71 96.90 188.61 86.68 114.35 103.33 285.53 133.94 93.93 138.79 110.90 126.71

Max. 297.50 157.90 358.10 241.32 179.96 134.33 638.33 158.29 255.83 166.01 150.30 491.43 169.33 225.56 220.35 1240.00 273.54 177.19 353.47 266.68 293.23

Min. 35.50 55.89 61.97 53.27 44.67 34.24 86.99 52.93 57.59 52.33 43.17 84.11 41.84 62.54 41.82 108.06 55.17 44.83 57.66 43.83 62.26

Std. dev. 85.15 21.28 73.75 46.05 29.76 20.82 154.20 25.47 45.40 29.40 22.11 99.50 32.25 34.35 49.49 199.02 46.93 29.42 69.94 47.61 54.44

Sample regime 2; March 7, 2008 – June 26, 2009 (N = 69) This table reports summary statistics for the CDS spreads (in basis points) of Greece and each of the sampled banks for sample regime 2 (March 7, 2008 until June 26, 2009). It reports the mean, median (med.), maximum (max.), minimum (min.) and standard deviation (std. dev.). Each sampled bank is abbreviated on the basis of its Bloomberg ticker symbol listed in Fig. (1)

Assuming that the yt time-series (in our case, log-levels or log-changes) follows an AR(k) process, the ADF test is specified as follows: yt = μ + γ t + αyt−1 +

k−1 

βj yt−j + ut

(1)

j =1

whereby  is the difference operator and ut is a white-noise innovation series. This test checks the negativity of the parameter α using its regression t ratio. The asymptotic distribution of the statistic is derived in Dickey and Fuller (1979) while Hall (1994) shows that the asymptotic distribution is insensitive to parameter selection based on standard information criteria. The PP test is based on the standard OLS regression estimate, a, ˆ from an AR(1) specification: yt = ay t−1 + ut

(2)

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Table 1c Summary statistics of CDS spreads (in basis points) CDS spread series Greece ACA BAC BARC BBVA BNP C CBK CSGN DBK GLE GS HSBA JPM LLOY MS RBS SAN UBSG UCG WFC

Mean 669.72 120.71 148.13 110.88 169.85 88.30 181.23 110.26 90.69 101.06 114.69 131.96 73.16 79.87 166.28 165.40 169.50 155.99 102.95 137.77 99.99

Med. 745.60 124.61 144.22 111.20 187.08 94.16 172.52 102.06 88.96 97.51 115.24 125.96 73.66 77.33 169.50 159.01 169.27 157.90 97.37 140.30 99.22

Max. 2174.10 233.34 210.53 177.45 305.26 146.46 408.81 228.23 153.94 177.10 189.37 217.47 107.82 130.89 235.73 300.00 239.02 284.00 173.41 234.70 147.17

Min. 107.80 66.28 100.54 74.02 67.87 48.93 120.00 53.50 53.92 67.50 66.65 91.86 52.42 47.73 103.12 112.36 103.36 66.69 70.81 75.13 72.45

Std. dev. 437.53 33.34 26.46 23.15 69.51 23.74 54.44 37.19 19.61 21.42 29.42 27.91 12.33 17.24 34.82 35.60 35.16 61.87 21.15 41.70 14.78

Sample regime 3; July 3, 2009 – June 24, 2011 (N = 104) This table reports summary statistics for the CDS spreads (in basis points) of Greece and each of the sampled banks for sample regime 3 (July 3, 2009 until June 24, 2011). It reports the mean, median (med.), maximum (max.), minimum (min.) and standard deviation (std. dev.). Each sampled bank is abbreviated on the basis of its Bloomberg ticker symbol listed in Fig. (1)

Using the OLS regression estimate a, ˆ the PP unit root statistics are estimated as follows9 : −1

T 1   1 2 2 Za = T aˆ − 1 − λˆ − s 2 yt−1 2 T2

(3)

t=1

−1/2

T λˆ 2  s 1 2 2 2 Zt = ta=1 λˆ − s − yt−1 ˆ 2 T2 λˆ

(4)

t=1

9 Castro

et al. (2015) provide an in-depth review and analysis of the PP test along with its advantages and disadvantages, focusing in particular on time-series data which display a strong cyclical component.

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Table 1d Summary statistics of CDS spreads (in basis points) CDS spread series Greece ACA BAC BARC BBVA BNP C CBK CSGN DBK GLE GS HSBA JPM LLOY MS RBS SAN UBSG UCG WFC

Mean 8992.56 241.87 251.01 187.54 345.05 209.64 206.25 230.11 143.75 160.37 269.26 236.40 120.14 119.24 255.37 301.37 267.24 329.24 157.13 406.69 105.03

Med. 7307.50 240.72 253.65 189.83 324.98 214.19 222.20 229.40 146.68 163.00 273.90 241.23 125.66 119.06 266.67 314.08 277.56 311.74 165.89 366.53 94.95

Max. 26089.20 403.78 483.06 278.64 492.73 359.59 323.38 349.19 207.36 311.60 432.08 419.94 183.53 183.16 375.83 523.62 395.94 455.66 244.85 687.10 178.45

Min. 1705.20 133.29 112.19 117.76 241.51 112.98 111.19 131.14 83.14 86.07 132.01 130.01 65.51 76.99 117.45 136.00 139.14 226.75 84.17 206.69 69.93

Std. dev. 6049.68 62.55 94.58 39.37 67.59 55.84 55.17 51.33 33.04 41.62 72.88 69.41 26.18 24.44 71.42 98.15 68.57 62.21 38.51 102.45 26.34

Sample regime 4; July 1, 2011 – February 22, 2013 (N = 87) This table reports summary statistics for the CDS spreads (in basis points) of Greece and each of the sampled banks for sample regime 4 (July 1, 2011 until February 22, 2013). It reports the mean, median (med.), maximum (max.), minimum (min.) and standard deviation (std. dev.). Each sampled bank is abbreviated on the basis of its Bloomberg ticker symbol listed in Fig. (1)

1/2  T  2 whereby ta=1 = s −1 aˆ − 1 and s 2 = T −1 Tt=1 uˆ 2t and λˆ 2 are ˆ t=1 yt−1 the estimators for the short- and long-run variances of {ut }.The test statistics all support the notion that log-levels contain a unit root (i.e. are non-stationary) while log-changes do not contain a unit root (i.e. are stationary). For the ADF test, the appropriate lag structure is atheoretical and more of an empirical question. Various lag structures are entertained (not tabulated) in order to check the robustness of the ADF test. In general, the test statistics at various lags consistently fail to reject the null hypothesis, H0 , of a unit root for log-levels while rejecting this null for log-changes. For the ADF test statistics reported in Table 2, the Akaike information criterion (AIC) is used to select the optimal lag structure. The PP test

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Table 1e Summary statistics of CDS spreads (in basis points) CDS spread series Greece ACA BAC BARC BBVA BNP C CBK CSGN DBK GLE GS HSBA JPM LLOY MS RBS SAN UBSG UCG WFC

Mean 1444.32 95.96 84.45 89.21 141.68 84.78 85.94 109.54 84.84 101.44 100.82 99.31 73.69 71.37 83.64 97.66 105.70 139.12 64.86 172.45 53.18

Med. 1199.20 77.84 76.98 76.53 121.30 75.91 82.72 99.67 77.39 89.15 86.93 92.76 71.30 70.39 67.63 87.50 89.46 121.82 60.84 141.88 53.25

Max. 11188.50 214.71 141.94 167.21 339.67 176.44 143.01 185.19 171.94 244.49 215.15 163.42 142.53 103.03 182.05 179.97 241.04 324.33 118.53 402.58 77.75

Min. 422.40 55.16 60.67 43.34 60.76 53.28 58.99 66.69 48.54 57.44 63.92 64.32 39.11 48.99 42.76 60.82 46.44 59.03 39.29 82.10 34.18

Std. dev. 1180.22 39.12 19.63 32.58 69.96 27.54 15.39 31.16 29.64 40.80 36.19 19.45 22.09 11.27 35.29 25.11 43.88 65.47 18.25 80.01 10.38

Sample regime 5; March 1, 2013 – July 15, 2016 (N = 177) This table reports summary statistics for the CDS spreads (in basis points) of Greece and each of the sampled banks for sample regime 5 (March 1, 2013 until July 15, 2016). It reports the mean, median (med.), maximum (max.), minimum (min.) and standard deviation (std. dev.). Each sampled bank is abbreviated on the basis of its Bloomberg ticker symbol listed in Fig. (1)

yields qualitatively analogous findings as the ADF test for both log-levels and logchanges.10 Whereas the critical values for the ADF and PP tests become larger (in absolute terms) when you move from a 10% to a 1% level of significance in rejecting the null, the ERS critical values become smaller. The ERS test seeks to modify the ADF test by de-trending the time-series so that explanatory variables are removed from the data prior to performing the test regression. De-trending the data is performed by quasi-differencing the time-series in question, yt .The quasi-difference of yt that

10 Various

kernel-based sum-of-covariances estimators and autoregressive spectral density estimators are entertained for all the CDS spreads to check the robustness of the PP test (they yield qualitatively analogous findings but are not tabulated for brevity). The choice of using a kernel-based estimator versus a spectral density estimator does not systematically affect the aforementioned findings in any substantive way.

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Table 2 Unit root tests CDS spread series Greece ACA BAC BARC BBVA BNP C CBK CSGN DBK GLE GS HSBA JPM LLOY MS RBS SAN UBSG UCG WFC

ADF Log levels −1.1984 −1.0983 −1.1146 −1.3482 −1.1819 −1.0852 −1.1004 −1.3716 −1.8968 −1.5419 −0.9877 −1.6054 −1.4357 −1.5718 −0.9777 −1.3039 −1.0917 −1.2320 −1.0954 −1.3694 −1.3668

PP

ERS

−1.1226 −1.2720 −1.1982 −1.6188 −1.2963 −1.5583 −1.1528 −1.9651 −1.8330 −2.0246 −1.2632 −1.6921 −1.7139 −1.8727 −1.2136 −1.4418 −1.4070 −1.3726 −1.3085 −1.6779 −1.4540

17.7772 26.7083 27.5457 29.0315 26.5942 27.5788 30.0886 20.0201 13.9572 20.4046 29.5557 17.0074 21.1148 14.0050 40.9554 27.0237 35.3527 24.8225 38.4536 21.9042 20.1303

ADF Log changes −7.0868∗ −6.2307∗ −10.1860∗ −10.1297∗ −28.4390∗ −10.6993∗ −12.1326∗ −9.8409∗ −10.9670∗ −9.8874∗ −11.4906∗ −13.8618∗ −10.2907∗ −6.3828∗ −9.9722∗ −9.9663∗ −10.4329∗ −28.7338∗ −10.7525∗ −10.1890∗ −5.0660∗

PP

ERS

−29.4486* −25.4113* −26.3353* −25.4277* −28.3341* −26.4007* −26.8576* −24.3304* −23.1858* −25.9238* −25.6084* −25.3819* −24.8643* −25.8550* −23.9358* −24.0236* −25.2321* −28.7307* −22.8068* −25.9110* −26.0416*

0.3021* 0.9853* 0.0667* 0.0036* 0.3497* 0.0915* 0.1269* 0.4447* 0.0919* 0.5984* 0.0346* 0.1294* 0.0167* 0.1818* 0.0003* 0.0002* 0.0355* 0.3365* 0.0670* 0.0078* 0.8276*

This table reports unit root test statistics for the log-levels and log-changes, respectively, of Greece’s sovereign CDS spreads as well as the CDS spreads for each sampled bank. Each sampled bank is abbreviated on the basis of its Bloomberg ticker symbol listed in Fig. (1). Augmented Dickey-Fuller (ADF), Phillips-Perron (PP) and Elliott-Rothenberg-Stock (ERS) tests are respectively conducted and test statistics are estimated for the full sample period (October 1, 2004 until July 15, 2016). Critical values for the ADF and PP tests are found in MacKinnon (1996) while critical values for the ERS test are found in Elliott et al. (1996). Lag lengths for the ADF and ERS tests are based on the Akaike information criterion (AIC). An asterisk (*) denotes rejection of the null hypothesis, H0 , of a unit root at the 5% significance level at least

depends on the value of a, which represents the particular point alternative against which we test the null:  if t = 1 yt (5) d (yt |a) = yt − ayt−1 if t > 1 The value for a is needed in order to obtain an ERS test statistic. This value can be obtained by an OLS regression with the quasi-differenced time-series d(yt | a) on the quasi-differenced d(xt | a): d (yt |a) = d(xt |a) δ(a) + ηt

(6)

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whereby xt contains either a constant or both a constant and trend, and where δ(a) is an OLS from this regression. The residuals, ηt (a), can be defined as ηˆ t (a) = d (yt |a) − d(xt |a) δ(a) while the of squared (SSR) residuals function, SSR(a),  sum can be defined as SSR(a) = ηˆ t2 (a). The ERS point optimal tests statistic, PT , tests the null (that yt contains a unit root), a = 1, against the alternative a = a. The test statistic is computed using SSR and the value for a from (6): PT = [SSR (a) − aSSR(1)] /f0

(7)

whereby f0 is the estimator for the residual spectrum at frequency zero. Similarly to the ADF and PP tests, the optimal lag structure for the test statistics reported in Table 2 for the ERS test are based on the AIC. Various lag structures entertained for the ERS test (not tabulated for brevity) support the notion that loglevels are non-stationary while log-changes are stationary. In summary, the ADF, PP and ERS test statistics are consistent with one another and this leads us to the next subsection where cointegration tests are performed in order to answer question (a).

2.3 Cointegration Tests Having established that CDS spreads are non-stationary in their log-levels and stationary in their log-changes, it is now of interest to see whether log-levels in CDS spreads between Greece and each G-SIB share a common stochastic trend. In other words is there a long-run cointegrating relation between them whereby disequilibria from this relation are transitory and random across various points in time (i.e. the residuals of this cointegrating relation are stationary). A priori, we have no way of knowing whether or not a long-run equilibrium relation exists. The appearance of comovement among the CDS spreads in Figs. 2 and 3 is not necessarily a condition for cointegration. If it is the case that all the twelve sampled CDS markets are cointegrated, a linear combination of any set of CDS spreads ought to be stationary. To ascertain this and to answer question (a), the multivariate cointegration framework of Johansen (1991, 1995) is implemented to find out whether pairwise combinations between the CDS spreads of Greece and each Bankj are cointegrated. Given that there are two variables (the CDS spreads of Greece and Bankj , respectively) there is the possibility of at most one cointegrating equation. The Johansen (1991, 1995) multivariate cointegration methodology begins with a vector autoregression (VAR) of order p: yt = A1 yt−1 + · · · + Ap yt−p + Bxt + εt

(8)

whereby yt is a k-vector of non-stationary variables, xt denotes a d-vector of deterministic variables, and εt is an n × 1 vector of innovations. In a more compact form, this VAR can be expressed as:

Credit Contagion Between Greece and Systemically Important Banks: Lessons. . .

yt = yt−1 +

p−1 

i yt−i + Bxt + εt

119

(9)

i=1

whereby:

=

p 

Ai − I and i = −

p 

Aj

(10)

j =i+1

i=1

For the coefficient matrix Π in (9) and (10) to have reduced rank r < k, there  must exist k × r matrices a and β with respective rank r, such that Π = αβ and  β yt are stationary series (Engle and Granger 1987). In this case, r is the number of cointegrating relationships (i.e. the cointegrating rank) while the elements of a are adjustment parameters. Each respective column of β represents a cointegrating vector. Johansen (1995) shows that for a given cointegrating rank, r, the maximum likelihood estimator for a cointegrating vector, β, describes an arrangement of yt − 1 that generates the r largest canonical correlations between yt with yt − 1 , following corrections for lagged differences and when deterministic variables, xt , are present (Hjalmarsson and Osterholm 2010). The Johansen methodology, (8) – (10), entails estimating the Π matrix using an unrestricted VAR and subsequently testing whether restrictions implied by the reduced rank of Π can be rejected. When estimating (8) through (10), there are two important statistics that are used to determine whether cointegration is present among non-stationary time-series and, if so, how many cointegrating equations there are at any given point in time: the trace test statistic and the maximum (max) eigenvalue test statistic, shown in Eqs. (11) and (12), respectively: LR trace (r|k) = −T

k 

log (1 − λi )

(11)

i=r+1

LR max (r|r + 1) = LR trace (r|k) − LR trace (r + 1|k) = −T log (1 − λr+1 ) (12) For (11) and (12), r is the number of cointegrating vectors, T denotes the sample size and λi is the i-th largest eigenvalue of the Π matrix in (9) and (10). The purpose of the trace statistic is to test the null hypothesis of r cointegrating relationships against an alternative of k cointegrating relationships whereby k represents the number of endogenous variables for r = {0, 1, . . . , k − 1}. The purpose of the max eigenvalue statistic is to test the null of r cointegrating relationships against the alternative of r + 1 cointegrating relationships. If the sampled series are not cointegrated, the rank of Π is zero. Tables 3a through 3e report results for the Johansen cointegration methodology described in (8) – (12) for the full sample under all five of the deterministic trend cases considered by Johansen (1995). Given that the purpose of the cointegration framework in (8) through (10) is to determine whether a long-run equilibrium relationship is present between the CDS spreads of Greece and each of the respective

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Table 3a Log level CDS have no deterministic trends and the cointegrating equations (CEs) do not have intercepts Trace test Max-Eigenvalue test Hypothesized Trace Max-Eigen no. of CE(s) statistic Cointegration? statistic Cointegration? None 8.5736 NO 8.5628 NO [p = 0.27] [p = 0.22] At most 1 0.0108 0.0108 2. (Greece, BAC) None 8.4989 NO 0.0137 NO [p = 0.20] [p = 0.15] At most 1 0.0521 0.0001 3. (Greece, BARC) None 7.0172 NO 6.9760 NO [p = 0.32] [p = 0.25] At most 1 0.0411 0.0411 4. (Greece, BBVA) None 7.6641 NO 7.5411 NO [p = 0.26] [p = 0.21] At most 1 0.1229 0.1229 5. (Greece, BNP) None 9.2734 NO 9.2607 NO [p = 0.15] [p = 0.11] At most 1 0.0127 0.0127 6. (Greece, C) None 7.4938 NO 7.3974 NO [p = 0.28] [p = 0.22] At most 1 0.0964 0.0964 7. (Greece, CBK) None 7.2902 NO 7.1959 NO [p = 0.30] [p = 0.23] At most 1 0.0942 0.0942 8. (Greece, CSGN) None 5.2628 NO 5.1821 NO [p = 0.53] [p = 0.45] At most 1 0.0806 0.0806 9. (Greece, DBK) None 6.6386 NO 6.4546 NO [p = 0.36] [p = 0.30] At most 1 0.0003 0.1839 10. (Greece, GLE) None 9.4958 NO 9.4957 NO [p = 0.14] [p = 0.11] At most 1 0.0001 0.0002 11. (Greece, GS) None 6.5557 NO 6.4768 NO [p = 0.37] [p = 0.29] At most 1 0.0789 0.0789 12. (Greece, HSBA) None 6.7383 NO 6.7107 NO [p = 0.35] [p = 0.27] At most 1 0.0276 0.0276 13. (Greece, JPM) None 5.8213 NO 5.8016 NO [p = 0.45] [p = 0.37] At most 1 0.0197 0.0197 14. (Greece, LLOY) None 9.2823 NO 9.2776 NO [p = 0.15] [p = 0.11] At most 1 0.0047 0.0047 Test pair (Greece, Bankj ) 1. (Greece, ACA)

(continued)

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121

Table 3a (continued) Test pair (Greece, Bankj ) 15. (Greece, MS)

Trace test Hypothesized Trace no. of CE(s) statistic None 7.0660

16. (Greece, RBS)

At most 1 None

0.1765 9.1659

17. (Greece, SAN)

At most 1 None

0.0224 7.7111

At most 1 18. (Greece, UBSG) None

0.1158 7.1399

19. (Greece, UCG)

At most 1 None

0.0025 7.0480

20. (Greece, WFC)

At most 1 None

0.2365 8.0069

At most 1

0.0642

Max-Eigenvalue test Max-Eigen Cointegration? statistic Cointegration? NO 6.8894 NO [p = 0.31] [p = 0.26] 0.1765 NO 9.1434 NO [p = 0.16] [p = 0.11] 0.0224 NO 7.5953 NO [p = 0.26] [p = 0.20] 0.1158 NO 7.1373 NO [p = 0.31] [p = 0.24] 0.0025 NO 6.8115 NO [p = 0.32] [p = 0.26] 0.2365 NO 7.9426 NO [p = 0.23] [p = 0.18] 0.0642

This table reports Trace and Max-Eigenvalue (Max-Eigen) statistics, derived respectively from (11) and (12) using the Johansen (1991, 1995) cointegration method described in (8) through (10) for the full sample period (October 1, 2004 until July 15, 2016). CE(s) denote the hypothesized number of cointegrating equations for each test pair. Since cointegration is being tested between Greece’s sovereign CDS spreads with the CDS spreads of each of the sampled banks listed in Table (1), we have the possibility that there is no cointegrating equation (‘None) or the possibility of at most one cointegrating equation (‘At most 1 ). The null hypothesis, H0 , of ‘None’ is rejected if the Trace and Max-Eigen statistics exceed their respective critical values over the desired confidence interval. Conversely, the null hypothesis cannot be rejected if the Trace and MaxEigen statistics are less than the desired critical values. For this table, the critical values, assuming the log level CDS spreads have no deterministic trends and the cointegrating equations (CEs) do not have intercepts, can be found in MacKinnon (1996) and are as follows for ‘None:’ 10.4746 and 9.4745 for the Trace and Max-Eigen tests, respectively, at the 10% level of significance. Likewise, they are 12.3209 and 11.2248 for the Trace and Max-Eigen tests, respectively, at the 5% level of significance. Failure to reject the null of no cointegrating equations (‘None’) for either the Trace or Max-Eigen tests leads to a conclusion of no cointegration (indicated by ‘NO’). Associated p-values for both respective tests (Trace and Max-Eigen) of no cointegration (H0 : ‘None’) are in square brackets

G-SIBs, the full sample (October 1, 2004 through July 15, 2016) is used to initially determine whether a vector error correction (VEC) framework with an adjustment factor is necessary or whether a VAR is sufficient in order to subsequently determine causal relationships (in order to test whether Greece’s credit risk is contagious for the G-SIBs and to answer questions (b) and (c), respectively). The five deterministic trend cases are described in Johansen (1995, pp. 80– 84) and are reported in each of the respective Tables (3a through 3e) for the full sample:

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Table 3b Log level CDS have no deterministic trends and the cointegrating equations (CEs) have intercepts Test pair (Greece, Bankj ) 1. (Greece, ACA)

Trace test Hypothesized Trace no. of CE(s) statistic None 12.9978

2. (Greece, BAC)

At most 1 None

3.1950 12.7448

3. (Greece, BARC)

At most 1 None

2.7147 11.2321

4. (Greece, BBVA)

At most 1 None

3.4831 12.5853

5. (Greece, BNP)

At most 1 None

3.4182 17.0424

6. (Greece, C)

At most 1 None

3.1220 10.5924

7. (Greece, CBK)

At most 1 None

2.8405 16.8692

8. (Greece, CSGN)

At most 1 None

3.1370 11.0959

9. (Greece, DBK)

At most 1 None

3.4612 12.5555

10. (Greece, GLE)

At most 1 None

3.3163 14.5979

11. (Greece, GS)

At most 1 None

3.0088 12.8753

At most 1 12. (Greece, HSBA) None

3.2263 12.2224

At most 1 None

3.3077 13.2127

At most 1 14. (Greece, LLOY) None

2.9087 12.2323

At most 1

2.8005

13. (Greece, JPM)

Max-Eigenvalue test Max-Eigen Cointegration? statistic Cointegration? NO 9.8027 NO [p = 0.36] [p = 0.35] 3.1950 NO 10.0300 NO [p = 0.38] [p = 0.33] 2.7147 NO 7.7489 NO [p = 0.52] [p = 0.58] 3.4831 NO 9.1670 NO [p = 0.39] [p = 0.41] 3.4182 NO 13.9204 NO [p = 0.13] [p = 0.11] 3.1220 NO 7.7519 NO [p = 0.58] [p = 0.57] 2.8405 NO 13.7322 NO [p = 0.14] [p = 0.11] 3.1370 NO 7.6346 NO [p = 0.53] [p = 0.59] 3.4612 NO 9.2391 NO [p = 0.40] [p = 0.41] 3.3163 NO 11.5891 NO [p = 0.25] [p = 0.21] 3.0088 NO 9.6490 NO [p = 0.37] [p = 0.36] 3.2263 NO 8.9146 NO [p = 0.43] [p = 0.44] 3.3077 NO 10.3039 NO [p = 0.34] [p = 0.31] 2.9087 NO 9.4318 NO [p = 0.42] [p = 0.39] 2.8005 (continued)

Credit Contagion Between Greece and Systemically Important Banks: Lessons. . .

123

Table 3b (continued) Test pair (Greece, Bankj ) 15. (Greece, MS)

Trace test Hypothesized Trace no. of CE(s) statistic None 11.8113

16. (Greece, RBS)

At most 1 None

3.3652 12.7937

17. (Greece, SAN)

At most 1 None

3.1507 12.8648

At most 1 18. (Greece, UBSG) None

3.2808 10.6721

19. (Greece, UCG)

At most 1 None

3.2635 16.6675

20. (Greece, WFC)

At most 1 None

3.6753 12.2226

At most 1

2.9395

Max-Eigenvalue test Max-Eigen Cointegration? statistic Cointegration? NO 8.4460 NO [p = 0.47] [p = 0.49] 3.3652 NO 9.6429 NO [p = 0.38] [p = 0.36] 3.1507 NO 9.5839 NO [p = 0.37] [p = 0.37] 3.2808 NO 7.4086 NO [p = 0.57] [p = 0.62] 3.2635 NO 12.9922 NO [p = 0.15] [p = 0.14] 3.6753 NO 9.2830 NO [p = 0.43] [p = 0.40] 2.9395

This table reports Trace and Max-Eigenvalue (Max-Eigen) statistics, derived respectively from (11) and (12) using the Johansen (1991, 1995) cointegration method described in (8) through (10) for the full sample period (October 1, 2004 until July 15, 2016). CE(s) denote the hypothesized number of cointegrating equations for each test pair. Since cointegration is being tested between Greece’s sovereign CDS spreads with the CDS spreads of each of the sampled banks listed in table (1), we have the possibility that there is no cointegrating equation (‘None) or the possibility of at most one cointegrating equation (‘At most 1 ). The null hypothesis, H0 , of ‘None’ is rejected if the Trace and Max-Eigen statistics exceed their respective critical values over the desired confidence interval. Conversely, the null hypothesis cannot be rejected if the Trace and MaxEigen statistics are less than the desired critical values. For this table, the critical values, assuming the log level CDS spreads have no deterministic trends and the cointegrating equations (CEs) have intercepts, can be found in MacKinnon (1996) and are as follows for ‘None:’ 17.9803 and 13.9059 for the Trace and Max-Eigen tests, respectively, at the 10% level of significance. Likewise, they are 20.2618 and 15.8921 for the Trace and Max-Eigen tests, respectively, at the 5% level of significance. Failure to reject the null of no cointegrating equations (‘None’) for either the Trace or Max-Eigen tests leads to a conclusion of no cointegration (indicated by ‘NO’). Associated p-values for both respective tests (Trace and Max-Eigen) of no cointegration (H0 : ‘None’) are in square brackets

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D. Koutmos

Table 3c Log level CDS have linear trends but the cointegrating equations (CEs) have only intercepts Trace test Max-Eigenvalue test Hypothesized Max-Eigen no. of CE(s) Trace statistic Cointegration? statistic Cointegration? None 11.4336 NO 9.0667 NO [p = 0.19] [p = 0.28] At most 1 2.3668 2.3668 2. (Greece, BAC) None 11.2370 NO 8.8242 NO [p = 0.20] [p = 0.30] At most 1 2.4127 2.4127 3. (Greece, BARC) None 9.6387 NO 7.2339 NO [p = 0.31] [p = 0.46] At most 1 2.4047 2.4047 4. (Greece, BBVA) None 10.9112 NO 8.8047 NO [p = 0.22] [p = 0.30] At most 1 2.1065 2.1065 5. (Greece, BNP) None 12.6871 NO 10.3815 NO [p = 0.13] [p = 0.18] At most 1 2.3056 2.3056 6. (Greece, C) None 9.1289 NO s6.4519 NO [p = 0.35] [p = 0.56] At most 1 2.6770 2.6770 7. (Greece, CBK) None 14.4875 NO 12.6153 NO [p = 0.07] [p = 0.09] At most 1 1.8721 1.8721 8. (Greece, CSGN) None 9.5625 NO 7.4958 NO [p = 0.31] [p = 0.43] At most 1 2.0666 2.0666 9. (Greece, DBK) None 10.7253 NO 8.9190 NO [p = 0.22] [p = 0.29] At most 1 1.8062 1.8062 10. (Greece, GLE) None 13.1188 NO 10.7654 NO [p = 0.11] [p = 0.17] At most 1 2.3535 2.3535 11. (Greece, GS) None 11.4086 NO 8.7257 NO [p = 0.19] [p = 0.31] At most 1 2.6828 2.6828 12. (Greece, None 10.7901 NO 8.5719 NO HSBA) [p = 0.22] [p = 0.32] At most 1 2.2182 2.2182 Test pair (Greece, Bankj ) 1. (Greece, ACA)

(continued)

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125

Table 3c (continued) Trace test Max-Eigenvalue test Hypothesized Max-Eigen no. of CE(s) Trace statistic Cointegration? statistic Cointegration? None 11.7604 NO 9.5936 NO [p = 0.17] [p = 0.24] At most 1 2.1668 2.1668 14. (Greece, None 10.6210 NO 8.3516 NO LLOY) [p = 0.23] [p = 0.34] At most 1 2.2693 2.2693 15. (Greece, MS) None 10.3440 NO 7.2702 NO [p = 0.25] [p = 0.45] At most 1 3.0737 3.0737 16. (Greece, RBS) None 11.1212 NO 8.7610 NO [p = 0.20] [p = 0.31] At most 1 2.3601 2.3601 17. (Greece, SAN) None 11.2125 NO 9.1977 NO [p = 0.20] [p = 0.27] At most 1 2.0148 2.0148 18. (Greece, None 9.1948 NO 6.5001 NO UBSG) [p = 0.35] [p = 0.55] At most 1 2.6946 2.6946 19. (Greece, UCG) None 14.4496 NO 12.0796 NO [p = 0.07] [p = 0.11] At most 1 2.3699 2.3699 20. (Greece, WFC) None 10.7245 NO 8.1108 NO [p = 0.23] [p = 0.37] At most 1 2.6136 2.6136 Test pair (Greece, Bankj ) 13. (Greece, JPM)

This table reports Trace and Max-Eigenvalue (Max-Eigen) statistics, derived respectively from (11) and (12) using the Johansen (1991, 1995) cointegration method described in (8) through (10) for the full sample period (October 1, 2004 until July 15, 2016). CE(s) denote the hypothesized number of cointegrating equations for each test pair. Since cointegration is being tested between Greece’s sovereign CDS spreads with the CDS spreads of each of the sampled banks listed in table (1), we have the possibility that there is no cointegrating equation (‘None) or the possibility of at most one cointegrating equation (‘At most 1 ). The null hypothesis, H0 , of ‘None’ is rejected if the Trace and Max-Eigen statistics exceed their respective critical values over the desired confidence interval. Conversely, the null hypothesis cannot be rejected if the Trace and Max-Eigen statistics are less than the desired critical values. For this table, the critical values, assuming the log level CDS spreads have linear trends but the cointegrating equations (CEs) have only intercepts, can be found in MacKinnon (1996) and are as follows for ‘None:’ 13.4287 and 12.2965 for the Trace and Max-Eigen tests, respectively, at the 10% level of significance. Likewise, they are 15.4947 and 14.2646 for the Trace and Max-Eigen tests, respectively, at the 5% level of significance. Failure to reject the null of no cointegrating equations (‘None’) for either the Trace or Max-Eigen tests leads to a conclusion of no cointegration (indicated by ‘NO’). Associated p-values for both respective tests (Trace and Max-Eigen) of no cointegration (H0 : ‘None’) are in square brackets

126

D. Koutmos

Table 3d Log level CDS and the cointegrating equations (CEs) have linear trends Trace test Max-Eigenvalue test Hypothesized Max-Eigen no. of CE(s) Trace statistic Cointegration? statistic Cointegration? None 12.2181 NO 9.8129 NO [p = 0.80] [p = 0.64] At most 1 2.4051 2.4051 2. (Greece, BAC) None 12.8049 NO 10.2298 NO [p = 0.75] [p = 0.59] At most 1 2.5750 2.5750 3. (Greece, BARC) None 10.2240 NO 7.3034 NO [p = 0.91] [p = 0.88] At most 1 2.9205 2.9205 4. (Greece, BBVA) None 11.4845 NO 9.3287 NO [p = 0.85] [p = 0.69] At most 1 2.1557 2.1557 5. (Greece, BNP) None 16.1553 NO 13.9027 NO [p = 0.48] [p = 0.26] At most 1 2.2526 2.2526 6. (Greece, C) None 10.0140 NO 7.1130 NO [p = 0.92] [p = 0.89] At most 1 2.9010 2.9010 7. (Greece, CBK) None 15.8282 NO 13.7369 NO [p = 0.51] [p = 0.27] At most 1 2.0912 2.0912 8. (Greece, CSGN) None 10.2698 NO 7.5665 NO [p = 0.91] [p = 0.86] At most 1 2.7032 2.7032 9. (Greece, DBK) None 12.4807 NO 9.3064 NO [p = 0.78] [p = 0.69] At most 1 3.1742 3.1742 10. (Greece, GLE) None 14.0286 NO 11.6039 NO [p = 0.66] [p = 0.45] At most 1 2.4246 2.4246 11. (Greece, GS) None 12.5747 NO 9.5694 NO [p = 0.77] [p = 0.66] At most 1 3.0053 3.0053 12. (Greece, HSBA) None 11.2751 NO 8.5942 NO [p = 0.86] [p = 0.76] At most 1 2.6808 2.6808 13. (Greece, JPM) None 12.4497 NO 10.0981 NO [p = 0.78] [p = 0.61] At most 1 2.3516 2.3516 Test pair (Greece, Bankj ) 1. (Greece, ACA)

(continued)

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127

Table 3d (continued) Trace test Max-Eigenvalue test Test pair Hypothesized Max-Eigen (Greece, Bankj ) no. of CE(s) Trace statistic Cointegration? statistic Cointegration? 14. (Greece, LLOY) None 12.1345 NO 9.5709 NO [p = 0.80] [p = 0.66] At most 1 2.5636 2.5636 15. (Greece, MS) None 11.9465 NO 8.6234 NO [p = 0.82] [p = 0.76] At most 1 3.3231 3.3231 16. (Greece, RBS) None 12.0318 NO 9.2888 NO [p = 0.81] [p = 0.69] At most 1 2.7429 2.7429 17. (Greece, SAN) None 11.6934 NO 9.5423 NO [p = 0.83] [p = 0.67] At most 1 2.1510 2.1510 18. (Greece, UBSG) None 9.8855 NO 6.8112 NO [p = 0.93] [p = 0.91] At most 1 3.0743 3.0743 19. (Greece, UCG) None 15.3972 NO 13.2162 NO [p = 0.54] [p = 0.31] At most 1 2.1809 2.1809 20. (Greece, WFC) None 11.8171 NO 8.8223 NO [p = 0.82] [p = 0.74] At most 1 2.9948 2.9948 This table reports Trace and Max-Eigenvalue (Max-Eigen) statistics, derived respectively from (11) and (12) using the Johansen (1991, 1995) cointegration method described in (8) through (10) for the full sample period (October 1, 2004 until July 15, 2016). CE(s) denote the hypothesized number of cointegrating equations for each test pair. Since cointegration is being tested between Greece’s sovereign CDS spreads with the CDS spreads of each of the sampled banks listed in table (1), we have the possibility that there is no cointegrating equation (‘None) or the possibility of at most one cointegrating equation (‘At most 1 ). The null hypothesis, H0 , of ‘None’ is rejected if the Trace and Max-Eigen statistics exceed their respective critical values over the desired confidence interval. Conversely, the null hypothesis cannot be rejected if the Trace and Max-Eigen statistics are less than the desired critical values. For this table, the critical values, assuming the log level CDS spreads and cointegrating equations (CEs) have linear trends, can be found in MacKinnon (1996) and are as follows for ‘None:’ 23.3423 and 17.2341 for the Trace and Max-Eigen tests, respectively, at the 10% level of significance. Likewise, they are 25.8721 and 19.3870 for the Trace and Max-Eigen tests, respectively, at the 5% level of significance. Failure to reject the null of no cointegrating equations (‘None’) for either the Trace or Max-Eigen tests leads to a conclusion of no cointegration (indicated by ‘NO’). Associated p-values for both respective tests (Trace and Max-Eigen) of no cointegration (H0 : ‘None’) are in square brackets

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D. Koutmos

Table 3e Log level CDS have quadratic trends and the cointegrating equations (CEs) have linear trends Trace test Max-Eigenvalue test Hypothesized Max-Eigen no. of CE(s) Trace statistic Cointegration? statistic Cointegration? None 10.8507 NO 9.6569 NO [p = 0.40] [p = 0.43] At most 1 1.1938 1.1938 2. (Greece, BAC) None 11.4969 NO 9.6879 NO [p = 0.35] [p = 0.43] At most 1 1.8089 1.8089 3. (Greece, BARC) None 9.2750 NO 7.0822 NO [p = 0.55] [p = 0.70] At most 1 2.1928 2.1928 4. (Greece, BBVA) None 10.3186 NO 9.2410 NO [p = 0.45] [p = 0.47] At most 1 1.0776 1.0776 5. (Greece, BNP) None 15.1053 NO 13.7502 NO [p = 0.14] [p = 0.15] At most 1 1.3551 1.3551 6. (Greece, C) None 8.6812 NO 6.5217 NO [p = 0.61] [p = 0.76] At most 1 2.1595 2.1595 7. (Greece, CBK) None 14.9618 NO 13.5907 NO [p = 0.14] [p = 0.15] At most 1 1.3711 1.3711 8. (Greece, CSGN) None 9.4118 NO 7.3236 NO [p = 0.53] [p = 0.67] At most 1 2.0881 2.0881 9. (Greece, DBK) None 11.6090 NO 8.7415 NO [p = 0.33] [p = 0.52] At most 1 2.8674 2.8674 10. (Greece, GLE) None 12.7124 NO 11.4077 NO [p = 0.26] [p = 0.28] At most 1 1.3047 1.3047 11. (Greece, GS) None 11.4080 NO 9.2855 NO [p = 0.35] [p = 0.46] At most 1 2.1221 2.1221 12. (Greece, HSBA) None 10.3826 NO 8.4623 NO [p = 0.44] [p = 0.55] At most 1 1.9203 1.9203 Test pair (Greece, Bankj ) 1. (Greece, ACA)

(continued)

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Table 3e (continued) Trace test Max-Eigenvalue test Hypothesized Max-Eigen no. of CE(s) Trace statistic Cointegration? statistic Cointegration? None 11.4238 NO 9.9519 NO [p = 0.35] [p = 0.40] At most 1 1.4718 1.4718 14. (Greece, LLOY) None 11.0270 NO 9.0148 NO [p = 0.38] [p = 0.49] At most 1 2.0122 2.0122 15. (Greece, MS) None 10.5956 NO 8.2075 NO [p = 0.42] [p = 0.58] At most 1 2.3880 2.3880 16. (Greece, RBS) None 10.9492 NO 8.8693 NO [p = 0.39] [p = 0.51] At most 1 2.0798 2.0798 17. (Greece, SAN) None 10.6693 NO 9.3808 NO [p = 0.42] [p = 0.45] At most 1 1.2885 1.2885 18. (Greece, UBSG) None 8.7556 NO 6.5250 NO [p = 0.60] [p = 0.76] At most 1 2.2306 2.2306 19. (Greece, UCG) None 14.4151 NO 13.2070 NO [p = 0.16] [p = 0.17] At most 1 1.2080 1.2080 20. (Greece, WFC) None 10.6278 NO 8.3234 NO [p = 0.42] [p = 0.57] At most 1 2.3043 2.3043 Test pair (Greece, Bankj ) 13. (Greece, JPM)

This table reports Trace and Max-Eigenvalue (Max-Eigen) statistics, derived respectively from (11) and (12) using the Johansen (1991, 1995) cointegration method described in (8) through (10) for the full sample period (October 1, 2004 until July 15, 2016). CE(s) denote the hypothesized number of cointegrating equations for each test pair. Since cointegration is being tested between Greece’s sovereign CDS spreads with the CDS spreads of each of the sampled banks listed in table (1), we have the possibility that there is no cointegrating equation (‘None) or the possibility of at most one cointegrating equation (‘At most 1 ). The null hypothesis, H0 , of ‘None’ is rejected if the Trace and Max-Eigen statistics exceed their respective critical values over the desired confidence interval. Conversely, the null hypothesis cannot be rejected if the Trace and Max-Eigen statistics are less than the desired critical values. For this table, the critical values, assuming the log level CDS spreads have quadratic trends and the cointegrating equations (CEs) have linear trends, can be found in MacKinnon (1996) and are as follows for ‘None:’ 16.1608 and 15.0012 for the Trace and MaxEigen tests, respectively, at the 10% level of significance. Likewise, they are 18.3977 and 17.1476 for the Trace and Max-Eigen tests, respectively, at the 5% level of significance. Failure to reject the null of no cointegrating equations (‘None’) for either the Trace or Max-Eigen tests leads to a conclusion of no cointegration (indicated by ‘NO’). Associated p-values for both respective tests (Trace and Max-Eigen) of no cointegration (H0 : ‘None’) are in square brackets

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1. (Table 3a): The log-level CDS spreads have no deterministic trends and the cointegrating equations have no intercepts: H2 (r) : yt−1 + Bxt = αβ  yt−1 2. (Table 3b): The log-level CDS spreads have no deterministic trends and the cointegrating equations have intercepts:  H1∗ (r) : yt−1 + Bxt = α β  yt−1 + ρ0 3. (Table 3c): The log-level CDS spreads have linear trends but the cointegrating equations have only intercepts:  H1 (r) : yt−1 + Bxt = α β  yt−1 + ρ0 + α⊥ γ0 4. (Table 3d): The log-level CDS spreads and the cointegrating equations have linear trends:  H ∗ (r) : yt−1 + Bxt = α β  yt−1 + ρ0 + ρ1 t + α⊥ γ0 5. (Table 3e): The log-level CDS spreads have quadratic trends and the cointegrating equations have linear trends:  H (r) : yt−1 + Bxt = α β  yt−1 + ρ0 + ρ1 t + α⊥ (γ0 + γ1 t) Tables 3a through 3e report the trace and max eigenvalue statistics, respectively, along with their corresponding 5% and 1% critical values. If we look at, say, Table 3c (which tends to be one of the more standard assumptions in empirical studies seeking to determine cointegrating relationships), and focus on the trace and max eigenvalue statistics for Bank of America (BAC) as an example. For the trace test, we see that the trace statistics of 2.4127 is well below its critical value and thus the null hypothesis, H0 , of no cointegration (‘none’) cannot be rejected (details of critical values are explained in the notes of each of the tables). The same holds true for the max-eigenvalue statistic for Bank of America. In fact, for all G-SIBs and under all assumptions, there is no evidence in favor of cointegration between the CDS spreads of Greece with those of the G-SIBs since we cannot reject the null of ‘none’ (r = 0), regardless of which of the assumptions we entertain. The closest (but still statistically weak) evidence we have of cointegration is when examining the pairwise CDS spreads of Greece and Commerzbank (CBK) for the third assumption (log-level CDS spreads have linear trends but the cointegrating equations have only intercepts) reported in Table 3c. We see that ‘none’ is rejected at the 7% and 9% levels for the trace and max-eigenvalue tests, respectively (p-value = 0.07 and 0.09, respectively). When considering all the evidence from the cointegration results (Tables 3a through 3e), the case for cointegration between the credit risks of Greece with those

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of the G-SIBs is weak. Thus, we can answer for question (a) that there is no evidence of cointegration despite the appearance of comovement between CDS spreads in Figs. 2 and 3. This finding echoes the findings of other studies which explore the timeseries properties of CDS spreads. For example, Chan-Lau and Kim (2004) find no evidence of cointegration in the CDS and corresponding bond markets of various sampled emerging markets. Other studies which examine CDS markets with their corresponding bond markets also document weak evidence for a long-run equilibrium cointegrating relation (Palladini and Portes 2011), a finding that goes against theoretical predictions. In the context of cointegration between sovereign and bank CDS spreads, Alter and Schüler (2012) find that cointegration may exist in some cases while not in others. After conducting subsample analysis and still failing to find convincing evidence of cointegration (trace and max-eigenvalue statistics not reported for brevity), the next section proceeds to answer questions (b) and (c) using a bivariate VAR between Greece’s CDS spreads with those of each of the respective G-SIBs without a vector error correction representation, which would capture short-term stochastic disequilibria in the cointegrating relation. Using a bivariate VAR approach will help us ascertain whether Greece’s credit risk is contagious for G-SIBs across the credit regimes. If it is contagious, we would expect to see credit risk transmissions from Greece to the other G-SIBs. By partitioning the full sample into the subsamples described earlier, we can also observe whether transmission channels shifted across credit regimes.

3 Modelling Contagion Measuring contagion is problematic both from an empirical and theoretical perspective. A high degree of correlation between CDS spreads, for example, is not a basis for causation. Thus, just because Greece’s CDS spreads are correlated with those of the other G-SIBs does not imply that shocks in one of them can cause changes in another. Establishing the theoretical nature of the transmission channels is also challenging because we are oftentimes limited to discussing them in relatively abstract and unquantifiable ways. In our case, since we seek to delineate the financial-sovereign nexus, with Greece taking center stage due to media insinuations that disproportionately brand it as the catalyst for the 2011–13 euro-area debt crisis, who is to say which entity (Greece of Bankj ) is the catalyst for credit risk transmissions? Does geographical proximity matter? Is the credit risk transmission unidirectional (one-way feedback) or bidirectional (two-way feedback)? These are not easy questions to answer and any empirical model that presumes some relation from the onset may be contaminated by noise. Bayoumi and Vitek (2013) argue that, although “at first blush, the solution to measuring spillovers across countries would seem fairly easy . . . although progress

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is being made, the financial sectors in large macroeconomic models are poorly developed and . . . there are no strong theories as to why financial markets are as closely linked as they appear to be in the data . . . ” (p. 3). From a practical standpoint, it is very difficult to establish a priori which entity within a system serves as the dominant transmission channel. For this reason, an unrestricted bivariate VAR is estimated, which, unlike structural models with simultaneous regression equations, presumes no specific structure in the pattern of the transmission channels between Greece and Bankj . Instead, all that is hypothesized a priori is that the CDS spreads of Greece with those of each bank affect each other in some way across time. By using a bivariate VAR to describe transmission channels, we are at a vantage point where we can identify whether Greece disproportionately transmits credit risk to each of the G-SIBs and how the pattern for credit risk transmissions shifts across credit regimes (i.e. what patterns do we witness in 2008–09 versus, say, 2011–13?). Without exogenous variables (the CDS spreads of Greece and each bank serve as endogenous variables), the VAR in (8) can be re-expressed compactly as follows: Yt = μ +

k 

AYt−p + εt

(13)

p=1

whereby the set of endogenous (Y) variables consists of the weekly log-level CDS spreads of Greece and each of the sampled banks. Using log-levels for CDS spreads is consistent with Alter and Schüler (2012, p. 3448) who argue that “ . . . if the tests do not clearly indicate that there is a long-run relation, we obtain the impulse responses from a VAR with the variables modelled in log-levels. Thus we do not cancel out the dynamic interactions in the levels, as opposed to modelling the variables in first differences, and leave the dynamics of the series unrestricted . . . ” Within this bivariate VAR framework, a ‘credit shock transmission’ can be defined as the fraction of H-week-ahead forecast error variance of a sampled bank’s log-level CDS spreads that can be accounted for by innovations (shocks) in Greece’s log-level CDS spreads. Conversely, and in an effort to detect two-way feedback effects, we also want to examine the fraction of H-week-ahead forecast error variance of Greece’s log-level CDS spreads that can be accounted for by innovations in a sampled bank’s log-level CDS spreads. Given that there are twenty sampled banks (see Fig. 1), there is a total of twenty pairs (Greece, Bankj ) that are examined for one-way and two-way feedback effects. The vector of constants, μ, is an n × 1 vector and A is an n × n matrix of parameters to be estimated. The residuals, ε, are an n × 1 matrix of serially uncorrelated disturbances and k is the order for the variables, Y. The estimates for A are determined by the following orthogonality conditions:    = 0n×n , p = 1, 2, . . . , k E {εt } = 0 and E εt |Yt−p

(14)

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The most widely used method to achieve orthogonal decomposition of the ε vector in time-series analysis is the Cholesky decomposition method. This method, despite some of its potential pitfalls (addressed in Sect. 5), traditionally serves as the standard workhorse for time-series analysis which implements VAR methodologies and is thus the method used to draw inferences here (Hamilton 1994; Wisniewski and Lambe 2015). As is explained by classics such as Hamilton (1994), the choice of the ordering procedure, k, for the endogenous variables Y is atheoretical in nature. In the case of mapping transmission channels between Greece and each of the G-SIBs, there is no one formal method that dictates whether Greek CDS spreads or the CDS spreads of any of the banks, ought to follow first in the Cholesky ordering scheme. There are no academic theories or policy reports that can provide guidance nor can we necessarily make an atheoretical undisputable proposition that one likely transmits to another and thus ought to follow first in the Cholesky ordering. Bearing this in mind, in the analysis that follows, Greece’s sovereign CDS spreads will follow first in Cholesky ordering and then, second, the CDS spreads of the sampled banks. The only reason being is that Greece is a sovereign nation and an important trade partner for the rest of Europe and the international community. If Greece experiences a crisis, it is likely to transmit, with some lag, credit risk to major international banks that are exposed to Europe’s political and sovereign risks.

4 Discussion of Results The purpose of a bivariate parameterization of the VAR in (13) is to quantify credit shock transmissions between Greece and each of the G-SIBs (in a pairwise fashion). As discussed, a credit risk transmission is defined as the fraction of H-week-ahead forecast error variance of a bank’s log-level CDS spreads that can be accounted for by innovations (shocks) in Greece’s log-level CDS spreads. Conversely, and in an effort to detect two-way feedback effects, we also want to examine the fraction of H-week-ahead forecast error variance of Greece’s log-level CDS spreads that can be accounted for by innovations in a sampled bank’s log-level CDS spreads. Before discussing the variance decompositions, it is essential to first examine pairwise Granger causalities between Greece and each bank. When performed for the full sample period, there is no evidence that Greece’s CDS spreads Granger cause changes in the CDS spreads of any of the banks. These results though (not reported for the sake of brevity but available upon request) do not provide the full picture because, as discussed earlier, the 2008–09 and 2011–13 periods (credit regimes 2 and 4, respectively) are extraordinarily unique in their nature and materially dissimilar relative to the whole sample. They thus merit particular attention and examination. Tables 4a and 4b provide a summary of pairwise Granger causality test results for credit regimes 2 and 4, respectively, using one, two, three and four lags. As mentioned, these causality tests are concerned with two-way feedback effects

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and, thus, there are two columns for both these tables: Greece → Bankj and Bankj → Greece, respectively. The Greece → Bankj column reports for which cases Greece’s sovereign CDS spreads Granger cause shifts in the CDS spreads of each of the G-SIBs. As mentioned, these causality tests are performed in pairwise fashion and, since there is a total of twenty sampled G-SIBs (Fig. 1), there is a total of twenty tested pairs: 1. (Greece  ACA), 2. (Greece  BAC), 3. (Greece  BARC), 4. (Greece  BBVA), 5. (Greece  BNP), . . . . . . . . . , 20. (Greece  WFC), in alphabetical order according to each bank’s abbreviation and until all pair combinations have been explored. Thus, there are twenty pair combinations. Likewise, the Bankj → Greece column reports which banks’ CDS spreads Granger cause shifts in Greece’s CDS spreads. Since there is no evidence (results available upon request) of Greece transmitting credit risk to each of the G-SIBs when using the full sample (October 1, 2004 until July 15, 2016), we instead focus our attention on the two OECD recession periods; regimes 2 and 4, respectively. By focusing on regime 2, we can answer question (b) as to whether there were one-way or two-way feedback effects and the extent to which Greece transmitted credit risk to the G-SIBs. Table 4a shows results for regime 2, which represents the 2008–09 financial crisis. In the column Greece → Bankj and when lag length = 1, we see that Greece’s credit risk transmits to BA, BBVA, BNP, C, CSGN, DBK, GLE, HSBA, JPM, SAN, UCG, WFC (a total of twelve out of twenty sampled banks, which equates to 60% of all possible cases). In fact, across all lag lengths (lags = 1, 2, 3 and 4, respectively) it appears that Greece transmits to 50% or more of the sampled G-SIBs. When we look at the Bankj → Greece column, we see that about 10% to 15% of the sampled GSIBs transmit credit risk to Greece; specifically Goldman Sachs (GS) and Morgan Stanley (MS) transmit when lag length = 2, 3 and 4, respectively, while Banco Bilbao (BBVA), GS and MS transmit when lag length = 1. Thus, to summarize Table 4a, it appears there are predominantly one-way feedback effects from Greece to the G-SIBs. The only case of two-way feedback effects is between Greece and BBVA with lag length = 1. Comparing these findings with those reported in Table 4b, we see stark differences between what happened in 2008–09 and 2011–13. Since the media has branded Greece as the instigator for the euro-area crisis, it is of interest to see the extent to which Granger causalities shift in 2011–13 (regime 4) relative to 2008–09 (regime 2). If the media’s portrayal is correct, the number of transmissions in the direction of Greece → Bankj ought to, at a minimum, rise relative to what we saw in Table 4a. Thus, and to help answer question (c) we see that one-way feedback effects are few in the direction of Greece → Bankj and the only case of two-way feedback is with Bank of America (BA) when lag length = 1 and 2, respectively. Instead, what we see is that the number of transmissions from Greece to the G-SIBs decreases substantially and, in the case of lag length = 3, there are no statistically significant credit risk transmissions (denoted by “Nil.”). In summary, the Greece → Bankj column of Table 4b shows that Greece transmits to between 0%

% cases with causal relationship 60% 50% 70% 60%

Lags (Lags = 1) (Lags = 2) (Lags = 3) (Lags = 4)

Bankj → Greece % cases with causal relationList of j ship banks 15% BBVA, GS, MS 10% GS, MS 10% GS, MS 10% GS, MS

Sample regime 2; March 7, 2008 – June 26, 2009 (N = 69) This table reports pairwise Granger causality tests between Greece’s CDS spreads and the CDS spreads of each of the respective sampled banks listed in Fig. (1) for sample regime 2 (March 7, 2008 until June 26, 2009). For each pairwise Granger causality test, one, two, three and four lags, respectively, are entertained (listed in the far left column). The middle column reports which j banks’ CDS spreads are Granger caused by Greece’s CDS spreads (Greece → Bankj ). The right-side of the column reports which j banks’ CDS spreads Granger cause Greece’s CDS spreads (Bankj → Greece). Each bank is abbreviated on the basis of its Bloomberg ticker symbol listed in Fig. (1). Banks with a single underline signify that the null hypothesis of ‘no causality’ is rejected at the 10% level while banks with a double underline signify rejection at the 5% level at least. Finally, for each direction of causality (Greece → Bankj and Bankj → Greece, respectively) I report the % of cases where a causal relation is detected between Greece and each of the banks at the 10% level at least. For each pairwise test, there are a total of twenty sampled banks and thus twenty possible cases of unidirectional significance

List of j banks BA, BBVA, BNP, C, CSGN, DBK, GLE, HSBA, JPM, SAN, UCG, WFC BBVA, BNP, CSGN, DBK, GLE, HSBA, JPM, LLOY, SAN, UCG BA, BBVA, BNP, C, CBK, CSGN, GLE, HSBA, JPM, LLOY, RBS, UBSG, UCG, WFC BA, BBVA, C, CSGN, DBK, GLE, HSBA, JPM, RBS, UBSG, UCG, WFC

Greece → Bankj

Direction of causality

Table 4a Pairwise Granger causality tests

Credit Contagion Between Greece and Systemically Important Banks: Lessons. . . 135

Greece → Bankj % cases with causal relationship 25% 10% 0% 10% List of j banks BA, GLE, JP, UBS, WFC BA, UBS Nil. RBS, UBS

Bankj → Greece % cases with causal relationship 45% 45% 10% 5%

List of j banks ACA, BA, C, CSGN, DBK, GS, JP, MS, UBS ACA, BA, C, CSGN, GS, JP, MS, UBS, WFC C, JP C

Sample regime 4; July 1, 2011 – February 22, 2013 (N = 87) This table reports pairwise Granger causality tests between Greece’s CDS spreads and the CDS spreads of each of the respective sampled banks listed in Fig. (1) for sample regime 4 (July 1, 2011 until February 22, 2013). For each pairwise Granger causality test, one, two, three and four lags, respectively, are entertained (listed in the far left column). The middle column reports which j banks’ CDS spreads are Granger caused by Greece’s CDS spreads (Greece → Bankj ). The right-side of the column reports which j banks’ CDS spreads Granger cause Greece’s CDS spreads (Bankj → Greece). Each bank is abbreviated on the basis of its Bloomberg ticker symbol listed in Fig. (1). Banks with a single underline signify that the null hypothesis of ‘no causality’ is rejected at the 10% level while banks with a double underline signify rejection at the 5% level at least. Finally, for each direction of causality (Greece → Bankj and Bankj → Greece, respectively) I report the % of cases where a causal relation is detected between Greece and each of the banks at the 10% level at least. For each pairwise test, there are a total of twenty sampled banks and thus twenty possible cases of unidirectional significance

Lags (Lags = 1) (Lags = 2) (Lags = 3) (Lags = 4)

Direction of causality

Table 4b Pairwise Granger causality tests

136 D. Koutmos

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137

and 25% of the sampled G-SIBs. Conversely, when we look at the Bankj → Greece column of Table 4b, about 5% to 45% of these G-SIBs transmit to Greece. The stark shifts in credit risk transmissions between regimes 2 and 4 beg the question, what changed? Although it is beyond the scope of this paper to examine in detail the reasons for this shift, it is plausible to reconcile these findings with the fact that G-SIBs reduced their exposure to Greece while the ECB took on more exposure. According to BIS (2011), most banks reduced their exposures to claims on Greek banks and claims to Greece’s public sector by the 4th quarter of 2010 (German banks reduced their exposure the most relative to other international banks). However, in the meantime, the ECB extended a substantial emergency lifeline of funding to Greece with the expectation that its fiscal reforms and austerity measures will help it recover from its dire state of economic affairs.11 Thus, it seems that our central banking system increased its direct exposure while the commercial banking system decreased its direct exposure. At a minimum, these findings suggest two things; first, we ought to examine more closely the reasons for the systemic risk buildup in Europe at large. The media has focused exclusively on Greece, branding it the “first domino” that can bring down the EU. But this may not be the case, at least not for the commercial banking industry. Second, we must distinguish between our central banking system and our commercial banking system and the roles they play in the grand scheme of things. It appears from these findings that our financial system at large will become more dependent on central banking and that central banks, such as the ECB, will become more concentrated in terms of the debts they hold on sovereign government securities and, ultimately, the roles they play in the fiscal and domestic affairs of sovereigns. With this concentration may come fragility for our global economy.12 Tables 5a, 5b and 5c report forecast error variance decompositions for the full sample, regime 2 and regime 4, respectively, for 2-, 4-, 6-, 8- and 10-week forecast horizons. While the Granger causality tests can be thought of as a step in identifying credit risk transmission channels, the forecast error variance decompositions can be thought of as measuring the bandwidth of such channels. This is because they show the fraction of H-week-ahead forecast error variance of a G-SIB’s log-level CDS spreads that can be explained by shocks in Greece’s log-level CDS spreads. Conversely, since we are interested in measuring two-way feedback effects, they can show the fraction of H-week-ahead forecast error variance of a Greece’s log-level CDS spreads that can be explained by shocks in G-SIB’s log-level CDS spreads.

11 The

emergency lifeline funding the ECB has extended Greece far exceeds that which it extended to Cyprus or Ireland (CNBC 2011; NYT 2015). While Greece’s then finance minister, Yanis Varoufakis, had requested that the ECB grant debt relief, ECB’s then president, Mario Drahi, declined to provide any citing that it would violate Eurozone rules which forbid the ECB from financing the deficits of sovereign governments. 12 A growing area of public policy and banking research is examining the concentration that is taking place in our financial system and, namely, the degree to which central banking involvement can create moral hazards in our economy; see footnote 2 for policy discussion papers on this by the Federal Reserve Bank of Richmond.

2 4 6 8 10

2 4 6 8 10

2 4 6 8 10

2 4 6 8 10

Greece

Greece

Greece

Greece

0.1005 0.1356 0.1621 0.1841 0.2030

0.1004 0.1355 0.1623 0.1846 0.2039

0.0999 0.1346 0.1609 0.1828 0.2018

0.1002 0.1350 0.1613 0.1830 0.2018

Response variable Horizon (weeks) S.E. Panel A: Greece as the response variable Greece 99.9957 99.9649 99.8469 99.6358 99.3339 Greece 99.9923 99.9602 99.8260 99.5814 99.2280 Greece 99.9745 99.9803 99.9330 99.8217 99.6461 Greece 99.9946 99.9725 99.8878 99.7372 99.5230

ACA 0.0043 0.0351 0.1531 0.3642 0.6661 BAC 0.0077 0.0398 0.1740 0.4186 0.7720 BARC 0.0255 0.0197 0.0670 0.1783 0.3539 BBVA 0.0054 0.0275 0.1122 0.2628 0.4770

Predictor variables (%) (Greece, Bankj )

Table 5a Forecast error variance decompositions of CDS spreads

BBVA

BARC

BAC

ACA

2 4 6 8 10

2 4 6 8 10

2 4 6 8 10

2 4 6 8 10

Response variable Horizon (weeks) Panel B: Bankj as the response variable

0.0643 0.0878 0.1057 0.1207 0.1337

0.0676 0.0944 0.1147 0.1316 0.1461

0.0634 0.0881 0.1071 0.1229 0.1366

0.0629 0.0879 0.1069 0.1227 0.1364

S.E. Greece 7.3939 7.3249 7.2835 7.2505 7.2213 Greece 4.0416 3.9408 3.8613 3.7897 3.7225 Greece 6.5363 6.5115 6.4822 6.4520 6.4219 Greece 10.7053 10.9534 11.1245 11.2675 11.3973

ACA 92.6061 92.6751 92.7165 92.7495 92.7788 BAC 95.9584 96.0592 96.1387 96.2103 96.2775 BARC 93.4637 93.4885 93.5178 93.5480 93.5781 BBVA 89.2947 89.0466 88.8755 88.7325 88.6027

Predictor variables (%) (Greece, Bankj )

138 D. Koutmos

2 4 6 8 10

2 4 6 8 10

2 4 6 8 10

2 4 6 8 10

Greece

Greece

Greece

Greece

0.1006 0.1360 0.1632 0.1859 0.2058

0.1003 0.1352 0.1618 0.1840 0.2033

0.1003 0.1355 0.1624 0.1848 0.2042

0.1000 0.1346 0.1607 0.1824 0.2011

Greece 99.9904 99.8495 99.5553 99.1149 98.5395 Greece 99.9790 99.9842 99.9498 99.8682 99.7382 Greece 99.9875 99.9548 99.7911 99.4921 99.0696 Greece 99.9986 99.9724 99.8779 99.7123 99.4790

BNP 0.0096 0.1505 0.4447 0.8851 1.4605 C 0.0210 0.0158 0.0502 0.1318 0.2619 CBK 0.0125 0.0452 0.2089 0.5079 0.9304 CSGN 0.0014 0.0276 0.1221 0.2877 0.5210 CSGN

CBK

C

BNP

2 4 6 8 10

2 4 6 8 10

2 4 6 8 10

2 4 6 8 10

0.0580 0.0828 0.1012 0.1161 0.1289

0.0658 0.0923 0.1115 0.1269 0.1399

0.0640 0.0886 0.1076 0.1235 0.1374

0.0646 0.0894 0.1081 0.1236 0.1370

Greece 7.7452 7.7756 7.8381 7.9093 7.9830 Greece 3.4600 3.3911 3.3011 3.2068 3.1127 Greece 6.5907 6.8845 7.1990 7.5192 7.8414 Greece 7.1733 7.3850 7.5114 7.6155 7.7102

(continued)

BNP 92.2548 92.2244 92.1619 92.0907 92.0170 C 96.5400 96.6089 96.6989 96.7932 96.8873 CBK 93.4093 93.1155 92.8010 92.4808 92.1586 CSGN 92.8267 92.6150 92.4886 92.3845 92.2898

Credit Contagion Between Greece and Systemically Important Banks: Lessons. . . 139

2 4 6 8 10

2 4 6 8 10

2 4 6 8 10

Greece

Greece

Greece

0.1000 0.1351 0.1619 0.1844 0.2041

0.0999 0.1344 0.1605 0.1821 0.2007

0.1002 0.1353 0.1621 0.1844 0.2039

Response variable Horizon (weeks) S.E. Panel A: Greece as the response variable

Table 5a (continued)

Greece 99.9987 99.9067 99.6897 99.3510 98.8991 Greece 99.9865 99.8535 99.5840 99.1822 98.6549 Greece 99.9994 99.9036 99.6677 99.2950 98.7956

DBK 0.0013 0.0933 0.3103 0.6490 1.1009 GLE 0.0136 0.1465 0.4160 0.8178 1.3452 GS 0.0006 0.0964 0.3323 0.7050 1.2044

Predictor variables (%) (Greece, Bankj )

GS

GLE

DBK

2 4 6 8 10

2 4 6 8 10

2 4 6 8 10

Response variable Horizon (weeks) Panel B: Bankj as the response variable

0.0641 0.0893 0.1081 0.1234 0.1364

0.0632 0.0882 0.1073 0.1232 0.1371

0.0631 0.0876 0.1059 0.1211 0.1341

S.E.

Greece 5.9715 6.0950 6.1965 6.2906 6.3811 Greece 7.8007 7.6625 7.5599 7.4696 7.3857 Greece 3.1082 3.2514 3.3244 3.3771 3.4212

DBK 94.0285 93.9050 93.8035 93.7094 93.6189 GLE 92.1993 92.3375 92.4401 92.5304 92.6143 GS 96.8918 96.7486 96.6756 96.6229 96.5788

Predictor variables (%) (Greece, Bankj )

140 D. Koutmos

2 4 6 8 10

2 4 6 8 10

2 4 6 8 10

2 4 6 8 10

Greece

Greece

Greece

Greece

0.1000 0.1351 0.1620 0.1845 0.2041

0.1001 0.1349 0.1612 0.1830 0.2018

0.1004 0.1359 0.1632 0.1862 0.2063

0.1005 0.1357 0.1627 0.1852 0.2048

Greece 99.9935 99.9773 99.8962 99.7450 99.5259 Greece 99.9819 99.8562 99.6180 99.2768 98.8428 Greece 99.9835 99.9827 99.9243 99.7960 99.5959 Greece 99.9892 99.9693 99.8532 99.6308 99.3047

HSBA 0.0065 0.0227 0.1038 0.2550 0.4741 JPM 0.0181 0.1438 0.3820 0.7232 1.1572 LLOY 0.0165 0.0173 0.0757 0.2040 0.4041 MS 0.0109 0.0307 0.1468 0.3692 0.6953 MS

LLOY

JPM

HSBA

2 4 6 8 10

2 4 6 8 10

2 4 6 8 10

2 4 6 8 10

0.0689 0.0975 0.1188 0.1363 0.1513

0.0636 0.0905 0.1109 0.1279 0.1428

0.0578 0.0799 0.0962 0.1094 0.1206

0.0617 0.0864 0.1050 0.1203 0.1335

Greece 7.8912 8.0639 8.1585 8.2308 8.2937 Greece 3.7551 3.8790 3.9897 4.0964 4.2015 Greece 6.9598 6.6561 6.4571 6.2893 6.1366 Greece 2.5923 2.5859 2.5672 2.5457 2.5233

(continued)

HSBA 92.1088 91.9361 91.8415 91.7692 91.7063 JPM 96.2449 96.1210 96.0103 95.9036 95.7986 LLOY 93.0402 93.3439 93.5429 93.7107 93.8634 MS 97.4077 97.4141 97.4328 97.4543 97.4767

Credit Contagion Between Greece and Systemically Important Banks: Lessons. . . 141

2 4 6 8 10

2 4 6 8 10

2 4 6 8 10

2 4 6 8 10

Greece

Greece

Greece

Greece

0.1006 0.1358 0.1625 0.1847 0.2040

0.1003 0.1356 0.1626 0.1851 0.2047

0.1005 0.1354 0.1618 0.1836 0.2024

0.1001 0.1349 0.1613 0.1832 0.2022

Response variable Horizon (weeks) S.E. Panel A: Greece as the response variable

Table 5a (continued)

Greece 99.9782 99.9787 99.9151 99.7754 99.5584 Greece 99.9639 99.9717 99.9128 99.7797 99.5737 Greece 99.9999 99.9750 99.8962 99.7604 99.5683 Greece 99.9695 99.8391 99.6123 99.2998 98.9115

RBS 0.0218 0.0213 0.0849 0.2246 0.4416 SAN 0.0361 0.0283 0.0872 0.2203 0.4264 UBSG 0.0001 0.0250 0.1038 0.2396 0.4317 UCG 0.0305 0.1609 0.3878 0.7002 1.0885

Predictor variables (%) (Greece, Bankj )

UCG

UBSG

SAN

RBS

2 4 6 8 10

2 4 6 8 10

2 4 6 8 10

2 4 6 8 10

Response variable Horizon (weeks) Panel B: Bankj as the response variable

0.0662 0.0915 0.1102 0.1255 0.1386

0.0647 0.0935 0.1150 0.1328 0.1482

0.0632 0.0862 0.1037 0.1183 0.1310

0.0683 0.0958 0.1168 0.1343 0.1497

S.E. Greece 7.1124 6.9696 6.8348 6.7053 6.5801 Greece 10.1623 10.3904 10.5663 10.7224 10.8687 Greece 6.5414 6.3240 6.1744 6.0440 5.9229 Greece 11.1545 11.7870 12.3201 12.8207 13.3052

RBS 92.8876 93.0304 93.1652 93.2947 93.4199 SAN 89.8377 89.6096 89.4337 89.2776 89.1313 UBSG 93.4586 93.6760 93.8256 93.9561 94.0772 UCG 88.8455 88.2130 87.6799 87.1793 86.6948

Predictor variables (%) (Greece, Bankj )

142 D. Koutmos

2 4 6 8 10

0.1002 0.1354 0.1623 0.1847 0.2043

Greece 99.9835 99.9783 99.9087 99.7660 99.5503

WFC 0.0166 0.0217 0.0913 0.2340 0.4498 WFC

2 4 6 8 10

0.0625 0.0869 0.1054 0.1208 0.1342

Greece 2.5940 2.6395 2.6300 2.6047 2.5735

WFC 97.4060 97.3605 97.3700 97.3953 97.4265

Full sample; October 1, 2004 – July 15, 2016 (N = 616) This table reports forecast error variance decompositions (expressed in %) of CDS spreads between Greece and each respective bank across a 10-week forecast horizon. Such a decomposition arises from the bivariate VAR described in (13) and (14) and is constructed using the full sample period (October 1, 2004 until July 15, 2016). In panel A (on the left-hand-side) are variance decompositions whereby Greece serves as the response variable while in panel B (on the right-hand-side) Bankj serves as the response variable. For both panels, the Cholesky ordering is, first, Greece and, second, Bankj . The standard error (S.E.) for each bivariate case is reported for both panels A and B, respectively

Greece

Credit Contagion Between Greece and Systemically Important Banks: Lessons. . . 143

2 4 6 8 10

2 4 6 8 10

2 4 6 8 10

2 4 6 8 10

Greece

Greece

Greece

Greece

0.0801 0.1162 0.1425 0.1634 0.1805

0.0827 0.1190 0.1446 0.1647 0.1812

0.0816 0.1194 0.1458 0.1664 0.1831

0.0813 0.1173 0.1437 0.1646 0.1817

Response variable Horizon (weeks) S.E. Panel A: Greece as the response variable Greece 99.5239 97.7752 95.9808 94.4970 93.3434 Greece 97.0161 95.2404 94.6492 94.3716 94.2126 Greece 99.9017 99.9278 99.7658 99.5141 99.2573 Greece 98.3000 95.1638 92.1713 89.6816 87.7022

ACA 0.4761 2.2248 4.0192 5.5030 6.6566 BAC 2.9839 4.7596 5.3508 5.6284 5.7874 BARC 0.0983 0.0722 0.2342 0.4859 0.7427 BBVA 1.7000 4.8362 7.8287 10.3184 12.2978

Predictor variables (%) (Greece, Bankj )

Table 5b Forecast error variance decompositions of CDS spreads

BBVA

BARC

BAC

ACA

2 4 6 8 10

2 4 6 8 10

2 4 6 8 10

2 4 6 8 10

0.0850 0.0956 0.1001 0.1030 0.1056

0.0900 0.1079 0.1165 0.1221 0.1263

0.0929 0.1147 0.1268 0.1348 0.1411

0.0704 0.0811 0.0840 0.0851 0.0857

Response variable Horizon (weeks) S.E. Panel B: Bankj as the response variable Greece 1.6965 1.4895 2.1210 3.1960 4.4528 Greece 14.7562 19.1440 24.3168 29.5239 34.3827 Greece 16.3827 18.4203 22.1193 25.9708 29.5339 Greece 21.6312 24.7631 28.9290 32.7747 35.9417

ACA 98.3035 98.5105 97.8790 96.8040 95.5472 BAC 85.2438 80.8560 75.6833 70.4761 65.6173 BARC 83.6173 81.5797 77.8807 74.0292 70.4661 BBVA 78.3688 75.2369 71.0710 67.2253 64.0583

Predictor variables (%) (Greece, Bankj )

144 D. Koutmos

2 4 6 8 10

2 4 6 8 10

2 4 6 8 10

2 4 6 8 10

Greece

Greece

Greece

Greece

0.0824 0.1189 0.1450 0.1655 0.1823

0.0809 0.1184 0.1453 0.1664 0.1836

0.0826 0.1193 0.1449 0.1648 0.1811

0.0812 0.1171 0.1433 0.1641 0.1811

Greece 99.3044 97.4325 95.6022 94.0755 92.8670 Greece 98.6458 98.3381 98.3415 98.4037 98.4747 Greece 98.1068 95.4918 93.4658 91.8646 90.6001 Greece 99.4977 99.6217 99.7223 99.6984 99.6378

BNP 0.6957 2.5675 4.3978 5.9245 7.1330 C 1.3542 1.6619 1.6585 1.5963 1.5253 CBK 1.8932 4.5082 6.5342 8.1354 9.3999 CSGN 0.5023 0.3783 0.2777 0.3016 0.3622 CSGN

CBK

C

BNP

2 4 6 8 10

2 4 6 8 10

2 4 6 8 10

2 4 6 8 10

0.0731 0.0891 0.0970 0.1031 0.1083

0.0795 0.0925 0.0972 0.0993 0.1004

0.1087 0.1354 0.1517 0.1633 0.1724

0.0792 0.0901 0.0943 0.0969 0.0991

Greece 9.5364 11.4813 15.1267 19.0447 22.6644 Greece 9.6575 13.8116 18.4400 23.1958 27.8245 Greece 8.3916 7.7165 8.6776 10.1426 11.7297 Greece 10.2953 20.4087 29.7884 37.4309 43.3593

(continued)

BNP 90.4636 88.5188 84.8733 80.9553 77.3356 C 90.3425 86.1884 81.5600 76.8042 72.1755 CBK 91.6084 92.2835 91.3224 89.8574 88.2703 CSGN 89.7047 79.5914 70.2116 62.5691 56.6408

Credit Contagion Between Greece and Systemically Important Banks: Lessons. . . 145

2 4 6 8 10

2 4 6 8 10

2 4 6 8 10

2 4 6 8 10

Greece

Greece

Greece

Greece

0.0819 0.1181 0.1439 0.1641 0.1805

0.0713 0.0996 0.1256 0.1509 0.1749

0.0831 0.1190 0.1444 0.1643 0.1806

0.0826 0.1196 0.1466 0.1678 0.1853

Response variable Horizon (weeks) S.E. Panel A: Greece as the response variable Greece 99.9063 99.9168 99.7504 99.5826 99.4596 Greece 100.0000 99.9997 99.9993 99.9989 99.9986 Greece 98.6753 96.4339 87.6616 77.6656 68.9820 Greece 99.1676 97.9240 97.0753 96.4678 96.0255

DBK 0.0937 0.0832 0.2496 0.4174 0.5404 GLE 0.0000 0.0003 0.0007 0.0011 0.0014 GS 1.3247 3.5661 12.3384 22.3344 31.0181 HSBA 0.8324 2.0760 2.9247 3.5322 3.9745

Predictor variables (%) (Greece, Bankj )

Table 5b Forecast error variance decompositions of CDS spreads

HSBA

GS

GLE

DBK

2 4 6 8 10

2 4 6 8 10

2 4 6 8 10

2 4 6 8 10

0.0721 0.0851 0.0924 0.0984 0.1037

0.1068 0.1361 0.1555 0.1693 0.1794

0.0704 0.0798 0.0838 0.0865 0.0886

0.0840 0.0955 0.1000 0.1031 0.1058

Response variable Horizon (weeks) S.E. Panel B: Bankj as the response variable Greece 32.1033 37.2644 41.4801 44.7443 47.3726 Greece 11.8965 16.8228 21.3391 25.2569 28.5831 Greece 10.0706 11.7746 12.3591 12.6448 12.8058 Greece 20.9050 30.1583 39.0689 46.1629 51.4765

DBK 67.8967 62.7356 58.5200 55.2557 52.6274 GLE 88.1035 83.1772 78.6609 74.7431 71.4169 GS 89.9294 88.2254 87.6409 87.3552 87.1942 HSBA 79.0950 69.8417 60.9311 53.8371 48.5235

Predictor variables (%) (Greece, Bankj )

146 D. Koutmos

2 4 6 8 10

2 4 6 8 10

2 4 6 8 10

2 4 6 8 10

2 4 6 8 10

Greece

Greece

Greece

Greece

Greece

0.0819 0.1182 0.1439 0.1640 0.1804

0.0820 0.1195 0.1459 0.1665 0.1835

0.0673 0.0960 0.1265 0.1570 0.1852

0.0829 0.1196 0.1456 0.1659 0.1825

0.0828 0.1189 0.1444 0.1643 0.1807

Greece 99.2103 99.0011 99.0271 99.0767 99.1219 Greece 99.7331 99.4074 99.2638 99.1844 99.1329 Greece 98.6480 94.8192 82.1596 70.4238 61.7895 Greece 98.5927 98.7251 99.0951 99.2987 99.3856 Greece 98.9770 97.6590 96.4964 95.5523 94.8070

JPM 0.7897 0.9989 0.9729 0.9233 0.8781 LLOY 0.2669 0.5926 0.7362 0.8157 0.8671 MS 1.3520 5.1808 17.8404 29.5762 38.2105 RBS 1.4073 1.2750 0.9049 0.7013 0.6144 SAN 1.0230 2.3410 3.5036 4.4477 5.1930 SAN

RBS

MS

LLOY

JPM

2 4 6 8 10

2 4 6 8 10

2 4 6 8 10

2 4 6 8 10

2 4 6 8 10

0.0804 0.0915 0.0966 0.1001 0.1029

0.1003 0.1186 0.1269 0.1316 0.1349

0.1354 0.1736 0.1940 0.2060 0.2135

0.1000 0.1266 0.1386 0.1458 0.1513

0.0743 0.0875 0.0937 0.0975 0.1003

Greece 18.8943 25.3956 30.2785 34.2173 37.4296 Greece 7.1502 7.3827 10.2909 14.3485 18.7676 Greece 10.4792 11.1028 11.3752 11.5481 11.6710 Greece 15.1027 17.1236 19.9439 22.7728 25.3799 Greece 20.4360 25.6801 30.7481 35.0817 38.6085 (continued)

JPM 81.1057 74.6044 69.7215 65.7827 62.5704 LLOY 92.8498 92.6173 89.7091 85.6515 81.2324 MS 89.5208 88.8972 88.6248 88.4519 88.3290 RBS 84.8973 82.8764 80.0562 77.2272 74.6202 SAN 79.5640 74.3199 69.2519 64.9183 61.3915

Credit Contagion Between Greece and Systemically Important Banks: Lessons. . . 147

2 4 6 8 10

2 4 6 8 10

Greece

Greece

0.0815 0.1182 0.1443 0.1648 0.1816

0.0825 0.1183 0.1437 0.1636 0.1798

0.0827 0.1180 0.1431 0.1630 0.1795

Greece 99.9978 99.8282 99.3623 98.8298 98.3445 Greece 99.7184 99.1212 98.5310 98.0181 97.5947 Greece 97.7034 95.3056 93.8036 92.6988 91.8513

UBSG 0.0022 0.1718 0.6377 1.1702 1.6555 UCG 0.2816 0.8788 1.4690 1.9819 2.4053 WFC 2.2966 4.6944 6.1964 7.3012 8.1487

Predictor variables (%) (Greece, Bankj )

WFC

UCG

UBSG

2 4 6 8 10

2 4 6 8 10

2 4 6 8 10

Response variable Horizon (weeks) Panel B: Bankj as the response variable

0.0979 0.1154 0.1231 0.1278 0.1314

0.0807 0.0981 0.1090 0.1175 0.1248

0.0983 0.1238 0.1355 0.1428 0.1481

S.E. Greece 9.8556 14.3673 18.9898 23.2912 27.1044 Greece 37.1913 47.5317 55.6657 61.6600 65.9692 Greece 12.4461 17.0416 21.7890 26.1909 30.0169

UBSG 90.1445 85.6327 81.0102 76.7088 72.8957 UCG 62.8087 52.4683 44.3343 38.3400 34.0308 WFC 87.5539 82.9584 78.2110 73.8091 69.9831

Predictor variables (%) (Greece, Bankj )

Sample regime 2; March 7, 2008 – June 26, 2009 (N = 69) This table reports forecast error variance decompositions (expressed in %) of CDS spreads between Greece and each respective bank across a 10-week forecast horizon. Such a decomposition arises from the bivariate VAR described in (13) and (14) and is constructed using sample regime 2 (March 7, 2008 until June 26, 2009). In panel A (on the left-hand-side) are variance decompositions whereby Greece serves as the response variable while in panel B (on the right-hand-side) Bankj serves as the response variable. For both panels, the Cholesky ordering is, first, Greece and, second, Bankj . The standard error (S.E.) for each bivariate case is reported for both panels A and B, respectively

2 4 6 8 10

Greece

Response variable Horizon (weeks) S.E. Panel A: Greece as the response variable

Table 5b (continued)

148 D. Koutmos

2 4 6 8 10

2 4 6 8 10

2 4 6 8 10

2 4 6 8 10

Greece

Greece

Greece

Greece

0.1413 0.1884 0.2149 0.2314 0.2422

0.1382 0.1838 0.2114 0.2296 0.2422

0.1353 0.1767 0.1996 0.2136 0.2228

0.1346 0.1753 0.1985 0.2139 0.2253

Response variable Horizon (weeks) S.E. Panel A: Greece as the response variable Greece 99.6692 99.2519 96.8176 92.8778 88.2583 Greece 99.1006 99.2948 99.1886 98.2232 96.3479 Greece 99.9787 99.4518 97.9032 95.7469 93.3706 Greece 99.4655 99.4239 99.5276 99.5913 99.6139

ACA 0.3308 0.7481 3.1824 7.1222 11.7417 BAC 0.8994 0.7052 0.8114 1.7768 3.6521 BARC 0.0213 0.5482 2.0968 4.2531 6.6294 BBVA 0.5345 0.5761 0.4724 0.4087 0.3861

Predictor variables (%) (Greece, Bankj )

Table 5c Forecast error variance decompositions of CDS spreads

BBVA

BARC

BAC

ACA

2 4 6 8 10

2 4 6 8 10

2 4 6 8 10

2 4 6 8 10

Response variable Horizon (weeks) Panel B: Bankj as the response variable

0.0520 0.0645 0.0707 0.0742 0.0763

0.0564 0.0717 0.0802 0.0854 0.0886

0.0575 0.0802 0.0982 0.1135 0.1269

0.0570 0.0739 0.0850 0.0929 0.0984

S.E. Greece 6.5198 5.1218 3.9393 3.3865 3.3393 Greece 1.0105 0.7133 1.9867 4.4448 7.5269 Greece 5.9279 5.2332 4.2746 3.8800 4.0335 Greece 8.2346 11.0204 13.2822 15.1666 16.6996

(continued)

ACA 93.4802 94.8782 96.0607 96.6135 96.6607 BAC 98.9895 99.2867 98.0133 95.5552 92.4731 BARC 94.0721 94.7668 95.7254 96.1200 95.9665 BBVA 91.7655 88.9796 86.7178 84.8335 83.3004

Predictor variables (%) (Greece, Bankj )

Credit Contagion Between Greece and Systemically Important Banks: Lessons. . . 149

2 4 6 8 10

2 4 6 8 10

2 4 6 8 10

2 4 6 8 10

Greece

Greece

Greece

Greece

0.1345 0.1763 0.2015 0.2192 0.2327

0.1375 0.1808 0.2060 0.2229 0.2350

0.1322 0.1689 0.1890 0.2029 0.2144

0.1368 0.1800 0.2045 0.2202 0.2312

Response variable Horizon (weeks) S.E. Panel A: Greece as the response variable

Table 5c (continued)

Greece 99.9192 99.5532 98.0051 95.4591 92.2813 Greece 98.5263 98.8913 97.6151 93.8535 88.1679 Greece 99.6766 99.6178 98.4587 96.3160 93.5378 Greece 99.7446 99.3305 96.9113 92.8933 88.0419

BNP 0.0808 0.4468 1.9949 4.5410 7.7187 C 1.4737 1.1087 2.3849 6.1465 11.8321 CBK 0.3234 0.3822 1.5413 3.6840 6.4622 CSGN 0.2554 0.6695 3.0887 7.1067 11.9581

Predictor variables (%) (Greece, Bankj )

CSGN

CBK

C

BNP

2 4 6 8 10

2 4 6 8 10

2 4 6 8 10

2 4 6 8 10

Response variable Horizon (weeks) Panel B: Bankj as the response variable

0.0546 0.0723 0.0841 0.0926 0.0987

0.0531 0.0693 0.0801 0.0878 0.0935

0.0528 0.0732 0.0888 0.1014 0.1116

0.0580 0.0764 0.0889 0.0981 0.1050

S.E. Greece 3.9289 2.6527 2.0528 2.2446 3.0062 Greece 2.2041 1.4231 1.0692 1.3113 1.9471 Greece 5.0055 4.6634 3.7956 3.1708 2.8448 Greece 6.4154 5.0760 3.8284 3.2769 3.3261

BNP 96.0711 97.3473 97.9472 97.7554 96.9938 C 97.7959 98.5769 98.9308 98.6887 98.0529 CBK 94.9945 95.3366 96.2044 96.8292 97.1552 CSGN 93.5846 94.9240 96.1716 96.7231 96.6739

Predictor variables (%) (Greece, Bankj )

150 D. Koutmos

2 4 6 8 10

2 4 6 8 10

2 4 6 8 10

2 4 6 8 10

Greece

Greece

Greece

Greece

0.1382 0.1818 0.2066 0.2227 0.2338

0.1340 0.1726 0.1939 0.2081 0.2191

0.1361 0.1787 0.2027 0.2178 0.2279

0.1357 0.1770 0.2005 0.2160 0.2273

Greece 99.7961 99.4385 97.5233 94.3087 90.3300 Greece 99.6831 99.6256 98.4119 96.1430 93.2148 Greece 99.7381 99.4795 97.3002 93.2731 88.0748 Greece 99.9858 99.1893 97.3841 94.9354 92.2027

DBK 0.2039 0.5615 2.4767 5.6913 9.6700 GLE 0.3169 0.3744 1.5882 3.8570 6.7852 GS 0.2619 0.5205 2.6998 6.7269 11.9252 HSBA 0.0142 0.8107 2.6159 5.0646 7.7973 HSBA

GS

GLE

DBK

2 4 6 8 10

2 4 6 8 10

2 4 6 8 10

2 4 6 8 10

0.0511 0.0675 0.0778 0.0848 0.0896

0.0569 0.0783 0.0936 0.1055 0.1147

0.0581 0.0760 0.0878 0.0962 0.1024

0.0579 0.0759 0.0883 0.0974 0.1041

Greece 2.8901 2.1472 1.6148 1.5986 1.9815 Greece 4.1612 2.6982 2.3536 3.1479 4.6930 Greece 2.2435 1.4228 1.1588 1.5703 2.4194 Greece 5.3698 5.2947 4.4909 3.8484 3.4470

(continued)

DBK 97.1099 97.8528 98.3852 98.4014 98.0185 GLE 95.8388 97.3018 97.6464 96.8521 95.3070 GS 97.7565 98.5772 98.8412 98.4297 97.5806 HSBA 94.6302 94.7053 95.5091 96.1516 96.5530

Credit Contagion Between Greece and Systemically Important Banks: Lessons. . . 151

2 4 6 8 10

2 4 6 8 10

2 4 6 8 10

2 4 6 8 10

Greece

Greece

Greece

Greece

0.1389 0.1844 0.2115 0.2293 0.2415

0.1344 0.1729 0.1947 0.2099 0.2221

0.1389 0.1842 0.2110 0.2285 0.2405

0.1321 0.1712 0.1928 0.2074 0.2188

Response variable Horizon (weeks) S.E. Panel A: Greece as the response variable

Table 5c (continued)

Greece 98.9983 99.1408 96.9434 92.4612 86.7109 Greece 99.8900 99.8882 99.4906 98.6415 97.4011 Greece 99.7676 99.5888 97.5145 93.4381 88.0275 Greece 99.9391 99.8837 99.3722 98.3901 97.0279

JPM 1.0018 0.8592 3.0566 7.5388 13.2891 LLOY 0.1100 0.1118 0.5094 1.3585 2.5989 MS 0.2324 0.4112 2.4855 6.5619 11.9725 RBS 0.0609 0.1163 0.6278 1.6099 2.9721

Predictor variables (%) (Greece, Bankj )

RBS

MS

LLOY

JPM

2 4 6 8 10

2 4 6 8 10

2 4 6 8 10

2 4 6 8 10

0.0512 0.0700 0.0825 0.0918 0.0990

0.0645 0.0923 0.1121 0.1273 0.1394

0.0557 0.0759 0.0898 0.1006 0.1091

0.0444 0.0592 0.0692 0.0764 0.0814

Response variable Horizon (weeks) S.E. Panel B: Bankj as the response variable Greece 0.3760 0.5839 1.6567 3.2254 5.0004 Greece 8.1656 7.1686 5.5270 4.4271 3.9298 Greece 2.7811 2.1495 1.4837 1.3921 1.7487 Greece 8.6454 7.5333 5.7637 4.6959 4.3849

JPM 99.6240 99.4162 98.3434 96.7746 94.9996 LLOY 91.8344 92.8314 94.4730 95.5729 96.0702 MS 97.2189 97.8505 98.5163 98.6079 98.2513 RBS 91.3546 92.4667 94.2363 95.3041 95.6152

Predictor variables (%) (Greece, Bankj )

152 D. Koutmos

2 4 6 8 10

2 4 6 8 10

2 4 6 8 10

Greece

Greece

Greece

0.1364 0.1820 0.2086 0.2258 0.2374

0.1391 0.1839 0.2100 0.2269 0.2381

0.1342 0.1742 0.1973 0.2127 0.2242

0.1412 0.1882 0.2145 0.2309 0.2418

Greece 99.3133 99.2904 99.4269 99.5019 99.5228 Greece 99.6681 99.4657 97.6197 94.1599 89.5575 Greece 99.8518 99.7717 98.9265 97.5610 96.0084 Greece 98.4558 98.8245 98.9638 98.3378 96.9585

SAN 0.6867 0.7096 0.5731 0.4981 0.4772 UBSG 0.3319 0.5343 2.3803 5.8401 10.4425 UCG 0.1482 0.2283 1.0735 2.4390 3.9916 WFC 1.5443 1.1755 1.0362 1.6622 3.0415 WFC

UCG

UBSG

SAN

2 4 6 8 10

2 4 6 8 10

2 4 6 8 10

2 4 6 8 10

0.0441 0.0592 0.0701 0.0786 0.0855

0.0623 0.0801 0.0891 0.0941 0.0969

0.0507 0.0679 0.0808 0.0910 0.0994

0.0517 0.0634 0.0692 0.0724 0.0743

Greece 8.4831 11.6170 14.0899 16.1093 17.7227 Greece 6.5292 4.7964 3.4334 3.1821 3.8119 Greece 10.0910 9.9984 8.9020 8.0773 7.6369 Greece 0.6526 0.7055 2.0218 4.2240 6.9291

SAN 91.5169 88.3830 85.9102 83.8907 82.2773 UBSG 93.4708 95.2036 96.5666 96.8179 96.1881 UCG 89.9090 90.0016 91.0980 91.9227 92.3631 WFC 99.3474 99.2945 97.9782 95.7760 93.0709

Sample regime 4; July 1, 2011 – February 22, 2013 (N = 87) This table reports forecast error variance decompositions (expressed in %) of CDS spreads between Greece and each respective bank across a 10-week forecast horizon. Such a decomposition arises from the bivariate VAR described in (13) and (14) and is constructed using sample regime 4 (July 1, 2011 until February 22, 2013). In panel A (on the left-hand-side) are variance decompositions whereby Greece serves as the response variable while in panel B (on the right-handside) Bankj serves as the response variable. For both panels, the Cholesky ordering is, first, Greece and, second, Bankj . The standard error (S.E.) for each bivariate case is reported for both panels A and B, respectively

2 4 6 8 10

Greece

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Variance decompositions are advantageous because instead of tabulating all the A coefficients from the VAR in (13), they provide a more compact and intuitive way of determining how shocks in one CDS series affects another CDS series. To estimate these decompositions, the Cholesky method is used (the merits of this method are revisited in Sect. 5 where generalize impulse responses are computed). For Tables 5a, 5b and 5c, two-way effects are entertained (in the left columns we see decompositions when Greece is the response variable while in the right columns we see decompositions when Bankj is the response variable). For the full sample (Table 5a) we can see that, when Greece is the response variable (and Greece and Bankj are predictor variables), the majority of its forecast variance is naturally explained by its own lagged shocks. In the case of Bank of America (BAC), for example, 99.96% of its forecast variance in the 4-week horizon can be explained by its lagged shocks while 0.04% for that same horizon is explained by shocks in BAC’s CDS spreads. Together, variance decompositions across any of the respective horizons sum to 100% by construction. In Table 5a, when Bankj is the response variable we see that shocks in Greece’s lagged CDS spreads account anywhere from about 2%, as in the cases of Morgan Stanley (MS) and Wells Fargo (WFC), to about 13%, as in the case of UniCredit (UCG), of G-SIB’s forecast variances. On average, the forecast variance that Greece contributes to all G-SIBs and across 2-, 4-, 6-, 8- and 10-week forecast horizons is approximately 6.56%. In Table 5b (regime 2), and consistent with the findings in Table 4a, we expect to see Greece contributing higher forecast variances given that the Granger causality tests show that Greece’s credit risk was more contagious for the G-SIBs during the 2008–09 financial crisis. The variance decompositions indeed show this; in the case of Bank of America (BA), for example, 14%, 19%, 24%, 29% and 34% of its forecast variance in the 2-, 4-, 6-, 8- and 10-week horizon, respectively, can be explained by shocks in Greece’s lagged CDS spreads. On average, the forecast variance that Greece contributes to all G-SIBs and across 2-, 4-, 6-, 8- and 10week forecast horizons is approximately 22.85%. This is significantly higher than the 6.56% that was estimated using the full sample (Table 5a). Thus, as Table 4a shows us that there are more credit risk transmission channels in the direction of Greece → Bankj , Table 5B shows that the bandwidth for such channels became larger. Finally, in Table 5c (regime 4), we would expect the bandwidth to shrink given that G-SIBs reduced their direct exposures to Greece. The forecast variance decompositions confirm this. On average, the forecast variance that Greece contributes to all G-SIBs and across 2-, 4-, 6-, 8- and 10-week forecast horizons is approximately 4.77%. This average is, of course, significantly lower than the average for regime 2 (Table 5b) and is lower than the average for the full sample (Table 5a).

5 Generalized Impulse Responses When performing variance decompositions in the preceding section, the Cholesky ordering scheme is, first, Greece and, second, the respective G-SIB. The reasoning is that Greece is a sovereign nation and an important trade partner for Europe and the

Credit Contagion Between Greece and Systemically Important Banks: Lessons. . . Response of ACA to Greece

.06 .04 .02 .00 -.02

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Response of BAC to Greece

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Response of BBVA to Greece

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Response of Greece to DBK

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Response of CSGN to Greece

.10 .08 .06 .04 .02 .00 -.02 -.04

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Response of Greece to CBK

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Response of C to Greece

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-.02

Response of Greece to BNP

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Response of Greece to BBVA

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Response of GLE to Greece

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Response of Greece to GLE

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Fig. 4a Generalized impulse responses to one S.D. innovations ±2 S.E Sample regime 2; March 7, 2008 – June 26, 2009 (N = 69) This figure reports generalized impulse response functions (blue lines) as those estimated in Koop et al. (1996) and which do not rely on a Cholesky ordering scheme. All the impulse functions are illustrated for a 10-week horizon and are reported in a pairwise fashion for each Bankj (i.e. response of Bankj to Greece and the response of Greece to Bankj ). Each sampled bank is abbreviated on the basis of its Bloomberg ticker symbol listed in Fig. (1). ±2 standard error (S.E.) bands are also shown (dashed red lines). The impulse response functions reported in this figure are constructed from sample regime 2 (March 7, 2008 until June 26, 2009)

international community at large. If Greece experiences a credit crisis, it is likely to transmit, with some lag, this credit risk to major international banks that are exposed to Europe’s political and sovereign risks and which may hold European debt. Thus, this is the reasoning for selecting this Cholesky ordering scheme when estimating the variance decompositions reported in Tables 5a, 5b and 5c, respectively. However, it is also of interest to check variance decompositions that do not rely on the ordering scheme of the variables. Thus, a generalized VAR á la Koop et al. (1996) and Pesaran and Shin (1998) is implemented for the sake of comparison and in order to extract generalized impulse response functions. The advantage of such

156

D. Koutmos Response of Greece to GS

Response of GS to Greece .10

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Response of JPM to Greece

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Response of SAN to Greece .08 .06 .04 .02 .00 2

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Response of UCG to Greece

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Response of UBSG to Greece

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Response of RBS to Greece

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Response of Greece to LLOY

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Response of LLOY to Greece

Response of Greece to SAN

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Response of Greece to MS

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Response of MS to Greece

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Response of HSBA to Greece

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Fig. 4a (continued)

an approach is that it does not rely on an ordering pattern for the variables in the VAR system and this is important if there is no criteria for establishing an ordering procedure. The disadvantage of this approach, however, is that structural shocks are not orthogonalized. In an analysis involving country spillover effects, IMF (2016) shows that Cholesky methods of decomposition yield qualitatively similar findings with the generalized approach. Thus, given their advantages and disadvantages, one cannot prove theoretically that a generalized method is superior to a Cholesky method, or vice versa, given that such a comparison can be highly data-dependent. Generalized variance decompositions echo the findings of the Cholesky variance decompositions reported in Tables 5a, 5b and 5c, respectively. They show that the bandwidth of credit risk transmissions in the direction of Greece → Bankj intensified during the 2008–09 financial crisis but subsided afterwards. These results (not reported for the sake of brevity but available upon request), show that Greece’s credit risk was contagious during the 2008–09 crisis but, after commercial banks reduced their exposure, was not contagious during the 2011–13 euro-area debt crisis.

Credit Contagion Between Greece and Systemically Important Banks: Lessons. . . Response of ACA to Greece

Response of Greece to ACA

.06 .04 .02 .00 -.02 -.04

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Response of BARC to Greece .06 .05 .04 .03 .02 .01 .00 -.01 -.02

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Response of Greece to BARC

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.06

2

2

Response of Greece to C .12 .10 .08 .06 .04 .02 .00 -.02 -.04

Response of CSGN to Greece

.16

Response of DBK to Greece

2

Response of C to Greece .06

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Response of Greece to BNP

Response of CBK to Greece

.04

.01

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-.04

2

Response of Greece to BBVA

.16

Response of BNP to Greece

.05 .04 .03 .02 .01 .00 -.01 -.02

Response of Greece to BAC

.06

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-.04

157

.00 2

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Fig. 4b Generalized impulse responses to one S.D. innovations ±2 S.E Sample regime 4; July 1, 2011 – February 22, 2013 (N = 87) This figure reports generalized impulse response functions (blue lines) as those estimated in Koop et al. (1996) and which do not rely on a Cholesky ordering scheme. All the impulse functions are illustrated for a 10-week horizon and are reported in a pairwise fashion for each Bankj (i.e. response of Bankj to Greece and the response of Greece to Bankj ). Each sampled bank is abbreviated on the basis of its Bloomberg ticker symbol listed in Fig. (1). ±2 standard error (S.E.) bands are also shown (dashed red lines). The impulse response functions reported in this figure are constructed from sample regime 4 (July 1, 2011 until February 22, 2013)

For brevity, generalized impulse response functions are graphically illustrated for regime 2 (Fig. 4a) and for regime 4 (Fig. 4b) with a ± 2 standard error confidence band. These impulses show how Greece and G-SIBs respond to a one standard deviation shock in one another’s CDS spreads. Impulse response functions are particularly interesting because we can see the extent of the shock and when it decays across the forecast horizon period. The impulse response functions are shown in pairs (i.e. the response of Bankj to Greece and, next to it, the response of Greece to Bankj ). For regime 2 (Fig. 4a) and regime 4 (Fig. 4b), we see that, on average, G-SIBs respond to credit transmissions

158

D. Koutmos Response of GS to Greece

.04 .02 .00 -.02 -.04

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Response of JPM to Greece .04 .03 .02 .01 .00 -.01 -.02 -.03

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Response of MS to Greece

.04 .02 .00 -.02 4

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Response of SAN to Greece

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Response of Greece to SAN

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Response of UCG to Greece .06 .05 .04 .03 .02 .01 .00 -.01 -.02

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Response of WFC to Greece

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Response of Greece to UBSG

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Response of UBSG to Greece .06

6

Response of Greece to RBS

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Response of RBS to Greece

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Response of Greece to LLOY .16

-.02 2

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Response of LLOY to Greece

.05

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Response of Greece to HSBA .16

.06

Response of Greece to MS

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Response of Greece to JPM

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Response of HSBA to Greece

Response of Greece to GS

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Fig. 4b (continued)

most from Greece in the first 2 weeks. After about 2 weeks, the credit risk innovation (impulse) from Greece begins to decay (or ‘die out’). Two cases that particularly stand out when looking at both these regimes is the way Greece responds to CDS innovations by Goldman Sachs (GS) and Morgan Stanley (MS) (especially in regime 2), respectively. We see in these two cases a sharp response is observed in the second week and, thereafter, the impulse persists throughout the forecast horizon while appearing to decay only in the tenth week.

6 Summary and Concluding Remarks This paper examines the credit risk transmission channels between Greece and too-big-to-fail banks across various credit risk regimes. By dissecting CDS interdependencies between Greece and banks, this paper seeks to answer these three questions: (a) Is there a long-run equilibrium relation between the CDS spreads

Credit Contagion Between Greece and Systemically Important Banks: Lessons. . .

159

of G-SIBs and the sovereign CDS spreads of Greece? (b) Was there one-way or two-way feedback effects between the credit risks of Greece and G-SIBs during the 2008–09 financial crisis? (c) Was there one-way or two-way feedback effects between the credit risks of Greece and G-SIBs during the 2011–13 euro-area debt crisis? There are two trends that serve as a motivation for this paper; firstly, there is a lack of evidence which seeks to demarcate the nexus between sovereigns and banks. As is discussed, too-big-to-fail banks have become a more influential force in our financial system and we must understand how their credit risks are intertwined with the credit risks of sovereigns. Secondly, the media has disproportionately focused on Greece as the catalyst for the 2011–13 euro-area debt crisis. When we intersect these two trends, the three aforementioned questions arise. This paper shows that Greece’s credit risk does not share a long-run equilibrium relation with the CDS spreads of each of the sampled banks. In addition, while Greece’s credit risk may have been contagious for G-SIBs during the 2008–09 financial crisis, it was not contagious during the 2011–13 euro-area debt crisis. In fact, it appears that the credit risks of G-SIBs became more contagious for Greece during the 2011–13 period. These findings are ascertained by means of cointegration and VAR analysis. It appears that the ECB has taken on a larger role in recent years and, although it is against Eurozone regulations for it to finance sovereign debts, has increased its exposure and roles in Greece’s domestic state of affairs. If central banks become more concentrated in terms of the roles they play in the global financial system, this could unintentionally increase moral hazards and spell trouble in the future.

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Cluster Analysis for Investment Funds Portfolio Optimisation: A Symbolic Data Approach Virginie Terraza and Carole Toque

1 Introduction Portfolio selection is an important problem for investors and risk managers. There are a variety of ways researchers and investors define an optimal portfolio in literature. The definition used depends on the objective behind constructing the portfolio (the degree of risk aversion, the time horizon for the investment). In the process of asset selection, correlation is frequently used to summarize investment opportunities, but reduction of risk is strongly associated with portfolio diversification. Mathematically, this corresponds to invest in financial products which have low correlations in their returns. For any practical use, it’s necessary to have reliable estimates for the correlations of returns of the assets making up the portfolio, which are usually obtained from historical return series data. However, several aspects of the effect of noise in the correlation matrices determined from empirical data on the classical portfolio selection have been investigated (see Elton et al. 2007) and the numerous references therein. In particular, prediction based on past data is very difficult, since finding elementary structures in data which are valid and persistent in the future is not really easy. One way to cope with the problem of noise is to impose some structure on the correlation matrix, which may certainly introduce some bias in the estimation, but effectively reduce the dimensionality of the problem. However, estimates of correlations are often noisy particularly in stress period.

V. Terraza () Department of Economics and Management, University of Luxembourg, Luxembourg e-mail: [email protected] C. Toque Ministère de la Transition écologique et solidaire, Paris - La Défense, France e-mail: [email protected] © Springer Nature Switzerland AG 2021 C. Zopounidis et al. (eds.), Financial Risk Management and Modeling, Risk, Systems and Decisions, https://doi.org/10.1007/978-3-030-66691-0_5

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From the perspective of machine learning, new approaches have been proposed in the literature of applied finance. Among these techniques, clustering has been considered as a significant method to capture the natural structure of data. To ensure that the portfolio is well-diversified, stocks are usually clustered in such a way that intra-cluster correlations are high, while inter-cluster correlations are low. Similarity measure based on correlation is the most obvious and straightforward approach. Ren (2005) uses cluster analysis to group highly correlated stocks and then uses those clusters to run mean-variance portfolio optimization. Rosen (2006) also grouped stocks based solely on their mutual correlation coefficients but the author follows a two-step approach in order to optimize stock portfolios. First, the author uses the K-means method to classify stocks into classes so that their expected returns and Value at Risk (VaR) are close to each other. A dynamic optimization algorithm is leaded to build a portfolio that has the highest average returns and lowest average VaR. All these approached based on correlation based clustering have some drawbacks. The value of correlation coefficients changes quickly with the overall market condition, probably more quickly than the distance between stocks in question. Marvin (2015) proposes an another clustering method based on some variables such as revenues divided by assets or income divided by assets in order to classify assets and diversified portfolios of high performing stocks can be created by picking assets with the highest Sharpe ratios from different clusters. Indeed, the use of the Sharpe ratio is probably the simplest index referring the investment return rate to its risk. But this approach is strongly dependent on the average of two financial ratios; dynamic purposes should be added to adjust portfolios. Most recently, in Korzeniewski (2018) the grouping methods used in the clustering process is the classical K-means and the PAM (Partitioning Around Medoids) algorithm. The technique is tested on data concerning the 85 biggest companies from the Warsaw Stock Exchange for the years 2011–2016. K-means algorithms are extremely easy to implement and very efficient computationally speaking. But the results obtained from K-means heavily depend upon the initial parameters and lead often to inconsistency results. PAM algorithms are less sensitive compared to k-means but in general the algorithms require the analyst to specify the number of clusters to be generated. The problem of determining the number of clusters, i.e. number of positions in the portfolio, is usually set arbitrarily in all of the related researches. In order to have more information on data, cluster analysis have been successfully applied (Pasha and Leong 2013) even to high-frequency data with the help of some econometric time series modelling. Dynamic clustering is one extension of the previous studies based on the Kmeans method in order to improve the selection of clusters. In this paper, we deal with a dynamic clustering procedure in the context of Symbolic Data Analysis to partition a set of histogram data, in a predefined number of clusters. Histogram data have been introduced in the context of Symbolic Data Analysis by Bock and Diday (2000) and they are defined by a set of contiguous intervals of real domain which represent the support of each histogram, with

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associated a system of weights (frequencies, densities). Symbolic Data Analysis (SDA) is a domain in Data Science aiming to provide suitable methods (clustering, factorial techniques, decision trees, etc.) for managing aggregated data described by multi-valued variables, i.e., where the cells of the data table contain sets of categories, intervals, or weight (probability) distributions (for further insights about the SDA approach, see Bock and Diday (2000), Billard and Diday (2007) and Diday and Noirhomme-Fraiture (2008)). Furthermore, symbolic data analysis (SDA) provides a recent way of thinking financial data with their internal variation. SDA builds new concepts like classes of assets by periods described by symbolic data. At the same time, SDA provides a range of methods for analyzing these new data like new classification methodologies for histogram valued data (Billard and Diday 2019). The symbolic K-means has a double advantage: to achieve the number of clusters, the algorithm is repeated on the number of classes, and these classes are described by histogram type variables. Very few papers are published on this subject. We can cite Toque and Terraza (2013) where SDA defines new measures of risk, more elaborated, and built upon more complete information of risk data. In our research, we partition a set of funds described by histogram-valued data and dynamical clustering is then proposed as a suitable method (see originally Diday (1971), Diday and Simon (1976), Diday (1988) and more recently Diday (2010), Brito and Chavent (2012), Diday (2013), Le-Rademacher and Billard (2013), Dias and Brito (2015), Diday (2016), Emilion and Diday (2018) and Kim and Billard (2018) to select funds samples from the clusters of funds in order to create funds’ portfolios. The process of asset allocation, portfolio selection, asset weighting and asset management are then optimized conforming to lower the overall risk of the portfolios. Portfolio optimization has been first developed by Markowitz (1952) in modern portfolio theory. Financial correlation matrices are the key input parameters to Markowitz’s classical portfolio optimization problem, which aims at providing a recipe for the selection of a portfolio of assets so that risk (quantified by the standard deviation of the portfolio’s return) is minimized for a given level of expected return. In this theory, with the variance or standard deviation as a risk measure, portfolio mean returns and risk are calculated and the efficient frontier represents various combinations of minimum portfolio risk for each return level. In this research, portfolios based on histogram-valued data are compared with the classical method of correlation and optimization, but risk is measured using Conditional Value at Risk to capture the extreme risk of the distribution. Indeed, since the last decades, the need has emerged for another type of risk measurement based on the larger and least likely losses, which are known as tail risks. The possibility to use Value at Risk (VaR) and related measures like the Conditional Value-at-Risk (CVaR) (see Rockafellar and Uryasev 2002) as criteria for optimal portfolio selection attend to attract some attention. The relevant literature includes Krokhmal et al. (2002), Basak and Shapiro (2001), Gaivoronski and Pflug (2000), Rockafellar and Uryasev (2000), Medova (1998) and sheds an interesting light on the properties of VaR optimal portfolio. We make computational comparisons on

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the CVaR of the funds of funds’ portfolios in order to evaluate the performance of the correlation based portfolio relative to the performance of the histogram based portfolio. We discuss the portfolio selection methods. The remainder of this paper is organized as follows. The methodology is described in Sect. 2, the empirical application is represented in Sect. 3, and Sect. 4 concludes the paper.

2 Methodology 2.1 The Symbolic Approach Based on Histogram-Valued Data and Clusters In many financial applications, we need to aggregate data by specific groups like periods (years, months etc.). But data aggregation raises the issue of information loss. To prevent a too important information loss when individual observations are aggregated, variability across records should be somehow kept. New data representations are to be considered and SDA suggests building distributions like histogram-valued data instead of means or medians that overwrite the internal variation of the data. For given bounds, it’s easy to calculate frequencies and then deduce histograms. In other cases, supervised or unsupervised discretization methods build histograms from continuous attributes (see Haddad 2016). The first stage of our approach is then to build a symbolic data table where, in each cell, we get a histogram and not a number for one specific group and one variable. As a second stage, dynamic clustering is used with the squared Euclidean distance for histogram-valued data (see Afonso et al. 2018). Dynamic clustering is an extension of K-means method for distributions like histogram-valued data. The classification process uses a random initialisation of clusters (known K), followed by assigning each individual to the ‘closest cluster’. Each update of the cluster re-centres, using the function of the minimisation of intra-class inertia and/or the maximisation of inter-class inertia. When they reach convergence on the inertia criterion, the spread no longer evolves and the algorithm stops. But the final result depends on the initialization. In practice, the algorithm is executed for different values of K, and for each K, the algorithm is executed several times. For each K, we fix a number of maximum iterations because it cannot converge. The best result according to the assignment criterion is retained for each K, and at the end between K. Another difference between classical K-means and dynamical clustering is that we use other kinds of centers to describe the obtained clusters then classical means. These are called ‘kernel’ (or ‘prototype’) and, in the case of SDA, these are symbolic descriptions like histogram-valued data. Through this process, the variation is retained and the information loss is therefore minimalized. Data to be clustered are histogram-valued data and ‘kernels’ are also histogram-valued data. The clustering method is run on these new data to partition it into groups. In the

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process of portfolio selection, a fund will be picked from each cluster. Since the clusters contain different information from each other, a portfolio containing a fund from each cluster will be diversified.

2.2 The Mean-CVaR Optimal Portfolio The objective of a risk manager is to minimize the risk and maximize the expected return of his portfolio. Optimal portfolio selection has been an area of great focus since the modern portfolio theory as proposed by Markowitz (1952). Markowitz mean-variance model shows how investors could achieve the lowest possible risk for any given target rate of return. On the basis of the variance-return framework, the optimization process is obtained by changing combinations of funds with the objective function to maximize the portfolio returns or to minimize the portfolio risk. In this study, we adopt the mean-CVaR approach to optimize the portfolios. Then, risk is measured using CVaR to capture the extreme risk of the distribution, rather than standard deviation. CVaR, is also known as mean excess loss, mean shortfall or tail Value at Risk. For a given time horizon and confidence level, CVaR is the conditional expectation of the loss above VaR, in other words, CVaR is calculated by the average of the return beyond VaR. It is shown by Acerbi and Tasche (2002) that CVaR is a coherent measure of risk as it fulfills all axioms proposed by Artzner et al. (1997). Rockafellar and Uryasev (2000) have shown that CVaR has other attractive properties including convexity. We consider a portfolio of funds with random returns. The portfolio vector of weights w is associated with the vector of the random events noted r. Let f(w,r) denote the loss function when we choose the portfolio W from a set of feasible portfolios. We assume that the random vector r has a probability density function denoted by p(r). For a fixed decision vector w, we compute the cumulative distribution function of the loss associated with that vector w. The probability of the loss f (w, r) not exceeding a given value L∈ R is given by:  F (w, L) =

∞

p(r)dr

(1)

f (w,r)≤L

Then, for a given confidence level α: – the VaR associated with portfolio W is given by:

V aR α = min {L ∈ R : F (w, L) ≥ α} α [0, 1]

– the CVaR associated with portfolio W is defined by:

(2)

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CV aR α =

1 1−α



∞

f (w, r) p(r)dr

(3)

f (w,r)≤V aR α

In Eq. 3, the probability that f(w,r) ≤ VaRα , is therefore equal to 1 –α. Thus, CVaRα comes out as the conditional expectation of the loss associated with W relative to that loss being CVaR or greater. The CVaR function in Eq. 3 is difficult to resolve, as it is a function of the VaR function. The primary contribution by Rockafellar and Uryasev (2000) is the derivation of a CVaR function that is independent of the VaR function, making the optimization process much less complicated. Their function is given by:

F (w, L) = L +

1 1−α



[f (w, r) − L]+ p(r)dr

(4)

where t + the term in the brackets in Eq. 4 is equal to the max (t,0). Equation 4 can be used since this function is convex with respect to α and that minimizing this function gives the same result as minimizing the CVaR (Uryasev and Rockafellar 2000). The minimization objective written in matrix form is described as follows: minCV aR α (w) = min F (w, L)

(5)

wT μ = r p

(6)

wT 1 = 1

(7)

subject to:

In Eq. (6), μ represent the vector of the average of fund’s returns and rp represent a predetermined level of average return of the portfolio. Eq. (7) is the budget constraint while the weight for any fund cannot be negative. We compare the performance of funds of funds portfolios using CVaR risk measure as described by Argawal and Naik (2004). This risk adjusted performance ratio gives us the Conditional Sharpe ratio (SharpeCVaR) in Eq. 8, where rf is the risk free rate: SharpeCV aR =

r − rf CV aR

(8)

The conditional Sharpe ratio is defined as the ratio of expected excess return to the expected CVaR. SharpeCVaR is able to discriminate portfolio funds’ downside performance. The main question with CVaR is to choose a methodology for calculation. The standard approach, the parametric method is to assume a normal

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distribution, in which case CVaR can be estimated directly from VaR by multiplying the standard deviation of returns by the relevant confidence factor. There are several alternative approaches for estimating CVaR in particular non parametric approaches. In this paper, CVaR will be estimated from the historical simulation method.

3 Application in Luxembourg Funds 3.1 Data Collection and Risk Measures Luxembourg is one of the most experienced and dynamic global investment fund centers. It has been very active in the latest developments of the European Undertakings for collective investment (UCI) industry. Funds existing under the laws of Luxembourg pay a subscription tax at the rate of 0.05 per cent per annum on their total net assets. UCIs set up under the 2010 European directive law are not subject to any Luxembourg ordinary income, capital gain, estate or inheritance taxes. In this paper we consider 17 Luxembourg funds collected from the Eikon database. These funds are not subject to the European directive tax. However, concerning the annual charge and the redemption charge no completely information is provided from the database. Then, these costs will not be considered in our analysis. We observe the fund’s net asset values from 01/01/2008 till 31/12/2016 representing 3388 observations for each fund return. This period is divided into sub-periods: during the crisis (2008–2009), after the crisis (2010–2012), and the non-crisis period (2013–2016). The analysis of sub-periods should measure the impact of clustering according the economic conjuncture. All of funds are shown by symbol in Table 1. The performance and descriptive statistics of funds returns are shown respectively in Fig. 1 and Table 2. From Fig. 1, we observe that in some period, volatility is relatively high and in others volatility is relatively low. Then volatility values tend to cluster together in time, with more or less smooth transitions from higher to lower volatility and conversely. Since volatility does not remain constant over time, it results that rolling estimations of covariance matrices will capture better the time varying character of the volatility. From Table 2, we can already notice some characteristics of funds’ returns. In particular, the mean returns approximate zero, the negative values of skewness in many funds suggest that the distributions are left-skewed. We expect higher probabilities in the negative returns tail compared to the positive returns tail. Moreover, the values of kurtosis are on average very high; the normality of returns is rejected as we expect a leptokurtic behavior, meaning higher probability around the mean and fatter tails.

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Table 1 Symbol of funds Luxembourg Funds LP60063450 LP60044241 LP60017799 LP60063754 LP60084565 LP60089810

LP60088510 LP60088034 LP60071418

LP60083956 LP60081330 LP60070661

LP60071398 LP60094177 LP60012698

LP60052246 LP60058385

Fig. 1 Performance of funds returns

Table 2 Statistics of fund returns over the period LP60063450 Mean 0.0003 Sd 0.012 Skewness 0.1531 Kurtosis 10.3252 LP60017799 Mean 0.0004 Sd 0.0111 Skewness 0.0962 Kurtosis 8.7029 LP60084565 Mean 0.0002 Sd 0.0106 Skewness −0.0117 Kurtosis 8.2712

LP60044241 0.0001 0.0149 −0.0522 5.0481 LP60063754 0.0005 0.0092 −0.9938 9.363 LP60089810 0.0003 0.0127 0.1451 10.3786

LP60088510 0.0002 0.0135 0.0402 7.7329 LP60088034 0.0003 0.0139 −0.3532 11.7601 LP60071418 0.0003 0.0228 −0.0133 3.1319

LP60083956 0.0003 0.01 −0.7872 12.8173 LP60081330 0.0004 0.0129 −0.4749 4.1305 LP60070661 0.0003 0.0113 −0.4177 6.4258

LP60071398 0.0004 0.0123 −0.0943 6.4261 LP60094177 0.0003 0.0101 −0.5538 6.198 LP60012698 0.0004 0.0118 −0.3785 5.7055

LP60052246 0.0001 0.0137 0.3524 13.259 LP60058385 0.0001 0.0124 −0.457 11.9651

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3.2 Constructing the Portfolio and Calculating the Efficient Portfolio 3.2.1

Portfolio Selection from the Correlation Matrix

A principal argument of standard portfolio optimization is that lower correlations provide scope for diversification within a portfolio, particularly for risk adverse investors who prefer a given expected return objective with minimum or acceptable downside volatility. In this approach, the level of diversification within a portfolio will matter a great deal and the selection of portfolios is based on the correlation matrix of the returns. In order to optimize the timing of the funds selection process using the above methodology, the portfolio is made up of 4 sub-periods of 2 years. Each subportfolio is rebalanced every 2 years in order also to limit transaction costs. Figure 2 gives the matrix of reordered correlations for the 17 funds for each sub-period. From Fig. 2, we observe in very light color the less correlated funds. In Table 3, we report the funds which constitute the four portfolios selected for each sub-period.

Fig. 2 Matrix of reordored correlations for the 17 funds by sub-periods

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Table 3 Selection of funds of funds’ portfolios

Period 2008–2009 LP60084565 LP60071418 Period 2010–2012 LP60071398 LP60071418 Period 2013–2014 LP60083956 LP60071418 Period 2015–2016 LP60083956 LP60071418

LP60070661 LP60070661 LP 60070661 LP60070661

Fig. 3 Histogram-valued data for the LP60063450 in 2008

3.2.2

Portfolio Selection Based on the Symbolic Data Approach

For portfolio selection, clustering is used for grouping data objects in similar groups according to their similarities. Our focus is on clustering from symbolic data, particularly from histogram- valued data. In this context of multivariate analysis, we need to aggregate fund returns by year. For each fund, we build histogramvalued data based on given bounds in order to build k return intervals. The selected values of these bounds are: “-0.009”, “-0.005”, “-0.003”, “0”, “0.003”, “0.005” and “0.009”. To illustrate the procedure, we give an example for the LP60063450 fund and for the 2008 year (see Fig. 3). From the series of 221 daily returns, we range the fund’s returns according the k return intervals, and we obtain 30.1% of daily returns less than “-0.009”, 10.7% between “-0.009” and “-0.005” . . . and 23.7% high than “0.009”. From this range of values, we can create a histogram-valued data table. For all our data collection, histogram-valued data table have a 17 funds x 9 years dimension. In Table 4, we give an extract of the symbolic data table for the 2008–2009 subperiod. Visualizing the histograms by the symbolic data table, gives us a first element of discrimination between funds concerning their similarities. Now, to identify clusters of funds, the second step of the SDA method is to run dynamical clustering for a

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Table 4 Extract from the symbolic data table between 2008–2009

number of classes between 2 and 8 and we measure the evolution of intra-class inertia (see Fig. 4 and Appendix). Concerning the 2008–2009 period, we observe a last significant loss in intraclass inertia between four and five clusters of funds. Or, five clusters correspond to a last significant elbow in the curve of intra-class inertia (Fig. 4). Table 5 resumes the symbolic data table obtained from this partition of 5 clusters followed by Table 6, the list of funds by cluster. In order to validate the partition into 5 clusters, we propose the (Calinski and Harabasz 1974) method extended to symbolic objects with the Euclidean distance for histogram-valued variables. More precisely, the Calinski and Harabasz method proposes the following index:

CH =

B/ (c − 1) W/ (n − c)

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number of classes 1

intraclass inertia 0.535 (=Tot Inert)

CH 0.25 0.2

2

0.222

21.21

3

0.125

23.01

4

0.066

30.85

5

0.04

37.19

6

0.039

28.03

7

0.041

20.12

8

0.035

18.40

0.15 0.1 5 classes 0.05 0 2

4

6

8

Fig. 4 Intra-class inertia and CH index for a number of classes between 2 and 8 Table 5 The symbolic data table for the five classes

Table 6 Funds by cluster C1 C2 C3 C4 C5

LP60052246 LP60071418 LP60017799 LP60044241 LP60012698

LP60058385 LP60088034 LP60063754 LP60070661

LP60063450

LP60071398

LP60081330

LP60088510

LP60083956

LP60084565

LP60089810

LP60094177

where n is the total number of units, c the number of clusters in the partition, B and W denote the total between-clusters sum of squared distances (about the centroids) and the total within-cluster sum of squared distances, respectively. In practice, the maximum value of the index is used to indicate the true number of clusters in the data set. For the period 2008–2009, we add the results in Table 5 and we validate the partition into 5 clusters. For the other sub-periods, the methodology is repeated in order to obtain the symbolic data tables and the lists of funds by cluster (see the Appendix).

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Table 7 Funds of funds portfolios selection Period 2008–2009 LP60052246 Period 2010–2012 LP60071398 Period 2013–2014 LP60071398 Period 2015–2016 LP60044241

LP60071418

LP60084565

LP60044241

LP60012698

LP60044241

LP 60012698

LP60012698

LP60083956

LP60044241

LP60012698

LP60071398

As a result, funds present similarities into each cluster. Then, the portfolio selection procedure is to select funds in different clusters to compose the portfolio of fund of funds in order to apply the diversification principle. As many funds compose each cluster, the adopted principle is reinvesting if possible in same funds in order to limit entrance and redemption costs. Table 7 gives the selection of portfolios for each sub-period.

3.2.3

Mean-CVaR Equal Weights Portfolios

Estimation of risks for portfolios measured by CVaR is listed in Table 8. Conditional Value at Risk is calculated by the historical simulation method for a 95% confidence level. For equal weights portfolios, differences exist due to the selection method of funds. The histogram valued method of fund’s portfolio selection gives lower risk for all periods. The difference is more pronounced during the crisis period (2008– 2009). In order to observe the dynamics of the evolution of extreme risks, rolling CVaR of portfolios with a window of 20 days are estimated for the two periods 2008–2009 and 2013–2014. Rolling CVaR on the “SDA portfolios” represented in black are shown in Fig. 5 with the rolling CVaR on the “correlation portfolios” shown in red, from the two sub-periods. These figures show how the correlation method portfolio selection exhibits extreme source of volatility especially during the crisis phase. There are three locations where there are large negative peaks compared to the CVaR issued of the ADS methodology: December 2008, April 2013 and June 2013. Now, to illustrate the relationship between extreme risk, as measured by CVaR, and mean returns for each period, we estimate the conditional Sharpe Ratio ignoring the risk free rate. We find that the correlation based funds’ portfolios have the best risk-adjusted performance in the most periods except for the 2013–2014 periods. This result is confirmed looking the rolling estimations given in Fig. 5. Indeed, the “SDA portfolio” gives more positive peaks of the SharpeCVaR ratios during the 2013–2014 sub-periods.

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Table 8 CVaR risk measures and Conditional Sharpe Ratios (in percent) Conditional value at risk Histogram based funds portfolio Correlation based funds portfolio Conditional Sharpe ratio Histogram based funds portfolio Correlation based fund’s portfolio

2008–2009

2010–2012

2013–2014

2015–2016

3.54 4.7

2.34 2.45

1.74 2.17

2.43 2.56

−0.847 −0.427

0.427 0.481

3.45 0.461

1.234 2.34

Fig. 5 Rolling CVaR and SharpeCVaR Ratios. (Red line: Correlation portfolio, black line: SDA portfolio)

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Table 9 Mean and risk measures on optimal portfolios (in percent) Period Mean Variance Histogram based portfolio selection 2008–2009 0.0 1.3 2010–2012 0.0 0.9 2013–2014 0.1 0.7 2015–2016 0.0 0.9 Correlation based portfolio selection 2008–2009 −0.02 1.62 2010–2012 0.02 0.96 2013–2014 −0.01 0.92 2015–2016 0.06 1.1

3.2.4

CVaR

VaR

Conditional Sharpe ratio

3.2 2.1 1.6 2.1

2.1 1.6 1.3 1.4

−1.0 0.6 3.7 1.4

4.2 2.25 2.14 2.44

2.57 1.58 1.4 0.84

−0.47 0.88 −0.46 2.45

Optimal Weights Portfolios

The study now considers the optimal weights for each method of portfolio selection. The portfolio optimization problem consists of minimizing CVaR subject to an expected return. Table 9 shows for each period and each selection method of portfolio, the amounts of expected return, volatility, Value at Risk and conditional Value at Risk for optimal weighted portfolios. Mean-CVaR optimization models are estimated, specifying the target return. We start from the equal weights portfolio defining previously and search a portfolio with the same returns, but a lower risk measured by the CVaR. Then, we can compute an optimized efficient portfolio which has the lowest risk for a given return. We consider only the long- mean-CVaR portfolios. In this case all the weights are bounded between zero and one. Applying the mean CVaR optimization method, we obtain a significant reduction of extreme risk beyond the VaR regardless the method used. Rolling CVaR portfolios of a mowing window of 20 days are estimated in Fig. 6. Overall, we observe more big drops for the correlation based portfolios in any time period. More particularly, we show that the correlation based portfolio have extreme risks beyond the VaR during the crisis period with a big drop near December 2008. After the crisis, in the 2010–2012 or in the 2015–2016 periods, more erratic results are observed between the two methods of selection of the portfolio. By contrast, in the crisis period, portfolios have less large peaks, due maybe to the systematic risk across all markets during the period. We observe many couple of high peaks and low peaks during these periods more pronounced for the correlation based portfolio selection method. These extreme peaks concern July 2011 and September 2015. This last method provides stronger and more frequent decreases. In order to evaluate the extreme risk adjusted to mean returns, we use the Rolling SharpeCVaR and we show that in overall, better SharpeCVaR ratios are obtained from the histogram valued method of the portfolio selection with more peaks above 0.4% for the 2010– 2012 period and for the 2015–2016 period.

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Fig. 6 Rolling CVaR and SharpeCVaR Ratios. (Red line: Correlation portfolio, black line: SDA portfolio)

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Table 10 Portfolios weights The global minimum correlation based portfolio weights Period 2008–2009 LP60084565 LP60071418 LP60070661 99.10% 0.90% Period 2010–2012 LP60071398 LP60071418 LP60070661 59.90% 4.10% 36% Period 2013–2014 LP60083956 LP60071418 LP 60070661 100% Period 2015–2016 LP60083956 LP60071418 LP60070661 25.10% 13.60% 61.20% The global minimum SDA based portfolio weights Period 2008–2009 LP60052246 LP60071418 LP60084565 42.80% Period 2010–2012 LP60071398 LP60044241 LP60012698 68.50% 19% 12.50% Period 2013–2014 LP60071398 LP60044241 LP 60012698 65.80% 15.60% 18.60% Period 2015–2016 LP60044241 LP60012698 LP60083956 3.90% 29.30% 38.90%

3.2.5

LP60044241 33.40%

LP60012698 23.70%

LP60071398 27.90%

The Global Minimum CVaR Portfolio

Now, we examine the global minimum CVaR portfolio which is the portfolio with the lowest risk. To estimate the portfolio, we only need to estimate the return variances and correlations. It is the only efficient stock portfolio whose composition does not depend on the expected returns. Table 10 gives the composition of the global minimum CVaR portfolio according the selection method. The efficient frontiers representing the set of optimal portfolios are observed in Figs. 7 and 8. Optimal Portfolios in light points are sub-optimal because they do not provide enough return for the level of risk and optimal portfolios in bold points, to the right of the efficient frontier, are also sub-optimal because they have a higher level of risk for the defined rate of return. A key finding of the theory is the benefit of diversification resulting from the curvature of the efficient frontier. Optimal portfolios that comprise the efficient frontier tend to have a higher degree of diversification than the sub-optimal ones, which are typically less diversified. Findings indicate larger risks and sub-optimal correlation based portfolios over the

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Fig. 7 Efficient frontiers for the 2008–2009 sub-period

Fig. 8 Efficient frontiers for the 2010–2012 sub-period

periods. Looking the composition of these portfolios, we notice that the global minimum CVaR portfolios are inefficient. Indeed, a problem of diversification appears in the selection of correlation based portfolios. For the two periods 2008– 2009 and 2013–2014, only one fund composes the optimal portfolios at 99% and at 100% respectively (see Table 10). This lack of diversification in the composition

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of the portfolios explain why during these periods, correlation based portfolios are more risky and present also a negative SharpeCVaR for the 2013–2014 period. Figure 8 illustrate the efficient frontiers of the portfolios for the 2010–2012 subperiod. Overall, it seems that the ADS based portfolio present a better relationship between mean returns and extreme risk as indicated by the SharpeCVaR (on the right hand side of the figures). Maybe as previously a diversification problem can explain this result. Indeed, if we examine carefully the composition of portfolios based on the correlation and the aggregation of funds into clusters given by the SDA methodology, we observe that for the two sub-periods 2010–2012 and 2013–2014, some funds appear in the same cluster. It’s the case for the LP60070661 and the LP60071398 funds and for the LP60083956 and LP60070661, which appear in the same cluster C1, respectively for the 2008–2009 and the 2013–2014 sub-periods. In the histogram valued method, these funds have a similar behavior and then move in the same way. As a result, the global minimum portfolios represented by red points in Figs. 7 and 8 show better results for these periods when investing in a portfolio based on the SDA approach.

3.2.6

Back-Testing Procedure

We assess the performance of our portfolios out of sample using a back-testing approach. Out of sample experiments permits to evaluate the potential of the efficient portfolios for actual risk management purposes. We consider the efficient portfolios computed on the last period (2015–2016) as described in the last section and we use the 250 daily observations of the last year of our sample rolling the window forwards through the 2017 year to conduct our back tests. The portfolios are optimized and then re-weighted with respect to this sliding data window and the results are determined by the sample values in this sliding data window. Back-testing of the different investment portfolio strategies generates a set of optimal weights and a comparison is conducted between the ADS portfolio and the correlation based portfolio running the global minimum CVaR optimization model. In order to evaluate the evolution of the portfolios out of sample, the inner products between the lagged portfolio weights and the subsequent returns have to be computed for the ADS portfolio and the correlation based portfolio. Supposing the initial wealth position is equal to 100, the returns factors can be estimated by means of the cumulative returns of each portfolio. From Fig. 9, we observe that for this back-test design, the ADS portfolio approach outperforms the correlation portfolio solutions. We observe high cumulative returns for the ADS portfolio during the 2007 year. CVaR statistics are given in Table 11 and we can conclude that in means, the two portfolios have the same average losses.

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Fig. 9 Trajectory and Relative Performance of portfolios

Table 11 Indicators of CVaR for the portfolios

Min 1st Qu Median Mean 3rd Qu Max

ADS portfolio 0.008 0.010 0.012 0.012 0.013 0.020

Correlation based portfolio 0.007 0.009 0.010 0.012 0.015 0.020

4 Conclusion In this paper, we have compared the correlation based portfolio selection method to a new method based on the symbolic data analysis. We have performed portfolio optimization by applying the symbolic approach in aggregating funds returns into histogram-valued data and in partitioning funds with dynamic clustering method. Funds returns to be clustered are described by histogram-valued data and the prototypes of each group of funds are also described by histogram-valued data. The symbolic data approach allows to partition funds with more complete information. One of the objectives of this paper was to investigate how a set of portfolios perform in terms of extreme risk beyond the VaR using the CVaR. Indeed, recently, Value at Risk (VaR) and Conditional Value at Risk (CVaR) have gained acceptance in world financial markets as appropriate risk measures in risk management. Furthermore, CVaR has advantage to be a coherent risk measure. We have shown that the portfolios obtained with the SDA selection method are less risky than with the correlation selection method for any selected period. The second objective of our study was to compare portfolios selection methods in the context of mean CVaR optimization, determining optimal weights into the portfolios. The examination of the global minimum CVaR portfolios provides further evidence that SDA methodology gives portfolios with lower extreme risks compared with portfolios based on the

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correlation method. Furthermore, examining the composition of funds’ portfolios based on the correlation matrixes, problems of diversification are highlighted: some funds appear in the same cluster defining by the SDA methodology. This proposed alternative method in term of clustering, keeping the maximum information into the structure of data, can provide interesting insights in the process of assets selection that the classical analysis fails to capture. Furthermore, out of sample back-testing of the analysis could be conducted to confirm the validity of our results. Further analysis could incorporate more data of funds from a wider universe. The larger universe will allow for more scope in terms of diversification benefits.

Appendix Period 2010–2012

number of classes 1

intraclass inertia 1.05 (=Tot Inert)

CH

0.8 0.6

2

0.694

3

0.266

20.63

4

0.189

19.74

5

0.159

16.81

6

0.134

15.04

7

0.134

11.39

8

0.108

11.21

7.69

0.4 0.2 0 2

4

Fig. A.1 Intra-class inertia for a number of classes between 2 and 8 Table A.1 The symbolic data table for the four classes

6

8

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Period 2013–2014

Table A.2 Funds by cluster C1 C2 C3

LP60017799 LP60071398 LP60012698 LP60044241

number of classes 1

LP60052246 LP60083956

LP60058385 LP60084565

LP60063450 LP60088034

LP60063754 LP60094177

LP60071418

LP60081330

LP60088510

LP60089810

intraclass inertia 1.35 (Tot Inert)

CH

LP60070661

0.6 0.5 0.4

2

0.534

22.92

0.3

3

0.294

25.14

0.2

4

0.245

19.54

5

0.222

15.24

6

0.19

13.43

7

0.171

11.49

8

0.163

9.36

0.1 0 2

4

6

8

Fig. A.2 Intra-class inertia for a number of classes between 2 and 8 Table A.3 The symbolic data table for the three classes

Table A.4 Funds by cluster C1 C2 C3

LP60017799 LP60071398 LP60012698 LP60044241

LP60052246 LP60083956

LP60058385 LP60084565

LP60063450 LP60088034

LP60063754 LP60094177

LP60071418

LP60081330

LP60088510

LP60089810

LP60070661

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Period 2015–2016

number of classes 1

intraclass inertia 1.32 (=Tot Inert)

CH

0.6 0.5 0.4

2

0.59

18.56

3

0.266

27.74

4

0.117

44.56

5

0.096

38.25

6

0.078

35.03

7

0.06

35.00

8

0.049

33.35

0.3 0.2 0.1 0 2

4

6

8

Fig. A.3 Intra-class inertia for a number of classes between 2 and 8 Table A.5 The symbolic data table for the five classes

Table A.6 Funds by cluster C1 C2 C3 C4

LP60044241 LP60012698 LP60083956 LP60017799 LP60071398 LP60094177

LP60071418

LP60052246 LP60081330

LP60058385 LP60084565

LP60063450 LP60088034

LP60063754 LP60088510

LP60070661 LP60089810

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Grey Incidence Analysis as a Tool in Portfolio Selection Tihana Škrinjari´c

1 Introduction Quantitative finance represents a set of mathematical, statistical and econometric models and methods combined with the financial theory for the purpose of investment analysis and portfolio management, with applications within three areas: investment analysis, portfolio construction and derivatives evaluation (Fabozzi et al. 2006). Thus, quantitative finance is a complex discipline due to much different knowledge required to apply from the area of quantitative disciplines, as well as finance theory. Performance evaluation and forecasting of crucial financial variables are important parts of the portfolio management. Many different quantitative methods and models have been developed (and are still in process of development) in order to achieve investment goals faster, with high-quality and on time. That is why the portfolio selection and the whole portfolio management process represent a difficult task today. Some of the most popular models and methods in academia and practice are financial econometrics with, e.g. (M)GARCH models, EVT; operational research with DEA and MCDA; ANN; multivariate analysis from statistics (clustering, PCA), etc. Different approaches have been established to tailor specific questions and investment goals. Combination of different approaches in the same analysis can be found today, due to each approach having some advantages and disadvantages compared to others. Fabozzi et al. (2007) conducted research on American and European institutional investors and found that in the last several

The author states that the views presented in this paper are those of the authors and not necessarily representing the institution she works at. T. Škrinjari´c () Croatian National Bank, Zagreb, Croatia e-mail: [email protected] © Springer Nature Switzerland AG 2021 C. Zopounidis et al. (eds.), Financial Risk Management and Modeling, Risk, Systems and Decisions, https://doi.org/10.1007/978-3-030-66691-0_6

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years the majority of profits made on financial markets were due to the expansion of quantitative methods. These methods have become more popular and applicable due to the rise of computational quality, data quality and good computer support. A relatively unknown methodology useful in finance and portfolio selection is the Grey Systems Theory (GST) with its models, incidence analysis and other useful methodology. Compared to some other methodology, it is a relatively newer one, due to being developed from the early 1980s (please refer to Liu et al. 2016 for a historical overview). This methodology is developed for usage within decision making process when data is scarce or uncertain, with incomplete information about some system’s elements, data or behaviour. That is why the terminology uses word grey, due to partially known available information. Since there is a lot of different information available to investors every day, with investor not being able to distinguish which is completely true or false, the GST methodology can be very useful to use in the portfolio selection and management process. Thus, the purpose of this study is twofold. Firstly, this research will, for the first time in the literature, give a critical overview of existing research which applies some of the GST methodology in the portfolio selection process. In that way, guidelines can be provided for future work. Secondly, the empirical analysis will be conducted in order to obtain more insights into the usefulness of GST methodology and how to apply it in answering concrete questions regarding investing. This second part brings a novelty in existing research, due to being grounded in the investor’s utility theory where investment decisions are made based on the asset evaluation according to investor’s preferences. This is rarely found in the existing applications (as it will be seen in the literature review part). The result of this chapter will be available for future work to extend upon with specific questions in the portfolio selection and future academic work will have in one place the majority of literature within this area of research. The GRA (Grey Relational Analysis) approach of modelling and other areas within Grey Systems is gaining some popularity over the last decade, not only within the finance area, but other economic, social and environmental areas of life as well. Some of the applications within finance area include evaluating financial performance of selected companies or banks (Kung and Wen 2007; Wu et al. 2010; Do˘gan 2013; Pashaki et al. 2018); bankruptcy prediction (Lin et al. 2009; Delcea et al. 2012, 2013a); financial sector comparisons (Delcea et al. 2013b); forecasting cash flows or revenues of companies (Khajavi et al. 2012; Ping and Yang 2004). Other areas of applications are: supplier decision making (Li et al. 2007); ranking of intellectual capital in public sector (Datta 2014); total economy ranking (Yildirim et al. 2015); regional economic performance (Wu et al. 2012); academic performance ranking (Ertugrul et al. 2016); football clubs’ performance (Sakınç 2014); consumer satisfaction (Canglin 2012; Pan and Leu 2016); telecommunication companies’ performance (Ping and Yang 2004); etc. For an overview of the bibliometric analysis of the Grey Systems Theory and applications over several decades, please refer to Camelia (2015a, b). Up until this day, the Grey System Theory is most interesting to the eastern countries, with the majority of the published research, data and conferences in the eastern economies (far East), with Western countries

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researchers being less interested in this methodology (Kayacan et al. 2010). Reasons are unknown, due to the straightforward approach of this methodology, the useful interpretations and different models within it. This chapter is structured as follows. The second section gives an extensive overview of the existing literature within the area of finance and portfolio investment which applies some of the GRS methodologies. In that way, insights in current research trends and conclusions can be provided, with guidance for future work. The third section describes the methodology used in this study, with empirical analysis provided in the fourth section. The empirical analysis is extensive, due to obtaining better insights into the possibilities of the GRS methodology within the portfolio selection. The fifth section discusses the results obtained in the previous section, and the final, sixth section concludes the chapter.

2 Literature Overview This section gives a critical overview of the relevant research within the Grey Systems methodology and approach in the financial applications, with a focus on portfolio management. Existing literature within this area is rising. However, it mostly consists of shorter articles in which only a brief glance is given about previous empirical research. Two major groups of papers can be formed. First one deals with the GRA approach of modelling, whilst the second one applies (some variant of) Grey Model1 GM(1,1). Some authors apply only the Grey methodology, while others combine other approaches as well. Here we include the Data Envelopment Analysis (e.g. Fang-Min and Wang-Ching 2010; Pashaki et al. 2018), Neural Network Forecasting (e.g. Chen et al. 2014), Average Autoregressive Exogenous modelling (Huang and Jane 2008) and other approaches. Majority of research is concentrated in China, where this methodology originates from (see Julong 1989). Some of the literature has natural questions, such as how does this relatively new methodology compare to the existing popular ones in some area of research. Then, the authors ask themselves how good and accurate the GRA modelling is in real life examples and problems. And one part of the literature works on extending the original models to those which have a better prediction or are more suited to particular data and real problems. Still, much more work has to be done within this field of research. A lot of research does not state the limitations of their analysis, which should be discussed at the end of the paper in order to enhance future work. In that way, researchers within this area could be provided with fuller information on the current state and possible guidelines for future work.

1 More on Grey Models, GM, can be found in Liu and Lin (2006). These models refer to differential

equations which are used to forecast future values of stock prices or indices. Since the methodology is based upon observing a positive sequence of numbers to be forecasted, return series cannot be modelled via GM.

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Combination of several methodologies was made in Huang and Jane (2008). Authors obtained substantial results for the quarterly data analysis (more than 25% and 34% yearly returns in several cases) in which investments were simulated based upon a hybrid model (see Table 1) as a combination of several approaches. The question here is how come that authors found such profitable strategy but this approach has not become popular in the literature and/or practice. There is a lack of explanation of used variables as criteria in the paper, as well a more detailed explanation of the whole procedure. Almost the same analysis was done in Huang et al. (2008), due to same data being used, with the GM model and clustering approach of modelling in order to simulate investing into the same stocks on the same market (in the same time period). Again, another similar paper is Huang and Jane (2009), in which authors observed the same data and time span, by combining Variable Precision Rough Set (VPRS) theory with the GS approach and ARX modelling. The data and time span in this study is the same as the previous two (see Table 1), but authors additionally observe Fuzzy C-means in order to construct automatic portfolio selection. Conclusions are similar as in the previous two papers: abnormal and substantial returns could be obtained by following the procedure which was simulated in these studies. These three studies are relatively short compared to some other work (all having 7 pages in total) and although they are often cited in the related literature, this framework has not yet become popular in applications or in the publications in countries with developed stock markets. A related study is Huang (2009), in which the same data set is used again. However, the author searches for an appropriate threshold parameter in the VPRS to combine with ARX and the GRS framework. As previous papers, part of the methodology used here is to predict future price movements, and part of it is used to classify and select stocks to invest in based upon several criteria. In Fang-Min and Wang-Ching (2010) a comparison of GSD (Grey System Decision) and DEA (Data Envelopment Analysis) was made for a sample of companies in the electronics sector. Namely, since DEA is used to rank the decision making units based upon their “inputs” and “outputs” of “production”, this methodology is complementary to the GRA approach. GRA is simpler to conduct and if similar rankings can be found by doing both approaches, the GRA approach could save time and money. Authors found that the GRA approach had almost 79% accuracy rate of discriminating between companies with good and bad performances. Thus, this approach has the potential to predict good and bad performance with less computation demand compared to other more popular approaches, such as the mentioned DEA. Li et al. (2010) combined the AHP (Analytic Hierarchy Process) methods with the GRA approach in order to evaluate companies on the Chinese stock market. Several financial ratios were used to obtain their rankings by the GRA for the second stage, AHP application. Rankings were commented on, but no investment strategies were applied (simulated) nor were suggestions given. AHP and GRA were combined in Salardini (2013) as well, on a sample of Teheran Stock Exchange stocks (16 stocks, fiscal year 2010). Several financial and stock market variables were used to rank the stocks based upon both approaches with the author’s conclusions that such rankings can be used in the portfolio selection. Thus, no

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Table 1 Overview of main findings and methods in the GRA approach and GM methodology Research Huang and Jane (2008)

Huang et al. (2008)

Huang and Jane (2009)

Huang (2009)

Fang-Min and Wang-Ching (2010) Li et al. (2010)

Hamzacebi and Pekkaya (2011)

Salardini (2013)

Chen et al. (2014)

Series Electronic stock data from new Taiwan economy database 1Q 2003 – 1Q 2007 (in and out of sample), ROE, EpS, etc. Electronic stock data from new Taiwan economy database 1Q 2003 – 1Q 2007 (in and out of sample) Electronic stock data from new Taiwan economy database 1Q 2003 – 1Q 2007; profitability ratio, individual share ratio, debt ratio, etc. Electronic stock data from new Taiwan economy database 1Q 2003 – 1Q 2007; profitability ratio, individual share ratio, debt ratio, etc. 122 Taiwanese companies (electronic sector) in 2005, 9 financial ratios 8 companies, steel industry, Chinese stock market; no time span found; profitability measures, EPS, P/E and other financial ratios 12 firms in financial sector index of Istanbul stock exchange; ROA, ROE, TDR, QR and other financial ratios; 2003–2007 time span Fiscal year 2010; 16 firms on Teheran stock exchange, 18 variables as criteria (financial ratios mostly) REIT returns, IIP, lending rate, dividend yield, stock Index, inflation rate, GDP growth rate, money supply growth rate, monthly data 2001–2006, 12 (developed) countries

Methodology GRG, ARX, GM, RS

Main conclusions Extraordinary returns achieved (e.g. 34.7% in 1 year)

FM(1,N), K-means clustering, RS

Extraordinary returns achieved

GRA, VPRS, ARX

Extraordinary returns achieved

GRA, VPRS, ARX

Extraordinary returns achieved

GSD, DEA

GSD and DEA give very similar ranking for normal and stressed companies. GRA used to determine weights of variables in AHP

AHP, GRA

MCDM, GRA

P/E ratio most important in for stock selection;

AHP, GRA

Just obtained ranking of stocks based upon criteria

GRA, ANN

GRA is used to rank the variables for prediction in the ANN model. IIP and interest rates found to be most significant variables for prediction, lowest ranked: Inflation. (continued)

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Table 1 (continued) Research Bayramoglu and Hamzacebi (2016) Yongzhong and Hongjuan (2005) Doryab and Salehi (2017)

Škrinjari´c and Šego (2019)

Series Beta, return, standard deviation and coefficient of variation for 9 companies on Turkish stock exchange, Dec 2011 – Dec 2012 Weekly prices of Shanghai Composite Index, Feb 2000 – Mar 2004 100 companies on Teheran Stock Exchange, 2005–2015, data: stock prices, cash return equity

55 stocks: Market data and financial ratios data in 2017 with out of sample 6 months in 2018, Zagreb stock exchange

Methodology GRA

Main conclusions Beta most important (greatest weight in the model)

GM(1,1), Verhlust GM

GM(1,1) better for short-term forecasts, Verhlust for long-term Nonlinear grey Bernoulli model most accurate to predict

GM, nonlinear GM, Bernoulli GM, Nash nonlinear GM, panel regression for comparison of model predictions GRA rankings with portfolio backtesting

GRA rankings indicate good portfolio structure, best portfolio performance when 2 and 3 portfolio return moments used in rankings

Note: GRA Grey Relational Analysis, GRG Grey Relational Grade, ARX Average Autoregressive Exogenous, RS Rough Set theory, GM Grey Model, ROE Return on Equity, EPS Earnings Per Share, EpS Equity per Share, ANN Artificial Neural Network, IIP Index of Industrial Production, GSD Grey Situation Decision, DEA Data Envelopment Analysis, P/E Price to Earnings ratio, VPRS Variable Precision Rough Set, TDR Total Debt Ratio, QR Quick Ratio, MCDM Multiple Criteria Decision Making

investment strategies were simulated in the study. No explanations on why were specific variables used in the analysis. Hamzacebi and Pekkaya (2011) chose the best alternative stocks among different firms by comparing their financial ratios on the Istanbul Stock Exchange. Several scenarios have been compared in order to obtain information on which criteria (ratio) is most important for investors when making decisions on which stocks should enter the portfolio. The goal of this paper was to establish the relevance of different criteria for investors. Thus, the authors did not focus on investment strategies and their simulations and comparisons. Chen et al. (2014) employ the GRA approach in combination with ANN in forecasting the REIT returns of 12 advanced economies. Authors focused on several relevant variables (see Table 1) for forecasting the returns by applying the GRA analysis of every variable and their linear combinations in order to rank their relevance for return forecasting. In the second step, the ANN is applied in order to forecast the returns and compare several combinations of observed variables. Authors check for robustness of results

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by comparing the forecasts by dividing the predictor variables in groups based upon their rankings. Bayramoglu and Hamzacebi (2016) focused on a sample of 9 companies on Bursa Istanbul and used 4 criteria in the GRA approach (return, standard deviation, beta and the coefficient of variation). Simulation results showed that the greatest weight in the modelling was obtained for the beta of the company. However, no trading strategies were suggested. Moreover, the title of the paper contains the phrase fundamental analysis and in the introduction, the authors state that the modelling procedure will be based upon the fundamental analysis approach. The used 4 criteria in the empirical analysis are not based upon the fundamental analysis. Furthermore, the coefficient of variation is calculated from upon the return and standard deviation. This could lead to potential problems in the analysis due to using variables which are constructed one depending upon another. Doryab and Salehi (2017) wanted to explore how good several specifications of the GM model predict abnormal returns on the Teheran Stock Exchange. Škrinjari´c and Šego (2019) observed the market and financial ratio data for 55 stocks on Croatian stock market in order to apply the GRA modelling and ranking of those stocks when making decisions on which stocks will enter the portfolio structure. Authors compared several variable combinations in order to achieve either the greatest portfolio return or the minimal risk (depending upon the investors’ goals). The results indicated that the potential of using GRA methodology exists when ranking the stocks according to the defined criteria. This research is based upon the finance theory and the investor’s utility function, which is rarely found in other existing research when choosing the variables in the analysis. Authors comment on shortfalls and future work extensions in the direction of Post Modern Portfolio Theory. The conclusions based upon this overview are that many studies do not rely on finance theory which is an important factor in the whole process of the portfolio selection and management. That is why future work should focus on implementing Grey Systems methodology within the finance theory framework to obtain advantages and benefits from both sides. Moreover, there are advantages and disadvantages to use only market data or only financial ratios data. By using only the market data, timely decisions on a daily basis could be made. However, some investors consider the fundamental analysis in their investment approach. But when using financial ratios data as well, investment decisions could be made on a quarterly basis at best.2 The research lacks linking the GS results with portfolio management as well. Thus, more work has to be done in the future regarding implementing the GS methodology as a helpful tool in portfolio management.

2 Not

all companies publish their financial reports on a quarterly basis as well.

196

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3 Methodology The GRA is applied in any area where alternatives have to be ranked based upon different criteria. The difference between this and other approaches of ranking the alternatives, such as Data Envelopment Analysis or Artificial Hierarchical Process methodologies is that GRA is simpler to apply, with less subjectivity when deciding upon weights given to different criteria in the whole optimization process. This methodology can be used for small and large samples of data, with no need of making distribution assumption requirements. The rest of described methodology here is based upon Liu and Lin (2006, 2010) and Kuo et al. (2008). Suppose investor has K behavioural sequence data on M alternatives which have to be ranked, k ∈ {1, 2, . . . , K}, m ∈ {1, 2, . . . , M}. The behavioural sequences refer to the criteria which upon alternatives have to be ranked, such as return series, volatility, financial ratios and other variables of relevance to the investor. The alternatives refer to financial assets, such as in case of this study stocks. Alternatives could be bonds and other assets as well. All of the collected data can be formatted into one matrix: ⎡

⎤ x1 (1) x1 (2) · · · x1 (K) ⎢ x2 (1) x2 (2) x2 (K) ⎥ ⎢ ⎥ X=⎢ . .. . . .. ⎥ , ⎣ .. . . . ⎦ xM (1) xM (2) · · · xM (K)

(1)

where rows refer to the alternatives and columns to the criteria which upon alternatives are ranked. Thus, (xm (1), xm (2), . . . , xm (K)) is the behavioural sequence for the m-th alternative. Before the ranking could be performed, normalization of data has to be done, in order to have correct comparisons. Huang and Liao (2003) explain that if the criteria on which upon alternatives are being compared one to another has different goals, the results of the analysis will be incorrect. If the observed sequence has to be the larger the better (e.g. odd return distribution moments such as return and skewness), then each sequence (xm (1), xm (2), . . . , xm (K)) is normalized as follows: ym (k) =

xm (k) − minxm (k) m

maxxm (k) − minxm (k)

.

(2)

m

m

The following normalizations are for the smaller the values of a sequence and the closer to a desired value x* (k) respectively: ym (k) =

maxxm (k) − xm (k) m

maxxm (k) − minxm (k) m

m

(3)

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197

and ym (k) =

|xm (k) − x ∗ (k)| . maxxm (k) − x ∗ (k)

(4)

m

In that way, the values for every alternative are in a specific range. E.g., when observing (2) and (3), all of the data is now normalized to the range [0,1]. If the original behavioural sequence is closer to the desired value (greater or smaller), now the “new” values, i.e. normalized ones are closer to unit value. In the next step, the normalized data ym (k) is compared to a referent sequence y* (k), which could be determined by the researcher based upon the problem which is being observed. Since the data is normalized to the range [0,1], with unit value being the best one, in this study we use the unit value for every criterion as the best referent sequence (for details see Kuo et al. 2008). The differences between values of ym (k) and y* (k) are calculated for every alternative and every criteria: ym (k) = |ym (k) − y∗ (k)|, with the Grey Relational Coefficient (GRC) calculated for every alternative as follows: Gm (k) =

min + pmax , ym (k) + pmin

(5)

with p being the distinguishing coefficient, p ∈ [0,1], min = min {y1 (k), . . . , yM (k)} ∀ k and max = max {y1 (k), . . . , yM (k)} ∀ k. The range of the Gm (k) can be expanded or compressed by varying the value p, but the rankings of alternatives do not change. Most often used value in empirical research of p is 0.5. In the last step, the Grey Relational Degree/Grade (GRD) is calculated as a weighted average of GRC-s in (5): GRD m =

K 

(6)

wk Gm (k)∀m,

k=1

where wk denotes weight for the criteria k. It holds that

K 

wk = 1. The GRDm

k=1

for every alternative m is interpreted as the degree of similarity between the mth alternative sequence behaviour and the referent sequence y* (k). The greater the value of GRDm in (6) is, the greater performance of the observed alternative is. Thus, the best alternative is selected as having the greatest similarity performance to the best sequence y* (k). Thus, based upon (5) and (6), the basic idea can be seen that the GRA is used to calculate the degree of similarity between data sequences which are being compared one to another to the referent sequence. Moreover, this methodology does not need to be used only to compare with the referent sequence. It can be used to compare any sequence to another to see the degree of similarity.

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4 Empirical Analysis 4.1 Data Description and Preparation For the purpose of empirical analysis on how to employ the results from Grey System Methodology, daily data on prices on 20 stocks quoted on the Zagreb Stock Exchange has been obtained from website Investing.com (2019). The period observed in this study ranges from 2 January 2017 until 29 April 2019. The stocks chosen in the analysis were the most liquid stocks at the time of making this analysis. Moreover, all of the abbreviations of stock names are given in Table A1 in the appendix, with sector classification of each stock. In that way, it can be seen that diversification possibilities are greater by having different stocks in the portfolio. Moreover, basic descriptive statistics for daily data on each stock is given in Table A2 in the appendix (Table A3). Weekly average returns, standard deviations, coefficients of skewness and kurtosis have been calculated for every stock in the sample. In total, 121 weekly data is available for every stock return distribution moment. Basic statistics for each moment is shown in Table 2. Bolded numbers denote the best values for every moment. Just by observing averages for the whole period, it can be seen that none of the stocks had the best performance regarding all 4 return distribution moments. Additionally, a Jarque-Bera test was performed in order to test for normality of the weekly return distributions. The null hypothesis of normal distribution was not rejected for only two stocks in the sample: ADGR and ADPL (test values 1.64 and 0.48 with p-values 0.44 and 0.79 respectively). All other stocks were found to have non-normal distributions at usual levels of significance. This adds to the decision that investors should incorporate higher moments of return distributions when making investment decisions. Graphical representations of non-normality are shown via quantile distribution plots in Fig. A1 in the appendix as well. The rationale on why this study observes the 4 return distribution moments is as follows. Utility function theory focuses on the investor’s utility functions depending upon the first m moments of return distributions (Jurczenko and Maillet 2005). A lot of early work within finance theory recognized the importance of the first three moments, such as Friedman and Savage (1948) or Arditti (1967), whilst the fourth moment has been included in the spotlight since the 1980s (see Müller and Machina 1987), when the von Neumann-Morgenstern utility functions of investors have been extended to the first m moments of return distributions. Investors prefer smaller even moments (standard deviation and kurtosis), while higher odd moments are better (average return and skewness) when making decisions on investing (Arditti and Levy 1975; Athayde and Flôres 1997, Hwang and Satchell 1999; Jurczenko and Maillet 2005; Jondeau and Rockinger 2006). Alderfer and Bierman (1970) have conducted an empirical poll in which investors were given several portfolios to choose from. All of the portfolios had similar risks and returns, but very different portfolio asymmetries. Authors found that investors had a greater preference for positive skewness even if the expected return was smaller compared to a portfolio

Average return 0.000 0.001 0.000 0.001 0.000 −0.001 −0.001 0.000 0.000 0.003 −0.001 0.000 0.003 0.001 0.000 0.000 −0.002 0.001 0.005 0.000

Max return 0.010 0.011 0.018 0.027 0.069 0.056 0.038 0.020 0.011 0.075 0.015 0.034 0.106 0.059 0.014 0.032 0.052 0.078 0.085 0.024

Note: SD denotes standard deviation

Stock/ Statistics ADGR ADPL AREN ATGR ATPL DDJH DLKV ERNT HT INGR KONL KRAR LKPC LUKA PODR RIVP TPNR ULPL VART ZBB

Min return −0.013 −0.008 −0.017 −0.023 −0.032 −0.040 −0.040 −0.028 −0.011 −0.040 −0.033 −0.019 −0.071 −0.062 −0.015 −0.016 −0.061 −0.056 −0.090 −0.039

Average SD 0.009 0.010 0.010 0.012 0.026 0.032 0.029 0.012 0.007 0.031 0.013 0.013 0.015 0.018 0.011 0.011 0.019 0.037 0.036 0.015

Table 2 Descriptive statistics for weekly data on each stock Max SD 0.040 0.042 0.041 0.042 0.183 0.105 0.101 0.044 0.024 0.107 0.040 0.051 0.090 0.088 0.052 0.036 0.086 0.167 0.190 0.060

Min SD 0.001 0.001 0.000 0.000 0.004 0.004 0.004 0.002 0.000 0.002 0.000 0.000 0.000 0.000 0.002 0.002 0.000 0.006 0.000 0.000

Average skewness −0.060 −0.054 0.031 0.049 −0.010 0.030 0.029 −0.023 −0.056 0.104 −0.028 −0.073 −0.088 −0.047 0.053 0.037 0.250 −0.021 −0.098 0.107

Max skewness 1.278 1.500 1.456 1.500 1.417 1.350 1.414 1.500 1.500 1.485 1.154 1.448 1.150 1.405 1.500 1.375 1.154 1.244 1.260 1.500

Min skewness −1.394 −1.500 −1.500 −1.500 −1.365 −1.359 −1.287 −1.456 −1.500 −1.324 −1.500 −1.500 −1.500 −1.466 −1.369 −1.285 −0.820 −1.425 −1.500 −1.022

Average kurtosis 1.99 2.01 1.85 1.94 2.01 1.95 1.95 1.93 2.10 1.84 1.76 1.77 1.46 1.59 1.96 1.97 1.51 1.69 1.56 1.86

Max kurtosis 3.11 3.25 3.25 3.25 3.13 3.08 3.14 3.25 3.25 3.23 3.25 3.25 3.25 3.20 3.25 3.07 2.67 3.14 3.25 3.25

Min kurtosis 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00

Grey Incidence Analysis as a Tool in Portfolio Selection 199

200

T. Škrinjari´c ADGR

ADPL

520

AREN

220

500

ATGR

600

200

480

500

ATPL

1,300

800

1,200

700

1,100

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1,000

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180 460 160 440

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300 I

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2017

II

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DDJH

I

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2019

II

III

IV

I

2017

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2018

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200 I

2019

II

III

IV

II

III

IV

2018

I

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10

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I

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3.6

900 I

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III

IV

I

2017

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III

IV

2018

KONL

I

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3.2

140 I

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IV

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2017

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2018

KRAR

900

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4.0

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Source: ZSE (2019)

Fig. 1 Prices of all stocks in the analysis Source: ZSE (2019)

with greater return but smaller skewness. The focus on portfolio (and individual return) kurtosis is greater from late 1980s, due to computational difficulties of computers before that period (see Graddy and Homaifar 1988). Before moving on to the GIA (Grey Incidence Analysis) and raking with investment simulations, a graphical representation of the prices of each of the observed stocks has been depicted in Fig. 1. It can be seen that in the observed period, different trends in stock price movements can be found. Some stocks experienced a decline in their values over the observed period; some had price reversions, whilst others had an increase of their values. The different behaviour of prices is somewhat good in this research in order to fully test the possibilities of investment strategies which will be observed in the next sections.

4.2 Grey Incidence Analysis Initial Results Every stock in each week was ranked based upon the normalized values of its every moment. The normalization was such that the values for the odd moments were calculated via formula (2) and even moments were transformed by using formula (3). As an example, the calculation for the return series for every stock in week 1 is shown in Table 3. Original return series are in column labelled “Return”. Then, the values have been normalized by using formula (2) and they are shown in the column “yi (return)”. Next, the distance from the optimal value of 1 is calculated in the column “1yi (return)”. It can be seen that the stock LUKA has the greatest return in week 1,

Grey Incidence Analysis as a Tool in Portfolio Selection Table 3 Initial calculations, example of return series, week 1

Stock ADGR ADPL AREN ATGR ATPL DDJH DLKV ERNT HT INGR KONL KRAR LKPC LUKA PODR RIVP TPNR ULPL VART ZBB MAX

Return 0.0015 0.0020 0.0071 0.0043 0.0030 0.0206 0.0055 0.0065 0.0018 0.0108 0.0088 −0.0002 −0.0101 0.0211 0.0030 0.0112 0.0132 0.0143 0.0060 0.0197 0.0211

201 yi (return) 0.3728 0.3883 0.5513 0.4632 0.4212 0.9843 0.5006 0.5316 0.3815 0.6691 0.6078 0.3174 0.0000 1.0000 0.4197 0.6844 0.7488 0.7811 0.5176 0.9542 –

1-yi (return) 0.6272 0.6117 0.4487 0.5368 0.5788 0.0157 0.4994 0.4684 0.6185 0.3309 0.3922 0.6826 1.0000 0.0000 0.5803 0.3156 0.2512 0.2189 0.4824 0.0458 –

Gi (return) 0.3073 0.3102 0.3451 0.3253 0.3167 0.4923 0.3335 0.3405 0.3089 0.3757 0.3591 0.2972 0.2500 0.5000 0.3164 0.3800 0.3996 0.4102 0.3373 0.4781 –

Note: Last row denoting MAX refers to maximal value of return in first column. Best stock (LUKA) has bolded values Table 4 Grey Relational Coefficients for stock ADGR, week 1 GADGR (return) 0.3073

GADGR (SD) 0.5

GADGR (Skewness) 0.5216

GADGR (Kurtosis) 0.5

GRD 0.4572

thus the distance from the optimal value of 1 is equal to 0. Finally, Grey Relational Coefficients (GRC) have been calculated via formula (5) and are shown in column “Gi (return)”. Being the best in week 1 in terms of return, LUKA stock has the greatest value. The same procedure is repeated for the rest of the weeks in the analysis. Moreover, a similar procedure is repeated for the other three moments for every stock and every week in the analysis. Now, with weekly data on all four GRC values for each stock, the Grey Relational Degree/Grade (GRD) was calculated via formula (6). As an example, GRC values for the first stock in week 1 are shown in Table 4. Finally, the GRD can be calculated based upon values in Table 4. One problem here is to choose weights which will be assigned to each normalized moment. Thus, in order to avoid any subjectivity, the focus will be on equal weights for every moment. Although this is also subjective, neither moment is given greater weight compared to others. In other strategies where the modelling process asks to give weights to the distribution moments, equal weights will be given as well in order to ensure fairness of comparison. The GRD

202 Table 5 Average Grey Relational Degree for every stock in week 1

T. Škrinjari´c Stock ADGR ADPL AREN ATGR ATPL DDJH DLKV ERNT HT INGR

GRD value 0.4572 0.3730 0.3633 0.3135 0.3590 0.4231 0.3603 0.3904 0.3448 0.3189

Stock KONL KRAR LKPC LUKA PODR RIVP TPNR ULPL VART ZBB

GRD value 0.3549 0.3616 0.3191 0.3437 0.3876 0.3864 0.4688 0.3702 0.3646 0.4077

value for the stock ADGR is in week 1 equal to 0.4572. This value is then compared to the same values of other stocks in the sample. An average of every GRD value for every stock in week 1 is shown in Table 5 as an example of how the rankings were utilized in strategies simulations. It can be seen that the GRD value was greatest for stock ADGR, whilst the smallest value was obtained for stock ATGR. Thus, in terms of the Grey Incidence Analysis approach, the best performance in terms of all four moments, on average, was found for stock ADGR in the first week of the analysis. Now, the investor can make his decisions based upon the results given in Table 5. He can tailor his strategy based upon choosing the best stocks which had the greatest values of GRD in Table 5 and rebalance his portfolio accordingly each week. The assumption in this analysis is that investor ranks each stock in week t and based upon those rankings he invests in week t + 1 according to the results in the previous week (not only for the GRD strategies, but in other benchmark ones as well).

4.3 Benchmark Strategies For comparison purposes, several benchmark strategies were simulated before the GRD strategies were obtained. In that way, the strategies which are not based upon GRD results can be compared to the ones observed in this study. Consequently, comments can be made on whether to include the GRD methodology in the decision making process or not. Here, several popular strategies from the finance literature are chosen, including passive and active ones. The description of each one is as follows, with the brief summarization in Table 6 afterwards. In total, 8 benchmark strategies are chosen for comparison purposes with the GRD strategies. For details, see Conrad and Kaul (1998).

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Table 6 Benchmark strategies summarized Name Equal weights

Abbreviation EW

Random weights 1 Random weights 2

RW_1 RW_2

Moving average

MA

Minimum variance

Min_var

w∗t =

Data envelopment analysis

DEA

Multiple criteria decision making 1

MCDM_1

Multiple criteria decision making 2

MCDM_2

Every week only stocks with maximum efficiency score enter the portfolio; equal weights. MOORA based ranking. Only best stock enters the portfolio in every week. See yj∗ formula (11). MultiMOORA based ranking. Only best stock enters the portfolio in every week. See Uj formula (12).

4.3.1

Weights Equal, 5% (20 stocks); fixed over entire time span Randomly assigned every week Randomly assigned at first week; fixed over entire time span Depending upon moving average criterion for every stock. Equal weights of those stocks which enter the portfolio. −1 t e e −1 t e

(see formula 7)

Type Passive Active Passive Active

Active Active

Active

Active

Equal Weights Strategy

In this strategy, equal weights are given to all of the stocks at the beginning of the simulation period. Thus, each stock makes 5% of the portfolio. The investor is holding the same structure of the portfolio until the end of the holding period. This is a buy and hold strategy, due to the investor not buying or selling any of the stocks in the portfolio. Advantage of such a strategy is that the investor does not need to rebalance his portfolio and he does not pay transaction costs. Moreover, sophisticated analysis is not needed as well. However, such a strategy can omit some potential gains on the market.

4.3.2

Random Weights Strategy 1

In order to avoid any subjectivity, random weights are given to each stock every week. Thus, the investor buys and sells stocks every week, according to the random new weights. This strategy does not require that investor analyses the market conditions constantly. However, as in the previous strategy, the investor could miss some good opportunity on the market.

204

4.3.3

T. Škrinjari´c

Random Weights Strategy 2

The second random weights portfolio strategy is similar to the first one. Here, the random weights are given in the first week of the analysis. The same random weights are fixed over the entire time period, as in equal weights strategy. Thus, this is another buy and hold strategy in which the weights are given randomly. Advantages and disadvantages of this strategy are similar to previously mentioned two strategies.

4.3.4

Moving Average Strategy

Moving average is a common strategy from technical analysis in order to compare with other strategies. The basic idea is that the current price or return of a stock is compared to a moving average of the same variable from previous h time periods. If the comparing value in period t is above or below the moving average value, a buying or selling signal is in place. In this research, the average weekly return in week t is compared to the average return over the last h = 4 weeks. If the return in week t is greater than the average return over the past 4 weeks, the investor buys a stock, else he sells it. All stocks which enter the portfolio have equal weights in the portfolio in week t.

4.3.5

Minimum Variance Strategy

The minimum variance strategy is based upon optimizing the Markowitz (1952) model in which the variance of the portfolio is minimized in each week, as follows: min w t t wt wt

s.t. e wt = 1 , wt ≥ 0∀t

(7)

where wt is the vector of stock weights in week t, t is the variance-covariance matrix in week t, and e is the (1•n) vector of unit values, where n is the number of stocks. Moreover, short sale is not allowed. Thus, investor rebalances his portfolio every week based upon finding the minimal risk portfolio. The optimal solution to problem (7) is given as w∗t =

−1 t e . e −1 t e

This model is chosen so that in the optimization process in each week we do not confront problems on which level of desired return to impose within constraints. More details on the minimum variance portfolio can be found in Haugen and Baker (1991), Clarke et al. (2006) or Scherer (2010).

Grey Incidence Analysis as a Tool in Portfolio Selection

4.3.6

205

Data Envelopment Analysis Strategy

Data envelopment analysis (DEA) is an area of Operations Research in which units of observation are compared one to another based upon their performances. The basic idea is that those units are “production” units (called decision making units, DMUs) in which they use inputs to produce outputs. Since the theory and applications were firstly developed for the production companies, the terminology remained from that area. DMUs are ranked based upon producing maximum output by using minimal inputs possible. There are many models which can be used within DEA methodology (see, for example, Cooper et al. 2011). This research uses the following basic model to utilize its results in decision making process regarding stock selection for the portfolio in week t. The odd moments of return distribution of each stock are observed as outputs, due to them being the average return and skewness. Even moments (risk and kurtosis) are observed as inputs. Thus, each stock is a DMU which “uses” inputs to “produce” outputs. It is assumed that investor has data on n DMUs on m inputs and s outputs in each week t. In the case of this research m = s = 2. Thus, the Xt ∈Mmn is the matrix for all DMUs of all inputs in week t and similarly, Yt ∈Msn is the matrix of all outputs in week t for all DMUs. Each DMU has its own vectors xot and yot which represent all inputs and outputs vectors in week t respectively. Basic models are the CCR (Charnes-Cooper-Rhodes) model in which constant returns to scale are assumed; and the BCC (Banks-Charnes-Cooper) model, which adds the assumption of variable returns to scale. Moreover, the model can be input oriented, depending upon the assumption that the unit wants to minimize the value of inputs used to obtain a certain level of output. Another approach is that the unit aims to maximize the output level based upon a certain level of inputs used (output oriented). The model applied in this study is the BCC-I (input oriented) model. The envelope form in each week of the first phase of the optimization of the model is as follows: min θt λ,θt

s.t. θt x ot − Xt λ ≥ 0 Y t λ ≥ y ot λ≥0 K  λk = 1, ∀t

(8)

k=1

where λ ∈RK is the vector of nonnegative constants. Value θ t radially reduces values of the input vector xot . Since the DMU has to remain within the production possibility set, first and second constraint enable just that. The last constraint is the convexity constraint. Optimal solution from (8) θ t * is the rate of input reduction, with θ t * ∈ (0,1). Thus, the main idea is to minimize the risk and the coefficient of skewness, whilst keeping a certain level of return and coefficient of asymmetry.

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The second phase of the model is to maximize the sum of input surpluses and output shortfalls for each DMU at week t, by using the value θ t * for each unit as follows: + max es − t + es t

λ,st− ,st+ s.t. θt∗ x ot

− Xt λ = st− Y t λ = y ot + st+ , λ ≥ 0, st− ≥ 0, st+ ≥ 0 K  λk = 1, ∀t

(9)

k=1

where st− is the vector of input excess and st+ vector of output shortfalls in week t. e is a vector of unit values. The optimal solution of (9) is the max-slack solution, with the DMU being called efficient if the optimal solution (θ t * , λt * , st−∗ ,st+∗ ) satisfies θ t * = 1 and vectors st−∗ and st+∗ are null-vectors. The basic idea to form a portfolio is that all of the stocks are ranked every week based upon the value of θ t * for every stock i. Only those stocks which had the efficiency score of value 1 (maximum) enter the portfolio in week t. Moreover, equal weights are assigned to all of the entering stocks. If the same stock has efficiency score of unit value in the next week, the stock stays in the portfolio; else the investor sells it and buys those which have θ t * = 1 in that week. Some of the applications of DEA on stock markets can be found in Chen (2008), Lim et al. (2013), Škrinjari´c (2014) or Gardijan and Škrinjari´c (2015).

4.3.7

Multiple Criteria Decision Making Strategy 1

Multiple Criteria Decision Making (MCDM) is a discipline within the area of Operations Research (OR) which is based upon mathematical models which facilitate decision making process based upon several (or many) different criteria. MCDM is used in order to aid in the decision making process when decision alternatives have to be evaluated based upon (often) conflicting criteria. The decision maker has to assign weights to the criteria, thus making this approach somewhat subjective. Since the portfolio optimization depends upon many different stock characteristics, it is not surprising that such an approach has become popular in the empirical applications. For a detailed justification of applications of MCDM within portfolio management, please see Hurson and Zopounidis (1995). As mentioned, in real life decision making the criteria is often conflicting. E.g., in finance and the application in this research, investor aims to maximize the return and minimize the risk of a stock or portfolio. Since these two stock characteristics are conflicting, it is not easy to make decisions on which stocks enter the portfolio or not. Furthermore, investors do not observe risk and return as the only criteria when comparing stocks. There exist a lot of different MCDM models and methods,

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depending upon the area of the application (environment – Lahdelma et al. 2014; finance and banking Figueira et al. 2005; etc. See, for example Mardani et al. 2015). Basic steps in the MCDM approach are as follows. Firstly, one has to define the stakeholders, the problem, objectives of the decision; secondly, problem needs to be formulated with identifying the alternatives. Thirdly, mathematical model needs to be formulated and solved. Finally, the results are presented to the decision maker. He can revisit some of the previous steps and readjust them in order to redefine the solution (Bigaret et al. 2017). In this research, as a first strategy, the MOORA (multi objective optimization by ratio analysis) is used, due to it being robust with respect to 7 different criteria explained in Brauers and Zavadskas (2010). The ratio system ranking is observed as follows. Consider a matrix of responses for every alternative j and objective i, Xij = [xij ], where i ∈ {1, 2, . . . , n}, j ∈ {1, 2, . . . , m}. The MOORA calculates the ratio between each response j, xij and all alternatives regarding objective i, as follows: xij∗ = 

xij m 

j =1

(10)

, xij2

where xij∗ is the normalized response of the i-th alternative, xij∗ ∈ [0, 1]. Next, the normalized assessment for every alternative j is calculated by adding all values of xij∗ in the case of maximization of an objective (return and asymmetry) (from 1 to g) and subtracting those which have to be minimized (risk and skewness) (from g + 1 to n): yj∗ =

g  i=1

xij∗ −

n 

xij∗ .

(11)

i=g+1

Now alternatives yj∗ can be ranked. Formula (11) gives equal weights to all objectives. However, the decision maker can give weights wij such that: vij∗ = wij · xij∗ and now weighted values are substituted to (11). Details on MOORA can be found in Belton and Stewart (2002) or Brauers (2004). Applications in portfolio selection can be found in Baležentis et al. (2012) or Xidonas et al. (2009). If we translate this to the portfolio selection problem observed in this study, the four return distribution moments are observed as objectives (i ∈ {1, 2, 3, 4}, and 20 stocks are the alternatives which are compared each week). Every response is normalized via (10) and normalized assessments yj∗ are obtained by adding xij∗ for return and asymmetry and subtracting those for risk and skewness. Equal weights are given to all of the moments. The best ranked stock in every week enters the portfolio. If the same stock is the best one in the next week, it stays in the portfolio, but if another is ranked the best, this new one enters the portfolio and the previous one leaves.

208

4.3.8

T. Škrinjari´c

Multiple Criteria Decision Making Strategy 2

The second approach of a MCDM strategy is the ranking of alternatives based on the MultiMOORA; composed of MOORA and Full Multiplicative Form of Multiple Objectives (FMFMO). The FMFMO is based on utility theory (see Miller and Starr 1969). The utility function for ranking the alternatives can be defined n  xij . When looking at objectives which need to be simultaneously as Uj = i=1

minimized and maximized, as the problem observed here, the following value of utility of alternative j is considered as: g 

Uj =

i=1 n 

xij∗

i=g+1

,

(12)

xij∗

where weighted values vij∗ can be used as well. The greater the value of Uj , the better the alternative is. In terms of stocks observed in this study, the four moments, as mentioned previously, are used in order to construct (12) for every stock in each week. The best ranking stock is then bought and put in the portfolio. Again, as for the MCDM 1 strategy, this stock is in the portfolio in the next week if it stays the best ranked one. If other stock outranks the one which is currently in the portfolio, the new best ranking one goes to the portfolio and the previously best one leaves it. Finally, a concise description of each benchmark strategy is given in Table 6. All of them with the exception of EW and RW_2 being active strategies. Although the active strategies are more comparable to the active strategies based upon GRD results, we include the two passive ones as well. This is in order to see if the problem of transaction costs could be avoided by not constantly buying and selling the stocks every week.

4.4 Grey Results Based (GRD) Strategies The portfolios which will be simulated based upon the results of Grey Relational Analysis are described as follows. In total, 11 GRD based strategies will be simulated for comparison purposes. First 7 strategies are simpler than the last 4, in which the GRD results are combined with other methodologies in order to see if a combination of several approaches could result with even better results for the investor.

Grey Incidence Analysis as a Tool in Portfolio Selection

4.4.1

209

Best GRD Strategy

The first strategy is called Best GRD, due to taking the best ranking stock in the portfolio each week. Namely, as described in Sect. 4.2., the stocks are ranked based upon their final GRD (Grey Relational Degree) in each week. Then, the best one is put in the portfolio and stays in the portfolio in the next week if the ranking shows that this is the best stock once again. However, if another stock is ranked the best, investor sells the previously best one which was in the portfolio and buys the new best one. This is repeated until the end of the simulation period. Thus, only 1 stock is present in the portfolio every week.

4.4.2

GRD Based Weights Strategy

The second strategy includes all of the stocks due to diversification purposes. Firstly, in every week the stocks are ranked from the highest to the lowest GRD value. Stocks which obtain best values in ranking have greater weights in the portfolio in the next week, compared to those with the worst ranking. The weights for every stock i in each week t are calculated as follows: wi,t =

GRDi,t ∀t. 20  GRD i,t

(13)

i=1

The relative proportion of GRDi,t is calculated in (13) which gives the proportions, i.e. weights in the portfolio.

4.4.3

3 Best GRDs Strategy

Only the 3 best ranked stocks in each week enter the portfolio. The weights are equal, thus one third of the portfolio consists of every stock: wi,t = 13 . If a stock is ranked first, second or third place in the next week as well, it stays in the portfolio. Otherwise, it is sold and new one is bought which is ranked among best ones.

4.4.4

Return-GRD Strategy

One best stock enters the portfolio each week, based upon GRDs being calculated by taking into account only the return series. Thus, stocks are ranked by their returns in week t and the best one enters the portfolio in the next one. As in previous strategies, if other stock outranks the current week best one, the new best one enters the portfolio, whilst the previous best one leaves it.

210

4.4.5

T. Škrinjari´c

Risk-GRD Strategy

Similar to the previous strategy, only one stock enters the portfolio each week. The criterion is only the minimal risk of the stock in week t.

4.4.6

Skewness-GRD Strategy

Again, only one stock enters the portfolio each week, based upon the criterion of greatest skewness.

4.4.7

Kurtosis-GRD Strategy

The final strategy is the kurtosis-GRD, in which only one stock makes the portfolio. Here, it is based upon only the coefficient of kurtosis.

4.4.8

Fuzzy-GRD Strategy

Since real life problems regarding any aspect of the economy include uncertainty, the fuzzy logic, set theory, models and applications have been developed in order to aid such decision making. Ever since the fuzzy set theory has been introduced in the literature in early 1960s (Zadeh 1962, 1964, 1965), this area has been growing rapidly. The fuzzy logic is widely used in the area of financial applications and portfolio selection (see Watada 1997; Li and Xu 2013; Dourra and Siy 2002), due to it being a useful tool in modelling uncertainty and grey events. The fuzzy set theory, summarized, can be expressed as an extension to the crisp set theory. Let A = {(x, μA (x)) | x ∈ X}, where μA (x) is the membership function of x in set A that maps X to the membership space. In this research, in the first step the Grey Relational Coefficients (GRC) are calculated each week for every stock for every moment. In the next step, we do not calculate the GRDs, but form membership functions for every GRC in order to define fuzzy sets for every moment. Since GRC values are constructed that the greater the value the better, 4 membership functions for every moment are defined in the simplest manner as follows: μmoment (x) ⎧ ⎪ ⎨ 0, = 1+ ⎪ ⎩ 1,

GRC i,moment < GRCmoment GRCi,moment −0.8GRC max,moment , GRCmoment ≤ GRC i,return 0.8GRC max,moment −GRCmoment

< 0.8GRC max,moment

GRC i,moment ≥ 0.8GRC max,moment

(14)

μmoment (x) is the membership function for a distribution moment, GRCi, moment is the value of the GRC for the i-th stock and a given moment; and GRCmoment is the average value of GRC for all stocks for a given moment. The basic criteria

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is that if a stock has GRCi, moment value below the average value for that moment based upon all 20 stocks in the week t, the value of the membership function is equal to 0; if the value GRCi, moment is above the average value but below the 80% value of the maximal GRC value for that moment, then a line function is defined in the second part of (14); and finally, if GRCi, moment is above 80% value of the maximum GRC value, then, the membership function is equal to 1. Such function was chosen in order to obtain somewhat simplicity of interpretations and results. Moreover, in order to have stocks which enter the portfolio each week, the average value of GRCs was chosen as the lower benchmark in (14). If we have chosen a fixed constant instead of average for every week, the membership function could have been equal to 0 for every stock in some weeks. In this way, we avoid such problems. In other words, the GRC values for every stock and every week are mapped via (14) in order to obtain membership of each stock and it’s GRC to the fuzzy set of a distribution moment. Four membership functions for all four distribution moments are constructed as in (14). In the next step, the Sugeno model (Sugeno 1985) is used, due to its simplicity in order to define the final crisp value of ranking of every stock based upon the fuzzy memberships defined previously. The fuzzy rule in the Sugeno model for two inputs is as follows: if x is A and y is B then z = f (x,y), where A and B are fuzzy sets and z is the crisp function. The functional form for z is usually a polynomial. Here, we use the first order Sugeno model, in which the function z is defined as the linear function of the four inputs (the four distribution moments). For simplicity sake, we define 2 rules. The first rule is that if GRCreturn is large and GRCrisk is large and GRCskewness is large and GRCkurtosis is large, then z is the sum of the mentioned values, otherwise, the negative values of each GRC are summarized. The final output of this model is then defined as: K 

Z=

βk zk

k=1 K 

,

(15)

βk

k=1

where β k is the degree of truthfulness of the premise of rule k, with K being the total number of rules. More details can be found in Jang et al. (1997) or Zimmermann (2001). We give equal weights to all the rules, as in previous strategies in which weights had to be given as well. The procedure is repeated every week and the stocks are ranked. Finally, the stocks which are chosen to enter the portfolio in week t are those which have their output values above the average value in (15). Those stocks which make the portfolio are given equal weights.

212

4.4.9

T. Škrinjari´c

DEA-GRD Strategy

The GRC values from the Grey Relational Analysis are used in the DEA-GRD strategy. As mentioned previously, the greater the GRC value of a stock is, the better is the ranking of the stock. All 4 GRC values are, in terminology of DEA modelling, then outputs. Since at least one input is needed in order to conduct DEA optimization, we choose the GRC values for the third moment (skewness) to transform into the ratio 1 over GRCskewness,i for every stock in every week. Thus, the new ratio is observed as the input variable in DEA, because the greater the value of GRCskewness,i is, the ratio 1 over that value is smaller. The DEA model described previously (see formulae 8 and 9) is used here as well to rank the stocks every week. Stocks which were found to be efficient (optimal value θ t * from the optimization process equal to 1) in week t enter the portfolio in the next week. All of the entering stocks have equal weights in the portfolio. If one stock is found to be inefficient in the next week, it leaves the portfolio. Another stock which is found efficient then enters the portfolio.

4.4.10

MCDM-GRD Strategy 1

The GRC values from the Grey Relational Analysis are observed as objectives in MCDM terminology. The MOORA approach is used to rank the stocks based upon every GRC value at week t. The best ranking stock enters the portfolio in the next week. The procedure is repeated every week.

4.4.11

MCDM-GRD Strategy 2

The GRC values from the Grey Relational Analysis are observed as objectives in MCDM terminology again. The MultiMOORA approach is used to rank the stocks based upon every GRC value at week t. The best ranking stock enters the portfolio in the next week. The procedure is repeated every week (Table 7).

4.5 Comparisons of Results Firstly, we present the simulations of the benchmark strategies. Each portfolio (benchmark and the GRD ones) starts with a unit value at date t = 0. Moreover, we include transaction costs for every transaction made, with them being equal to 5% of the total transaction value. Since the MA strategy obtained much better values compared to other benchmark strategies, for better visibility, this strategy is shown in a separate figure, namely – Fig. 2. Best values were obtained, as mentioned, for the MA strategy, followed by MCDM_1 and DEA strategies (see Fig. 3). Only 5 strategies resulted with portfolio

Abbreviation Best

GRD_weighted

3_best Return_GRD Risk_GRD Skew_GRD Kurt_GRD Fuzzy_GRD DEA_GRD MCDM_GRD_1 MCDM_GRD_2

Name Best GRD strategy

GRD based weights strategy

3 best GRDs strategy Return-GRD strategy Risk-GRD strategy Skewness-GRD strategy Kurtosis-GRD strategy Fuzzy-GRD strategy DEA-GRD strategy MCDM-GRD strategy 1 MCDM-GRD strategy 2

Table 7 GRD based strategies summarized

i=1

GRDi,t 20  GRD i,t

∀t.

3 best ranked stocks, with equal weights, i.e. wi,t = 13 . 100% to the best stock; only return considered. 100% to the best stock; only risk considered. 100% to the best stock; only skewness considered. 100% to the best stock; only kurtosis considered. Sugeno model for the Grey relational coefficients; equal weights to best ranking stocks. Every week only stocks with maximum efficiency score enter the portfolio; equal weights. MOORA based ranking of GRC values. Only best stock enters the portfolio in every week. MultiMOORA based ranking of GRC values. Only best stock enters the portfolio in every week.

All stocks enter, greater weights given to those which have greater GRD value: wi,t =

Weights 100% to the best stock, all four moments considered.

Grey Incidence Analysis as a Tool in Portfolio Selection 213

214

T. Škrinjari´c

1,9 1,7 MA

1,5 1,3

3-Apr-19

3-Jan-19

3-Oct-18

3-Jul-18

3-Apr-18

3-Jan-18

3-Oct-17

3-Jul-17

3-Apr-17

0,9

3-Jan-17

1,1

Fig. 2 MA benchmark strategy value 1,15

1,1

1,05

1

0,95

0,9

EW

RW_1

RW_2

Min_var

DEA

MCDM_1

3-Apr-18

3-Jan-18

3-Oct-18

3-Jul-18

3-Apr-18

3-Jan-18

3-Oct-17

3-Jul-17

3-Apr-17

3-Jan-17

0,85

MCDM_2

Fig. 3 Benchmark strategies portfolio values

values greater than the starting unit value (besides the three mentioned, RW_1 and EW are included in the 5 best ones). However, the gains obtained in those strategies were not that substantial because the majority of the strategies had the portfolio value just barely above the unit value (see Fig. 3).

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215

5,4 4,9 4,4 3,9 3,4

2,9 2,4 1,9 1,4

BEST

3_best

Return_GRD

Fuzzy_GRD

3-Apr-19

3-Jan-19

3-Oct-18

3-Jul-18

3-Apr-18

3-Jan-18

3-Oct-17

3-Jul-17

3-Apr-17

3-Jan-17

0,9

DEA_GRD

Fig. 4 GRD strategies portfolio values

Thus, the MA strategy could be the best one regarding the portfolio value to compare with GRD strategies. Moreover, the only two passive strategies (EW and RW_2) did not perform that well, although almost no transaction costs were included in these two strategies. The EW is included in the top 5 strategies, but the portfolio value is rather poor due to not paying almost any transaction costs. Next, the GRD strategies portfolios have been depicted with their values in Figs. 4 and 5. Since several strategies obtained greater portfolio values compared to others, for the purpose of the better depiction, the strategies with greater values are shown in Fig. 4. The rest of the portfolios are shown in Fig. 5. The greatest portfolio value was obtained for the Return_GRD strategy. Since this strategy could have been taken without the GRD approach just by comparing best returns each week, we look at other strategies as well. The second best strategy is the BEST one. This is the GRD approach in which in each week all of the stocks are ranked based upon the Grey approach by using all four moments for comparisons. This indicates that the GRD approach can be very useful when making decisions on how to structure a portfolio in order to obtain great portfolio values over time. The next three strategies are: Fuzzy_GRD, DEA_GRD and 3_Best strategies. All three seem to follow similar trend over the entire period (please see Fig. 4). The Fuzzy_GRD seems to have a slightly higher value over the majority of the period compared to other two mentioned strategies. The 3_Best strategy is the simplest one to construct between all three. This means that using only the GRD approach could obtain similar results as some other approaches which include more sophisticated methodologies combined with GRD.

216

T. Škrinjari´c

1,25 1,20 1,15 1,10 1,05 1,00 0,95 0,90 0,85

GRD_weighted

Risk_GRD

Skew_GRD

Kurt_GRD

MCDM_GRD_1

MCDM_2_GRD

3-Apr-19

3-Jan-19

3-Oct-18

3-Jul-18

3-Apr-18

3-Jan-18

3-Oct-17

3-Jul-17

3-Apr-17

3-Jan-17

0,80

Fig. 5 GRD strategies portfolio values, continued

Finally, the last six GRD strategies are shown in Fig. 5. The bottom three include: MDCM_GRD_2, Risk_GRD and MCDM_GRD_1. These three strategies obtained portfolio values less than unit value at the end of the period. It is not surprising that one of the worst portfolio values is for the Risk_GRD strategy. This strategy aims to invest in the stock which had the smallest risk in week t. Thus, the returns could have been very small for the least risky stocks. The other two strategies are combination of MCDM and GRD. Thus, it could be said that based on the results here, it is not advised to combine the two approaches in portfolio selection as they were in this study. Other possibilities should be explored in future work to see how these two approaches can be used in order to achieve better results. Since the Risk_GRD strategy aimed to minimize the risk of the portfolio by looking at only one stock best in terms of minimal risk, we compare this portfolio to the minimum variance portfolio which was optimized via Markowitz model every week. The comparison is shown in Fig. 6. Although the portfolio value of Min_var was greater over time (due to diversification), the Risk_GRD followed it quite closely. This indicates that GRD methodology can be useful in risk minimization with obtaining a certain level of return. However, since the strategy here was a simple one (only one best stock with respect to the risk criterion), future work should extend upon combining the GRD approach and the minimum variance criterion. Next, for comparison purposes in terms of Modern Portfolio Theory, the efficient frontier was constructed based upon the Markowitz portfolio optimization problem. A random week was chosen to compare the results, week 115. The frontier is shown in Fig. 7. Additionally, values of risks and returns for all of the simulated portfolios/trading strategies have been calculated for the same week. The points

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217

1,02 1 0,98 0,96 0,94 0,92

Min var

3-Mar-19

3-Jan-19

3-Nov-18

3-Sep-18

3-Jul-18

3-May-18

3-Mar-18

3-Jan-18

3-Nov-17

3-Sep-17

3-Jul-17

3-May-17

3-Mar-17

3-Jan-17

0,9

Risk_GRD

Fig. 6 Comparison of minimum variance portfolio and the Risk_GRD strategy

0,025

0,02

0,015

0,01

0,005

0 0

0,005

0,01

0,015

0,02

0,025

0,03

0,035

0,04

-0,005 Efficient frontier DEA Return_GRD Fuzzy_GRD

EW BEST Risk_GRD DEA_GRD

RW_1 GRD_weighted Skew_GRD MCDM_GRD_1

Fig. 7 Efficient frontier compared to all strategies’ portfolios, week 115

RW_2 3_best Kurt_GRD MCDM_2_GRD

218

T. Škrinjari´c

Table 8 Percentage of time the GRD strategy has greater portfolio value compared to benchmark ones GRD/Benchmark BEST GRD_weighted 3_best Return_GRD Risk_GRD Skew_GRD Kurt_GRD Fuzzy_GRD DEA_GRD MCDM_GRD_1 MCDM_GRD_2

EW 100% 100% 100% 100% 0% 57% 100% 100% 100% 48% 4%

RW_1 100% 100% 100% 100% 0% 57% 100% 100% 100% 50% 5%

RW_2 100% 100% 100% 100% 18% 58% 100% 100% 100% 71% 12%

Min_var 100% 100% 100% 100% 0% 57% 100% 100% 100% 62% 13%

DEA 100% 100% 100% 100% 0% 1% 100% 100% 100% 12% 2%

MCDM_1 100% 55% 100% 100% 2% 6% 54% 100% 100% 1% 5%

MCDM_1 100% 100% 100% 100% 42% 69% 100% 100% 100% 77% 20%

MA 100% 5% 100% 100% 2% 2% 13% 100% 86% 2% 1%

represent portfolios which have been added to Fig. 7. Since this is just 1 week out of the whole period, we can only make conclusions for that week. Best performing strategies in terms of risk that week were the Risk_GRD, Skew_GRD and Kurt_GRD because they were achieving lower risk for almost the same portfolio return compared to portfolios near the minimum variance one. Bad performing ones were, e.g. those which realized negative portfolio returns (RW_1, RW_2, EW, etc.) or those which had a positive return, but the risk was much higher compared to the efficient frontier (e.g. Return_GRD or MCDM_GRD_1). As mentioned, such performance was recorded in the week 115. Thus, we move on to the performances in the entire period. Portfolio values were compared one to another by counting how much of the total time a GRD strategy has greater portfolio value compared to all of the benchmark ones. The results are shown in Table 8, with bolded values indicating that the GRD strategy has better portfolio value at least 50% of the time. It is not surprising that the majority of the GRD portfolios have greater values compared to the benchmark ones, due to the previously commented figures. It is also not surprising that the Risk_GRD portfolio has smaller values compared to others, due to this being the risk minimizing portfolio. Since investor is interested in the portfolio risk as well, Table 9 compares the values of portfolio risks. Again, percentages are interpreted as percentages of time each of the GRD portfolio had lower risk compared to benchmark ones. Now, only the MCDM_1 and 2 strategies are worse than any of the GRD strategies; meaning that these two had greater portfolio risk majority of the time. The best performing GRD strategy is the GRD_weighted one. This is due to including all of the stocks in the portfolio, which contributed to the diversification. The Min_var portfolio, unsurprisingly, had lower risk compared to all GRD portfolios. However, the results from Table 9 indicate that GRD strategies which include more stocks in the analysis could contribute to lower portfolio risks. Future work should focus more on how to

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219

Table 9 Percentage of time the GRD strategy has lower portfolio risk compared to benchmark ones GRD/Benchmark BEST GRD_weighted 3_best Return_GRD Risk_GRD Skew_GRD Kurt_GRD Fuzzy_GRD DEA_GRD MCDM_GRD_1 MCDM_GRD_2

EW 21% 50% 20% 23% 28% 28% 26% 12% 26% 21% 23%

RW_1 23% 62% 21% 23% 28% 27% 26% 16% 28% 15% 18%

RW_2 23% 62% 21% 23% 28% 27% 26% 16% 28% 15% 18%

Min_var 15% 28% 10% 17% 12% 12% 12% 6% 10% 12% 16%

DEA 24% 52% 20% 23% 27% 27% 26% 14% 26% 21% 24%

MCDM_1 50% 83% 56% 50% 70% 69% 66% 48% 63% 53% 56%

MCDM_1 46% 81% 57% 53% 69% 68% 65% 51% 60% 52% 55%

MA 28% 69% 30% 26% 40% 38% 36% 21% 33% 26% 30%

Table 10 Percentage of time the GRD strategy has greater CEa compared to benchmark ones GRD/Benchmark BEST GRD_weighted 3_best Return_GRD Risk_GRD Skew_GRD Kurt_GRD Fuzzy_GRD DEA_GRD MCDM_GRD_1 MCDM_GRD_2

EW 59% 88% 68% 98% 0% 14% 98% 96% 94% 8% 0%

RW_1 63% 79% 67% 98% 0% 14% 98% 96% 95% 7% 0%

RW_2 66% 81% 71% 98% 0% 14% 98% 96% 94% 8% 0%

Min_var 55% 64% 61% 98% 0% 14% 98% 96% 95% 7% 0%

DEA 55% 75% 64% 98% 0% 14% 98% 96% 94% 7% 0%

MCDM_1 25% 26% 28% 100% 7% 10% 55% 100% 100% 2% 4%

MCDM_1 MA 97% 7% 98% 7% 98% 7% 100% 100% 50% 2% 74% 2% 100% 13% 100% 98% 100% 84% 74% 1% 20% 1%

a Certainty

Equivalent is the value which gives equal utility to the investor as the expected utility of an uncertain gamble. For a derivation of the expression CE ≈ E(μ)-0.5γσ2 , where E(μ) denotes average return of the portfolio, γ the coefficient of absolute aversion towards risk and the σ2 portfolio risk, please see Cvitani´c and Zapatero (2004), Varian (1992) or Chen (2016). The value of γ was chosen to be 1

construct portfolios in order to achieve better diversification. This could be achieved by including the diversification measures either in the process of optimization or in the refining of the results. Next, Certainty Equivalent (CE) values have been calculated in every week for all of the strategies due to it representing the utility investor obtains based upon the portfolio return and risk. As in the previous two tables, we calculate the percentage of time when the CEs for GRD strategies were greater than other benchmark ones. Results are shown in Table 10. By looking at CEs, risk and return are observed simultaneously and more details can be obtained on how investor values every strategy.

220

T. Škrinjari´c

Best strategies were Return_GRD, Fuzzy_GRD, DEA_GRD and Kurt_GRD (see bolded values) since these strategies obtained greater utility values for majority of the time compared to all benchmark strategies. This indicates that maybe the Fuzzy logic approach and DEA methodology combined with GRD could be observed in future work so that best strategies could be advised for (potential) investors. Besides the percentages of time we have observed until now, other performance measures have been calculated based upon the whole time sample. This performance is shown in Table 11. Based upon weekly performance, average, minimum and maximum returns and standard deviations have been calculated, as well as average CE and the total portfolio return. Not surprisingly, the Min_var portfolio is best in terms of standard deviation, by achieving minimal average and minimal max portfolio standard deviation. Comparing the statistics for the return series, not one strategy dominates the others. However, average portfolio returns were actually losses for RW_2, Min_var, MCDM_2 as benchmark ones, and Risk_GRD and both MCDM with GRD from the Grey strategies. Average Certainty Equivalents values are compared in the column labelled CE. The average utility was greatest for Return_GRD, Fuzzy_GRD and DEA_GRD strategies. Finally, total returns at end of the period were calculated, with the best value of Return_GRD strategy. However, there does exist some potential in using the GRD approach either by itself or combined with other methodologies in order to achieve better results in terms of performance in Table 11. Additionally, the correlations between portfolio values have been calculated and are shown in Table A3 in the appendix. In that way, interested investors could compare which strategies behave in the most similar manner. This could be useful to see which strategy could be of most interest to follow based upon investor’s preferences, but he can choose to follow simpler strategy in terms of modelling and forecasting. Some investors are mostly focused on risks. Thus, we add comparison of the portfolio risk (standard deviation) between the best one from the benchmark portfolios, i.e. the Min_var and the GRD_weighted portfolio as the best one (in terms of minimal portfolio risk) from GRD strategies. Comparison is shown in Fig. 8. Despite the two spikes (April 2017 and September 2018), the both portfolio risks move in a very similar manner. Spike in April 2017 was due to the crisis of the company/concern Agrokor in Croatia;3 and the second spike in September 2018 was due to several big companies switching to the Prime market from the Regular market. The results from Fig. 8 are promising in terms that the GRD strategies have potential in achieving lower portfolio risks with not much scarifying portfolio returns.

3 For

details, please see Škrinjari´c (2018a, b) or Škrinjari´c and Orlovi´c (2019).

Average return 0.00002 0.00004 −0.00028 −0.00033 0.00076 0.00002 −0.00039 0.00459 0.00948 0.00151 0.00559 0.01266 −0.00051 0.00046 0.00138 0.00609 0.00531 −0.00042 −0.00116

Max return 0.00941 0.01180 0.01164 0.00572 0.01050 0.09356 0.04148 0.01460 0.06631 0.01261 0.02887 0.05562 0.01001 0.06623 0.08209 0.04951 0.03825 0.04565 0.04639

Min return −0.04383 −0.04354 −0.04354 −0.04582 −0.04397 −0.04979 −0.04979 −0.05129 −0.03091 −0.04301 −0.03910 −0.03043 −0.04979 −0.04979 −0.01129 −0.03814 −0.04247 −0.04060 −0.04249

Average SD 0.00568 0.00591 0.00591 0.00418 0.00578 0.01528 0.01698 0.00725 0.01537 0.00574 0.01119 0.01608 0.00914 0.01049 0.01148 0.01706 0.01056 0.01738 0.01667

Max SD 0.02424 0.02411 0.02411 0.01105 0.02280 0.06442 0.11421 0.02214 0.05845 0.02277 0.04672 0.07512 0.03135 0.13903 0.10368 0.16715 0.04451 0.11421 0.11421

Note: Bolded values indicate best performance by column; italic values indicate worst performance by column

Portfolio/Performance EW RW_1 RW_2 Min_var DEA MCDM_1 MCDM_2 MA BEST GRD_weighted 3_best Return_GRD Risk_GRD Skew_GRD Kurt_GRD Fuzzy_GRD DEA_GRD MCDM_GRD_1 MCDM_GRD_2

Table 11 Portfolio performance of simulated investment strategies Min SD 0.00056 0.00109 0.00109 0.00060 0.00042 0.00109 0.00109 0.00147 0.00100 0.00124 0.00097 0.00100 0.00065 0.00065 0.00065 0.00210 0.00174 0.00037 0.00037

CE −0.00282 −0.00292 −0.00324 −0.00242 −0.00213 0.04442 −0.06315 0.25280 0.00180 −0.00136 0.00000 0.84999 −0.06859 −0.03023 0.06572 0.33137 0.27456 −0.04193 −0.10127

Total return 0.00201 0.00443 −0.03440 −0.04004 0.09177 0.00219 −0.04768 0.55553 1.14746 0.18312 0.67663 1.53168 −0.06156 0.05556 0.16673 0.73662 0.64311 −0.05044 −0.13984

Grey Incidence Analysis as a Tool in Portfolio Selection 221

222

T. Škrinjari´c

0,025

0,020

0,015

0,010

0,005

GRD_weighted

3-Apr-19

3-Jan-19

3-Oct-18

3-Jul-18

3-Apr-18

3-Jan-18

3-Oct-17

3-Jul-17

3-Apr-17

3-Jan-17

0,000

Min var

Fig. 8 Portfolio risk comparison of Min_var and GRD_weighted portfolios

Based upon values in Table 11, rankings have been made for every strategy’s returns, risks, CEs and total returns. Strategy with highest return was ranked the first (Return_GRD); and the smallest return strategy MCDM_GRD_2 was ranked the last. Then, the procedure is repeated for other performance measures in Table 11. The final ranking was then calculated as equally weighted measure from all of the rankings. Thus, as a simple measure, this average ranking based upon total results in terms of risk and return could be used in order to make final comparisons and conclusions. The new average ranks were compared to the average return of each strategy in Fig. 9 and with average CEs in Fig. 10. In Fig. 9 it can be seen that the better the ranking is (lower values on y axis), the greater is the average return (x axis). The results are in line as previously commented tables and figures, thus making the results robust. Figure 10 shows a similar pattern: better ranking of a portfolio is characterized with greater CE value.

5 Discussion Based upon the results in the previous section, several conclusions and recommendations can be made. Active trading strategies could obtain greater portfolio values even with transaction costs when compared to passive ones. This is due to exploiting the best characteristics which are in the focus of a strategy. Even simpler strategies such as focusing only on one return distribution moment can

Grey Incidence Analysis as a Tool in Portfolio Selection

223

16 MCDM_2 14

12

Risk_GRD

MCDM_GRD_2 MCDM_GRD_1

Random_2 MCDM_1 Skew_GRD 10 Min_Var Random 1 EW DEA 8

MA

DEA_GRD Kurt_GRD

Fuzzy_GRD GRD_weighted

3 BEST

6

BEST

R² = 0,5991 Return_GRD R² = 0,5491

4 -0,002

0

0,002

0,004

0,006

0,008

0,01

0,012

0,014

Fig. 9 Comparison of rankings (y axis) based upon values in Table 11 with the average portfolio return (x axis)

16 MCDM_2 14

Risk_GRD

MCDM_GRD_2 MCDM_GRD_1

12

Random_2 Skew_GRD MCDM_1 Min_Var Random 1MA EW DEA

10

8

DEA_GRD

Fuzzy_GRD GRD_weighted

3 BEST Kurt_GRD 6

R² = 0,3666 Return_GRD

BEST

R² = 0,3064 4

-0,2

0

0,2

0,4

0,6

0,8

1

Fig. 10 Comparison of rankings (y axis) based upon values in Table 11 with the average CEs (x axis)

224

T. Škrinjari´c

achieve specific investment goals. If we focus only on the GRD approach in the portfolio selection, there exists a potential to exploit this methodology. Portfolio BEST which included the one best stock with respect to GRD ranking obtained a substantial portfolio value and return over time. However, investors are focused on the diversification possibilities when investing as well. Thus, other strategies were observed, such as the 3 BEST which included only the three best ranking stocks from the Grey Relational Analysis. This strategy obtained similar results as some other more complex approaches, such as combining the Fuzzy logic and DEA approaches with GIA. This indicates that the Grey Relational Analysis, as a rather simplistic approach, is able to distinguish good and bad performance in terms of distribution moments which have been examined in this chapter. Thus, possibilities exist in terms of extending the existing strategies with some specific investor’s goals. A specific strategy cannot be recommended for all investors, due to their preferences. However, the results indicate that those who are focused on returns could obtain substantial results, as well as those investors who are more aiming towards risk mitigation could obtain lower portfolio risk with GRD approach. Moreover, the methodology observed in this study can be used in the dynamic setting that is the financial market, and especially stock market; where changes and shocks are always taking place. Specific investment requirements could be achieved by including many different variables in the GRA analysis approach since the methodology is flexible and can be used dynamically. Next, the portfolio values of Grey strategies obtained in this study were, in the majority of cases, greater than values of those strategies based upon technical analysis. This represents valuable information for potential investors and those interested in speculating on stock markets. Moreover, Certainty Equivalent values which take into consideration both return and risk of a portfolio have indicated several potential strategies which could be the stepping stone for future research. Since many of the observed strategies included equal weights for the best performing stocks, future work should extend the current findings by trying to determine the best allocation of portfolio weights. This can be either throughout the optimization process in the modelling, or by including the decision maker to refine the results in several cycles.

6 Conclusion Quantitative finance today represents a complex discipline due to much different knowledge needed to apply from the area of quantitative disciplines, as well as finance theory. Some of the most important steps in the portfolio management are the performance evaluation and forecasting of crucial financial variables. Since

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225

many different quantitative methods and models have been developed in order to answer specific investor questions, finding the optimal combination of theory and quantitative methods represents a difficult task today. The Grey Systems theory is one possible way to use quantitative methods in the portfolio management, due to it being suitable for uncertain systems because of many uncertainties on financial markets. This research focused on the Grey Incidence Analysis when comparing different investment alternatives. The rationale of using this methodology is found in its simplicity compared to some other approaches in which many calculations, estimations and data manipulation are necessary in order to obtain results. Investors should aim to achieve their goals as fast as possible with lowest costs which can be achievable. The Grey Systems approach could provide some of the mentioned goals, due to it being computationally relatively easier compared to some other approaches. It could be said that it is a more parsimonious approach compared to some areas of operational research or quantitative econometrics. However, this does not imply that the mentioned approaches should be ignored. On the contrary, some complementarity exists between all of the approaches examined in this chapter. In order to obtain initial insights into the usefulness of the Grey Incidence Analysis, this research opted to start parsimoniously as well. This was achieved by focusing on the first four moments of the return distributions of return series when calculating the Grey Relational Grades every week. Thus, it was assumed that investor changes the structure of his portfolio every week based upon the rankings in the previous week. In that way, a dynamic approach was made so that more realistic results could be obtained for the analysis. A chance was given to the GIA approach, due to 11 different investment strategies which were simulated in the study. So, it can be said that initial results are somewhat reliable due to many approaches which were assumed that investor could take based upon the ranking results. This is what represents a gap in the literature. Existing work does not focus so much on implementing the results from GIA in the portfolio management; and especially in extending the results with additional analysis with other quantitative approaches. Moreover, the basis in this analysis was the utility function theory with focus on investor’s utility functions. This also was not found in the majority of existing research. It should be noted that some methodology should be used just by itself, but in conjunction with finance theory in order to obtain best possible results for the investor and his goals. However, there were some shortfalls of this study. Firstly, we observed only 20 stocks. Investors are often confronted with many more on different markets. The emphasis was made into seeing if Grey System methodology is applicable in the context of portfolio selection as it was done in this chapter. Since the calculations were made in environment R, real life problems with many stocks can be analysed as in this chapter with almost no problem. Furthermore, only return distribution moments have been the crucial criteria when calculating the Grey

226

T. Škrinjari´c

Relational Degree. This was chosen due to the utility function theory, but other work exists which incorporates financial ratios into the analysis as well. The problem with including other variables as criteria for ranking the stocks is that financial ratios are available on a quarterly basis at best. Thus, all of the analysis which was done in this research could not be performed. However, it is reasonable to assume that other factors besides return moments could potentially influence portfolio selection. Finally, portfolio restructuring was based upon the rankings of stocks in the previous week. This means that investor assumes the same behaviour from past is going to continue in the future as well. Other models within Grey System methodology exist which could be used to forecast future stock price movements in order to facilitate restructuring portfolios ever better. This is also open for future extensions. Future work has more to do besides the mentioned issues. Firstly, there is a shortage of research which tries to connect results from the methodology explored in this study with the portfolio management and portfolio restructuring. Thus, future research should focus on investment strategies which incorporate the Grey System methodology as one part of the analysis. Moreover, other variables which investors consider when making investment decisions have to be explored in order to find best possible investment strategies based upon individual preferences, goals and limitations. The Grey System methodology is useful for speculating (almost on a daily basis) as well. Thus, many possibilities exist here to incorporate this methodology into the technical analysis. This is true not only for the Grey Relational Analysis done in this study, but for other methods and models within Grey System framework. As it can be seen, there remains a need to continue exploring this area.

Grey Incidence Analysis as a Tool in Portfolio Selection

227

A.1 Appendix

Table A.1 Stock abbreviations with full names Abbreviation Full name ADGR Adris Group d.d. for managing and investing ADPL Ad Plastik d.d. for motor vehicles parts production and plastic mass products AREN Arena Hospitality Group d.d. for tourism and hospitality ATGR Atlantic Group d.d. for domestic and foreign trade ATPL Atlantska plovidba d.d. group for international transport of people and goods DDJH Ðuro Ðakovi´c group d.d. DLKV Dalekovod d.d. for engineering, production and construction ERNT Ericsson Nikola Tesla d.d. for telecommunication system and device production HT Hrvatski Telekom d.d. INGR Ingra d.d. for construction of investment objects, imports, exports and dealerships KONL Konˇcar electroindustry d.d. KRAR

Kraš food industry d.d.

LKPC

PODR

Luka Ploˇce d.d. for maritime traffic services, port services, goods storage and shipping Luka Rijeka d.d. for maritime traffic services, port services, goods storage and shipping Podravka food industry d.d.

RIVP TPNR ULPL VART ZBB

Valamar Riviera d.d. for tourism Tankerska Next Generation shipping d.d. Uljanik Plovidba d.d. Maritime transport Varteks d.d. Varaždin textile industry Zagreb bank d.d.

LUKA

Sector Management activities Other parts and motor vehicles parts Hotels and similar accommodation Non specialized wholesale Maritime and coastal transport

Management activities Construction of electrical power lines and telecommunication Telecommunication equipment production Wired telecommunications activities Engineering and related technical consultation Electric motors, generators and transformers production Cocoa, chocolate and confectionery products production Cargo handling

Cargo handling

Other food processing, fruit and vegetables conservation Hotels and similar accommodation Maritime and coastal transport Maritime and coastal transport Production of other clothes Other money intermediation

Source: Investing (2019) and Zagreb Stock Exchange (2019). Note: d.d. denotes joint stock company

Mean 0.0000 0.0005 −0.0003 0.0008 0.0002 −0.0023 −0.0011 −0.0001 0.0000 0.0016 0.0003 −0.0005 0.0011 0.0001 0.0001 0.0001 −0.0020 0.0002 0.0049 0.0002

Median 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

Maximum 0.0513 0.0485 0.0514 0.0670 0.3427 0.2393 0.1358 0.0760 0.0460 0.1657 0.0539 0.0807 0.1498 0.1069 0.0610 0.0556 0.0690 0.1276 0.2752 0.0531

Minimum −0.0383 −0.0568 −0.0713 −0.0586 −0.0839 −0.1926 −0.1560 −0.0711 −0.0312 −0.1384 −0.0576 −0.0760 −0.0713 −0.0801 −0.0546 −0.0532 −0.0822 −0.3164 −0.1542 −0.1089

SD 0.010 0.012 0.012 0.015 0.030 0.037 0.032 0.013 0.008 0.034 0.016 0.015 0.023 0.023 0.013 0.012 0.023 0.042 0.045 0.017

Skewness 0.381 −0.006 −0.105 0.244 2.655 0.434 0.260 0.059 0.676 0.498 −0.060 0.027 2.126 0.429 0.306 0.403 −0.107 −0.889 1.170 −0.659

Note: SD denotes standard deviation. N denotes number of available data in the observed period

Stock/Statistics ADGR ADPL AREN ATGR ATPL DDJH DLKV ERNT HT INGR KONL KRAR LKPC LUKA PODR RIVP TPNR ULPL VART ZBB

Table A.2 Descriptive statistics for daily data return Kurtosis 5.833 6.220 7.235 5.513 31.222 9.218 5.592 7.109 8.294 5.893 3.980 6.972 13.998 6.126 6.347 5.648 4.721 11.465 9.435 7.726

JB 201.58 237.62 376.89 137.09 19312.09 870.53 162.48 387.17 719.04 181.34 15.84 279.47 1668.37 108.61 265.72 183.58 25.56 1365.32 576.22 524.50

p-value 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000

N 562 550 503 502 562 530 558 550 578 465 390 425 288 248 551 575 204 438 295 523

228 T. Škrinjari´c

0.928

1.000

1.000

5

0.259

0.298

0.466

0.347

0.269

0.210

0.627

0.434

0.285

0.342

0.359

0.041

8 MA

9 BEST

10 GRD_weighted

11 3_best

12 Return_GRD

13 Risk_GRD

14 Skew_GRD

15 Kurt_GRD

16 Fuzzy_GRD

17 DEA_GRD

18 MCDM_GRD_1

19 MCDM_GRD_2

0.952 0.937

0.291 −0.450 −0.568

0.198 −0.538 −0.636

0.167

0.721

1.000

0.999

0.986

0.971

0.992

1.000

9

0.994

0.996

0.981

1.000

0.975

0.988

1.000

10

0.989

1.000

11

1.000

12

0.106

0.991

0.981

0.859

0.785

0.141

0.995

0.991

0.856

0.775

0.179

0.990

0.971

0.870

0.840

0.184

0.996

0.987

0.850

0.780

1.000

13

0.115

0.099 −0.228

0.157

0.854

0.837

1.000

15

0.173

0.988

1.000

16

0.151

1.000

17

0.622 −0.622 −0.731 −0.828 −0.829

0.790

0.737

0.915

1.000

14

0.994 −0.703

0.983 −0.737

0.854 −0.477

0.782 −0.262

0.589 −0.870 −0.834 −0.775 −0.802 −0.867

0.525

0.651 −0.430

0.699 −0.356

0.517 −0.286

0.341 −0.378

0.206

8

0.269 −0.724 −0.729 −0.628 −0.725 −0.722

0.687 −0.483

0.656 −0.399

0.586 −0.400

0.691 −0.416

0.750 −0.732 −0.695

0.193

0.956

0.279 −0.465 −0.574

0.163

0.924

0.240 −0.487 −0.588

0.240

0.888

0.343 −0.292 −0.386

0.472

0.900

0.516 −0.101 −0.191

7

0.699 −0.481

0.828 −0.517 −0.712

0.986

0.396 −0.344 −0.468

0.698

0.940

0.239 −0.494 −0.600

0.174

1.000

0.582 −0.391 −0.222 0.934

0.539

0.187 −0.548 −0.642

0.255

6

0.203

1.000

18

1.000

19

Note: Fist row contains numbers instead of names so the table can fit on the page. No 1 refers to first strategy in the first column, EW, the second number (2) refers to RW_1, etc. until the last one (19) – MCDM_GRD_2

0.099

7 MCDM_2

0.506

0.581

5 DEA

0.547

0.675

4

1.000

0.507

4 Min_var

1.000

3

−0.213 −0.233 −0.664 −0.715

0.639

3 RW_2

6 MCDM_1

0.951

2 RW_1

2

0.493 −0.230 −0.361

1.000

1

1 EW

Strategy

Table A.3 Correlations between portfolio values, all strategies

Grey Incidence Analysis as a Tool in Portfolio Selection 229

230

T. Škrinjari´c ADPL

.000 -.004 -.008

ATGR

.005 .000 -.005

.01

.00

-.01

-.010

-.012 -.015 -.010 -.005 .000 .005 .010 .015

-.015 -.010

-.02 -.005

Quantiles of ADGR

.000

.005

.010

.015

DDJH

.04

.02 .01 .00 -.01 -.02

-.02

-.01

Quantiles of ADPL

.00

.01

.02

-.02

.00

-.02

-.01

.00

.01

.02

.03

-.04

Quantiles of ATGR

ERNT

.04

.02

-.04 -.03

Quantiles of AREN

DLKV

.06

ATPL

.03

Quantiles of Normal

.004

AREN .02

Quantiles of Normal

.010

Quantiles of Normal

.015

.008

Quantiles of Normal

Quantiles of Normal

ADGR .012

-.02

.00

HT

.02

.02

.04

.06

.08

Quantiles of ATPL

INGR

.010

.04

-.02

.02

.00

-.02

.01

.00

-.01

Quantiles of Normal

.00

Quantiles of Normal

.02

Quantiles of Normal

Quantiles of Normal

Quantiles of Normal

.04 .005

.000

-.005

.02

.00

-.02

-.04 -.06

-.04 -.02

.00

.02

.04

.06

-.04

-.02

.00

.02

.04

-.03

-.02

-.01

.00

.01

.02

-.010 -.012 -.008 -.004 .000 .004 .008 .012

.03

.04

KRAR

LKPC

LUKA

PODR

.00 -.01

.08

.01 .00 -.01

.06

.04

.00

-.04

-.02

-.03 -.01

.00

.01

.02

.02 .00 -.02

.01

.00

-.01

-.04

-.03 -.02

-.08 -.02

-.01

.00

.01

.02

.03

.04

-.06 -.08

-.04

.00

.04

.08

.12

-.02 -.08

-.04

.00

.04

.08

-.02

-.01

.00

.01

Quantiles of KONL

Quantiles of KRAR

Quantiles of LKPC

Quantiles of LUKA

Quantiles of PODR

RIVP

TPNR

ULPL

VART

ZBB

.04

-.01

-.02 .01

.02

.03

Quantiles of RIVP

.04

.02

.03 .02

.00 -.02 -.04

.00

-.04

.04

.00

-.04

.01 .00 -.01 -.02

-.06 .00

.08

.04

Quantiles of Normal

.00

.08

.02

Quantiles of Normal

.01

Quantiles of Normal

Quantiles of Normal

.02

.08

.02

.04

Quantiles of Normal

.02

Quantiles of Normal

.03

-.01

.00

Quantiles of INGR

KONL

.01

-.02

-.04

Quantiles of HT

.02

-.03

-.08

Quantiles of ERNT

.03

-.04

-.04

Quantiles of DLKV

-.02

Quantiles of Normal

-.02 -.06

Quantiles of DDJH

Quantiles of Normal

-.04

Quantiles of Normal

Quantiles of Normal

-.06

-.08 -.08

-.04

.00

.04

Quantiles of TPNR

.08

-.08 -.08

-.04

.00

.04

Quantiles of ULPL

.08

-.03 -.10

-.05

.00

.05

Quantiles of VART

.10

-.04

-.02

.00

.02

.04

Quantiles of ZBB

Fig. A.1 Quantile plots of stock returns, compared to normal distribution

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Investors’ Heterogeneity and Interactions: Toward New Modeling Tools Souhir Masmoudi and Hela Namouri

1 Introduction The inability of the maximization of the standard expected utility of rational agents in the efficient markets context has triggered the research on behavioral finance to explain some empirical inconsistencies. The issue of rationality is a common element in the efficient market hypothesis and behavioral finance. For the proponents of the efficient market theory, rationality perfectly characterizes the behaviors and expectations of economic agents. I Irrational agents are potentially quickly eliminated because of the losses that their strategies generate due to the intervention of arbitrageurs who converge the price to its fundamental value. Regarding the supporters of behavioral finance, any valid model or theory should consider the irrational part of behavior. Behavioral finance that has become a part of mainstream finance suggests that investors’ psychological biases are important factors that help to better understand financial price evolution. In this context, several researchers have attempted to highlight the behavioral and emotional biases explaining investors’ irrationality (e.g, Barberis and Thaler 2003; Shiller 2000). Several researchers have found that investor sentiment, as part of emotional biases, can explain sustainable misalignments of prices (Fisher and Statman 2003; Brown and Cliff 2004; Chen 2011; Lux 2011; Ni et al. 2015; Namouri et al. 2017 etc.).

S. Masmoudi University of Lyon, Lyon, France COACTIS, UJM-Saint-Etienne, Saint-Etienne, France e-mail: [email protected] H. Namouri () ESDES Ecole Supérieure pour le développement Economique et Social, Lyon, France e-mail: [email protected] © Springer Nature Switzerland AG 2021 C. Zopounidis et al. (eds.), Financial Risk Management and Modeling, Risk, Systems and Decisions, https://doi.org/10.1007/978-3-030-66691-0_7

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It turns out that investors’ heterogeneity, triggered by the sentimental component, creates inertia effects and complex price dynamics1 In this context, alternative approaches attempt to consider the behavioral heterogeneity model to explain the misalignment of prices. The objective of this chapter is to present a critical analysis and a synthesis of three modeling frameworks that are able to reproduce the main characteristics inherent to financial market dynamics while considering the heterogeneity across agents and the interactions among them. First, nonlinear models and, in particular, regime-change processes, are more appropriate for modeling market returns and reproducing the dynamic adjustment of financial prices from fundamentals while reflecting behavioral inertia. Second are the agentbased models and the computational approaches to finance that constitute alternative tools of analysis to analytical models. Agent-based modeling consists of simulating complex systems involving agents and studying the effects that arise from their interactions in an explicit manner. Finally, this tool can be combined with network approaches that govern the interactions between these heterogeneous and connected agents. To the best of our knowledge, this work is the first in this research area. This work is conducted in two steps. In the first step, a literature review shows that behavioral finance permits a better explanation of the reality of financial markets. Durable price deviations from fundamentals, followed by crashes along with heuristics, are factors that have prompted several researchers to introduce more sophisticated models that consider psychological approaches (Kirman 1992, 1993; Brock and Hommes 1998; Black 1986; De Long et al. 1990b; Kirman 2014b). Such models have confirmed that agents’ heterogeneity eludes the traditional representative agent theory. In the second step, we outline some alternative research approaches cited above to better explain recent economic developments that traditional methods were unable to represent. The remainder of this chapter is structured as follows. The second section is largely devoted to a study of the literature concerning investor rationality since it is mainly on this point that behavioral finance, from which market sentiment arises, opposes classical finance. The notions of behavioral heterogeneity and noise traders allow us to address rationality in its collective dimension and to have a slightly different perspective on the phases of euphoria and pessimism. Subsequently, we define market sentiment by emphasizing the diverse approaches and issues posed by the use of the representative investor. We finally introduce the notion of mimicking behavior, with which we can analyze and explain periods of euphoria, followed by financial market crashes. Section 3 presents new modeling tools that are able to reflect the complex dynamics of financial market returns, as well as the interactions between agents, and explains the price deviations by retaining the hypothesis of behavioral heterogeneity. The last section concludes the study.

1 As

Shefrin (2005) documented, “In finance, sentiment is synonymous with error” (p. 213).

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2 The Paradox of Efficiency A “perfect” market is supposed to give the most complete results. This means that there is no arbitrage opportunities. An alternative definition of such a market is therefore a market which is fully efficient. In other words, observed prices are reliable signals for resources allocation. Efficiency can thus be defined as the market’s achievement of its function (Gillet 2006). Accordingly, prices should reflect the information available to all investors. Traditional financial theory is predominantly based on Efficient Market Hypothesis (EMH). This hypothesis primarily postulates that investors are rational, as they aim at maximizing their expected utility, by accounting for risk in the information they have.

2.1 Questioning Rationality According to the assumption of investors’ rationality, any investor is usually able to process the received information at any moment, revise his or her proper choices, and act in such way as to maximize his or her own satisfaction. However, people might tend to apply cognitive shortcuts to make a judgment. It is often this question of cognitive biases that guides the judgment in a predictable way, and sometimes it is a matter of heuristics that fixes it permanently.

2.1.1

Heuristics

Research on this subject dates back to the 1970s and was initially conducted by Tversky and Kahneman (1973, 1975), who identified three heuristics: representativeness,2 availability, and anchoring.. In fact, the heuristics of representativeness bias is about “to categorize a person, object or event in a category if these entities appear as representative of the category” Lemaire (2006). Individuals who mobilize this heuristic usually refer to the trend when it comes to making a judgment in a bid to generalize what is particular (Tversky and Kahneman 1973). They usually rely on stereotypes for the sake of establishing general laws. As a result of representativeness, investors tend to neglect the basic probabilities and follow the similarities observed with other typical or representative events. It is this notion that leads investors to frequently make quick, irrational opinions (Shefrin 2005). Individuals tend to evaluate the occurrence of an uncertain future event based on the degree to which it resembles a recently observed phenomenon. Thus, representativeness bias helps greatly to explain how prices over-react to past 2 Individuals

who mobilize this heuristic usually refer to the trend when it comes to making a judgment in a bid to generalize what is particular.

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consistent information by suggesting to investors that they are in line with long-term trends. In this respect, Fisher and Statman (2003) analyzed several opinion surveys conducted over the period of 1998–2001. Relying on the Gallup surveys conducted on behalf of the Paine Webber index of investors’ optimism, they showed that, during the last months of the Internet bubble, individual investors were aware that there was still sufficient time to make investment decisions. The authors concluded that investors were subject to over-optimism. Thus, investor optimism turns out to be strongly enhanced and powered by representativeness bias prompting them to think that very high past returns bode well for high future returns. Hence, representativeness bias helps indicate that individuals tend to make use of simple elements, easily accessible to memory, in a bid to achieve their estimates. Yet, these estimates turn out to be too biased due to such immediately available information. The availability heuristic documented by Tversky and Kahneman (1975) as the general principle by which individuals assess the probability associated with an event based on the ease with which examples of such an event come to mind. In terms of financial choices, the availability heuristic may occur whenever the uninformed individual proves to use more analogical reasoning than logic reasoning to make judgments. Several empirical studies revealed that the availability heuristic helps greatly influence the financial analyst’s behavior. In this context, Ganzach (2001) concluded that throughout the return assessment of thinly traded stocks, analysts tend to base their judgments on a global attitude. For instance, if stocks are perceived as good, they are judged to have a high return and low risk, whereas if they are perceived as bad, they are judged to have a low return and high risk. Primarily, Lee et al. (2008) discovered that analysts are relatively optimistic about their long-term forecasts of benefits once the economy is perceived to be expanding, and they are relatively pessimistic whenever the economy is noted to be in a state of recession. According to the authors, such results prove to be highly consistent with the availability heuristic, indicating that analysts tend to overweigh the current state of the economy when making forecasts of future profits. Regarding the anchoring, Hirshleifer (2001) defined it as “the phenomenon that people tend to be unduly influenced in their assessment of some quantity by arbitrary quantities mentioned in the statement of the problem, even when the quantities are clearly uninformative”. In any assessment case, the interviewee has been asked to compare his estimates with another figure that can be either serious or totally random. The compared figure is called an anchor. This anchor has been discovered to remarkably affect the interviewee’s choice. The anchoring lies in the observation that the comparison drawn between the interviewee’s reached figure and the questionnaire’s figure proves to influence the study responses. Kahneman and Tversky (1979) considered that the individuals were formulating their estimates by starting from an “initial value and by adjusting it to give their final answer”. Hence, the newly obtained information can be insufficiently taken into account, as it may lead to errors in judgment and puts rationality into question. Moreover, anchoring is considered as an individual over-confidence with regard to previous information.

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Hence, it follows that the three above described heuristics indicate how individuals deal with available information. The responsive action seems biased, representing a primary deviation from the rationality hypothesis of individuals operating in the market. More recently, a better understanding of brain functioning has enabled us to have a new conception of the decision-making process. In this respect, neuroeconomics undertakes to confirm that the human brain functions by making various shortcuts. This can be explained through the process in which several choices are made reflexively.

2.1.2

Neuroeconomics

Neuroeconomics can be defined as the science that studies decision making and economic activities using experimental methods to make a direct observation of brain activity. It helps in providing a better understanding of rationality and the preferences guiding the economic agents’ decisions. The neuroeconomics’ major achievement lies in highlighting the emotions’ crucial role in economic decision making (Bechara and Damasio 2005). Furthermore, Akerlof and Shiller (2010) provide an explanation of the economy relating emotional reasoning through the animal spirit’s elements. They thus contribute in providing a clearer understanding of the limits of rationality. In fact, they defended that individuals pursue their economic interests but they also do it for non-economic reasons. The authors concluded that the individuals’ presumed rationality does not explain the current economic and financial crisis context. Hence, investors do not stand as perfectly rational, their emotions represent an integral part of their decisions. In some situations, emotions can guide judgments or even determine them.

2.2 Price Predictability Relating Anomalies Several empirical studies have predominantly revealed that future returns are discovered to be partly predictable from past returns. Trend movements have characterized both aggregate markets and individual stocks. Hence, two anomalies have been identified; “Momentum” and “reversal,” suggesting investors tend to predominantly under-react to the present information while over-reacting to past information. Culter et al. (1991) found monthly autocorrelation to be significantly positive in the short-term regarding 13 stock markets studied over the period 1960–1988. This result reflects a momentum effect, indicating that performance is continuing in the short run. Jegadeesh and Titman (1993) also showed a momentum effect regarding US stocks over 13 to 12-month periods during 1965–1989. The authors showed that 25% of the excess return enjoyed by past winners appears to occur during the

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quarterly earnings announcement periods. Furthermore, the momentum effect is more important for securities with extreme performance. On comparing the NYSE listed stock returns over the period 1926–1982, De Bondt and Thaler (1985) showed that, in the long-term, winning stocks recorded a potential decline. They also found that the correction of past over-reaction proves to be rather sensitive for losers and that this phenomenon would often occur especially during the month of January. So, Jegadeesh and Titman (1993) and DeBondt and Thaler (1985) suggested there is primarily a persistence of abnormal stock performance, subsequently followed by a reversal of this past trend. In the same context, Lee and Swaminathan (2000) concluded that regarding the period 1965–1995, the winning stocks over 6 months continued their outperformance for almost 1–3 years before underperforming. The reversal of long-term performances indicates that the momentum effect, reflecting the investors’ underreaction, would eventually lead to their over-reaction. More recently, analyzing the profitability of momentum and reversal strategies over the period 1964–2008, Alwathainani (2012) constructed the winners’ and losers’ portfolios as follows: While the first set involves financial shaving achieved the best monthly performance, the second consists of financials that have recorded poor performance over the past 2–4 months. The pursued strategy consists of buying winning financials and selling losing ones, while maintaining this position over a holding period of 1–5 years, whose performance is measured by the yearly average monthly return. Such a strategy is likely to generate positive abnormal returns over a 1-year holding period and negative returns over the remaining 4 years. Such findings confirm the short-term momentum effect as well as the long-term reversal effect. It turns out that stock prices do not really follow a random path, given the observation that returns seem to be positively correlated in the short term and negatively correlated in the long term. Strongly related to the investors’ psychological patterns, this cyclical development seems hardly compatible with the rationality assumption, which is also called into question by the heuristics and neuroeconomics. In compliance with market conditions, investors usually undergo various emotional states. Thus, emotions turn out to play a particularly important role in the decisionmaking process whenever basic crucial information seems to be lacking. It thus appears necessary to quantify the investors’ emotions, which is the challenge of behavioral finance and market sentiment.

3 Behavioral Heterogeneity in Financial Markets Behavioral finance can be defined as the stream that appeals to the results of work in psychology and sociology and applies them to finance to develop more precise theories on investor behavior. Several definitions have been attributed to behavioral finance: Mangot (2004) stated this stream is the product of collaboration between psychology and finance since it takes into consideration the influence of

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the individuals’ feelings about their decisions, thus allowing a better understanding of financial markets. According to Tadjeddine (2013) “The behavioral finance trend proposes to reconsider the behavioral hypotheses by abandoning the axioms of the rational decision and the hypothesis of the market efficiency”. Among the channels of behavioral heterogeneity appears investor sentiment (Chiarella et al. (2011), He and Li (2008), He and Shi (2012)). Emotions can remarkably influence individual behavior: In fact the same information is differently interpreted by heterogeneous investors (optimistic, pessimistic, overconfident). the sentiment impacts the expectation and thus the decisions of investors. The literature highlights not only that investor sentiment might affect stock market dynamics but also that investor sentiment changes according to the investors who dominate the market. Accordingly, the same information is differently interpreted by each investor (Daniel et al. 1998). the sentiment risk thus impacts the expectations and the decisions of investors. It follows that the investor sentiment is the main source of investors’ heterogeneity (Barberis et al. 1998; Namouri et al. 2017). In this context, several studies have emphasized that investor sentiment can best describe the reality of these complex financial markets (Lee et al. 2002; Qiang and Shu-e 2009; Schmeling 2009; Sheu et al. 2009; Chung et al. 2012; Corredor et al. 2013; Jawadi et al. 2018).

3.1 Emotions, Moods, and Decisions Unlike classical theory, several psychological studies have shown that the individual is far from being placid. Investors’ decisions are often biased due to their predominating emotions and false reasoning. They often make systematic errors stemming from their limited mental capacity as human beings. Emotions have an important place in the reasoning process. Individuals are able to make judgments and decisions on the basis of the mental images with which they associate positive or negative feelings. Finucane et al. (2000) described reasoning based on emotions as an “affect heuristic”. They conducted an experiment to determine how the risks or benefits related to information manipulation influence perception, despite the complete absence of any logical connection between the provided information and the second variable. The heuristic model’s predictions were confirmed with respect to the entirety of situations. New information has been discovered to change the perception of non-manipulated variables in a direction opposite to the manipulated variable’s direction. Such a finding supports the idea that risk judgments are partially and jointly determined by a global effective evaluation. Consequently, the shares of companies enjoying a positive image (a glamour field) are more likely to be bought than those of negatively perceived ones. It is this overall positive feeling aroused among investors that causes them to

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underestimate the risk and overestimate the expected return. Emotional evaluation might take precedence over cognitive assessment if the investor lacks experience. Experienced investors are more cognitively able to control their behaviors. Emotions are dependent on the investor’s successes and failures, along with his or her role in such situations. For every emotion, there is a reflex response allowing the investor to respond quickly to each situation, while setting the goal for improving such a situation. Loewenstein et al. (2001) suggested that cognitive assessments of risk and perceived risk are divergent. The cognitive assessment process is most often based on probabilities relevant to different scenarios, as well as on the results emanating from each scenario. Affective perception of risk is mainly focused on results since they can be imagined more easily. The more extreme that possible outcomes seem to the individual, the more automatic that his or her responses will be, regardless of the actual probabilities attached to such extreme situations. Loewenstein (2000) revealed that emotions experienced during the decision-making process tend to remarkably influence investor behavior in the sense that they are different from those dictated by cost constraints or long-term benefits. It seems reasonable, therefore, to assume that the investor’s emotions can influence the asset price setting process. According to Dowling and Lucey (2005), two areas have proved to highlight the impact of sentiments on investors’ decisions. The first one covers the “mood-misattribution effect.” This research undertakes to study the impact of such environmental factors as weather, human body biorhythms, and social factors on financial assets’ returns. This area is based on psychological research works advancing the idea that people decisions are partly guided by their sentiments, implying that sentiments induced by factors such as weather influence even complex decisions, including risks and uncertainties. Concerning the second research area, it emphasizes the image’s impact on the decision-making process; the argument put forward by this research trend concludes that the image of a stock affects investors’ emotions and, therefore, their behaviors. As general emotional states, moods influence financial decisions by skewing anticipations. In general, a good mood is discovered to yield better results since it allows for better understanding of information and better resolution of problems. A positive mood is likely to induce an individual’s optimism about the future. As a result, good humor would enhance acting as a buyer and reduce risks. Accordingly, moods would kindle the effect of changing expectations as regards returns and risks. It is widely documented that good weather usually helps people to enjoy a good mood. Therefore, if moods help to encourage investors to become buyers, sunny days should then be distinguished by higher returns, which was confirmed by Hirshleifer and Shumway (2003), who, on investigating 26 stock markets, concluded that the better that the weather is, the better that the returns will be. As Rick and Loewenstein (2008) documented, “bad weather should lead to negative emotions which should in turn lead to negative price movements since negative emotions can exert conflicting effects on risk-taking”. With weekends, days off also put investors in good moods, thus helping to increase market returns. Several empirical studies have confirmed that markets

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outperform historical averages during the days preceding vacations (Ariel 1990; Frieder and Subrahmanyam 2004). This outcome is called the holidays effect. The returns observed with respect to American markets revealed that this effect is rather remarkable on Christmas Eve. Other researchers, such as Tetlock (2007), have investigated the mass media’s linguistics and found that media pessimism predicts price decreases. Tetlock et al. (2008) further showed that earnings and stock returns are predicted by the proportions of negative words used in news stories. Another non-economic phenomenon affecting investor decisions is sports scores. In this context, Edmans et al. (2007) used football results as a mood variable to investigate the impact of an international football match on 39 national indices during the day after a game. The empirical study showed that there exists a positive “abnormal return” of 5 basis points for the winning countries, along with a significantly higher loss of 8.4 basis points for the losing countries. It follows that investors’ decisions are often biased by their erroneous feelings and reasoning; they often make systematic errors that find their origins in the limited mental capacities of human beings.

3.2 The Role of Noise Traders The concept of the investor sentiment is based on the behavioral model as considered by De Long et al. (1990a) or the “DSSW model”, introducing the “noise trader risk” or what is called investor sentiment. In fact, De Long et al. (1990a) developed a model whereby the noise traders’ integration within the entirety of acting investors could be maintained. The model involves two types of investors. On the one hand, it includes noise traders and, on the other, arbitrageurs or sophisticated investors who are highly aware of the stocks’ fundamental value. The DSSW model revealed that the noise traders’ behaviors predominantly based on their sentiment has an impact on stock returns while limiting the arbitrageurs’ actions. It is now possible to model such behaviors while integrating them it into the market movements’ general review. This suggests a growing interest placed on the investor sentiment related area and the relevant works undertaken to investigate the stock market dynamics field. Moreover, noise traders don’t withhold or make use of all relevant and available information likely to generate potential benefits. According to Black (1986), “Noise trading is trading on noise as if it were information. People are willing to trade even though from an objective point view they would be better off not trading. Perhaps, they think the noise they are trading is information. Or perhaps, they just like to trade”. According to Daniel et al. (1998), all investors could have the same information but use it differently, mainly due to the over-confidence of informed investors: “Uninformed individuals can infer all the signals perfectly from market prices. The uninformed end up with the same information as the informed traders but use it differently as they are not overconfident about these signals”.

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Efficiency supporters tend to defend the idea that noise traders should be discarded rather rapidly. For instance, Fama (1965) argued that noise traders must be excluded mainly because they act wrongly with arbitrageurs who are most often right since they are well informed and have correct information. Hence, these arbitrageurs would eliminate uninformed investors. Nevertheless, this reasoning will not hold unless the noise traders performed a small part of the transactions, and their action was not overriding. Similarly, De Long et al. (1990a) argued that arbitrageurs are unable to take sufficient risks to rule out noise traders. Their risk-aversion causes the removing of these noise traders take longer. They added that arbitrageurs are hesitant to sell or buy whenever noise traders buy or sell in a bullish or bearish market since they might not achieve the maximum gain by buying or selling too early. Furthermore, arbitrageurs often seem unable to predict the noise traders’ reactions since noise traders do not often rely on effectively relevant information. In other words, noise traders can lead prices to retain their bullish or bearish nature over longer periods. However, it is equally likely that their opinion would suddenly veer according to their sentiments. Sentiments’ disruptive nature is likely to produce an additional risk relevant to their exchanged assets. The noise trader risk or sentiment risk renders assets riskier. Accordingly, arbitrageurs would certainly require a higher risk premium to invest in assets that noise traders made too risky. Kogan et al. (2006) examined the link between long-run survival of the noise traders and their influence on asset prices. They noted that noise traders can significantly impact asset prices even when their health goes to zero. These results are similar to that documented by Mendel and Shleifer (2012), who also demonstrated that noise traders have an effect on equilibrium price regardless of their size in the market. Consequently, the noise trading approach seems to highlight that ignorant strategies help to influence markets and are not canceled out automatically. Noise traders might dominate the market in matters of transaction volume, relying heavily on the illusion that they are acting rationally. Thus, noise traders could generate higher returns than those achieved by rational investors (De Long et al. 1990a). Correspondingly, arbitrage might be unable to absorb all of the demand-related shocks in so far as the noise traders’ sentiment unpredictability might restrict the shares of arbitrageurs to take action against the noise traders’ devised strategies. As a result, asset prices might diverge permanently from the fundamental value. As Zhang (2008) indicated, “the noise trader model posits that if there are limits to arbitrage and investor beliefs are correlated, then noise unrelated to fundamentals, such as sentiment, may lead asset prices to deviate from what is expected from the benchmark of market efficiency”.

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3.3 Investor Sentiment and Financial Returns Dynamics The investor sentiment concept serves mainly to depict how investors form their expectations, and it attempts to explain their reactions. In this respect, accessible and intuitive as it might seem, the subject constitutes a complex concept that seems to be distinctively defined. In this respect, Broihanne et al. (2004) defined investor sentiment as the set of behavioral phenomena likely to help explain how investors form beliefs on the basis of which they evaluate assets. Zouaoui (2008) confirmed this definition and added, “the investor sentiment represents investor expectations that are not justified by the fundamentals”. Regarding Baker and Wurgler (2007), they defined the sentiment as “a belief about future cash flows and investment risks that is not justified by the facts at hand”. According to Zhang (2008), “sentiment corresponds to erroneous beliefs that investors have against some kind of objective benchmark”. Investor sentiment can be interpreted as being the variable that helps to generate investor evaluation errors, along with their anticipation of financial markets, emanating from the subjective aspects involved in asset evaluation. Although there should be only a single referential objective price for each asset, a certain subjectivity also appears to prevail in attempting to estimate such prices. Hirose et al. (2009) applied margin trading to investigate the Japanese market by studying the link binding sentiments and returns. They found that variations in the margin buying volume are positively correlated with the previous period’s registered returns. Moreover, they concluded that the margin purchases’ volume increases whenever the market expanded in the recent past and the concerned company’s shares registered a poor performance. Qiang and Shu-e (2009) revised the DDSW model in the Chinese market over May 1998 – December 2006. Using a generalized autoregressive conditional heteroskedasticity in mean model (GARCH-M), they found a significant investor sentiment impact on stock prices. They also noted that the positive impact of change in investor sentiment on stock prices proves to be stronger than that of a negative one. Sheu et al. (2009) studied the causal link between daily sentiments and returns in the Taiwan stock market over the period 2003–2006. They used a threshold model to account for different market states. Their results further confirmed that noise traders affect market behavior. The authors found that sentiment, measured by the ARMS index, is an important indicator once the market is more bearish. Yet, they noted that when sentiment is measured by the put-call trading volume and option volatility index, its effect is noticed once the market more bullish. In line with this, Lux (2011) examined the German stock market and found that investor sentiment might forecast returns; however, the impact of sentiment decreases during large market movement periods. ¨ Daszy´nska-Zygadło et al. (2014) studied the nexus between investor moods and excess market returns in eight emerging markets. They noted a positive contemporaneous relationship between excess returns and investor sentiment only

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in Brazil and China. They also found that the impact of the change in investor sentiment on excess returns is stronger during periods of negative moods than that of positive moods in Brazil, China, India, and Mexico. Focusing on Chinese stock market from January 2005 to September 2011, Ni et al. (2015) used a panel quantile regression model to examine the effect of investor sentiment on returns. They found a significant asymmetric impact of investor sentiment on stock returns lasting from 1 to 24 months. While starting from the limits of individual rationality, these studies highlight that investor sentiment can best describe the reality of financial markets. Other studies on behavioral finance take into account rationality in its collective dimension and show that humans are influenced by their environment. Indeed, some investors are not perfectly rational and their interventions are correlated. The notion of mimicking behavior allows thus to handle the interaction of irrational behavior and to have a slightly different look at the phases of euphoria followed by financial market crashes.

3.4 Mimicking Behavior Imitation is an attitude of humans that is frequently observed in everyday decision making and represents an aspect of social life. Everyone practices imitation to some extent, without even being aware that they are doing so (to find a dentist, a plumber, to buy a new car, a computer, etc.). Robert Shiller (1984) emphasized the idea that imitation is a human behavior widespread in social life and more particularly in financial markets, as already observed by Poincaré (1908), who argued that people have an intrinsic tendency to behave like sheep. It has only been recently that the focus of economists has moved toward imitation. However, the study of imitation has a long history. Already in 1952, Asch and other scientists and psychologists emphasized this point. For social and human sciences, mimicking behavior is described as a voluntary or unconscious imitation of behavioral models with which we attempt to empathize or identify, and it can be thought of as a process of adaptation to the standards of the group.3 According to Mannoni (1994), the behavior of individuals in crowds derives from several psychological mechanisms intrinsic to the crowd, on the basis of the contributions of (Freud 1921; Le Bon 1895; Miller and Dollard 1941; Moscovici 1985). These mechanisms have shown that, in crowds, individuals develop behaviors that they would not have contemplated were they alone. This finding allows us to infer that the characteristics of collective behavior differ markedly from those of individual behavior. In this respect, Kirman (2014a) asserted that individuals exemplified by ants “produce aggregate phenomena by their interaction that are very different from

3 Grawitz

(2004), Lexique des sciences sociales, 2004, 8ème édition, Dalloz, p.276.

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those that could be anticipated by studying individuals in isolation”. In this sense, individuals can be pushed to develop herd behavior and their decisions to be based on imitation. While imitating success, as ants follow the crowd to food sources, might be perfectly rational, it can also be the case that the mimetic behaviors present in financial markets can lead to excessive behavioral biases, ranging from simple periods of rumors to periods of mass hysteria that cause speculative booms. Empirical studies have detected herd behavior on the part of investors in financial markets with a more pronounced tendency for this behavior to occur among those operating in emerging financial markets (Chang et al. 2000; Wang 2008). When the information that people seek is contained in others’ choices, imitation can represent completely rational behavior. Theoretical works by Orléan (1989a, b, 1994) and Bikhchandani et al. (1992) have contributed to the reintegration of imitation as a legitimate study in finance. By incorporating these perspectives into their decision making, agents can decide in line with an opinion or a movement of opinion, rather than simply pursuing analyses of situations and values. Therefore, the explosion in prices is inconsistent with what traditional theory would suggest. Difficulties in interpreting and understanding economic and financial information induce people to imitate each other with the objective of homogenizing their behaviors. Some investors might also consider that it is too costly to access the available information on the market, so they prefer to rely on the decisions expressed by some leaders in their profession or on the studies approved by their superiors. In this context, Trichet (2001) noted that “some operators have come to the conclusion that it is better to be wrong along with everybody else, rather than take the risk of being right, or wrong, alone”, reflecting an earlier idea of Keynes. Ideas revolving around mimetic behavior accept the concept that economic agents are not in complete command of information about the market and prices. They are primarily interlinked with others. Their anticipation is the result of the evaluation of the anticipations of other agents in the economy and of the evaluation of their potential impacts on them. The existence of such behavior sometimes creates a significant departure of asset prices from what might be considered “fundamentals”. If one accepts that the term “fundamental” has a real meaning, then it is a source of inefficiency and joint increases of risk and fragility in financial markets. Since mimetic behavior can lead to erroneous assessments of assets, studying the extent to which it is present in transactions on financial markets could help to explain several events (deviations of asset prices from fundamentals, excessive volatility, extreme values, etc.). Mimicking behavior is at the root of phases of price increases and also of periods of crisis, when asset price bubbles burst. The anticipation of a broad sell-off on the market generates a contagion effect and a financial panic. This information contagion is self-reinforcing in periods of crisis, as the expected decrease in prices leads to a generalized sale, which in turn, pushes prices lower. To illustrate this point, Keynes (1936) used the famous beauty contest analogy, comparing it to the functioning of financial markets. This contest consists of its participants electing a woman among a hundred photographs of faces. The winner is the one whose vote was the closest to the average choice. Therefore, the goal is not to vote for

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the woman whom we find the most beautiful but the woman who would be most likely to obtain the largest number of votes, and everyone thinks this way. This analogy is what is referred to as the “common knowledge” problem, and there are infinite levels of reasoning. In this sort of situation, agents’ utility depends on the decisions of other agents. Everyone forms his or her own expectations in terms of what others anticipate; while others do the same, indicating that their decisions are mutually reinforcing. The final winner is then potentially different from the person who would have been designated in the case of voting for the most beautiful woman by each of the judges. This example aims to demonstrate that the asset price does not depend on fundamentals but is directly tied to the perceptions and expectations of the market participants. Contagion behavior occurs when traders attempt to predict, as in Keynes’ beauty contest, “what average opinion expects average opinion to be”. This principle is also related to Kirman’s model of opinion formation. Thus, it is more important to predict the future value of the asset generated endogenously by the market than to find its fundamental value, considered exogenous to the market. Although mimetic behavior has been widely discussed in the academic literature, it is relatively difficult to empirically validate models of mimetic behavior since this behavior cannot be tested directly.In summary, the presence of participants who exhibit mimetic behavior, even if not irrational from their point of view, can lead to substantial deviations of prices from what are often considered to be their “fundamental” values. This deviation, in turn, contributes to the fragility of financial markets and confirms the deficiency of traditional theory. In light of all of the above, it is reasonable to believe that financial markets are considered complex systems in which several competing investment strategies meet (Kirman 2017). It would be impossible to control all of their components and the relations that exist between them at a given time. Indeed, everyone can observe the ubiquity of complex systems composed of interacting parts in the real world. Complexity is characterized by aggregate phenomena, which are the result of the interaction between a large number of components in the system. In fact, when it is no longer possible to completely divide the system into independent parts, complexity takes over. As we have observed, the resulting aggregate behavior emerges from the complicated interaction among components at the micro-level. The interdependence of its components is reflected in a non-linear interaction network, which is the source of the complexity. Aggregate features are more than only the sum or average of the components of the system, such as cells, ants, social networks, internet or economic and financial systems.

4 New Modeling Tools To be able to investigate financial markets, it is essential to develop models of them that reflect their complex aspects. We should integrate the behavioral complexity of investors into these models. In a first time, we present non-linear models and, in

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particular, regime-change processes that are most appropriate for modeling market returns empirically and reproducing the dynamic adjustment of financial prices from fundamentals. In a second time, we introduce agent-based modelling that constitute alternative tool of analysis to analytical models. This tool can be combined with network approach that governs the interactions between agents. The advantage of these approaches is that they allow one to control the behavioral aspects of investors and hence to study the effects of various behavioral assumptions in complex financial markets. These models allow us to better understand the functioning of financial markets.

4.1 Switching Transition Regression Models The use of linear models is linked to restrictive assumptions (the assumption of the absence of transaction costs, the homogeneity of investors’ anticipations, and information symmetry), implying a rapid and symmetric adjustment of prices toward fundamentals, with a constant speed of convergence. However, the presence of rigidities in financialmarkets often prevents prices from adjusting in a continuous and linear way. According to Franses and Van Dijk (2000), the asymmetry characterizing most market data renders linear price adjustment unlikely. Thus, economically, linearity has been questioned by the presence of transaction costs (Anderson 1997), mimicking behavior (Orléan 1990, 1992), behavioral heterogeneity of market participants (De Grauwe and Grimaldi 2005) and information asymmetry (Artus 1995). In this section, we focus on the heterogeneity of investors induced by investor sentiment as a source of nonlinearity. In fact, most linear models assume the existence of a representative agent and do not consider investor psychology or market sentiment. Actually, investors have heterogeneous expectations and can switch from one regime to another while creating interpersonal interaction. Thus, the emotional component (sentiment) affects agents’ reactions after the arrival of new information, also causing price-adjustment delays, which cannot be represented by simple linear models. In fact, many studies, such as Chung et al. (2012) and Ni et al. (2015), have confirmed the presence of asymmetry in the link between investor sentiment and stock market returns. Moreover, Boswijk et al. (2007) showed the persistence of asset price deviations. They focused on the processes bringing these deviations to equilibrium in the presence of operators with heterogeneous expectations. They concluded the superiority of non-linear models toward linear models to consider such market friction (Chen 2011; Chung et al. 2012). In the literature, many channels have been explored to model nonlinear dynamics of financial markets such as deterministic statistics, bifurcations, fractals (Shiryaev 1999). We can distinguish between two types of models: nonlinear variance models and nonlinear mean models, including regime-switching models. Models that allow for state-dependent or regime-switching behavior have been most popular over the

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last few years. In this context, several theoretical and empirical studies using regimeswitching models have highlighted not only that investor sentiment might affect financial market dynamics but also that investor sentiment changes according to the investors who dominate the market (arbitrageurs or noise traders), which might be presented by regimes. We can distinguish between two main classes of models existing in time series: Markov switching models and threshold models. In the context of Markov models, the transition mechanism is based on an unobservable state variable, which is supposed to follow a Markov chain. At each period, there is therefore a certain probability of belonging to a given regime. In contrast, for threshold models, the transition mechanism is carried out using an observable transition variable, a threshold, and a transition function. A smooth transition model has the advantage of containing a continuum of regimes. Then, belonging to a regime depends on the transition function and on the distance between the threshold and the transition variable. The main distinctive special feature of such model is to consider smooth transition between regimes which enable investors to switch smoothly between regimes while taking behavioral inertia into account. Indeed, this smoothing effect can be justified by the fact that investors do not adjust immediately to the new regime level but gradually converge. Moreover, some studies have shown the superiority of smooth transition autoregressive (STAR) models toward the Markov switching models (Phillips 1991; Sarantis 1999; Deschamps 2008). STAR models (smooth transition autoregressive models) include only lagged endogenous variables as explanatory variables, whereas the introduction of other exogenous variables in the STAR model defines a model called the STR model (smooth transition regression), developed by Granger and Teräsvirta (1997). Formally, a two-regime STR model corresponds to: yt = α Wt + θ Wt F (st , γ, c) + ut

(1)

γ > 0, where ut →N(0,σ2 ), i = 0,1, γ > 0,ut → N(0, σ2 ),  i = 0, 1, ∼  ∼ 1, Wt and Wt = Wt is a vector of p explanatory variables, Wt =    1, x1t , x2t , , x3t , . . . ., xp,t , α = (α0 , α1 , α2 , . . . . . . αp ) denotes the coefficients  of the first part, θ = (θ0 , θ1 , θ2 , . . . . . . θp ) denotes the parameters of the second part, and F is the transition function, which is continuous and ranges between 0 and 1. This model depends on the transition variablest , which can take several forms: either a lagged dependent variable yt − d , an exogenous variable xt or also a time variable. This function also depends on the threshold value c, which delimits two possible regimes, and the parameter γ, which measures the speed between regimes. In this regard, the higher that γ is, the fast that the transition; however, if γ = 0, the model becomes linear.

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In fact, the function F could be an exponential function or a logistic function. The models obtained are called, respectively, ESTR (exponential STR) and LSTR (logistic STR). An exponential function is defined as: ⎧ ⎛ ⎞2 ⎫ ⎪ ⎪ ⎪ ⎪ ⎨ ⎜ ⎟ ⎬ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ F ⎝ s γ, c⎠ = 1 − exp −γ⎝s − c⎠ γ > 0 t , ⎪ ⎪ ⎪ ⎪ ⎭ ⎩ t ⎛

⎞

(2)

The exponential function tends to be canceled for values of st close to the threshold c, whereas it is equal to 1 when st departs from c from below, rather than from above. There will be two external regimes of the same dynamics that correspond to the phases of expansion and recession and an intermediate regime. In other words, the transition from a phase of expansion or recession toward the central regime occurs in the same way. At the same time, a logistic function corresponds to: ⎞⎞⎫−1 ⎪ ⎪ ⎜ ⎜ ⎜ ⎟⎟⎬ ⎟ ⎟ = 1 + exp ⎜−γ ⎜s − c⎟⎟ F⎜ s γ, c ⎝ , ⎝ ⎝ t ⎠⎠⎪ γ > 0 ⎠ ⎪ ⎪ ⎪ ⎭ ⎩ t ⎛

⎞

⎧ ⎪ ⎪ ⎨

⎛

⎛

(3)

The logistic function is canceled when st moves away from c and tends toward 1 when the transition variable is higher than c. The logistic function defines two regimes associated with high and low values of st relative to the threshold. The steps of specification, estimation and validation of STR process were described by Teräsvirta (1994), while their recent developments were presented by Van Dijk et al. (2002). The use of investor sentiment as a threshold variable would enable switching to be endogenously governed by changes and shocks affecting investor sentiment. Moreover, the explicit consideration in this modeling of behavioral heterogeneity leads to a more realistic presentation. STR models allow for refining the study of financial market dynamics through the detection of regimes with smooth transitions. This modeling is interesting because market returns series are often characterized by dynamics with abrupt changes. To refine their analysis of financial market dynamics, Namouri et al. (2017) united the advantages of panel data and those of nonlinear models. The authors employed the Panel Smooth Transition Regression (PSTR) model proposed by González et al. (2005). This regime-switching model with smooth transitions in panel data allows for nonlinear behavior of the price adjustment process with respect to the equilibrium value to be modeled, while nonlinearity and heterogeneity are considered. They found, on the one hand, that nonlinearity can be generated by three regimes and, on the other hand, that the impact of investor sentiment depends on the regime being considered. Their results suggested the existence of a normal regime

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in which investor sentiment is not significant (arbitrageurs’ regimes). However, they emphasized two other regimes dominated by noise traders (optimism and overoptimism). Jawadi et al. (2018) analyzed the impact of heterogeneity of agents before and after the subprime crisis in time series, using the smooth transition regression (STR) model developed by Granger and Teräsvirta (1997). Their results showed that smooth transition threshold models can provide a relevant alternative to linearity and can better explain the exposure of stock market returns to investor sentiment. Additionally, they found that stock market returns dynamics can be presented by two regimes (arbitrageurs and noise traders), and they highlighted that the sentiment effect depends on the country, as well as on the regime under consideration. From an empirical point of view, STR models are therefore more appropriate than standard linear models to describe the dynamics of financial market series and to consider their asymmetry. However, agent based models have proven their usefulness and relevance in helping filling the theoretical void raised by policymakers in crisis periods. The following section explains this modeling approach in more details.

4.2 Agent-Based Modeling Agent-based modeling is a new and, still in some disciplines, unfamiliar approach that consists of simulating complex systems involving heterogeneous and connected agents. However, several fields are increasingly using this approach, which is often called the “third way” of doing science (Axelrod and Tesfatsion 2006). Agent-based modeling has become a frequently used approach to modeling and simulating financial markets. For survey papers on agent-based financial market models, see (Bookstaber and Kirman 2018; Lux 2018; Chiarella et al. 2009a; Chen et al. 2012; Lux 2009; Hommes 2006; LeBaron 2006). This approach represents agents and their behaviors in an explicit way and studies the effects that arise from their interactions. The aim of this approach is to overcome the weaknesses of traditional theories in describing and explaining anomalies in financial markets. Indeed, agent-based model dynamics attempt to replicate, at least in part, the dynamics of today’s financial markets. Being able to replicate the stylized facts of financial markets can be considered a form of empirical validation (Westerhoff and Reitz (2003)). Their designs are in compliance with economic reality. Agents use heuristic and competing trading strategies, such as chartist and fundamentalist trading methods. This distinction is based on the observation that it is not possible to explain some instabilities of asset prices by an approach entirely based on market “fundamentals”. Agents also interact directly with each other and can influence the actions of others. Thus, agent-based models and heterogeneous agent models can provide insight into the forces driving the stylized facts characterizing financial markets and help to provide explanations for financial instability. This is precisely what Jean Claude

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Trichet, then president of European Central Bank and others in policy making positions have suggested. First, we have to think about how to characterise the homo economicus at the heart of any model. The atomistic, optimising agents underling existing models do not capture behaviour during a crisis period. We need to deal better with heterogeneity across agents and the interaction among those heterogeneous agents. We need to entertain alternative motivations for economic choices. Behavioural economics draws on psychology to explain decisions made in crisis circumstances. Agent-based modelling dispenses with the optimisation assumption and allows for more complex interactions between agents. Such approaches are worthy for our attention. Jean-Claude Trichet (2010)

We should build models of financial markets as complex systems of interacting agents. Using computational models enables us incorporate the heterogeneity across agents and to capture the collective dynamic that emerges from their interactions. Networks that govern those interactions are the subject of what follows in the next sub-section.

4.3 Networks “Social networks permeate our social and economic lives. They play a central role in the transmission of information about job opportunities and are critical to the trade of many goods and services” (Jackson (2008)). In financial markets, the behavior of an investor can be heavily influenced by the behavior of his or her neighbors. Investors form their demands based on the strategy that they use to forecast future prices; but agents are linked to others in a network. Because of the interaction and communication between agents, these strategies can change. The result is that they copy one another’s investment choices. That networks play a significant role in agents’ behavior and interactions in financial markets and thus in replicating the stylized facts of financial time series has been recognized in the literature (Alfarano and Milakovi´c 2008). Considerable work regarding financial networks has shown that the structure of social networks that connect traders has a relevant impact on information dissemination and aggregation and therefore on the corresponding price dynamics (Hein et al. 2012; Hoffmann and Jager 2005; Ladley and Bullock 2008; Panchenko et al. 2013). Interdisciplinary statistical physicists have also influenced this literature by their contributions: Cont and Bouchaud (2000) and Iori (2002), among others, considered network structures in their financial market models. An interactive network is any set of entities that interact individually with each other. These networks can be very large and can include such different networks as social networks, internet networks, protein networks, business networks and traders’ networks, among others. Networks are modeled using graphs. A node represents a social entity and can be a person, a cell, a device, a business, an investor, and so on. An edge represents a link between two nodes having a social interaction with each

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other. In a network, the degree of a node is the number of edges linking this node to other nodes. Whereas local interactions are usually well defined, the aggregate result from these interactions is still poorly understood. Kirman (2010) argued that. The outcome of the process through which the market organises itself would have been impossible to predict by looking at the individuals in isolation and is clearly linked to the structure of the graph of relations which emerges [ . . . ] When we consider this interaction, we have also to look at the structure of that interaction. In other words, the network that links people together can have an important impact on the outcome of the whole system.

Until the late 1990s, network analysis was based on the random graphs model defined in the 1950s by Erdos and Reyni. Two new models were proposed in the late 1990s and aimed to change the study of networks and even more ambitiously to create a science of networks. In what follows, we provide a brief presentation of each of these network structures. • Random graphs Random graphs were introduced by Erdos and Renyi (1959). The Erdos-Renyi model assumes that the existence of each edge in the network is independent of the others, and each edge can exist with probability p. In this case, the degrees of the vertices follow a Poisson distribution. However, it has been shown that the distribution of the degrees of many networks in everyday life seems far from a Poisson low; for example, regarding the internet, Faloutsos and Faloutsos (1999). Newman (2003) showed how the model of Erdos-Renyi could be generalized to the case of specific degree distributions. He considered the following procedure to generate the random graph. Each node has a number of “stubs” (ends of edges emerging from this node). Pairs of these stubs are then chosen randomly and joined together to form complete edges. When all “stubs” are used, the graph that results is a random graph with the intended degree sequence. There are several different ways of generating each network because there are many possible permutations of the stubs. Basically, the bottom line is that there are many models of what can be characterized as random graphs. • The small world network Milgram (1967) performed an experiment that provided the basis for the theory of “six degrees of separation”. He aimed to demonstrate that any person could easily be linked to another by a chain of social relationships. The purpose was to show how small our world is. Milgram’s experiment was run as follows. A stockbroker from Boston was chosen as a target individual. Three groups of hundreds of people were randomly selected. The first group was composed of residents of Boston chosen at random. The second group was composed of residents of Nebraska chosen at random, and the third group was composed of residents of Nebraska but who were also shareholders. Each individual received a file including a description of the experiment and the profession and the place of residence of the target individual. Each participant was asked to send this file by mail, either directly to the target

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Fig. 1 Frequency of the lengths of the completed chains. The number of intermediaries required to link starters and target define the “chain length”. The mean of the distribution is 5.2 links. Adapted from Milgram (1967)

individual if he or she personally knew him or to a close acquaintance who was more likely to know the target individual. “If you know the target person on a personal basis, mail this folder directly to him (her). Do this only if you have previously met the target person and know each other on a first name basis. If you do not know the target person on a personal basis, do not try to contact him directly. Instead, mail this folder to a personal acquaintance who is more likely than you to know the target person. You may send the booklet on to a friend, relative, or acquaintance, but it must be someone you know personally.4 ” Of the 296 starting persons, 217 participated in the experiment; 64 of the files reached the target. The completed chains had variable lengths. The average length was 5.2 links, as shown in Fig. 1. This finding led Milgram to conclude that there are six degrees of separation between any pair of individuals. In 1998, Watts and Strogatz (1998) reversed this approach. Their question was not whether a network is “a small world” but was to convert a network into a small world. The method that they used to generate the graph was as follows. They considered a random rewiring method. They started from a regular ring lattice of N

4 (Milgram

1967) The small-world problem, Psychology Today 1967.

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Fig. 2 Normalized clustering coefficient and average path length as functions of the rewiring probability p. N = 1000 and k = 10. Adapted from (Watts and Strogatz 1998)

* vertices. Each node was connected to k 2 nodes on each side by undirected edges, as shown in Fig. 3. Then, they rewired each edge randomly with probability p. For p = 0, the graph is regular. The degree of disorder increases with increasing p until, for p = 1,all of the edges are rewired randomly, and the network becomes random. The graph represents a small-world network for intermediate values of p (0 < p < 1). Watts and Strogatz (1998) introduced the formal notion of a clustering coefficient, which “measures the cliquishness of a typical neighborhood”, or in other words, it expresses how well the neighbors of a node i are interconnected. It is the ratio of the number of links between the neighbors of i and the maximum number of links that could exist between the neighbours of i. The clustering coefficient of agent i is i defined as Ci = ki (k2 ie−1) in an undirected network and Ci = ki (keii−1) in a directed network, where ki is the number of neighbors of I, and ei is the number of connected pairs between the neighbors of i. It should be noted that, while the clustering coefficient represents a local property of the network, the average path length represents a global property. The characteristic path length “measures the typical separation between two vertices in the graph”. In other words, it provides the shortest distance on average between any two nodes i and j in the network: L(i, j). Watts and Strogatz (1998) found that, in the small world network, the clustering coefficient remains high as the rewiring probability increases, but the characteristic path length decrease rapidly, as shown in Fig. 2. Figure 3 below shows the model for the regular network at p = 0, which is a highly clustered large world, the random network at p = 1,which is a poorly clustered small world, and the small-world network for 0 < p < 1,which gives rise to the appearance of two properties both exhibiting high clustering and being a small world. • Scale-free networks

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Fig. 3 Random rewiring procedure with N = 20 and k = 4. Adapted from (Watts and Strogatz 1998)

A scale free network was introduced by Barabási and Albert (1999). The degree distribution in this type of network is a power law. A scale free network contains a few strongly connected nodes and a very large number of weakly connected nodes. To this end, the authors proposed a dynamic network model5 based on the preferential attachment mechanism. When an agent joins the network, he or she tends to connect to the most connected agents. The algorithm underlying the model of Barabási-Albert is the following. Growth: They start with a small number (m0 ) of nodes. At every time step, they add a new node i with m (≤m0 ) edges that link the node to m different nodes already present in the system. Preferential attachment: They assume that the probability that a new node will be connected to node i depends on the degree ki of node i, such that (ki ) = kik . j j

After t time steps, this procedure results in a network with (N = t + m0 ) nodes and mt edges.

4.4 Combining Networks and Agent-Based Models in Financial Markets The examination of financial markets with an approach combining networks and agent-based models has only very recently begun to receive the attention of researchers. Hoffmann and Jager (2005) provided a framework built in line with Day and Huang (1990), considering investors’ needs, decision-making processes and network structures’ effects. Hoffmann and Eije (2007) used a multi-agent based social simulation approach with two different network topologies: the regular network and the scale free network according to the model of Takahashi and Terano

5 Another

node is added to the network at every time step.

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(2003). They found that an artificial stock market based on a scale free network does not display volatility clustering. This outcome could result from the superior information diffusion capacities of this network structure, facilitating the absorption of market shocks so that their influence quickly disappears. Hein et al. (2012) introduced agent communication through small world networks into the model of Lux and Marchesi (1999). Their results indicated that price volatility and kurtosis increase as the rewiring probability increases. Tedeschi et al. (2009) introduced an order-driven market with traders that imitate each other through a random communication network that can evolve dynamically. They showed that the imitation of a fixed guru can generate the phenomenon of volatility clustering. Following from the model of (Chiarella et al. 2009b; Tedeschi et al. 2012) implemented an endogenous mechanism of imitation by introducing a preferential attachment process based on agents’ performance. They found that imitative behaviors of traders result in herd behavior and large fluctuations in prices. Panchenko et al. (2013) expanded the model of Brock and Hommes (1998) and studied the effects of different network topologies on asset price dynamics. Masmoudi (2014) employed a chartist-fundamentalist approach considering the influence of different imitation rules in the interaction between these two trader types in a fully connected network. Modeled within a multi-agent framework, the agents switch their trading strategies and consequently their expectations of prices according to their past performances based on two different mimicking rules: the most profitable rule and the average rule. This study found that, as market participants interact with one another, this stochastic process generates alternating periods of generally dominating chartists or generally dominating fundamentalists i.e., cyclical dynamics derivable from the way in which they interact. Furthermore, this simulation model reveals the existence of periods of tranquility dominated by fundamentalists and unstable trading phases when chartists dominate. Yeh and Yang (2015) proposed an agent-based artificial stock market in which agents are interconnected with each other through different network structures. They varied the strength of imitation and found that, when imitation is not very strong, the effects arising from the network characteristics are reduced. More recently, Iori and Porter (2018) showed how agent based models in financial markets have evolved from simple zero-intelligence agents into sophisticated connected agents. They also presented examples of how agent based models have been successful at providing useful insights for policy making. Therefore, the development of heterogeneous, boundedly rational agents’ models, which attempt to capture such limited rational behavior, is attracting increasing academic attention. In fact, the unsatisfactory nature of the full rationality hypothesis, together with the elaboration of computational tools, agent-based modeling and networks, which have permitted researchers to build and analyze market models with heterogeneous agents, have given further momentum to the expansion of this stream of research.

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5 Conclusion Financial markets gather actors of an extremely heterogeneous nature. Apart from the heterogeneity of actors operating in the market, these actors might have heterogeneous expectations and thus use distinct trading strategies. In situations of uncertainty, agents make assumptions about how asset prices are determined and try, make mistakes, learn and adapt to each other and to the environment. The strategies that they adopt may occasionally be optimal. However, since the market is not stable, this optimality does not last indefinitely. In this way, heterogeneous agents compete in asset markets due to information asymmetry and the heterogeneity of analysis information. In fact, the same information might be interpreted in a subjectively different way by each investor. Investor sentiment is thus an intuitive tool that affects the asset price formation process proposed by behavioral finance. In this context, we must use models with complex heterogeneity. Agents have heterogeneous anticipations due to their sentiment but also can change their strategies over time by imitating more successful strategies. Within this context, it is not possible to explain some fluctuations of asset prices by an approach purely based on the market fundamentals. Models, based on the hypothesis that investors have heterogeneous expectations, were developed using alternative modeling tools. These models are able to replicate real market behavior better than traditional ones. This chapter outlines that agent-based models and network theory provide insight into the forces driving the stylized facts that characterize financial markets. Prices instabilities are thus endogenous and can arise from the interactions among these heterogeneous investors and the positive feedback effects deriving from their interdependence. Moreover, we emphasized that nonlinear models can explain price misalignments with respect to fundamentals. In particular, the smooth transition regression “STR” model is used to provide a better reproduction of the different regimes for market returns triggered by investor sentiment. This study contributes to the growing literature on behavioral finance linked to modeling and forecasting of financial return dynamics. We highlighted that such new modeling tools would be able to refine price dynamics with the assumption of limited rationality and heterogeneity of investors. We need to accept that financial markets are constantly changing without tendencies to self-stabilize and thus to rethink how to regulate the activity of individuals, institutions and markets in order to get a better understanding of the functioning of fina ncial markets.

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On the Underestimation of Risk in Hedge Fund Performance Persistence: Geolocation and Investment Strategy Effects William Joseph Klubinski and Thanos Verousis

1 Introduction The last three decades have seen a gradual but significant increase in interest in Alternative Investment Funds (AIFs) (commonly known as hedge funds). The extreme expansion of the industry has seen its value increase from approximately US$118.2bn in 1997 to US$3.55tn in November 2017 (Prequin 2018). In this paper, we investigate the impact of geolocation and investment strategy effects on the estimation of risk in performance persistence measurement dynamics. An accurate appraisal of AIF performance must recognise that AIFs’ risk exposure to investment styles is constantly shifting as managers are able to change the fund’s focus. In that respect, risk management in AIFs is prone to systematic biases as exposure to risk factors is changing (see Bollen and Whaley 2009). Further, AIFs’ strategies expose investors to high correlation risk (see Buraschi et al. 2014). Since their inception in the 1950s, AIFs were always looked to for their astonishing performance (Bridgewater, Soros, and Citadel)1 which in turn has gradually elevated their reputation to ‘the money-making machines’ (Rittereiser and Kochard 2010, pp. 196). The industry did not thrive without controversies, and more specifically significant exposure to left-tail risk (see Agarwal and Naik 2004) and defaults (Amaranth Advisors, LTCM, and Tiger Management).2

1 Bridgewater: (net gains) approx. $50bn since 75 , Soros: approx. $42 (73 ), Citadel: approx. $25bn

(90 ).

Advisors losses = approx. $6.5bn, LTCM = approx. $4.6bn, Tiger Management = approx. $2bn. 2 Amaranth

W. J. Klubinski · T. Verousis () Essex Business School, University of Essex, Colchester, UK e-mail: [email protected]; [email protected] © Springer Nature Switzerland AG 2021 C. Zopounidis et al. (eds.), Financial Risk Management and Modeling, Risk, Systems and Decisions, https://doi.org/10.1007/978-3-030-66691-0_8

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The literature related to the performance persistence of AIFs has grown exponentially in the last two decades. Nevertheless, despite its wide coverage of all the years from approximately the late 1977s until 2018, utilisation of all major databases and variety of methodologies, risk management with respect to the measurement of performance persistence remains largely unexplored. One of the areas where AIF risk management is crucial is geolocation, as the majority of academic research focuses on one (or a combination of) of the following approaches in data analysis: The globally aggregated approach (all AIFs in one portfolio), the investment strategies (all AIFs aggregated in portfolios based on their primary investment strategy), or the data clusters (some of which are based on the fundspecific properties, e.g. low, medium or high return portfolios). The only studies that we have come across that disrupted the aforementioned pattern, focused on the Asian and Australian (Koh et al. 2003), Italian (Steri et al. 2009) and solely Australian (Do and Veeraraghavan 2010) AIF universes. Therefore, in this chapter, we are going to assess the performance persistence of AIFs in the sphere of geolocation and identify whether the country of domicile and the investment strategy impact on their risk dynamics. The additional side objective of this investigation is to contribute to the scarce literature concerning the previously noted non-US AIFs domiciles (Koh et al. 2003; Steri et al. 2009; Do and Veeraraghavan 2010). In order to provide an adequate perspective for the analysis of performance persistence, we have employed both non-parametric contingency tables and parametric regressions. The analysed sample of AIFs in this study comes from the EurekaHedge database. The sample data aggregates 5619 AIFs (post-processing) and spans January 1995 to October 2016. Interestingly, the period covered in our analysis consists of two major economic events (the Russian financial crisis of 1998 (combined with the LTCM’s collapse) and the sub-prime mortgage crisis of 2007), what may be of interest particularly to the potential AIF investors. In our analysis, we have focused on the world’s four most saturated domiciles (USA, CAYI, LUX and IRL) and the four most commonly employed strategies (LSE, CTA, FIX and MLTI).3 We have several findings to report. We show that metrics based on the individual domiciles and (separately) the investment strategies indicate the existence of shortterm performance persistence. However, as we move to consider a combination of both domicile and the investment strategy, we can observe diminished persistence as well as its loss and reversal. Interestingly, one can draw a parallel between the geo-strategic combinations exhibiting high risk and the positive level of persistence. To provide greater depth into our analysis, we have further employed a twostep parametric regression method. In the first instance, we have computed the performance persistence on raw data without consideration for risks crystallising in the AIFs. The results reveal dominant and statistically significant negative performance persistence in portfolios such as IRL and the USA (a result previously

3 Table

1 provides a list of abbreviations.

On the Underestimation of Risk in Hedge Fund Performance Persistence. . . Table 1 Abbreviations

Abbreviation AIF/s AIFM/s AuM CTA

FIX FOHFs HFR LSE MLTI

267

Explanation Alternative investment fund/s Alternative investment fund manager/s Assets under management Commodity trading advisors are primarily AIFs trading futures contracts Fixed-income Funds of hedge funds Hedge fund research Long-short-equity Multi-strategy

unseen under the non-parametric approach). The same goes for the geo-strategic combinations and domiciles employing either the LSE or MLTI strategies. In the second instance, we have enhanced our parametric method to account for the risks materialising in the AIFs. The accountability for risk has completely changed the outcomes for some of the individual domiciles and the investment strategies, as they have all moved into a positive and statistically sig. Territory (except for IRL). As to the cross combinations, we no longer observe any negative performance persistence across domiciles practising the LSE approach. A similar reversal and in effect a dominance of the positive β p coefficients occur at the MLTI level. The results of our analysis for both the non-parametric and parametric approaches uncovered differences in performance persistence between the general overview of the domicile, investment strategy and a combination of two. Furthermore, we prove that the sole reliance on either the general domicile or on the investment strategy level focused clusters can be grossly misleading and lead to undesirable consequences. The definition of risk propagated by the participants in the AIFs industry very often varies. Therefore, the results of this study are specifically relevant to AIF investors. Primarily, the performance persistence of the AIFs is far more important than in mutual funds, as it has a bigger impact on the fund’s survival (Agarwal and Naik 2000a). Secondarily, the results of our study allow potential investors for more educated investment decisions. We clearly show that the sole reliance on either the general domicile or on the investment strategy level focused clusters can be grossly misleading and lead to undesirable consequences. The rest of the chapter is organised in the following way: Section 2 discusses the previous literature; Section 3 analyses the database and provides descriptive statistics; Sect. 4 discusses the methodology; and Sect. 5 provides the interpretations of the results; Sect. 6 concludes.

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2 Performance Persistence This section discusses the literature on the performance persistence of the AIFs. In general, we show that the magnitude of performance persistence amongst AIFs exhibits a high degree of variation that is conditional on the country of domicile and investment strategy. We classify papers depending on whether the country of domicile is defined or undefined. To provide more clarity on the literature around AIFs, the data has been dissected based on the results: short and long-term persistence.

2.1 Undefined Domiciles The following sub-sections aggregate all studies which do not explicitly denote the domicile of the AIFs they have analysed. Since the domicile focus is unknown/undefined, it is assumed that the entire databases (pre/post-cleaning) were collated to reflect the AIF industry.

2.1.1

Short-Term Persistence

Ever since the inception, the research into the performance persistence of the AIFs has rarely explored its full potential. The researchers were mostly focused on either the aggregation of the global hedge fund universe under one umbrella or/and the division based on the investment strategy. The frequent omission or underestimation of the domicile factor has not provided a complete risk-accountability, much needed in the case of the AIFs. The modern performance persistence analysis of the AIFs began with the research of Park and Staum (1998). Their research was not only one of the first to focus on performance persistence but also controlled for the survivorship bias.4 In their results, they have shown the evidence of performance persistence at annual horizons (with substantial variations from year to year) within the aggregated universe of the AIFs pursuing the CTA strategy. In the following year, Brown et al. (1999) focused again just like their predecessors, on the aggregated universe of AIFs, this time domiciled outside of the United States, identifying performance persistence in years 1991–1993, which reversed in the next two years.

4 Survivorship

bias refers to one of the most frequent and momentous weaknesses in statistical data analysis. The omission of its existence can result in erroneous investment decisions, which derive from statistically distorted data. It can be specifically responsible for overstating active hedge funds/mutual funds’ performance and in effect misleading investors. In the literature, survivorship bias is depicted in a two-dimensional spectrum: as a disparity in returns between live and defunct funds and/or the disparity between live & the aggregated universe (live + defunct) (e.g. Fung and Hsieh 1997; Ackermann et al. 1999; Liang 2000; Malkiel and Saha 2005).

On the Underestimation of Risk in Hedge Fund Performance Persistence. . .

269

Their research was one of the first to depart from a commonly adopted aggregation of the all-in-one portfolio, focusing only on non-US funds. For approximately the same period but with significantly larger sample size, Edwards and Caglayan (2001) identified persistence with both winning and losing AIFs at both annual and biannual horizons, which differs significantly by the investment style. They have also indicated, that the performance persistence of the AIFs can be attributed to the exploitation of market inefficiencies, which can be attained due to a relative lack of regulatory oversight. Other researchers pointed also towards interesting factors influencing performance persistence. Thus, with Liang (1999) we can learn that the performance of AIFs can be enhanced by the incentivisation of the AIFMs. While Boyson (2003) shows that young-skilled AIFMs are the driving force behind quarterly performance persistence. Bares et al. (2003) show that Relative Value and Specialist Credit focused AIFs exhibit the strongest persistence amongst all six of the analysed strategies. Others, such as Amenc et al. (Amenc et al. 2003) identify 8 out of 9 analysed investment strategies exhibiting performance persistence (i.e. exceeding 0.5 baselines in the Hurst Index [HI]) with Managed Futures being the only strategy below 0.5 in the HI (0.465), i.e. a mere 0.025 below the baseline. Brown and Goetzmann (2003) further show that the performance persistence of AIFs varies significantly across investment strategies. Another approach, which continuously focuses on the aggregation of the AIF universe comes from Capocci and Hubner (2004), who identified persistence only for the mid-range (average return portfolio) AIFs. This result was further confirmed by Capocci et al. (2005). Moreover, the authors show that Global Macro and Market Neutral were able to consistently outperform market returns. The supportive study comes from Harri and Brorsen (2004) and also shows, that Market Neutral and FoHFs exhibit the strongest (short-term) persistence with Event-Driven and Global/Macro (see also Agarwal and Naik (2000a), Hentati-Kafell and Peretti (2015) and Gonzalez et al. (2016)). Kosowski et al. (2007) and Joenvaara et al. (2012) further show that some investment strategies exhibit stronger persistence (on the annual horizon); Long-Short Equity, Directional Traders, Relative Value and FoHFs. Their cluster-size focused analysis shows, that the small AIFs exhibited strong annual persistence, whereas large AIFs persistence is much weaker. Moreover, they have identified that persistence amongst AIFs is sensitive to fund-specific limitations, e.g. share restrictions or the AuM.

2.1.2

Long-Term Persistence

In relation to long-term performance persistence, Kouwenberg (2003) has identified persistence on a three-year horizon, noting that the selection of persistently performing AIFs has been suppressed by a large number of funds disappearing from the market (see also Jagannathan et al. (2010)). While, Sun et al. (2012) demonstrated that AIFs exhibit strong persistence within five years of their inception. The other

270

W. J. Klubinski and T. Verousis

factors, influencing the performance persistence were identified by Bae and Yi (2012), who has shown that AIFs with inflow/outflow restrictions exhibit superior (winning) performance over the other funds. Finally, Ammann et al. (2013) showed that AIFs’ characteristics (AuM and leverage ratio) impact upon their long-term performance persistence. Their findings reaffirmed Kouwenberg’s (2003) results, indicating (Alpha) performance persistence on the horizons of up to 36 months with statistically significant over 6 months and substantial (yet insignificant) during 24 months for all three analysed strategies: Equity Market Neutral, Global Macro and Emerging Markets.

2.2 Defined Domiciles The following sub-section aggregate all studies, which denote the domicile of the AIFs they have analysed. It is worth noting that there are no studies with defined domiciles that investigate the long-term performance persistence of AIFs. Agarwal and Naik (2000a) were one of the first proponents to analyse AIFs based on domicile. In their research, they have identified significant quarterly performance across all ten investment strategies, which successively diminished at bi-annual and annual levels. Their other research identified quarterly persistence attributable to continuously losing, rather than winning AIFs (Agarwal and Naik 2000b). Interestingly, they have underlined that analysing performance persistence amongst AIFs is far more critical than that of mutual funds, due to its impact on their longevity (i.e. default rates). Chen and Passow (2003) continued reliance on the US-based AIFs market, showing that the AIFs with lower exposure to the factors identified by Agarwal and Naik (2000b) exhibited superior performance during both adverse and advantageous market conditions. Further work by Baquero et al. (2005) also built on Agarwal and Naik’s (2000b) research and found that performance analysis can be hampered by significant attritions in databases (mainly due to the fund’s liquidations or the lack of continuous reporting to the database). In the Asian and Australian AIFs universe, Koh et al. (2003) employed single and multi-period persistence analysis, identifying performance persistence at monthly and quarterly intervals. The same result has been achieved by Henn and Meier (2004) who also identified significant persistence on the monthly and quarterly bases, which diminished towards the annual horizon. It is important to notice that despite describing and providing statistical descriptions of specific investment strategies, their non-parametric (contingency table) persistence analysis focused solely on the aggregated universe. Steri et al., (2009) have also analysed the European environment, focusing on their analysis on the Italian AIFs, confirming monthly persistence but demonstrating that this persistence differs on quarterly and semi-annual horizons. In an important note, the peculiarity of the Italian AIFs industry is that 95% of AIFs are FoHFs.

On the Underestimation of Risk in Hedge Fund Performance Persistence. . .

271

Another, this time solely focused on the Australian market study by Do and Veeraraghavan (2010) have shown that the Australian AIFs exhibit short-term monthly persistence. Overall, the review of the literature uncovers significant limitations in terms of geolocation focus. Majority of the aforementioned research focuses on either globally aggregated approach, i.e. all AIFs under one umbrella, usually divided based on the investment strategy, or the data clusters based on the fund-specific properties, such as the AuM, returns, flows. Given the scarce literature concerning defined domiciles, this chapter will analyse the performance persistence of the AIFs in the sphere of geolocation and identify whether the country of domicile and the investment strategy matter.

3 Data 3.1 Database The Alternative Investment Funds (AIF) data used in this research comes from the EurekaHedge5 database. EurekaHedge is the world’s largest alternative investment data provider and consists of more than 28,500 investment vehicles (as of January 2017) according to Capocci (2013). Additionally, EurekaHedge provides a much more comprehensive reflection of the contemporaneously reporting hedge funds universe than (for example) Lipper, HFR or MorningStar, as noted by Joenvaara et al. (2012). Currently, the largest AIFs data providers on the market are EurekaHedge, Lipper, HFR, Morningstar, Barclays Hedge, and CISDM (see Table 2). Thus, from the perspective of a single data source, this research utilises the dataset with the highest saturation of contemporaneously reporting AIFs in the world. The research timeframe covers the period from January 1995 to October 2016. Before the analysis was undertaken, we filtered the data to retain the AIFs domiciling solely in the United States, Cayman Islands, Luxembourg and Ireland (due to Table 2 World’s primary AIFs databases

Database EurekaHedge Lipper HFR MorningStar Barclays hedge CISDM

# of live AIFs 9722 7500 7200 7000 6366 5000

# of defunct AIFs 12,138 11,000 16,000 12,000 17,965 11,000

Note: The figures refer to the total number of contemporaneously reporting AIFs (as of January 2017)

5 For

more detailed description, please visit www.eurekahedge.com

272

W. J. Klubinski and T. Verousis

the extensive saturation of these domiciles). We have further limited our dataset by selecting the four most prominent investment strategies within each domicile: LongShort-Equity (LSE), Fixed-Income (FIX), Commodity-Trading-Advisors (CTA), and Multi-Strategy (MLTI). This way we have reduced the initial dataset from 16,678 AIFs to 11,197.6 Further reductions occurred due to missing/not-disclosed observations in sections such as management and performance fees, assets under management (AuM) and lockup and redemption periods. Another important aspect of the data cleaning process is the potential existence of duplicate funds, previously identified by Aggarwal and Jorion (2010), and Bali et al. (2011), whose analysis eliminated duplicate fund classes and all other funds of which correlation was either equal to or exceeded 0.99. Therefore, we investigated our database and removed all duplicate classes and all AIFs where the correlation was either equal to or greater than 0.99. For the robustness check, we have also analysed the data where the correlation threshold has been set at 0.95 and subsequently at 0.90. This operation (0.99) as well as the removal of all funds with a lifespan equal to or shorter than six months limited our collective data set to 5619 AIFs across four domiciles (USA 2302, CAYI 2034, LUX 853, IRL 430) or four investment strategies (CTA 1212, FIX 912, LSE 2928, MLTI 567).

3.2 Descriptive Statistics In this section, we are looking at the descriptive statistics of the aforementioned domiciles and their associated investment strategies. Table 3 comprises the USA (Panel A) and CAYI (Panel B), LUX (Panel C) and IRL (Panel D). Furthermore, each domicile has been divided into four most commonly employed strategies (within the EurekaHedge database). The data gathered in this table aggregates 5619 AIFs. A significant proportion of the AIFs domiciled in the USA and CAYI can be classed as defunct as they did not report any returns in October 2016. The case of the other two domiciles is much less severe, nevertheless in almost all cases across IRL (except CTA) and LUX more than 50% of the AIFs are classed as defunct. Furthermore, the negative skew of the returns dominates all domiciles and strategies apart from the CTA (all domiciles) and LSE (USA, CAYI and IRL) strategies. In addition, the kurtosis has exhibited non-normal properties across all domiciles and strategies. With regards to the average returns, the USA and its strategies dominate all other cases with LUX and IRL generating the lowest returns.

6 The

null hypothesis of the unit root is uniformly rejected. The results are available upon request.

5.33

0.77

7.02

35.86

29.52

Std. Dev. of r

AVG r

Age [yrs]

AVG AuM

MED AuM

4.45

0.44

6.54

Std. Dev. of r

AVG r

Age [yrs]

102.1

2.14

Kurtosis

113

0.13

Skewness

MED AuM

0.41

Negative skew %

AVG AuM

0.73

Dead/alive

Cayman Islands

114.50

132.65

5.23

1.29

4.71

5.32

Min

0.00

0.10

Max

1788.00

2203.50

21.90

15.01

−3.47

1.10

73.90

48.70

−1.64

0.29

5.63

−5.86

336.81

338.78

6.35

0.73

1.98

5.92

−0.14

0.52

0.63

2218.79

2208.07

4.30

0.60

1.57

9.00

1.76

0.50

0.49

521.35

553.46

4.67

1.22

3.09

4.25

1.00

0.50

0.45

S.D.

0

0.5

1.2

−3.99

7659

7734.4

21.9

9.319

22.3

37.557

−1.40

0.67

4.753

1

1

−5.90

0

0

159.28

165.91

5.95

0.62

2.84

7.73

−0.44

0.60

0.65

260.76

252.11

3.87

1.24

5.26

11.98

2.00

0.49

0.48

S.D.

FIX [Obs.230]

3.30

Kurtosis

1.23

1.00

0.00

1.00

Mean

0.18

Skewness

0.49

0.00

CTA [Obs.262]

0.40

Negative skew %

0.46

S.D.

Mean

0.70

Panel B

Max

FIX [Obs.187]

Min

Mean

S.D.

CTA [Obs.787]

Mean

Dead/alive

United States

Panel A

Table 3 Descriptive statistics

0.00

0.30

1.20

−3.97

0.04

−0.93

−8.15

0.00

0.00

Min

0.00

0.10

1.20

−1.26

0.07

−0.97

−7.98

0.00

0.00

Min

6.26

1.00

1.00

6.93

1.00

1.00

1863.00

1821.20

19.40

14.71

73.32

86.99

Max

29903.00

29776.90

21.90

5.62

12.06

69.61

Max

285.23

355.35

5.01

1.58

4.18

4.54

0.98

0.50

0.45

84.31

95.40

6.35

0.53

4.02

2.47

−0.01

0.56

0.76

Mean

166.83

178.58

4.08

0.83

2.84

4.19

0.94

0.50

0.42

S.D.

LSE [Obs.1275]

64.36

75.54

7.34

0.74

4.39

2.69

0.06

0.49

0.72

S.D.

LSE [Obs.1159]

0.00

0.10

1.20

−9.35

0.40

−1.20

−3.50

0.00

0.00

Min

0.00

0.10

1.10

−46.22

0.36

−1.52

−4.40

0.00

0.00

Min

2024.00

2127.50

21.90

7.15

36.09

70.36

6.73

1.00

1.00

Max

7710.00

9437.80

21.90

5.17

107.54

72.08

6.42

1.00

1.00

Max

506.22

561.79

5.31

0.66

2.69

6.62

1.39

0.50

0.43

176.78

204.32

6.43

0.48

3.94

4.63

−0.08

0.52

0.78

Mean

400.11

456.28

4.12

0.93

4.09

8.19

1.51

0.50

0.42

S.D.

MLTI [Obs.267]

190.22

212.81

7.74

0.70

3.37

4.79

−0.26

0.57

0.75

S.D.

MLTI [Obs.169] Mean

0.00

0.30

1.20

−3.54

0.44

−1.20

−7.27

0.00

0.00

Min

0.00

0.20

1.30

−2.69

0.31

−1.15

−6.35

0.00

0.00

Min

(continued)

3471.00

3870.60

19.70

5.60

47.95

72.80

6.81

1.00

1.00

Max

5262.00

5843.00

21.90

3.38

19.67

52.90

5.28

1.00

1.00

Max

On the Underestimation of Risk in Hedge Fund Performance Persistence. . . 273

0.62

1.09

3.83

−0.08

Kurtosis

Std. Dev.

1137.01

1138.01

5.91

0.15 2000.87

127.69

141.88

4.61

0.54

1.51

3.86

0.99

0.49

0.50

0.00

1.00

1.10

826.00

832.46

20.60

1.68

−1.23

21.54

−1.09

6.45

4.02

−2.28

0.74

1.00

1.00

0.00

0.00

446.48

455.24

4.95

0.28

1.54

2.13

−0.29

0.66

0.73

662.16

675.74

2.55

0.34

0.91

3.84

0.77

0.48

0.45

S.D.

0.00

1.00

1.20

−0.80

0.03

−0.65

−2.67

0.00

0.00

Min

1.00

1.00

1.20

−0.66

0.03

−0.90

−4.39

0.00

0.00

Min

3340.00

3122.68

13.50

2.57

4.70

27.19

2.97

1.00

1.00

Max

8806.50

8770.60

22.70

3.40

5.66

35.15

3.42

1.00

1.00

Max

246.94

292.38

2.88

0.54

1.87

6.22

0.92

0.48

0.50

145.50

152.77

5.23

0.29

3.17

2.00

−0.17

0.63

0.53

Mean

314.94

315.38

3.75

0.52

2.09

5.00

0.93

0.48

0.50

S.D.

LSE [Obs.218]

168.17

201.14

4.75

0.26

2.79

1.86

−0.20

0.63

0.46

S.D.

LSE [Obs.276] Mean

0.00

1.00

1.10

−2.12

0.44

−1.11

−3.61

0.00

0.00

Min

1.00

1.00

1.10

−1.91

0.62

−1.08

−8.97

0.00

0.00

Min

3623.00

3728.08

21.90

1.49

17.66

58.17

6.57

1.00

1.00

Max

2048.50

1696.80

16.30

2.55

11.45

92.48

3.96

1.00

1.00

Max

2660.18

2686.33

154.90

166.26

3.40

0.01

2.02

1.18

−0.31

0.71

0.52

Mean

2.41

0.26

1.49

4.49

0.88

0.45

0.50

S.D.

282.49

290.07

2.79

0.49

1.82

1.76

0.69

0.46

0.51

S.D.

MLTI [Obs.31]

987.94

1006.92

4.68

0.12

1.67

1.82

−0.35

0.73

0.50

Mean

MLTI [Obs.100]

0.00

1.00

1.20

−1.64

0.30

−0.83

−2.06

0.00

0.00

Min

1.00

1.00

1.10

−0.85

0.26

−1.14

−4.64

0.00

0.00

Min

2.81

1.00

1.00

1.05

8.64

7.36

1.32

1.00

1.00

1563.00

1587.41

13.10

Max

16018.00

16200.90

16.80

1.02

11.66

29.62

Max

Note: The Dead/Alive: denotes the percentage of AIFs, which have not reported any results in Oct 2016. The Negative Skew %: percentage of AIFs with negative skewness. Skewness and Kurtosis: the average skew/kurt value for a given strategy. Std. Dev. of r: standard deviation of the returns. The AVG r: average returns. The Age [yrs]: the average age of AIFs for a given strategy. While the AVG and MED AuM: average and median assets under management in $US millions

75.92

0.24

AVG r

MED AuM

3.24

Std. Dev. of r

5.22

1.67

Kurtosis

90.81

0.20

Skewness

AVG AuM

0.40

Negative skew %

Age [yrs]

0.42

S.D.

3.85

0.35

0.83

4.28

0.99

0.46

0.44

1999.38

FIX [Obs.124]

Max

1414.00

1454.70

21.90

1.62

1.30

2.77

−0.44

Mean

Min

0.00

1.00

1.10

−2.84

11.94

37.90

−0.92

0.56

4.82

−1.57

0.69

0.26

CTA [Obs.57]

Dead/alive

Ireland

172.58

201.97

4.14

3.92

0.68

1.00

1.00

0.00

0.00

S.D.

Mean

93.91

MED AuM

Panel C

104.83

AVG AuM

Age [yrs]

5.54

2.37

0.01

Skewness

0.50

0.48

Negative skew %

0.50

0.58

AVG r

Max

FIX [Obs.371]

Min

Mean

S.D.

CTA [Obs.106]

Mean

Dead/alive

Luxembourg

Panel C

Table 3 (continued)

274 W. J. Klubinski and T. Verousis

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275

4 Methods The investigation of performance persistence relies on two different approaches: contingency tables (non-parametric) and regressions (parametric). We undertook all our tests at monthly intervals for the timeframe between January 1995 and October 2016. The non-parametric method consists of widely utilised contingency tables (see Brown and Goetzmann 1995; Agarwal and Naik 2000a; Eling 2009; Do and Veeraraghavan 2010). The anchor value which serves as a performance benchmark is the median return of all funds across all four domiciles and specific investment strategies. Thus, the fund which exceeds (is below) the median return is considered a winner (loser) and denoted as WW (LL). Whereas, the winner (in the first period), transforms into a loser (in the second period) as WL or LW if the opposite is true. This non-parametric measure uses three different metrics: cross-product ratio (CPR), Z-statistic (Z) and Chi-square (X2 ). The CPR defines the odds ratio of the funds, which exhibit performance persistence as opposed to those that do not. Its fundamental null hypothesis is CPR = 1, implying no persistence (when WW = 25%, LL = 25%, WL = 25%, LW = 25%). Carpenter and Lynch (1999) conclude that X2 test based on the number of winners and losers is well specified, powerful and more robust to the presence of biases compared to other non-parametric methodologies. The CPR can be denoted as:

CP R =

(W W xLL) (W LxLW )

(1)

The statistical significance of the CPR has been measured through the application of the standard error of the natural logarithm (α ln(CPR) ) what results in a Z-statistic, which is the ratio of α ln(CPR) to the standard error of the ln x ≡ loge x. Thus, in parallel to Z ~ N (0,12 ) ➔ Z, whenever the value of 1.96 or 2.58 (for 5% and 1% confidence interval respectively) is exceeded, significant performance persistence occurs. The Z-statistic can be denoted as:

Z=

ln(CP R) =

aln(CP R)

ln(CP R) 1 WW

+

1 WL

+

1 LW

(2) +

1 LL

Lastly, the chi-square (X2 ) compares the observed frequency distribution of all four denominations with the expected frequency distribution. Thus, if the value of X2 for one d.f. exceeds 3.84 or 6.64 (for 5% and 1% confidence interval respectively), we can observe a significant performance persistence. The chi-square can be denoted as (where n is the number of funds in a given period):

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W. J. Klubinski and T. Verousis

X2 =

  2 W +LW ) W W − (W W +W L)(W n  +

(W W +W L)(W W +LW ) n

LW −



(LW +LL)(W W +LW ) n

(LW +LL)(W W +LW ) n



+

  2 L+LL) W L − (W W +W L)(W n

2

 +

(W W +W L)(W L+LL) n



(LW +LL)(W L+LL) n (LW +LL)(W L+LL) n

LL −

2

(3) Furthermore, we have computed the percentage of repeating winners (PRW).

P RW =

WW WW + WL

(4)

On the contrary, the parametric approach employs the XR to identify performance persistence. Unlike Do and Veeraraghavan (2010), our XR calculation measures the XR of an individual AIF in contrast to the median (and not the average) return of all AIFs within the same domicile and strategy. The reason for this change lies within the predominantly skewed return distributions of the analysed AIFs (see Table 3). The XR approach is then further enhanced into AXR to account for the risks associated with the AIFs investments. The AXR measures the XR of an individual AIF in contrast to the median (and not the average) return of all AIFs within the same domicile and strategy. It is further divided by the residual standard deviation from a linear regression of the AIF’s return on median returns from AIFs within the same domicile and strategy. XR it = an Dn + ap Dp + βi,n Dn XR i,t−1 + βi,p Dp XR i,t−1 + εit

(5)

Dn = 1 where XR i,t−1 < 0 and Dp = 1 where XR i,t−1 > 0 AXR it = an Dn + ap Dp + βi,n Dn AXR i,t−1 + βi,p Dp AXR i,t−1 + εit

(6)

Dn = 1 where AXR i,t−1 < 0 and Dp = 1 where AXR i,t−1 > 0. With regards to the dummies of Dn and Dp , they stand for negative (lose) and positive (win) returns. While the β i, n and β i, p identify the level of return autocorrelation of the AIFs amongst the negative and positive cases respectively.7

7 E.g.,

the β i, n with a significant positive figure implies the existence of the autocorrelation or persistence of the negative (lose) cases. On the contrary, the β i, p implies the autocorrelation or persistence amongst positive (win) cases.

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277

5 Empirical Results 5.1 Non-Parametric Methods The following sub-sections outline the results of the two approaches. The first individually examines domiciles and investment strategies while the second deals with the combination of both. The results unequivocally confirm the existence of short-term performance persistence across all of the examined universes, regardless of whether it is the individual domicile/strategy or a combination. However, when we increase granularity and begin to focus on smaller clusters, we observe the equal number of persistent cases (WW versus LL) in the USA (CTA & FIX), CAYI_FIX and IRL (LSE & FIX) registered funds as well as the loss and reversal of persistence in places such as LUX (all strategies) and IRL_MLTI.

5.1.1

Domiciles and Investment Strategies

Tables 4 and 5 present results of the non-parametric method with regards to the mean and total number of the AIFs exhibiting winning (WW) and losing (LL) cases of persistence (Sect. 5). Tables 4 and 5, each consists of two panels which reflect the domicile (Panel A) and separately the strategy (Panel B) of the analysed AIFs. On the contrary, Tables 6 and 7 consists of 4 different panels (A: USA, B: CAYI, C: LUX and D: IRL) reflecting the domiciles combined with the investment strategies, which are directly associated with Tables 4 and 5 and provide the statistics for the non-parametric test. The timeframe of for this data is January 1995 through to October 2016 (262 months) and aggregates 5619 AIFs. The initial examination of Table 4 shows us that in all cases, regardless of whether we are considering the domicile or the investment strategy alone, the number of funds denoted as WW dominates all other instances (i.e. LL, WL or LW). Such an outcome implies positive performance persistence at the very start of our analysis; as such we examine further the statistical results of the CPR, X2 , Z-statistics and the PRW. The domicile focused analysis (Table 5, Panel A) indicates that the CPR and X2 show statistical significance at 5% (1%) in 126 (112) and 181 (159) out of 262 months for the USA domiciled AIFs. The PRW is greater than 50% in 165 out of 262 cases (or 63%). The average (total) CPR of all USA based AIFs is 1.79 (1.30), rejecting the null hypothesis of no persistence in 196/262 cases. Whereas the total (average) X2 for the entire sample, is 26.96 (1.64), which reaffirms that the AIFs domiciled in the USA exhibit short-term (monthly) performance persistence. Similarly, the funds domiciled in the CAYI exhibit the CPR and X2 in 123 (102) and 160 (135) out of 262 months respectively. Their mean and total CPR stands at 1.95 and 1.49 implying performance persistence in 196 out of 262 months. The mean and total X2 exceed the value of 1.96 for the sig. at 5%, further demonstrating

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W. J. Klubinski and T. Verousis

Table 4 Non-parametric performance persistence Panel A Domicile USA Mean Total CAYI Mean Total LUX Mean Total IRL Mean Total Panel B Investment strategy LSE Mean Total CTA Mean Total FIX Mean Total MLTI Mean Total

WW 171.43 44,572 155.62 40,462 57.09 14,216 25.85 6694

LL 170.07 44,218 152.53 39,657 56.77 13,852 24.89 6396

WL 149.92 38,979 126.65 32,928 50.66 12,411 23.07 5930

LW 149.23 38,801 126.19 32,810 50.62 12,452 23.18 5956

WG 4.22 586 4.01 557 2.75 151 1.55 68

LG 6.16 875 6.14 970 2.86 206 1.68 126

NEW 4.41 975 4.23 934 3.01 352 1.63 165

NEL 4.03 878 4.74 1009 3.72 499 2.18 261

WW 147.12 38,250 94.34 24,528 72.02 18,652 45.20 11,753

LL 143.96 37,429 92.85 24,142 70.84 18,206 44.10 11,465

WL 123.45 32,097 88.99 23,138 49.67 12,764 36.07 9379

LW 123.16 32,021 88.70 23,062 49.89 12,822 36.01 9362

WG 3.72 514 3.07 362 2.35 167 2.18 172

LG 5.71 890 3.85 500 2.60 268 2.31 238

NEW 4.29 919 3.07 577 2.42 336 1.82 264

NEL 4.84 1026 3.08 569 3.38 571 2.09 287

Note: This table presents the mean and total number of winning [WW] and losing [LL] periods over the 262 months between Jan 1995 and Oct 2016. Furthermore, it also provides the number of winners-gone [WG] and losers-gone [LG] as well as the new-entrant-winner [NEW] and new-entrant-loser [NEL].

persistence. The PRW, in this case, is much higher (than in the USA) and is equal to 195 (or 74%). The number of months where LUX based AIFs exhibit significance at 5% (1%) for CPR and X2 stands at 79 (66) and 127 (99). The mean (2.68) and total (1.27) CPR differ from the value of 1 and as it can be seen with Z-stat (13.91) exhibit persistence. Lastly, the CPR and X2 of the IRL domiciled funds show statistical significance at 5% (1%) in 63 (39) and 109 (64) out of 262 months. With the mean (total) CPR of 3.27 (1.20) and the Z-stat of 7.59 they do exhibit performance but to a lesser magnitude than the other domiciles. In Table 5, Panel B, we can observe the same number of the AIFs (5619), however, this time they have been dissected based on their investment approach: LSE, CTA, FIX and MIRL. All strategies defy the null hypothesis of the CPR and report more than 190 out of 262 months (in every case), representing the existence of performance persistence. The total Z-stats is significant in all cases. Furthermore, as it was the case with domiciles, every single type of strategy generates PRW >50%.

CPR

196 190 213 213

194 190 224 200

Mean/Total CPR

1.79/1.30 1.95/1.49 2.68/1.27 3.27/1.21

2.00/1.39 1.68/1.11 3.19/2.07 2.54/1.53

1.78/30.87 0.48/8.01 2.5/44.85 1.31/21.81

1.64/26.96 2.16/37.58 0.90/13.91 0.57/7.59

Mean/Total Z-s

115 [102] 97 [77] 136 [115] 100 [78]

126 [112] 123 [102] 79 [66] 63 [39]

Z@5% [1%]

23.39/955.35 14.97/64.23 20.22/2033.83 8.54/477.32

24.99/727.68 22.96/1417.15 12.05/193.78 6.76/57.72

Mean/Total X2

167 [143] 159 [130] 160 [134] 126 [96]

181 [159] 160 [135] 127 [99] 109 [64]

X2@5% [@1%]

173 [0.66] 138 [0.53] 198 [0.76] 179 [0.68]

165 [0.63] 195 [0.74] 159 [0.61] 161 [0.61]

PRW [PRW%]

Note: This table provides the results of the non-parametric test for a collective sample of 5619 AIFs from January 1995 to October 2016 [monthly intervals]. The first column shows the average and total CPR, the second column shows the number of months different from CPR’s null hypothesis, the third column shows the average and total Z-stat, the fourth column counts the number of months where Z-stat is sig. at 5 and 1%, the following column shows the average and total X2 figures and the sixth column counts the number of significant cases. Lastly, PRW shows the number and percentage of AIFs considered repeating winners

Domicile Panel A USA CAYI LUX IRL Panel B LSE CTA FIX MLTI

Table 5 Non-parametric performance persistence

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W. J. Klubinski and T. Verousis

Table 6 Non-parametric performance persistence: Domicile combined with the investment strategy Panel A United states USA_LSE Mean Total USA_CTA Mean Total USA_FIX Mean Total USA_MLTI Mean Total Panel B Cayman Islands CAYI_LSE Mean Total CAYI_CTA Mean Total CAYI_FIX Mean Total CAYI_MLTI Mean Total Panel C Luxembourg LUX_LSE Mean Total LUX_CTA Mean Total LUX_FIX Mean Total LUX_MLTI Mean Total Panel D Ireland IRL_LSE Mean Total IRL_CTA Mean Total IRL_FIX Mean Total IRL_MLTI Mean Total

WW 103.40 26,883 64.34 16,728 16.31 4224 16.70 4342

LL 101.70 26,442 63.63 16,543 15.69 4016 16.08 4180

WL 89.18 23,187 60.35 15,690 11.08 2815 13.09 3404

LW 88.67 23,054 60.10 15,625 11.04 2804 13.07 3397

WG 2.77 338 2.31 236 1.45 45 1.54 60

LG 4.18 552 2.92 333 1.55 87 1.21 70

NEW 3.13 589 2.38 391 1.24 82 1.23 74

NEL 2.60 507 2.22 344 1.40 101 1.17 82

WW 100.30 26,078 20.02 5204 20.33 4941 21.97 5668

LL 98.23 25,539 19.19 4969 19.55 4654 21.18 5444

WL 82.60 21,477 18.95 4928 13.60 3182 17.80 4467

LW 82.30 21,398 18.91 4916 13.55 3184 17.63 4442

WG 2.88 374 1.44 82 1.22 44 1.53 81

LG 4.14 637 1.53 112 1.77 113 1.64 131

NEW 3.15 623 1.43 130 1.23 87 1.38 138

NEL 3.44 637 1.41 121 1.54 143 1.50 126

WW 19.99 4098 7.15 1794 28.67 7282 7.01 1479

LL 21.85 3911 7.64 1613 31.18 6922 10.55 1319

WL 20.72 3585 7.50 1709 25.18 5641 10.53 1306

LW 20.55 3576 7.49 1707 24.91 5680 10.64 1309

WG 1.57 47 1.36 30 1.81 47 1.93 29

LG 1.91 86 1.30 35 1.91 61 1.38 22

NEW 1.98 131 1.41 48 2.32 137 1.63 49

NEL 1.88 145 1.36 57 2.38 233 1.55 51

WW 14.27 3583 3.58 917 11.16 1942 1.82 4098

LL 14.16 3369 3.17 767 10.85 1790 2.02 3911

WL 12.54 3136 3.52 883 10.66 1673 2.08 3585

LW 12.52 3143 3.49 877 11.00 1694 2.06 3576

WG 1.31 38 1.00 18 1.25 15 1.25 47

LG 1.40 67 1.33 16 1.21 23 1.09 86

NEW 1.38 90 1.09 25 1.37 41 1.25 131

NEL 1.64 126 1.15 30 1.66 83 1.31 145

Note: This table presents the mean and total number of winning [WW] and losing [LL] periods over the 262 months between Jan 1995 and Oct 2016. Furthermore, it also provides the number of winners-gone [WG] and losers-gone [LG] as well as the new-entrant-winner [NEW] and newentrant-loser [NEL]

Panel A USA USA_LSE USA_CTA USA_FIX USA_MLTI Panel B Cayman Island CAYI_LSE CAYI _CTA CAYI _FIX CAYI_MLTI Pane C Luxemburg LUX_LSE LUX_CTA LUX_FIX LUX_MLTI Panel D Ireland IRL_LSE IRL_CTA IRL_FIX IRL_MLTI

CPR 200 191 224 212

CPR 194 212 221 202

CPR 216 233 229 238

CPR 213 217 232 241

Mean/Total CPR 2.02/1.33 1.61/1.13 3.93/2.15 2.77/1.57

Mean/Total CPR 2.29/1.45 1.70/1.07 3.73/2.27 2.53/1.56

Mean/Total CPR 2.57/1.25 3.36/0.99 3.35/1.57 3.03/1.14

Mean/Total CPR 3.25/1.22 2.57/0.91 3.97/1.23 2.42/1.30

Mean/Total Z-s 0.43/5.82 −0.06/−1.41 0.36/4.294 0.09/2.21

Mean/Total Z-s 0.49/6.864 0.05/−.167 1.14/17.98 0.1/2.42

Mean/Total Z-s 1.61/28.39 0.15/2.31 1.58/25.35 .91/15.52

Mean/Total Z-s 1.36/22.43 0.45/7.69 1.30/22.11 0.83/13.86

Z@5% [1%] 46 [27] 6 [1] 25 [14] 1 [0]

Z@5% [1%] 30 [20] 26 [18] 72 [59] 23 [13]

Z@5% [1%] 114 [94] 44 [26] 93 [58] 72 [45]

Z@5% [1%] 116 [105] 82 [65] 79 [45] 70 [41]

Mean/Total X2 4.19/33.9 1.85/1.98 4.82/18.46 1.82/4.9

Mean/Total X2 4.15/47.16 3.75/0.03 11.02/324.63 4.91/5.88

Mean/Total X2 16.23/808.27 4.15/5.32 5.81/651.58 4.5/241.92

Mean/Total X2 18.7/503.79 9.26/59.21 4.57/494.73 3.77/192.95

Table 7 Non-parametric performance persistence: Domicile combined with the investment strategy

X2@5% [@1%] 80 [55] 40 [10] 58 [37] 16 [1]

X2@5% [@1%] 45 [31] 72 [39] 113 [91] 54 [31]

X2@5% [@1%] 151 [122] 86 [52] 105 [67] 93 [55]

X2@5% [@1%] 171 [147] 134 [99] 101 [55] 89 [54]

PRW [PRW%] 139 104 110 143

PRW [PRW%] 129 128 177 149

PRW [PRW%] 174 138 200 171

PRW [PRW%] 171 146 204 173

PRW % 0.53 0.40 0.42 0.55

PRW % 0.49 0.49 0.68 0.57

PRW % 0.66 0.53 0.76 0.65

PRW % 0.65 0.56 0.78 0.66

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5.1.2

W. J. Klubinski and T. Verousis

Domiciles Combined with Investment Strategy

The combination of domiciles and investment strategies allowed us to provide significantly greater granularity. The initial assessment of Table 6 already reveals that all of LUX strategies and IRL_MLTI are dominated with losing (LL) cases of performance persistence. The panels A-D of Table 7 correspond to the following domiciles, each with four specific strategies (LSE, CTA, FIX and MLTI): the USA, CAYI, LUX and IRL. The total X2 and Z-stats of all strategies in the USA (Panel A) is highly significant at 5%. Moreover, the percentage of repeating winners above 50% dominates across all strategies. The trends in CAYI (Panel B) are similar to the USA across all strategies except CTA. The CTA’s total CPR stands at 1.07 which confirms the default null hypothesis of no persistence. While the total Zstats stands at 2.31 which is approximately 10 times lower than the other strategies (such as FIX and LSE) within this domicile. The Z-stat at 5% shows only 44 out of 262 months of persistence. Therefore, this particular strategy (CTA in CAYI) exhibits weak performance persistence. In contrast to previously described domiciles, the results for the European ones, LUX (Panel C of Table 7) and IRL (Panel D) differ significantly. Immediately apparent are the LUX_CTA and IRL_CTA which generate the total CPR that is in line with the null hypothesis of no persistence. Neither LUX nor IRL CTA strategy exhibits significance at 5% for either the Z-stat or the X2 . Therefore, they do not exhibit significant performance persistence. Moreover, the PRW in LUX is below the 50% threshold for both LSE and CTA strategies. Similarly, the IRL’s CTA and FIX strategies are at PRW 40 and 42 respectively with the remaining two at 53 (LSE) and 55 (MLTI) per cent. We have evaluated performance persistence through the idea of comparing ‘winning’ and ‘losing’ alternative investment funds returns in each period over 262 months. Moreover, this comparison has been enhanced with statistical measures of the CPR, X2 and Z-statistic at both 1 and 5 per cent significance. We have seen that the analysis based individually on either the domicile or the investment strategy of the AIFs does not provide a full overview of the risks lurking for potential investors. After expanding the scope of the analysis, we have shown that the individual strategies combined within domiciles such as IRL and LUX tend to underperform and do not maintain significant performance persistence.

5.2 Parametric Methods 5.2.1

Non-Risk Adjusted

The Domicile and Investment Strategies In this section, we analyse the results of a non-risk-adjusted parametric performance persistence test for the individual domiciles (Panel A) and investment strategies

On the Underestimation of Risk in Hedge Fund Performance Persistence. . .

283

(Panel B) presented in Table 8. Panel A shows that the majority of the AIFs across LUX and CAYI dominate with positive β i, p and statistically sig. (at 5%) cases over the number of β i, n coefficients. The exception to this is the USA and IRL, where the number of positive and statistically sig. β i, n casesdominate β i, p . Despite no signs in our non-parametric analysis, in this case, the USA and IRL exhibit negative performance persistence. In terms of the investment strategies (Panel B), the only approach where the β i, n cases dominate is MLTI – the difference between the significant cases is minimal and stands at 316/315 cases.

Domicile Combined with Investment Strategy Continuing with our more in-depth perspective, we turn to Table 9, which aggregates the combination of domiciles and the investment strategies. Table 9, Panel A (LSE) shows that the number of funds exhibiting positive β i, p amongst those domiciled in the USA, stands at 792 out of 1159 with 654 sig. at 5% level, while for CAYI it stands at 937 out of 1275 with 783 statistically sig. Concerning the other two domiciles, LUX exhibits positive β i, p at 197/276 with 178 sig. at 5% and IRL at 137/218 with 118 sig. at 5%. The contrarian, negative β i, n coefficient implies that 579 (USA), 730 (CAYI), 130 (LUX) and 120 (IRL) AIFs exhibit significant (at 5%) losing performance persistence. The exception is again the IRL domicile, which when combined with the LSE strategy continues to minimally exhibit dominant losing properties. Overall, the application of the XR performance persistence method indicates some short-term persistence, specifically of a positive magnitude (except IRL). Table 9, Panel B represents the second most populated investment strategy in our analysis, namely the CTA with 1212 total AIFs: USA (787), CAYI (262), LUX (106) and IRL (57). In this case, Panel B shows that the number of positive β i, p coefficients (sig. at 5%) dominates over the negative ones in all cases, which correlates with the results from Table 8 (Panel B). Furthermore, Panel C aggregates 912 AIFs employing the FIX strategy: USA (187), CAYI (230), LUX (371) and IRL (124). Panel C shows that the number of funds exhibiting positive (at 5%) β i, p (β i, n ) in the USA stands at 94 (88), LUX at 228 (189), while the on the contrary, negative cases (losers) dominance can be seen in CAYI at 117 (129) and IRL at 61 (73). Lastly, Table 9, Panel D gathers the lowest number of the AIFs in our dataset, pursuing the MLTI strategy with the total number of 567 funds: USA (169), CAYI (267), LUX (100) and IRL (31). Focusing on panel D we can observe that the number of positive β i, p (β i, n ) (at 5%) coefficients for the USA stands at 89 (97), IRL at 15 (17), while LUX at 64 (60) and CAYI 147 (142). Simultaneously, making CAYI the only domicile, which is capable of delivering positive performance persistence while employing the MLTI investment strategy.

290

647

0.962

0.215

0.413

IRL

294

1599

619

1484

268

Adj R2

770

501

14

1.521

27

2901 48

864 19

548

780

402

1019

1088

1559

1840

6.634

0.460

0.145

256

282

479

630

11.786

1.344

0.271

177

195

316

372

2.750

0.608

0.169

342

359

706

853

3.796

0.480

0.201

840

865

1733

2063

5.391

0.444

0.185

242

249

500

663

4.554

0.624

0.312

172

176

315

391

3.063

0.514

0.193

0.992

0.163

0.471

CTA

LSE

0.996

0.204

0.430

FIX

0.959

0.161

0.445

MLTI

0.961

0.189

0.418

Note: This table provides the results of the parametric (XR) test for a collective sample of 5619 AIFs from January 1995 to October 2016 [monthly intervals]. The first two columns refer to the dummy variables which separate negative (Alpha n) and positive (Alpha p) cases, the third column (Beta n) implies the existence of the auto-correlation or persistence of the negative (losing) cases, while the fourth column (Beta n) implies the auto-correlation or persistence amongst positive (winning) cases, the last column provides the adjusted r-squared figures

2756

3.018

0.118

432

Sig @ 0.05

1165

1198

2.158

2.492

26.817 47.553 39.250 3.695

2.237

1.312

Negative

66

59.368

3.849

3.074

665

142

5.794

1.844

3.902

Sig @ 0.05

172

29.432

1.746

−1.523

CTA

47

4.385

2.014

−0.895

CTA

Positive

MLTI

156

162

229

−27.820 −22.413 −16.007 −14.149 −17.032 −5.586 −2.927 −2.109 −50.693 −9.922 −30.356 −6.445 −8.119 −3.088 −2.704 −3.232 −0.324 −0.336 −0.776 −1.097

LSE

534

550

1204

Min

FIX

225

234

537

28.085

βp

681

703

1284

Max

MLTI

124

136

240

2.925

LSE

603

0.985

0.200

0.401

LUX

Sigma

FIX

269

0.996

0.163

0.439

CAYI

−2.134

βn

858

0.996

0.155

0.474

USA

−2.702

MLTI

25

5.391

0.673

0.153

Mean

LSE

19

1387 1156

4.313

0.454

0.223

Adj R2

CTA

FIX

42

563 440

2.612

0.588

0.299

IRL

αp

22

1378

3.806

0.444

0.176

CAYI

−5.449 −8.119 −2.704 −3.232 −2.763 −0.502 −1.097 −0.719 −0.776

4.827

0.653

0.250

LUX

FIX

MLTI

412

405

0.455

0.191

USA

βp

αn

LSE

1844

2015

0.961

0.273

IRL

CTA

XR InvStra

Panel B

802

811 924

Sig @ 0.05

2134

2280

Negative

18 1183

190

1.297

Sig @ 0.05

51

47.553 8.358

1.587

0.079

168

9.708

2.646

2.090

Positive

59.368

1.508

2.978

−2.078

3.131

3.335

1.500

−27.820 −10.925 −18.056 −11.405 −17.032 −2.404 −5.586 −2.927 −50.693 −9.922

4.385

1.572

3.520

Min

5.794

2.121

−1.823

6.634

CAYI

3.695 11.786

LUX

29.432

1.659

−1.923

USA

βn

Max

IRL

2.637

CAYI

Sigma

LUX

−1.616

USA

αp

−2.228

IRL

Mean

CAYI

LUX

USA

XR Domicile α _ n

Panel A

Table 8 Parametric performance persistence [non-risk-adjusted [XR]]

−22.413 −9.583

60

Min

Positive

25.387

IRL

−27.820 −10.925 −17.694 −6.836

25

Min

Positive

675

251

53

9.692

7

780 4

102

1.512

0

262

3.695

1.856

0.055

USA

6.634

0.439

0.196

CAYI

4.827

0.537

0.200

IRL

3.806

0.385

0.141

USA

βp

1.568

0.395

0.226

LUX

4.313

0.461

0.229

CAYI

5.391

0.623

0.112

IRL

0.9592

0.1459

0.4663

USA

Adj R2

0.9207

0.1497

0.4243

CAYI

0.9159

0.1989

0.4547

LUX

0.9135

0.2217

0.4451

IRL

1.780

0.535

0.328

LUX

115

127

130

149

1.642

0.377

0.204

CAYI

387

405

730

870

1.848

0.517

0.201

IRL

67

72

120

146

3.796

0.499

0.171

USA

βp

358

367

654

792

2.523

0.572

0.357

LUX

77

79

178

197

1.687

0.372

0.206

CAYI

329

338

783

937

1.140

0.399

0.296

IRL

76

81

118

137

0.992

0.1497

0.4885

USA

Adj R2

0.9741

0.1613

0.4616

CAYI

0.8993

0.2040

0.4051

LUX

0.9616

0.1979

0.3998

IRL

−9.922 −1.359 −0.974 −3.088 −0.846 −2.191 −2.763 −0.5019 −0.3477 −0.7193 −0.7762

1.867

0.755

0.052

LUX

3

54

485

279

24

25

61

81

80

84

155

178

19

21

30

36

233

245

447

542

25

26

67

80

71

75

157

187

13

13

35

44

(continued)

−2.281 −50.693 −1.511 −0.858 −1.208 −8.119 −0.694 −0.980 −0.536 −0.3235 −0.1266 −0.2523 −0.1783

15.960 5.425

2.635

−17.032 −2.404 0.040

59.368

2.107

2.122

IRL

βn

450

302

Sig @ 0.05

99

4

0.251

4.359

3.474

CAYI

2

216

Negative

11

4.368

1.364

2.563

LUX

15

1260

419

7

0.385

2.448

4.353

3

273

Sig @ 0.05

762

28.085

Max

2.267

3.205

−1.805

Sigma

−2.589

−2.556

−2.824

USA

CAYI

LUX

USA

αp

7

1152

αn

Mean

XR CTA

Panel B

212

6

3.003

0.352

484

Sig @ 0.05

1172

103

1.536

26.817 8.358

2.246

0.101

USA

βn

−0.988 −5.586 −0.135 −1.763

9.708

1.636

2.683

IRL

Negative

273

0.461

2.380

−18.056 −11.405 −2.584

4.385

1.678

3.032

CAYI

579

3

0.175

2.030

2.153

LUX

Sig @ 0.05

1099

3.830

Max

1.722

2.106

3.412

Sigma

−2.317

−2.237

−2.230

Mean

−1.993

USA

IRL

αp

CAYI

LUX

αn

USA

XR LSE

Panel A

Table 9 Parametric performance persistence [non-risk-adjusted [XR]]

Adj R2

−14.149 −7.224 −11.945 −8.067 −2.109 −1.960 −0.178 −1.112 −1.382

27

Min

Positive

28

4

7

93

5.000

1

266

33.105

7

24

7.424

1.599

107

2.117

0.405

58

2.232

0.435

0.132

CAYI

53

64

129

166

4.381

0.613

0.217

1.834

0.651

0.618

IRL

33

37

73

87

2.077

0.837

0.269

3.063

0.445

0.215

USA

βp

36

36

94

151

2.282

0.482

0.379

1.749

0.621

0.265

LUX

93

99

228

272

2.612

0.688

0.345

2.284

0.471

0.166

CAYI

60

60

117

170

1.962

0.470

0.275

2.952

0.743

0.072

IRL

53

54

61

70

4.554

0.813

0.181

CAYI

CAYI

0.939

0.9223

0.1497 0.1613

0.4885 0.4616

USA

Adj R2

0.9964 0.9961

0.2130 0.1917

0.5036 0.4940

USA

0.816

0.1696

0.3767

IRL

0.8825

0.2040

0.4051

LUX

0.9612

0.1979

0.3998

IRL

−0.3359 −0.2714

0.9845

0.1927

0.3718

LUX

31

33

60

67

83

94

142

173

5

6

17

25

54

55

89

114

30

30

64

70

74

77

147

190

14

14

15

17

−6.445 −2.078 −0.626 −1.166 −2.686 −3.232 −1.227 0.0762 −1.0972 −0.2233 −0.2513

2.750

1.054

0.212

LUX

99

105

189

266

11.786

1.118

0.438

Note: This table provides the results of the parametric (XR) test for a collective sample of 5619 AIFs from January 1995 to October 2016 [monthly intervals]. The first two columns refer to the dummy variables which separate negative (Alpha n) and positive (Alpha p) cases, the third column (Beta n) implies the existence of the auto-correlation or persistence of the negative (losing) cases, while the fourth column (Beta n) implies the auto-correlation or persistence amongst positive (winning) cases, the last column provides the adjusted r-squared figures

235

165

39.250

3.077

62

Sig @ 0.05

96

3

0.897

1.030

Negative

32

0.723

3.545

97

4

5.794

1.859

0.120

Sig @ 0.05

142

1.966

1.916

1.314

Max

1.459

3.013

1.895

1.063

Sigma

−1.508 2.731

USA

−1.253 −1.722

βn

71

−1.371

IRL

13

Mean

CAYI

3

USA

LUX

28

αp

4

111

LUX

IRL

119

111

2.248

2.296

αn

CAYI

186

227

6.311

1.178

USA

XR MTLI

Panel D

334

343

47.553

3.734

76

Sig @ 0.05

131

183

4.268

0.737

Negative

5

13.919

1.540

0.007

88

44

3.131

0.916

1.228

Sig @ 0.05

37

1.397

2.107

2.073

56

IRL

Positive

CAYI

−5.487 −16.007 −3.962 −0.906 −0.701 −1.053 −2.927 −30.356 −3.965 −1.390 −5.449 −1.081 −2.704 −1.728 −2.168 0.0364 0.0281

LUX

−9.374

1.050

0.829

USA

Min

βp

3.720

IRL

29.432

CAYI

Max

LUX

2.539

−1.042 1.390

USA

Sigma

βn

−0.983 −1.006

IRL

−0.485

CAYI

Mean

LUX

USA

IRL

αp

CAYI

LUX

αn

USA

XR FIX

Panel C

Table 9 (continued)

On the Underestimation of Risk in Hedge Fund Performance Persistence. . .

5.2.2

287

Risk-Adjusted

The Domicile and Investment Strategies Further to the previous non-risk-adjusted parametric approach, we provide here riskadjusted analysis (AXR). In the domicile only scenario (Panel A of Table 10), the IRL is no longer dominated by the negative values and instead regains its positive dominance with 230 cases for β i, p (sig. at 5%) versus 197 for β i, n . This reversal implies that the AIFs located in IRL regain their positive performance persistence after being adjusted for risk. Another peculiar case refers to the LUX domicile, which in this environment begins to underperform and generates 427 negative versus 417 positive cases. In the realm of investment strategies only (Panel B of Table 10), there is no more dominance of negative persistence as it was the case in the XR analysis (MLTI strategy). Despite the positive performance persistence, the number of statistically significant cases which exhibit persistence is much lower than it was in the non-riskadjusted analysis (e.g. CTA down from 706 to 578, LUX 1733 to 1464, LSE 500 to 470 and MLTI 315 to 283).

Domicile Combined with Investment Strategy In this sub-section, we provide the risk-adjusted (AXR) analysis of domiciles combined with the investment strategies. Table 11, Panel A indicates that all of the domiciles employing the LSE strategy exhibit performance persistence. In Table 11, Panel B (CTA) we can observe that the persistence trend for the CTA strategy in LUX and CAYI reverses in post-risk-adjustment case. Thus, the LUX is dominated by negative values in 56 (β i, p ) to 41 (β i, n ) and CAYI 123 to 129. The FIX strategy (Panel C) exhibits trend reversal in performance persistence when comparing nonrisk-adjusted and risk-adjusted approaches. The domiciles CAYI and IRL where positive performance persists in XR reverses into negative territory in AXR. While the same reversal occurs in the USA and LUX which no longer generate positive persistence in the post-risk-adjusted scenario. Lastly, Panel D shows that the MLTI strategy for LUX domiciled funds has been dominated by the AIFs exhibiting losing performance persistence. In summary, from the autoregressive perspective, we have found performance persistence amongst all strategies. Furthermore, in certain instances, we have observed trend reversals between the XR and AXR parametric approaches. Our results vary and cannot unilaterally confirm Do and Veeraraghavan (2010) nor Agarwal and Naik’s (2000b) outcomes, which held that the majority of the persistence is on the negative side. Lastly, the applicability of the risk-adjusted testing proves that the simple approach (excluding risk) of the XR can be misleading in assessing performance persistence of the AIFs.

2.478

7.325

−32.997 −9.999

191

Sigma

Max

Min

Positive

−32.997 −23.006 −28.547 −15.357 −1.856 −5.236

46

Min

Positive

1172

491

12

23

2905 15

897

0.709

450

0.406

0.010

FIX

378

403

427

1034

0.376

0.010

LSE

969

1000

980

11

556

0.829

0.008

USA

βp

205

1217

βp

1029

1085

1145

3.197

0.272

0.017

3.254

0.783

−0.024

MLTI CTA

210

225

197

441

9.722

0.349

0.014

FIX

395

412

417

597

593

1496

1378

1432

1419

480

402

432

456

288

268

279

275

619

555

593

578

1543

1326

1385

1464

IRL

0.369

238

MLTI

183

192

230

495

399

417

470

299

249

268

283

0.999

0.178

0.415

CAYI

0.981

0.218

0.365

LUX

0.884

0.226

0.387

IRL

0.176

0.454

CTA

Adj R2

0.989

0.179

0.425

FIX

0.942

0.190

0.394

MLTI

−0.856 −0.480 −1.139 −1.032

0.999

0.220

0.386

LSE

−1.139 −0.910 −1.032 −0.934

0.995

0.169

0.456

USA

Adj R2

7285.249 0.979

305.683 −4.105 −9.992

2.542

0.241

−0.007 12.879

LSE

922

974

1003

1060

−9.992 −1.638

9.722

0.606

−0.006 0.056

CAYI

7285.249 3.173

249.296

8.532

LUX

−5.316 −4.511 −8.467 −2.741 −22.605 −2.968

1317.945 18.300 13.641 4.587

55.255

−48.429 −6.409

51.408

2.899

0.929

0.037

IRL

13.641 18.300 27.972

0.405

0.007

CAYI

Note: This table provides the results of the parametric (AXR) test for a collective sample of 5619 AIFs from January 1995 to October 2016 [monthly intervals]. The first two columns refer to the dummy variables which separate negative (Alpha n) and positive (Alpha p) cases, the third column (Beta n) implies the existence of the auto-correlation or persistence of the negative (losing) cases, while the fourth column (Beta n) implies the auto-correlation or persistence amongst positive (winning) cases, the last column provides the adjusted r-squared figures

738

1200

132.712 30.967

2.297

615

Sig @ 0.05

2742

76

2.022

5.418

0.008

CTA

βn

1084

Negative

174

7.325

1.897

4.845

MLTI

17

413

4.587

0.321

0.015

LUX

−8.467 −3.180 −3.004 −2.741 −22.605 −4.105

7.586

0.451

0.006

USA

βn

568

186

35.118

1.516

1.408

LSE

16

2018

−5.236

30.967

2.175

2.252

IRL

Sig @ 0.05

1166

1.296

Max

2.167

3.187

2.675

4.111

Sigma

−1.572

−2.149

−2.820

Mean

−0.929

CTA

FIX

αp

MLTI

FIX

LSE

21

832

αn

7

2295

−6.409 −48.429 −4.704

CTA

AXR InvStra

Panel B

404

26

2.658

3.097

CAYI

1130

Sig @ 0.05

1829

205

45.113

3.027

LUX

132.712 1317.945 51.408

4.266

3.691

USA

αp

Negative

793

1.617

−28.547 −9.176

35.118

1.539

−1.819

IRL

1114

60

3.184

2.319

−1.916

CAYI

Sig @ 0.05

2111

−1.654

−2.328

Mean

1.577

LUX

USA

AXR Domicile α n

Panel A

Table 10 Parametric performance persistence [risk-adjusted [AXR]]

100

250

53

3

7

99 1

261 1

56

373

400

414

Sig @ 0.05

763

784

Negative

4 350

12

7.586

0.544

Sig @ 0.05

6

1.498

17.438 6.104

2.523

IRL

42

46

56

60

0.543

0.409

127

131

129

131

1.913

0.280

0.955

−0.031

USA

βp

24

24

33

33

344

376

381

411

18.300 3.254

2.408

549 528

154

660

CAYI

586

615

622

119

IRL

97

99

112

60

61

41

45

0.671

0.231

130

133

123

129

0.930

0.243

21

23

33

34

0.837

0.289

−0.027 −0.013 0.021

LUX

115

122

148

0.979

0.1598

0.4778

USA

Adj R2

24

2.107

132.712 9.926

6.435

CAYI

610 582

Positive

0.249

1.522

LUX

119 112

−0.003 −0.037 −0.015 0.344

USA

622 606

99 96

0.9757

0.1648

−32.997 −9.999 −19.167 −8.246 −1.856 −0.925 −0.380 −0.178 −5.316 −3.180 −1.675 −0.819 −22.605 −1.052 −1.911 −1.638 −0.856

1.015

2.358

2.420

IRL

138 130

653 615

9.722

0.819

Min

0.739

2.166

3.483

CAYI

βn

530

138 132

3.173

0.295

0.4480

USA

0.9893

0.1720

0.4009

LUX

0.8102

0.2100

0.4329

CAYI

LUX

0.8594

0.2015

0.3762

0.7965

0.2200

0.3588

IRL

−0.9338

0.8476

0.2262

0.4361

IRL

(continued)

−0.3238 −0.3438 −0.4089

0.9099

0.1824

0.433

CAYI

−2.595 −2.418 −1.385 −1.1393 −0.9098 −0.67

2.814

0.300

0.131

Adj R2

2.871

2.627

LUX

6

606

2.152

0.246

−0.004 0.000

IRL

1.296

−1.878 4.642

13

212

0.319

−0.015 0.010

13.641 2.052

0.482

0.008

CAYI

Max

−2.514 −2.596

−3.004

1

1262

1.377

0.332

0.021

LUX

Sigma

LUX

USA

USA

3

αp

IRL

211

αn

CAYI

1170

Mean

AXR CTA

Panel B

273

275

0.339

553

Sig @ 0.05

1088

1156

2.606

28.275 30.967 4.585

2.244

Negative

7

9.893

1.672

576

105

24.691

2.345

0.013

Sig @ 0.05

3

0.599

1.595

2.859

71

35.118

2.307

3.150

Positive

3.184

1.724

2.233

USA

−23.006 −9.811 −14.825 −9.176 −0.492 −0.163 −4.704 −5.236 −4.511 −3.026 −3.004 −2.240 −2.968

βp

Min

IRL

2.480

CAYI

Max

LUX

2.184

−2.270 3.517

USA

Sigma

βn

−2.251 −1.979

IRL

−2.289

CAYI

Mean

LUX

USA

IRL

αp

CAYI

LUX

αn

USA

AXR LSE

Panel A

Table 11 Parametric performance persistence [risk-adjusted [AXR]]: Domicile combined with the investment strategy

−5.591 −28.547 −4.123 0.170

−5.234

64

Min

Positive

−15.048 −7.140 −15.357 −8.425 −6.409 0.030

32

Min

Positive

107

28

1

168

0

100

0.989

0.146 0.630

0.154

0.009

IRL

0.469

0.092

0.006

USA

βp

2.542

0.314

−0.013

LUX

172

0.541

0.164

0.008

LUX

162

114

2.065

0.211

0.012

CAYI

109

116

108

60

102

USA

βp

83

85

95

0.907

0.545

189

724.872

72.868

LUX

176

182

177

2

265 8

23

86

80

53

44

47

52

136

127

131

128

13

17

18

12

132

94

74

75

87

53

44

47

51

0.451

0.144

0.9945

0.2267

72

IRL

50

52

72

USA

Adj R2

0.720

0.9986

0.2042

0.4608

LUX

0.9809

0.2093

0.3210

CAYI

0.8626

0.1854

0.3282

IRL

0.9395

0.1508

0.942

0.1689

0.4243

LUX

0.7758

0.2347

0.3278

CAYI

0.8841

0.2953

0.3214

IRL

116

128

132

139

15

18

13

13

−9.992 −1.255 −0.2138 −0.4795 −1.0316 −0.3697

0.213

0.242

−0.042 −0.075 0.3996

CAYI

90

98

126

27.972 7285.249 2.165

2.155

−0.051 0.171

IRL

57

64

56

−0.328 −0.402 −1.137 −0.803 −0.570 −2.741 −1.249 −0.415

3.197

0.324

199 187

USA

Adj R2 −0.028 0.4629

IRL

−2.740 −0.988 −0.1544 −0.0015 −0.4795 −0.3878

0.677

0.227

0.005

CAYI

Note: This table provides the results of the parametric (AXR) test for a collective sample of 5619 AIFs from January 1995 to October 2016 [monthly intervals]. The first two columns refer to the dummy variables which separate negative (Alpha n) and positive (Alpha p) cases, the third column (Beta n) implies the existence of the auto-correlation or persistence of the negative (losing) cases, while the fourth column (Beta n) implies the auto-correlation or persistence amongst positive (winning) cases, the last column provides the adjusted r-squared figures

232

1.739

18.490 1317.945 30.573 7.901

3.082

83

Sig @ 0.05

94

3

1.617

131.025

0.043

USA

βn

74

Negative

35

0.604

2.206

1.416

IRL

2

122

83

6

0.230

1.949

3.110

CAYI

0

230

4.587

0.314

0.019

CAYI

−0.903 −8.467 −1.113 −0.477 −0.878 −0.361 −4.105

2.866

0.670

Sig @ 0.05

137

2.022

1.963

Max

1.226

2.078

14.290

Sigma

−1.507 2.625

−1.367 −1.735

LUX

−1.446

USA

αp

13

Mean

IRL

0

LUX

CAYI

112

358

USA

AXR MLTI α n

Panel D

177

187

LUX

−0.033 0.027

USA

βn

80

Sig @ 0.05

326

12

0.983

51.408 5.604

3.940

−48.429 0.244

15.336 6.969

2.894

1.318

IRL

Negative

53

0.246

1.565

2.343

CAYI

105

45

0.860

0.887

0.696

LUX

Sig @ 0.05

123

1.717

7.325

Max

2.410

1.254

Sigma

0.943

−1.041 −0.999

−0.525

Mean

−1.076 1.731

USA

IRL

αp

CAYI

LUX

αn

USA

AXR FIX

Panel C

Table 11 (continued)

On the Underestimation of Risk in Hedge Fund Performance Persistence. . .

291

6 Conclusion The value of the AIF industry has increased from approximately US$118.2bn in 1997 to US$3.55tn in November 2017. Equally, there is a large increase in the number of studies focusing on the performance persistence of AIFs. However, to our knowledge, the area of risk management with respect to the measurement of performance persistence remains largely unexplored. In this paper, we have analysed four of the world’s most saturated AIFs domiciles and four of the most commonly employed investment strategies for the period between January 1995 and October 2016. We employ parametric and non-parametric analysis. Our objective was to investigate the impact of geolocation and investment strategy effects on the estimation of risk in performance persistence measurement dynamics. We show new evidence regarding the performance persistence rankings when total (combined) risk is taken into consideration. The results unequivocally confirm the existence of short-term performance persistence. However, we show that some domicile/strategy combinations do not represent attractive investment opportunities. In that respect, pre-adjusted performance persistence analysis that looks at risk in isolation can lead to erroneous investment decisions and loss of the investment capital. The results of this study are primarily relevant to AIF investors. We clearly show that the sole reliance on either the general domicile or on the investment strategy level focused clusters can be grossly misleading and lead to undesirable consequences.

References Ackermann C, McEnally R, Ravenscraft D (1999) The performance of hedge funds: risk, return, and performances. J Financ 54(3):833–874 Agarwal V, Naik NY (2000a) Multi-period performance persistence analysis of hedge funds. J Financ Quant Anal 35(3):327–342 Agarwal V, Naik NY (2000b) On taking the alternative route: risks, rewards, and performance persistence of hedge funds. J Altern Invest 2(4):6–23 Agarwal V, Naik NY (2004) Risks and portfolio decisions involving hedge funds. Rev Financ Stud 17(1):63–98 Aggarwal RK, Jorion P (2010) The performance of emerging hedge funds and managers. J Financ Econ 96(2010):238–256 Amenc N, El Bied S, Martellini L (2003) Predictability in hedge fund returns. Financ Anal J 59(5):32–46 Ammann M, Huber O, Schmid M (2013) Hedge fund characteristics and performance persistence. Eur Financ Manag 19(2):209–250 Bae KH, Yi J (2012) Performance persistence and flow restrictions in hedge funds. Working Paper, York University Bali TG, Brown SJ, Caglayan MO (2011) Do hedge funds’ exposures to risk factors predict their future returns? J Financ Econ 101(1):36–68 Baquero G, Ter Horst J, Verbeek M (2005) Survival, look-ahead bias and the persistence in hedge fund performance. J Financ Quant Anal 40(3):493–517

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Bares PA, Gibson R, Gyger S (2003) Performance in the hedge funds industry: an analysis of short and long-term persistence. J Altern Invest 6(3):25–41 Bollen NPB, Whaley RE (2009) Hedge fund risk dynamics: implications for performance appraisal. J Financ 64:985–1035 Boyson NM (2003) Do hedge funds exhibit performance persistence? A new approach. Working Paper, Krannert Graduate School of Management Brown S, Goetzmann W (1995) Performance Persistence. J Financ 50(2):679–698 Brown SJ, Goetzmann WN (2003) Hedge Funds with Style. J Portf Manag 29(2):101–112 Brown SJ, Goetzmann WN, Ibbotson RG (1999) Offshore Hedge Funds: Survival and Performance 1989–1995. J Bus 72(1):91–117 Buraschi A, Kosowki R, Fabio T (2014) When There Is No Place to Hide’: Correlation Risk and the Cross-Section of Hedge Fund Returns. Rev Financ Stud 27(2):581–616 Capocci D (2013) Complete guide to hedge funds and hedge fund strategies (Global financial markets). (2013th edn). London, Palgrave Macmillan, p 63 Capocci D, Hubner G (2004) Analysis of hedge fund performance. J Empir Financ 11(1):55–89 Capocci D, Corhay A, Hübner G (2005) Hedge fund performance and persistence in bull and bear markets. Eur J Financ 11(5):361–392 Carpenter JN, Lynch AW (1999) Survivorship bias and attrition effects in measures of performance persistence. J Financ Econ 54(3):337–374 Chen K, Passow A (2003) quantitative selection of long-short hedge funds. FAME Research Paper, Geneva Do V, Faff R, Veeraraghavan M (2010) Performance persistence in hedge funds: Australian evidence. J Int Financ Mark Inst Money 20(4):346–362 Edwards F, Caglayan M (2001) Hedge fund performance and manager skill. J Futur Mark 21(11):1003–1028 Eling M (2009) Does hedge fund performance persist? Overview and new empirical evidence. Eur Financ Manag 15(2):362–401 Fung W, Hsieh D (1997) Empirical characteristics of dynamic trading strategies: the case of hedge funds. Rev Financ Stud 10(2):275–302 Gonzalez MO, Papageorgiou NA, Skinner FS (2016) Persistent doubt: an examination of hedge fund performance. Eur Financ Manag 22(4):613–639 Harri A, Brorsen BW (2004) Performance persistence and the source of returns for hedge funds. Appl Financ Econ 14(2):131–141 Henn J, Meier I (2004) Performance analysis of hedge funds. In: Dichtl H, Kleeberg JM, Schlenger C (eds) Handbuch hedge funds. Uhlenbruch, Bad Soden/Ts, pp 435–466 Hentati-Kafell R, Peretti P (2015) Generalized runs to detect randomness in hedge funds returns. J Bank Financ 50(1):608–615 Jagannathan R, Malakhov A, Novikov D (2010) Do hot hands exist among hedge fund managers? An empirical evaluation. J Financ 65(1):217–255 Joenvaara J, Kosowski R, Tolonen P (2012) New ‘stylized facts’ about hedge funds and database selection bias. Working Paper, Imperial College Business School. Koh F, Koh WTH, Teo M (2003) Asian hedge funds: return persistence, style, and fund characteristics. Working Paper, Singapore Management University Kosowski R, Naik N, Teo M (2007) Do hedge funds deliver alpha? A Bayesian and bootstrap analysis. J Financ Econ 84(1):229–264 Kouwenberg R (2003) Do hedge funds add value to a passive portfolio? J Asset Manag 3(4):361– 382 Liang B (1999) On the performance of hedge funds. Financ Anal J 55(1999):72–85 Liang B (2000) Hedge funds: the living and the dead. J Financ Quant Anal 35(3):309–326 Malkiel BG, Saha A (2005) Hedge funds: risk and return. Financ Anal J 61(6):80–88 Park JM, Staum JC (1998) Performance persistence in the alternative investment industry. Working Paper, Paradigm Capital Management Prequin (2018) Prequin Global Hedge Fund Report 2018. Available at: www.preqin.com (Accessed on 20 Jan 2019)

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Equal or Value Weighting? Implications for Asset-Pricing Tests Yuliya Plyakha, Raman Uppal, and Grigory Vilkov

JEL G11, G12

We gratefully acknowledge comments from Andrew Ang, Elena Asparouhova, Turan Bali, Hank Bessembinder, Michael Brennan, Oliver Boguth, Ian Cooper, Victor DeMiguel, Engelbert Dockner, Bernard Dumas, Nikolae Gârleanu, Will Goetzman, Amit Goyal, Antti Ilmanen, Ivalina Kalcheva, Philipp Kaufmann, Ralph Koijen, Lionel Martellini, Stefan Nagel, Stavros Panageas, Andrew Patton, David Rakowski, Tarun Ramadorai, Paulo Rodrigues, Bernd Scherer, Norman Seeger, Eric Shirbini, Mungo Wilson, Michael Wolf, Josef Zechner, and participants of seminars at the EDHEC-Risk Days Europe Conference, Endowment Asset Management Conference at the University of Vienna, European Summer Symposium in Financial Markets at Gerzensee, Edhec Business School (Singapore), Goethe University Frankfurt, Multinational Finance Society Conference (Krakow), Norges Bank Investment Management, S&P Indices, University of Innsbruck, and University of Southern Denmark. Yuliya Plyakha is from University of Luxembourg, Faculté de Droit, d’Economie et de Finance, 4, rue Albert Borschette, L-1246 Luxembourg; e-mail: [email protected]. Raman Uppal is from CEPR and EDHEC Business School, 10 Fleet Place, Ludgate, London, United Kingdom EC4M 7RB; e-mail: [email protected]. Grigory Vilkov is from Frankfurt School of Finance & Management, Adickesallee 32–34, 60322, Frankfurt am Main, Germany; e-mail: [email protected]. Y. Plyakha MSCI Inc., Frankfurt, Germany e-mail: [email protected] R. Uppal EDHEC Business School, London, UK e-mail: [email protected] G. Vilkov () Frankfurt School of Finance and Management, Frankfurt, Germany e-mail: [email protected] © Springer Nature Switzerland AG 2021 C. Zopounidis et al. (eds.), Financial Risk Management and Modeling, Risk, Systems and Decisions, https://doi.org/10.1007/978-3-030-66691-0_9

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1 Introduction On the one hand, the value-weighted “market” portfolio has played a central role in asset pricing, for instance in the Capital Asset Pricing Model of Sharpe (1964). On the other hand, the use of equal-weighted mean returns is ubiquitous in empirical finance.1 Does the choice between equal- and value-weighting impact inferences when testing asset-pricing models? Our main contribution is to answer this question, which we do in three steps. First, we show that there is a substantial difference in the performance of equal- and value-weighted portfolios. Second, we identify the source of this difference in performance. Finally, we demonstrate that, because of this difference in performance, the inferences drawn from tests of asset pricing models are substantially different, depending on whether one performs these tests on equal- or value-weighted test assets. Below, we explain these three steps in greater detail, and relate them to the existing literature. Comparing the performance of the equal- and value-weighted portfolios, and also the performance of price-weighted portfolios,2 we show in the first step of our analysis that with monthly rebalancing the equal-weighted portfolio outperforms value- and price-weighted portfolios in terms of total mean return and one- and four-factor alphas, even after allowing for transaction costs of fifty basis points.3 The equal-weighted portfolio, however, has a significantly higher volatility and kurtosis compared to the value- and price-weighted portfolios. Despite the unfavorable volatility and kurtosis, the Sharpe ratio and certainty-equivalent return of the equal-weighted portfolio are higher than those of the value- and priceweighted portfolios.

1 Equal-weighted

mean returns are used in a large number of papers on empirical asset pricing (see, for example, the classical work of Fama and MacBeth (1973), Black et al. (1972), and Gibbons et al. (1989)), almost all event-studies, and the research that relates mean returns to firm characteristics (for reviews of this literature, see Campbell et al. (1997) and Kothari and Warner (2006)). Asparouhova et al. (2013, p. 666) write: “For example, examining papers published in only two premier outlets, The Journal of Finance and The Journal of Financial Economics, over a recent 5-year (2005 to 2009) interval, we are able to identify 24 papers that report EW mean returns and compare them across portfolios.” 2 We consider the price-weighted portfolio for robustness even though it is used only occasionally as an index (for example, the Nikkei index, or the Dow Jones 30 Index), and almost never for asset-pricing tests. 3 DeMiguel et al. (2009) show that the performance of the equal-weighted portfolio is no worse than that of portfolios based on mean-variance optimization, such as Markowitz (1952) and its extensions, because of the error in estimating parameters used by the optimizing portfolios; Jacobs et al. (2013) extend this finding to other datasets and asset classes. However, DeMiguel et al. (2009) do not explain how the equal-weighted portfolio would perform relative to value- and price-weighted portfolios. Given that equal-, value-, and price-weighted portfolios do not rely on estimated parameters, it is not clear that one will perform better than the others. In fact, the CAPM suggests that the value-weighted portfolio should outperform the equal- and price-weighted portfolios.

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In the second step of our analysis, in order to identify the reasons for this difference in performance, we construct equal-, value-, and price-weighted portfolios from stocks randomly selected from the constituents of the S&P 500 index over the last forty years. We use the standard four-factor model (Fama and French 1993; Carhart 1997) to decompose the total returns of these portfolios into a systematic component, which is related to factor exposure, and alpha, which is unrelated to factor exposure. We find that of the total excess mean return earned by the equal-weighted portfolio over the value-weighted portfolio, 58% comes from the systematic component, including compensation for exposure to smaller stocks, as one may have expected; however, 42% comes from the difference in alphas. In contrast, of the total excess mean return earned by the equal-weighted relative to the price-weighted portfolio, only 4% comes from the difference in systematic returns and 96% comes from the difference in alphas.4 We then show that the higher alpha and less negative skewness of the equalweighted portfolio are a consequence of the rebalancing required to maintain constant weights for the equal-weighted portfolio, which is a contrarian strategy.5 Therefore, if one were to form a passive portfolio simply overweighting small stocks, one would fail to achieve the return of the active equal-weighted portfolio, which is rebalanced each month to maintain the equal weights. Moreover, it is not the initial equal weights that are important, but the monthly rebalancing for maintaining constant weights that is responsible for the alpha of the equal-weighted portfolio.6 Finally, in the third step of our analysis, we demonstrate that the inferences drawn from tests of asset-pricing models are substantially different depending on whether one performs these tests on equal-, value-, or price-weighted portfolios. We illustrate this by examining four asset-pricing tests. One, we examine the classical

4 Including the reversal factor in addition to the four factors reduces the alpha of the equal-weighted

portfolio by 11%, but does not affect the alphas of the value- and price-weighted portfolios. 5 For the literature on momentum and contrarian strategies, see Jegadeesh (1990), Conrad and Kaul

(1998), Jegadeesh and Titman (1993, 2002), Lo and MacKinlay (1990), DeMiguel et al. (2013), and Asness et al. (2009). 6 We check the robustness of these results along a variety of dimensions. When selecting a sample of stocks from the S&P 500 index, we don’t consider just one portfolio with 100 stocks, but we resample to select 1,000 portfolios, and all the results we report are based on the performance metrics averaged across these 1,000 portfolios. In addition to the results reported for portfolios with 100 stocks, we consider portfolios with 30, 50, 200, and 300 stocks (again, with resampling over 1,000 portfolios). Besides the stocks sampled from the S&P 500 for large-cap stocks, we also consider stocks from the S&P 400 for mid-cap stocks and the S&P 600 for small-cap stocks. We also test the sensitivity of our results to different time periods and economic conditions: we study the performance of the equal-weighted portfolio relative to the value- and price-weighted portfolios if one had invested in the strategy at the peak of the business cycle (March 2001 or December 2007) or the trough (November 2001). Finally, we use four methods to correct for potential biases arising from noisy prices and liquidity differences across stocks, as suggested in Blume and Stambaugh (1983), Asparouhova et al. (2010, 2013), and Fisher et al. (2010). We find that our results are robust to all these variations, and therefore, our findings about the differences in the returns of equal- and value-weighted portfolios are complementary to theirs.

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CAPM and find that the Gibbons et al. (1989) test fails to reject the CAPM for value-weighted portfolios, but it rejects the CAPM if one were to use equal- or price-weighted portfolios. Two, following the methodology developed by Hansen and Jagannathan (1991), we show that the stochastic discount factor in the space of equal-weighted excess returns is better at pricing excess returns of individual stocks than the stochastic discount factor in the space of value-weighted excess returns. Three, we use the traditional (Fama and MacBeth 1973) multivariate test for the relation between expected returns and various asset characteristics, and show that the economic significance of the relation between a particular characteristic and returns may change substantially depending on the weighting applied to the first (cross-sectional) stage of the procedure. Four, we test the relation between expected returns and expected idiosyncratic volatility, a topic that has been the focus of extensive empirical work in recent years.7 We use both the nonparametric univariate monotonicity-relation tests developed by Patton and Timmermann (2010) and the weighted (Fama and MacBeth 1973) multivariate test, and we find that with equal-weighted observations, higher idiosyncratic volatility is associated with higher returns (with a one-sigma difference in idiosyncratic volatility in the crosssection associated with an extra return of 0.17%), whereas with value-weighted observations, idiosyncratic volatility is either not priced (in Fama-MacBeth tests) or is priced negatively (in monotonicity-relation tests for value-weighted portfolios). For price-weighted observations, we find no evidence that idiosyncratic volatility is related to returns. In summary, while there is a large literature that studies returns from different trading strategies (see, for example, Fama and French (2008)) and reports results for both equal- and value-weighted portfolios (see, for instance, Li et al. (2008), Li et al. (2009), Bali et al. (2011), and Asparouhova et al. (2013)), we identify the proportion of the excess return of the equal-weighted portfolio relative to the value- and price-weighted portfolios that comes from differences in alpha and the proportion that comes from differences in systemic risk; we find that the size and value effect is present even for large stocks that comprise S&P 500; and we show that the source of the higher alpha of the equal-weighted portfolio is a consequence of the rebalancing required to maintain equal weights. More importantly, we show that the choice of equal vs. value weights affects inferences in a wide variety of empirical asset-pricing tests, and we link these differences in inferences to the alphas and systematic returns of the equal- and value-weighted portfolios. The rest of the article is organized as follows. In Sect. 2, we describe the data on stocks that we use in our analysis and the resampling procedure we use to build portfolios so that our results do not depend on the particular set of stocks that we select for our analysis. The three main steps of our analysis are in Sects. 3, 4, and 5: in Sect. 3, we compare the empirical performance of equal-, value-, and price-

7 Recent

papers that test the relation between expected returns and expected idiosyncratic volatility include Ang et al. (2006, 2009), Spiegel and Wang (2007), Bali and Cakici (2008), Fu (2009), Huang et al. (2010), and Han and Lesmond (2011).

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weighted portfolios; in Sect. 4, we explain the reasons for the differences in the performance of these portfolios; and, in Sect. 5, we explain the implications of these differences in performance for empirical asset-pricing tests. Section 6 concludes the paper. Appendix 1 gives the details of the construction of the various stock characteristics that we use in our analysis, Appendix 2 explains the data filtering and resampling technique used to compute the test statistics, and Appendix 3 describes the robustness tests we undertake.

2 Data Description and Methodology We construct equal-, value-, and price-weighted portfolios consisting of N = 100 stocks that are in the S&P 500 index in the period from February 1967 to December of 2009 using monthly returns from The Center for Research in Security Prices (CRSP). For robustness, we consider also portfolios with 30, 50, 200, and 300 stocks instead of N = 100, and stocks belonging to the MidCap S&P 400 index from July 1991, and the SmallCap S&P 600 index from November 1994, where the choice of starting month is dictated by the date on which a given index was initiated. Note that the samples from the S&P 500, S&P 400, and S&P 600 consist of relatively large and liquid stocks.8 The company characteristics used in our analysis, such as size, book-to-market, momentum, reversal, liquidity, and idiosyncratic volatility, are constructed using the monthly and daily CRSP and COMPUSTAT databases. The method for constructing each characteristic is described in Appendix 1; summary statistics for these characteristics are provided in Table 1. To ensure that our results are not driven by the choice of stocks, rather than studying just one sample of stocks, we use resampling to form 1, 000 randomly chosen portfolios of a given size N from a given stock index. If a stock that was in our portfolio is removed from the stock index (S&P usually announces such decisions five days before removing the stock), then we remove this stock from our portfolio and randomly choose another stock to replace it. We also describe the data filtering steps and the resampling procedure in Appendix 2.

8 For

instance, compared to the larger sample of 3,762 stocks used in Asparouhova et al. (2013), we see that the median firm size in their sample is approximately equal to the median firm size in our S&P 600 small-cap sample. Moreover, we also note that even in the S&P 600 small-cap sample the stocks are about two times more liquid than in the larger CRSP sample (using the reciprocal of the Amihud’s liquidity measure as a rough proxy for Amivest’s liquidity measure). Our S&P 500 large-cap sample has larger and more liquid stocks than the sample consisting of all CRSP stocks, and is relatively free from the microstructure and liquidity biases. To ensure that our results are not affected by microstructure biases, we implement four methods to remove potential biases arising from microstructure noise in stock prices that can influence the return of the equalweighted portfolio (see Asparouhova et al. (2010, 2013)); these robustness tests are discussed in Appendix “Bias in Computed Returns”.

Characteristic Size Book-to-market Momentum: 3 months Momentum: 12 months Reversal Liquidity Idiosyncratic volatility

S&P 400 Mean 1.9668 0.2745 0.0318 0.1095 0.0107 2.9629 0.4232

Median 1.6395 0.1836 0.0235 0.0695 0.0076 1.6640 0.3960

Std. 1.4659 0.3773 0.1774 0.3765 0.1036 6.5298 0.1762

S&P 500 Mean 8.1143 0.4550 0.0324 0.1245 0.0107 8.3305 0.3552 Median 3.6323 0.2646 0.0253 0.0953 0.0076 3.6366 0.3276

Std. 14.9701 1.4948 0.1459 0.3129 0.0851 19.2228 0.1443

S&P 600 Mean 0.6501 0.4049 0.0342 0.1154 0.0109 1.0526 0.5199

Median 0.5287 0.2534 0.0182 0.0501 0.0051 0.4885 0.4961

Std. 0.4917 0.7032 0.2290 0.4855 0.1317 2.6315 0.1965

Table 1 Summary of the characteristics of the data. In this table we summarize the characteristics of our data for S&P 400, S&P 500 and S&P 600 stocks. The table reports the mean, median, and standard deviation of the following characteristics: size, book-to-market, 3-month momentum, 12-month momentum, reversal, liquidity, and idiosyncratic volatility

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3 Identifying Differences in Performance of the Portfolios We now analyze how different weighting rules affect portfolio performance. We start by describing in Sect. 3.1 the performance metrics used to compare the out-ofsample performance of the equal-, value-, and price-weighted portfolios. Then, in Sect. 3.2, we report the performance of these three portfolios, which is based on the average metrics from the 1,000 portfolios constructed for each portfolio-weighting rule, as described above.

3.1 Performance Metrics For each portfolio-weighting rule we compute various performance metrics that can be divided into three groups. First, as measures of return we use the mean return, the systematic return, and the alpha based on the one- and four-factor models (Fama and French 1993; Carhart 1997). We also compute the outperformance frequency, which is the average fraction of times that the equal-weighted portfolio has a higher cumulative return than the value- and price-weighted portfolios within twelve months from the beginning of each such period. Second, to measure risk we compute the volatility (standard deviation), skewness, and kurtosis of the portfolio return, as well as the average maximum drawdown, defined as the time-series average of the maximum percentage loss of the portfolio value V (τ ) over any period from τ1 to τ2 during the last twelve months: T −1   V (τ ) 1 1 − 1 × 100. 0, Max Drawdown = max t−11≤τ1 0 , RVk,t = − rk,t−τ ∗ 1rk,t−τ f xj mN mD i∈N j ∈D

where mN and mD denote the number of non-failed and failed cases, f (xi ) is the output of a failure Prediction model for the input case i (i.e., posterior class membership probability or prediction score), and I[·] is an indicator function such that equals 1 if f (xi ) > f (xj ), otherwise it equals 0. • H-measure (H): though the AUROC is widely used as a metric of classification performance, recently has been under some critisism that the metric is essentially incoherent. The reason is that it treats the relative severities of misclassifications or misclassification costs differently when different classifiers are used. In order to correct the incoherence of AUROC, we further consider the H-measure proposed by Hand (2009). • Kolmogorov-Smirnov distance (KSD): This metric is defined as the difference between the cumulative distribution functions of the performance scores for cases in different classes. For a binary classification setting, the KS distance is defined as: KSD = max |CN (f ) − CD (f )| where CN (f ) and CD (f ) are the cumulative distribution functions of the value scores for non-failed and failed cases, respectively.

5 Results This section presents the results of the analysis. The discussion covers the different specifications of the predictor variables, the methods used in the analysis as well as the prediction results over different periods prior to failure.

5.1 Results by Variables’ Settings Table 5 presents the results for the different input variables used in the analysis. We can observe that the first scenario (CAMELS) for all the metrics (AUROC, Hmeasure, KSD) achieves very good results, which are further improved by adding the diversification variables. On the contrary, the addition of the regional proxies to the CAMELS variables does not improve the results at the same degree as the diversification variables. In the end, the use of the full set of variables outperforms all the previous ones. An important aspect of bankruptcy prediction models is their ability to provide early warning signals of failure. Table 6 presents results over different prediction

Bank Failure Prediction: A Comparison of Machine Learning Approaches Table 5 Overall results for different specifications of the predictor variables

Specifications CAMELS CAMELS + div CAMELS + states CAMELS + div + states

Table 6 Overall results on prediction horizon

Prediction horizon 1 year 2 years 3 years

AUROC 0.860 0.906 0.872 0.912

AUROC 0.957 0.885 0.820

361 H-measure 0.467 0.574 0.500 0.593

H-Measure 0.747 0.507 0.347

KSD 0.612 0.705 0.642 0.719

KSD 0.826 0.652 0.531

Fig. 1 AUROC results for different sets of attributes and prediction horizons

horizons, up to three years prior to the event of failure. These results are averaged over all methods and scenarios for the predictors. It is evident that one year prior to failure, the predictive power of the models is quite strong. For instance, AUROC is higher than 95%. However, the performance of the models deteriorates significantly for mid and long-term prediction periods. Figure 1 presents further results focusing on the AUROC performance metric, for different prediction horizons and different specifications of the attributes. In the short-term (one year prior to failure) all specifications with different sets of attributes perform remarkably well, with the best results achieved with the full set of predictors (AUROC = 0.961). For two and three years prior to failure, the addition of the diversification indicators leads to noticeable improvement over the models that do not consider diversification. Interestingly, the improvements get larger as we move further away from the time of failure. For instance, the CAMELS+diversification specifications have an average AUROC of 0.855 versus 0.769 for the simple CAMELS models and 0.793 for the models that combine CAMELS indicators and regional dummies. The full models provide slightly better results overall, but this is clearly due to the consideration of diversification, which

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adds important information about the viability of the banks in the long run. Similar results and conclusion have been obtained with the two other measures (H-measure and KSD).

5.2 Results by Classification Method Table 7 summarizes the overall results for all methods considered in the comparative analysis, averaged over all specifications of predictor attributes and prediction horizons. Based on the experimental results from the 100 bootstrap runs, the Tukey’s honest significant difference test is used to rank the methods in ascending order from the best (rank 1) to the worst. The results reported in Table 7 indicate that the nonlinear SVM model (SVM-RBF) yields the best overall results in all performance metrics, followed by the two ensemble models (XGB and RF). The two linear models (LR and SVM-Linear) follow, whereas NB and ANN yield the worst results. Table 8 presents additional results over the different predictions horizons considered in the analysis. For short-term predictions, random forests (RF) provide the best results on all performance indicators. The relative performance of the other methods depends on the performance metric chosen. For instance, according to the H-measure LR and ANN are the second-best performers, whereas NB provides the poorest results. Nonetheless, the KSD metric indicates that the RF is followed by SVM-RBF and LR, with XGB, ANN, and NB performing worst. The mid-term prediction results (two years prior to failure) indicate that SVM with radial kernel and random forests are the best classifiers, while naïve Bayes and ANN are the worst ones. Moreover, the differences between the methods are larger compared to the ones observed in the results derived for one year prior to failure. For the long-term prediction horizon (three years prior to failure), the non-linear SVM model is again the strongest classifier, followed by the two ensembles (extreme gradient boostingXGB and random forests-RF). Naïve Bayes and ANN are found again to provide the worst results. Therefore, it is evident that state-of-the-art machine learning models such non-linear SVMs and ensembles provide the best and most robust results over different prediction horizons.

Table 7 Overall results for the machine learning techniques Method LR SVM-linear SVM-RBF NB XGB RF ANN

AUROC 0.885 0.891 0.916 0.876 0.894 0.897 0.854

Rank 3 2,3 1 4 2 2 5

H-measure 0.525 0.528 0.583 0.490 0.538 0.564 0.509

Rank 2,3 2,3 1 4 2 1 3

KSD 0.658 0.670 0.722 0.646 0.673 0.686 0.630

Rank 3 3 1 4 3 2 5

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Table 8 Comparison of machine learning models over different prediction horizons Prediction horizon 1 year prior To failure

2 years prior To failure

3 years prior To failure

Method LR SVM-linear SVM-RBF NB XGB RF ANN LR SVM-linear SVM-RBF NB XGB RF ANN LR SVM-linear SVM-RBF NB XGB RF ANN

AUROC 0.961 0.958 0.957 0.953 0.956 0.970 0.947 0.878 0.887 0.921 0.871 0.893 0.902 0.844 0.815 0.829 0.869 0.805 0.833 0.819 0.771

Rank 2 3 3 4 3 1 5 5 4 1 6 3 2 7 3 2 1 4 2 3 5

H-measure 0.752 0.735 0.741 0.721 0.745 0.786 0.752 0.495 0.502 0.577 0.452 0.510 0.546 0.468 0.328 0.345 0.430 0.297 0.358 0.361 0.307

Rank 2 4 3,4 5 3 1 2 4 3,4 1 6 3 2 5 3 2,3 1 5 2 2 4

KSD 0.825 0.818 0.841 0.808 0.819 0.849 0.819 0.635 0.651 0.719 0.621 0.654 0.680 0.603 0.513 0.543 0.607 0.509 0.547 0.530 0.469

Rank 3 4 2 5 4 1 4 4 3 1 5 3 2 6 3 2 1 4 2 2,3 5

6 Conclusions The prediction of bank failures is a complicated problem and tis importance is enhanced by the volatility in the global financial system and the importance of banks for economic stability. In this paper, up-to-date data are used from the USA to analyze the predictive performance of popular machine learning approaches for developing early warning systems for bank failures. The results demonstrate that even though high prediction rates can be achieved when focusing on short-term estimations, long-term assessments are more challenging. Standard financial ratios become much weaker indicators of failure when used to make long-term forecasts, whereas indicators that describe the diversification of the banks’ activities are particularly useful. As far as the performance of different methods is concerned, non-linear SVMs and ensembles were found to provide the most robust results and outperforming other approaches. The differences between the methods were found to be higher for long-term prediction horizons. Future research on this subject could cover various issues. For instance, the set of prediction attributes could be extended to cover corporate governance as well as specific macro-economic indicators. The latter could further be examined in the context of bank stress testing exercises, which can incorporate failure prediction

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assessments in combination with the capital adequacy estimations currently being employed. Market-based data, such as credit default swap spreads and stock market indicators could also be relevant, whereas system risks, contagion effects, and with the interrelationships among banks, should be considered in a macro-prudential context for banking supervision. Finally, methodological advances in machine learning and analytics, such as deep learning and big data, could be employed to further improve the design of early warning systems, mainly over longer prediction horizons, providing dynamic assessments.

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From Calendar to Economic Time. Deciphering the Arrival of Events in Irregularly Spaced Time Kalaitzoglou Iordanis

1 Introduction The Efficient Market Hypothesis (EMH), as it is first mathematically introduced by Bachelier (1900), rediscovered by Samuelson (1965) and conceptualized by Fama (1965), suggests that asset prices incorporate all relevant information and, therefore, they are the best predictor of future prices. Any subsequent price change is the result of the arrival of new information, which arrives randomly and cannot be predicted. This conceptual framework is developed in order to describe previous empirical observations that prices follow a completely random pattern with deviations of certain magnitude. All these empirical observations have a common denominator, they arrive at fixed time intervals. The time in between the observed events is fixed. However, finance theory has developed considerably, over the last decades providing new insights into market structure and price formation. The availability of Ultra-high-Frequency (UHF) data offers the opportunity to examine the trading process at a new level, but it also poses a new challenge, not previously considered in the early stages of EMH; the arrival of events at irregular time intervals. This random arrival of events converts “calendar” time into another variable that contributes to information and affects price formation. At this level, information assimilation slows down and the impact of time becomes crucial. This creates predictable market frictions (e.g., Madhavan 2000) that make prices deviate from their efficient level. This challenges directly both the assumptions and the applicability of the EMH, opening up a new area of research about the role of time on intraday price formation. In particular; how can the irregularly spaced time of arrival of various events be

K. Iordanis () Audencia Business School, Nantes, France e-mail: [email protected] © Springer Nature Switzerland AG 2021 C. Zopounidis et al. (eds.), Financial Risk Management and Modeling, Risk, Systems and Decisions, https://doi.org/10.1007/978-3-030-66691-0_11

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translated into price-meaningful information, a term known as “economic” time, and how might this affect intraday price formation? Garman (1976) introduced the term “market microstructure” in a suggestive manner in order to highlight that the principles that govern price formation on that level might significantly differ from the ones that govern a lower frequency trading: the reference point for the development of the EMH. EMH operates under three assumptions that do not hold on a High Frequency Trading (HFT) setup: (i) information is immediately incorporated into prices, because (ii) it reaches all market participants at the same time and (iii) they are homogenous in their beliefs. In contrast, several market microstructure studies recognize the existence of different types of agents with respect to the timing of their access to information or their trading motives. Informed agents (e.g., Kyle 1985) are the first to receive the information and to act upon it. Their actions increase trading volume (Easley and O’Hara 1992) and this signal is identified by technical traders (e.g., Admati and Pfleiderer 1988) who act upon it till the information goes public and makes uninformed agents adjust their asset allocation or trade for liquidity reasons. These agents do not receive information at the same time, nor do they trade the same way upon receiving it and therefore, information is not simultaneously incorporated into prices. This process introduces price frictions and this deviation from an unconditional application of the EMH highlights the importance of time. More precisely, when focusing on a trade-by-trade, event-by-event, frequency level, time itself carries information because it is not fixed. It might run faster or slower than “calendar” time and the speed of this new notion of “economic” time has the potential to reveal how information from a granular level can be aggregated into price discovery and ultimately into a lower-frequency efficient price. This raises several questions that will be the focus of this chapter: 1. Does the arrival time of events reveal any information about the trading process? (a) (b) (c) (d)

Does “economic” time exhibit any patterns? What kind of information can be extracted from these patterns? The arrival of what type of events carries relevant information? Can “economic” time fluctuations be linked to the presence of different agents?

2. Is the information extracted from the arrival time of events priced? (a) How do the identified patters affect information/uncertainty resolution? (b) How do the identified patterns affect information and liquidity risk premia? These questions link liquidity, information, their relative risk premia and price discovery. The field of market microstructure delves into the mechanics that govern how these are intertwined. This chapter does not intend to cover the breadth of the market microstructure literature, especially with respect to intraday or continuous time pricing, but an attempt to highlight the importance of time in HFT. In particular,

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section 2 presents how the EMH is understood with respect to available information and how intraday price discovery and the formation of intraday risk premia challenge structurallty its fundamental assumptions. Then, section 3 introduces the notion of “economic time” and its economic significance, while the last section concludes.

2 Market Efficiency and High Frequency Trading . . . the Demon of Chance drew a random number . . . and added it to the current price to determine the next . . . price Kendall (1953)

Back in 1900, the French mathematician Louis Bachelier was one of the first to observe that stock prices, p, change randomly and that the absolute price changes have a certain magnitude that depends on the time interval, Δt, of observation (Bachelier 1900). He develops the notion of the Brownian motion, W = (Wt )t ≥ 0 with EWt = 0 and EWt2 = t, with which he describes price changes as Δpt = σ Wt , with σ denoting a fixed magnitude of price change. The Brownian motion sets the foundation for the development of the random walk (Pearson 1905, Kendall 1953) concept, which suggests that prices only change randomly and these changes or their logarithm (Samuelson 1965) cannot be predicted. Fama (1965) combines this concept with the martingale property (Lévy 1934; Ville 1939) and puts forward the EMH, which in brief implies that prices are martingales with respect to an information set. In more detail, considering a probability space (, F, P ) and a filtration process F = (Ft ) that defines an information set (, F, F = (Ft ) , P ), prices are considered to be martingales with respect to the filtration Ft , i.e., E (pt+1 |Ft ) = pt and, therefore, E (Δpt+1 |Ft ) = 0.1 Heuristically, this means that, if prices changes due to information Ft , then the current prices incorporate all relevant information and they are the best predictor of future prices. They only change when F changes and thus, when there is new information. Following the random walk hypothesis, new information, i.e., innovations, εt ~(0, σ ε ), arrives randomly and prices are described as the sum of these innovations, pt = p0 + tt=1 εt . The explicit contribution of Fama (1965) is that he distinguishes three different types of information with consecutively nesting filtration processes Fpast prices ⊆ Fpublic ⊆ FAll that correspond to the  information that can be extracted from (i) past prices , (ii) from public information, observing past prices Fpast prices = Ft

is the space of all possible elementary outcomes and F is some σ-algebra sub-set of Ω. If F evolves over time, Ft is a filtration that describes the history of F up to time t. Then P is a mapping of F into [0, 1]. This is a formal definition of observable information that can be collected up to time t and be used in expectations. 1Ω

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  public and (iii) all conceivable information FAll = FtAll including Fpublic = Ft inf o

private information. Then, there is an efficient, according toan information set Ft inf o inf o , which is the with info = (past prices, public, All), price, μt = E υt |Ft conditional expectation of the “true” value of the asset, υt . If the prices are equal to inf o inf o μt , pt = μt , then they are said to be efficient with respect to the information set they are conditional on. Fama (1965) distinguishes three levels of market efficiency. The weak form is used to describe asset prices that incorporate information extracted from past prices. This implies that no technical trading can be profitable. The semi-strong form is used to describe asset prices that incorporate all public information, such as public news. This implies that no trading on public information can be profitable. Finally, in its strictest version, the strong form is used to describe asset prices that incorporate all available information, even non-publicly disclosed, such as private information accessible only to insiders. According to this level of efficiency no trading strategy can consistently beat the market because prices change due to new information, which arrives randomly. Overall, the EMH implies that in efficient markets prices equal the efficient price and reflect all available information. Consequently, price changes are random.2 pt = μt and Δpt = Δμt = εt ∼ (0, σε )

(1)

Inevitably, this theory is developed under some rather strict assumptions, which are not entirely confirmed by empirical observations. (i) Prices are assumed to incorporate new information immediately, which (ii) is assumed to be received simultaneously by (iii) homogenous rational investors. Previous literature openly challenges the last two, suggesting that the existence of various biases – such as the marginal cost of information (e.g., Jensen 1968) or behavioural biases (e.g., De Bondt and Thaler 1985) among many that have been discussed over the years – 2 This could also be written in a continuous time mathematical formulation, as a zero drift Brownian

motion Δpt = σ Wt . This approach usually focuses on the properties of volatility aggregation. For example, price change series that exhibit martingale or semi-martingale (have a predictable component) properties need to assume a volatility time deformation. This poses the following dilemma (e.g., Barndorff-Nielsen and Shiryaev, 2015), if a simple process, like W, is selected for the volatility, then a jump process needs to be employed for its time deformation, in order to account for the empirical properties of the price changes. In the opposite case, if a simple process, like the Poisson, is selected for the time deformation, then W is no longer a suitable candidate. This renders the continuous time notation rather inappropriate for this study for two reasons. First, the objective here is to describe and explicitly model “economic time” rather than assume an arrival process for it, with or without jumps. Second, the conceptual objective of this study is to highlight the importance of intraday market frictions, which arise even in a perfectly efficient market, where prices are governed by a simple W. Consequently, the focus is on predictable market microstructure frictions, rather than on the properties of ε, which would render W redundant.

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make prices deviate from their efficient level because not all investors access simultaneously the same level of information and, even if they do, they might not be homogenous or rational in analysing it. Consequently, phenomena of over- or under-reaction (e.g., Jegadeesh and Titman 1993) might delay prices in converging to their efficient levels. These phenomena might become more intense in a UHF setting because the assumptions of the EMH might no longer be plausible due to structural issues. The field of market microstructure, a term introduced by Garman (1976), focuses on the deviations from the EMH due to phenomena that are manifested in an intraday setting. At this level of trading activity where the time between events is measured in micro-seconds and that mechanical (algorithmic) trading is the norm rather than the exception, it would be absurd to assume that everybody has simultaneous access to the same level of information and that they are homogenous in analysing it. Instead, intraday price discovery is understood to be governed by a continuous interaction (e.g., O’Hara 1995) between liquidity (Tinic 1972; Tinic and West 1972) and information (Bagehot 1971; Glosten and Milgrom 1985; Kyle 1985). Market microstructure focuses on how liquidity, which becomes quintessential in this setup, continuously changes the market-wide supply and demand curves and facilitates convergence, rather than an immediate adjustment as the EMH would dictate, to a Walrasian (Walras 1874) equilibrium (Biais et al. 2005). This continuous liquidity provision, constantly trying to avoid exposure to better informed agents is a risk that needs to be managed, not only by designated market makers, but also by limit order traders, in their continuous price/quote setting.

2.1 Intraday Market Frictions I: Liquidity and the Cost of Immediacy ... suppose that all buyers of an asset arrive on Monday and all sellers on Tuesday... [they] may all agree on the “fundamental value“ of the asset, but . . . no trade will take place on Monday . . . [or] on Tuesday; . . . a role emerges for a market intermediary . . . O’Hara (2003)

On a lower frequency, the reference prices refer to closing prices. Trade execution issues become irrelevant at this scale. However, in an HFT setting, price formation is determined by structural issues and by the algorithm that matches and executes orders. Modern markets facilitate trading either with the existence of dedicated market makers or by the use of limit orders (market making on one side of the spread). Market makers have the obligation, in exchange for some price benefits, to stand there being ready to provide liquidity. This immediacy comes at a cost, either in the form of exchange fees, order processing, etc. (e.g., Demsetz 1971; Stoll 1978) or in the form of holding and managing inventories (e.g., Tinic 1972; Garman 1976). This cost is recovered through trading by charging a small fee, the bid-ask spread, to all transactions. Consequently, even in a fully efficient market where μt is a martingale, the transaction price might be affected by frictions. These frictions

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are customarily written as st = sqt , where s ≥ 0 represents one half of the spread, and qt = + 1 (−1) for a buy (sell), is a trade initiation variable (Madhavan 2000). This can be represented as: pt = μt + st and Δpt = Δμt + Δst = εt + sΔqt

(2)

More recent studies investigate the composition (e.g., Roll 1984; Stoll 1978; Ho and Stoll 1981, 1983) of st as well as its intertemporal characteristics (e.g., Cohen et al. 1980, 1983). Despite their notable differences, all of them recognize two major characteristics for liquidity frictions. First, since they are not linked to information, they do not affect the beliefs about the efficient price, μt , and therefore their price impact is only transitory. Second, since they are linked to liquidity their magnitude per trade is reversely related to liquidity. In the case of fixed costs, they carry a lower importance when a higher number of trades are executed. Along the same lines, market makers face the risk of intense directional demand, which might put pressure on their inventories. Reversing this pressure and, consequently, the cost of taking such an action should be lower when it is easier to do so, i.e., upon higher liquidity.

2.2 Intraday Market Frictions II: Information and Adverse Selection The market maker always loses to [informed] transactors, [but] . . . always gains in transactions with liquidity-motivated transactors. . . . [the] gains from liquidity-motivated transactors must exceed . . . losses to information-motivated transactors. Bagehot (1971)

In a seminal study, Bagehot (1971) argues that spreads would exist even in the absence of explicit trading costs, st . Even in an infinitely liquid market, where liquidity-induced costs become insignificant per transaction, transaction prices should still be expected to deviate from a fully efficient (martingale) price, because at this high-speed level of events, the second assumption cannot hold unconditionally. Information is understood to arrive randomly and even if everybody receives it at the same point in time, analyse it homogenously and submit it at the same time, orders can only be sequentially executed due to latency issues (Hasbrouck and Saar 2013). Consequently, the orders that are executed first, before information is fully price-resolved, are better informed compared to the remaining trades. This structural issue, even if the assumptions (ii) and (iii) hold in principle, makes them non-plausible because it “structurally” creates different agent groups with respect to their access to information, or at least their ability to use it timely. This also directly challenges assumption ( i) because an equilibrium price cannot be instantly reached and thus, prices cannot fully reflect all available information at all times.

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Several studies investigate this issue and recognize the existence of informed agents versus a group of liquidity motivated traders (e.g., Kyle 1985; Glosten and Milgrom 1985). Informed agents are understood to possess price-relevant information prior to anybody else and therefore they have an incentive to use it timely. They only appear in the market when this private information arrives, which is assumed to happen randomly, and their actions are revealed to the rest of the market through excessive liquidity (e.g., Easley and O’Hara 1992). This information revelation and its incorporation into prices is gradual and depends on how ‘naïve’ the uninformed investors are (O’Hara 2003). Admati and Pfleiderer (1988) recognize that some of the uninformed agents observe the market continuously and try to extract information signals before they are incorporated into prices. When they (believe that they) do, then they discretionarily trade on the newly extracted information and they act as better informed to the remaining uninformed agents. Their learning ability and their subsequent actions are also revealed through excessive liquidity and they drive the price into an equilibrium. This interaction between liquidity and information is at the core of intraday pricing (O’Hara 2003). Collectively, previous literature recognizes that intraday prices might deviate from their fully efficient prices and a purely random walk approach, even in the complete absence of liquidity frictions. The reason for that is that, in reality, when focusing on an event-by-event level of detail, information cannot be assumed to reach everybody simultaneously and thus, it cannot be instantaneously incorporated into prices; instead it is gradually revealed and incorporated. The direct implication of this postulate is that there exist patterns that can be identified and exploited. This is a direct violation of the simple martingale property and implies that there exist a predictable component, also conditional on the same level of information. It is customary in previous literature to dissect the revision in beliefs (or else, the arrival of new information), Δμt , into a purely unpredictable component of new (public) information innovations, εt ~(0, σ ε ), but alsoa predictable component, . Δ = (M (q)|F ), that is a predictable function M .. of the trade initiation t

t

t

variable, q, extracted from observing past information, Ft . pt = μt + st and Δpt = Δμt + Δst = εt + (Mt (q)|Ft ) + sΔqt

(3)

here represents the sensitivity of price changes to information extracted by observing the trading history up to time t (depending on the specification, it might be information up to t − 1). Market makers, who are also considered to be uninformed, will lose when trade with better informed agents and therefore, have the incentive to observe the market and try to identify their presence. They can only recover their losses either by trading with less-informed agents (e.g., Kyle 1985) or by making it costly for the informed agents to exploit minor price advantages (e.g., Bagehot 1971). They use the predictable component of prices as a reference pricing and, therefore, becomes their means for recovering potential losses from trading with better-informed agents. then becomes the information component of half the spread they charge.

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Inevitably, previous literature investigates how informed trades can be timely identified and be incorporated into prices. Previous approaches model Δμt with a wide spectrum of specifications varying from a purely random walk, εt ~(0, σ ε ) (Roll 1984), to information revealed in previous trades’ direction, Δμt = εt + Δqt − 1 (Huang and Stoll 1997), or in an ex-post regret-free setup, Δμt = εt + (qt − E (qt |Ft−1 )) (Madhavan et al. 1997). Although they might differ in their assumptions, all of them recognize the following: Information is revealed through the direction of trades. Second, this information refers to the “true” price of the asset and therefore, it revises the expectation of the efficient price. Consequently, its impact is permanent. These approaches, although insightful, disregard a major issue that will be discussed in the following section, the interaction between information and liquidity. They consider that information can only be revealed through the direction of trades. However, other studies challenge this view and suggest that information cannot be thought independently of liquidity.

2.3 A more Detailed View: The Role of Time . . . sometimes time flows very rapidly in financial markets while in other periods it moves slowly . . . Russel and Engle (1998)

The discussion so far highlights the challenges that market microstructure poses on the EMH. When the level of interest is every single event, the structural design of the market has a significant impact on how and, most importantly, when information is incorporated into prices. Previous studies on the EMH and several empirical anomalies employ observations of a much lower frequency, such as daily, weekly, monthly or annually. The basic characteristic of these observations is that the time in between them is of fixed duration and that all information and its impact on price discovery is aggregated. In sharp contrast, the availability of UHF data enables a completely disaggregated view, where each event contributes individually to price discovery and, most importantly, its arrival time carries economic significance. This shift from an aggregated to a granular approach challenges the foundations of the EMH because the assumptions that might hold on an aggregated level do not seem plausible at this level, because the dimension of time becomes an integral part of the pricing process. This, irregularly spaced time, challenges the previous lower frequency setup on multiple fronts. First, the assumptions of the discrete timing econometrics do not hold unconditionally when the interval between observations is not fixed. This requires a new methodological approach. Second, information does not simply arrive; it arrives in time and it takes time to be price-resolved. Therefore, it has a duration itself. Due to the sequential nature of the algorithm that clears transactions (e.g., price or time priority), this lifespan of information results in some trades being executed at preferential rates, compared to subsequent transactions and,

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therefore, creates a classification of trades according to their access to information; a direct violation of the second assumption of the EMH. This is in the case of public information which is immediately dispersed. Third, when private information arrives into the market it is understood to be accessible only to a limited group; the informed traders. According to previous literature (e.g., Easley and O’Hara 1992) they only appear in the market when they possess exploitable information that is not price-resolved. Consequently, liquidity rises temporarily – the lifespan of private information – from its “normal” levels and their information is revealed through their actions. This crucial point, which is largely ignored in the adverse selection price component, suggests that the arrival rate of events, i.e., how fast they arrive – the arrival of volume (e.g., Easley and O’Hara 1987), the arrival of transactions (frequency) (Diamond and Verrechia 1987), etc. – carries information that can be deciphered by observing past history. Fourth, because information itself has a lifespan that also affects the arrival rate of events – for example, volume accumulates faster when there is private information – their arrival times might be clustered, in a way that might be conditionally predicted. Overall, it becomes imperative to consider the transition from calendar time that simply lapses to the notion of economic time, which is instead used to describe the arrival of events. Unlike calendar time, economic time might be expanded or contracted, depending on how fast events arrive. The speed of the arrival of events is where the information and liquidity market forces meet (O’Hara 1995) and constitutes the synthetic material for price discovery. Consequently, the speed of the arrival of the events becomes informative and acquires economic significance. In order to account for the properties of economic time, previous methodological approaches need to adjust accordingly and move from calendar time, t, to event time, i. The tool that has been mostly used for this time deformation is the theory of point processes. A point process is a probabilistic model for random scattering on a space/time dimension (Daley and Vere-Jones 2003). Of particular interest is the stochastic process of arrival times, where each point of the process, in the timeline t, represents the arrival of an event, i. This creates a time-series of arrival times {t0 , t1 , . . . , ti , . . . } with t0 < t1 < . . . < ti < . . . , t ∈ T, which now shifts the interest from simply t to ti . This implies that the counting of events, N(ti ), is not fixed in fixed time intervals Δt (as it is the case in lower frequency observations), or simply that the inter-event time, xi = ti − ti − 1 called duration, is not fixed. This formulation takes into consideration that the arrival time of events is irregularly spaced and offers a wide range of modelling it from a completely random series to a conditionally clustered one. This can be done by considering that durations xi are not fixed and that arrival times are distributed according to f (t), t > 0, which is a positive support distribution (e.g., the Poisson distribution) with a cumulative distribution function F(t). The stochastic nature of this process can be fully described by its “conditional intensity”, λ(t), which is the probability of an event to happen now, given that it has not happened so far. Mathematically, this can be expressed using the distribution of arrival times as: f (t) (t)) λ(t) = lim P (N (t+Δt)>N = 1−F Δt (t) . Then the expected number of events over Δt→0

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Δt can be given by E [N (tt+Δt ) − N (tt )] =

t+Δt 1

λ(t)dt. This formulation can also

t

be conditional on past information up to point i, Fi , taking the form: f (ti |Fi−1 ) P (N (ti + Δt) > N (ti ) |Fi−1 ) = Δt→0 Δt 1 − F (ti |Fi−1 )

λ (ti |Fi−1 ) = lim

(4)

The conditional intensity, also known as the “hazard” rate, is very flexible and can be parameterized in various ways to capture the potential conditionally clustering of the arrival of events, which as it has been discussed above is essentially the way information is diffused in an intraday context. What makes the conditional intensity, λ (ti |Fi−1 ), an appropriate tool to investigate the intraday dynamics of the arrival of various events is that it converts the flow of events – like the arrival of volume or volatility or number of orders, etc. – into a “rate” of arrival. This rate is the inverse of the waiting time and is now a variable that can be observed and predicted. Consequently, arrival time now  becomes part of the  history, Ft , which is no longer observed at fixed Δt. Ft :=

ˇ

Zt

−→ Fi :=

ˇ

ˇ

Z i , x i , in order to denote that

ˇ

ˇ

the history of the vector Z t = {Z 1 , . . . , Z t }, is now updated at event time i, Z i = ˇ

{Z 1 , . . . , Z i }, and that it includes the history of waiting times x i = {x1 , . . . , xi }, or ˇ

arrival times t i = {t1 , . . . , ti }, too.

From now on, all notation will use the index i, instead of t, in order to denote the time deformation and the move from “calendar” to “economic” time.

Consequently, it would be more appropriate to express the intraday pricing in event, rather than in calendar time, which would take into consideration that Δt is not fixed: pi = μi + si and Δpi = Δμi + Δsi = εi + (Mi (q)|Fi ) + sΔqi

(5)

3 Economic Time Modelling: Deciphering the Arrival of Events One of the most prominent approaches in modelling economic time is the Autoregressive Conditional Duration (ACD) model of Engle and Russell (1998), which estimates the conditional intensity, λ (ti |Fi−1 ), of the arrival of intraday events by using the ratio of realized durations xi – a waiting time in between two consecutive events – over their conditional expectations, ψ i = E (xi |Fi−1 ), where

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377

Fi = {x1 , . . . , xi }. The ACD model can be formulated as.  xi = ψi εi , with ψi = E xi |xˇi−1 , εi ∼ i.i.d.and E (εi ) = 1

(6)

The novelty of this modelling comes from offering a wide range of parameterizations of the conditional intensity of the arrival times, λ (ti |Fi−1 ), by expressing it as a function of the waiting times, xi , λ (ti |Fi−1 ) := λ (xi |Fi−1 ). The new conditional intensity function can now be expressed by using the conditional distribution of durations, i.e., waiting times, f (xi |Fi−1 ), and their cumulative distribution function f x |Fi−1 ) . Consequently, both F (xi |Fi−1 ), as λ (ti |Fi−1 ) := λ (xi |Fi−1 ) = 1−F( ix |F ( i i−1 ) the conditional mean of waiting times, ψ i , and the distribution of the innovations, f (εi |Fi−1 ) = f (xi |Fi−1 ) ψi −1 – called standardized durations, εi – can be modelled with a plethora of specifications according to the requirements of each market/setup. Partially due to this flexibility, but also its close resemblance (Pacurar 2008) to Autoregressive Conditional Heteroskedasticity, ARCH (Engle 1982), and Generalized ARCH, GARCH (Bollerslev 1986), specifications, the ACD framework was rapidly adopted in order to investigate phenomena related to economic time and expanded in order to incorporate more complex intraday stylized factors. Three main extensions are of particular interest to my work, mainly referring to: (i) the conditional mean; (ii) the conditional density function; and (iii) the inclusion of multiple layers/levels of information.

3.1 Arrival of Events: Asymmetry and Non-Linearity In the original ACD model, Engle and Russell (1998) purport that the stochastic properties of economic time, i.e., the conditional intensity of waiting times, is exogenously determined. They remain consistent in this argument even in later work where the durations interact with other marks such as price changes (e.g., Russell and Engle 2005) and volatility (e.g., Engle 2000). Although convenient for estimation purposes, this notion of complete exogeneity, or no reverse (Granger) causality of time might be rather unrealistic when considering the higher moments of durations (e.g., Bauwens et al. 2004; Bauwens and Veredas 2004). One of the first extensions of the model, toward this direction, refers to the ability of the conditional mean specification, initially and ARMA type specification (Engle and Russell 1998), to capture higher order complexities that might be present in the empirical data. A major issue addressed is potential non-linearities, with the specifications varying from a logarithmic, Log-ACD (Bauwens and Giot 2000), to an exponential and a Box-Cox, EXACD and BCACD (Dufour and Engle 2000a) transformation. In addition, other empirical specifications consider that at a UHF level trade clustering might exhibit a very long memory which should also be accounted for, but with a parsimonious lag-structure, like the Fractionally Integrated ACD, FIACD (Jasiak 1999). Another issue that is also addressed in the literature is

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the potentially asymmetric response of trading to different events, mostly captured by discrete (e.g., the Threshold-ACD (ACD), Zhang et al. 2001) or smooth transition (e.g., the Smooth Transition-ACD (ST-ACD), Meitz and Teräsvirta 2006) regimeswitching models. All these approaches share a deterministic structure, which according to Ghysels et al. (2007) is notably insufficient in capturing the higher moments of the Data Generation Process (DGP) of durations, which should also be included in the modelling. They develop the Stochastic Volatility Duration (SVD) model, which like the Stochastic Duration (SD) model of Bauwens and Veredas (2004), introduces an innovation term in the conditional mean specification that refers to (over-) under-dispersion of the conditional expectations relative to the innovations εi . Overall, Bauwens and Giot (2000) suggest that an appropriate conditional mean specification contributes more to fitting than the conditional density specification, probably because it accounts for observable factors that can be explicitly modelled. Recent studies (e.g., Kalaitzoglou and Ibrahim 2013a; Kalaitzoglou 2018) follow this proposition by introducing higher degrees of non-linearities without necessarily challenging the exogeneity assumptions of the initial ACD framework, and without the need of a new innovation term in the conditional expectations (e.g., Bauwens and Veredas 2004). Overall, the drastic improvement of model fitting, especially when additional factors are considered, emphasizes the importance of market transparency measures that would improve the quality and quantity of observable factors. These factors can be used to improve economic time modelling and, thus, reduce the magnitude of liquidity frictions – due to better predictability and thus better liquidity risk management – and, consequently, improve market efficiency.

3.2 Arrival Time and Agent Types When focusing on a UHF setting, the disaggregated nature of the irregularly spaced time might pose a direct challenge to the first assumption of the EMH, that prices reflect all relevant information instantaneously. A key idea is the role of time in information resolution, and more precisely when and for how long information is exploitable. When focusing on the process, rather than the content of information, markets can be seen as being efficient, in the sense that they rationally incorporate information, but imperfectly, in the sense that it takes some time from the moment that information hits the market until it is fully incorporated into prices. Public information is assumed to be immediately accessible by everybody, but due to the sequential nature of order execution some trades are executed at preferential rates. Consequently, public information is only gradually incorporated into prices, but at a rate that is much faster than the one of private information. That is because private information needs to be extracted first, after observing trading history. In both cases, but especially when private information arrives in the market, this period of “price adjustment” provides the opportunity to some traders to act before everyone else and make a profit. Consequently, the information benefit is now translated

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into a “timing” benefit. Modelling such a time dimension of information allows for identifying informed trades/traders in a natural way, based on past observable information. The natural modelling part that allows for a link between trading patterns and the existence of latent groups is the second component of the ACD modelling (i.e., conditional density), which, unlike the conditional mean that is used in order to model observable factors, is usually associated with latent determinants of the DGP of durations. Inevitably, this constitutes another area of extension of the original ACD. Early studies criticize the inadequacy of simple distributions with a low number of free shape parameters, like the Exponential or the Weibull that were used by Engle and Russell (1998), suggesting more elaborate counterparts, such as the Generalized Gamma (Zhang et al. 2001), the Pareto (De Luca and Zuccolotto 2006) and the Burr (Grammig and Maurer 2000) distributions. Although, increasing complexity is rewarded with better fit, Bauwens et al. (2004) argue that a single distribution is rather restrictive in capturing all the latent factors associated with it. Several studies address this concern by employing a mixture of distributions and can be generally classified into two broad categories. The first assumes that the latent factors included in the innovations are highly correlated with different observable factors whose regimes determine which distribution durations are drawn from (e.g., De Luca and Zuccoloto 2006). The second only considers latent factors, whose states determine the nature of the distribution. The modelling varies from a discrete version (e.g., De Luca and Gallo 2004) with a Markov chain (Hujer and Vuleti´c 2007) and expand with an increasing complexity in the use of copulas (e.g., De Luca et al. 2008). The development of the mixture of distribution models is based on the idea that the agents’ base is not homogenous and, therefore, not all transactions come from the same group. The original group, to which a transaction belongs, cannot be identified directly, but it should be partially revealed by its characteristics. More precisely, Hujer and Vuleti´c (2007) conjecture that the instantaneous arrival rates – or else the hazard function or the conditional intensity – of the transactions of each group should be distinct, i.e., flat for the uninformed, decreasing for the informed and increasing for traders who observe the market and act upon signals (Gerhard and Hautsch 2007). This is a crucial link between economic time modelling and the identification of intraday phenomena, and a characteristic example of how the arrival rate of events can be used in order to extract information signals from past trading activity. Kalaitzoglou and Ibrahim (2013b) combine these two and suggest a modelling that uses observable variables in order to extract information about the existence of different agent groups. The concept is based on the idea that the existence of different types of agents is expressed in their trading characteristics. Consequently, the identification of the agent types can be “reverse engineered” by observing different classifications of arrival rates, i.e., conditional intensities.

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K. Iordanis

Information

Information

Information

Episode P1

Episode P2

Episode P3

t0

t1

t2

t3

Exogenous

Informed traders

Discretionary

Information ceases to

information

start to exploit

liquidity traders act

be exploitable (goes

arrives

their information

(after observing t1

‘public’). No incentive

(transaction)

(or enough similar

for any of them to

transactions))

trade.

Let the first arrow represent the overall trading activity of a market. When there is no private information, which would instigate an information episode, Pin , in = (1, . . . , IN), the “normal” trading activity and, consequently, the “normal” arrival rate of trades should be time invariant (e.g., Hujer and Vuleti´c 2007), because it is not related to private information and, thus, it should represent the arrival of uninformed trades. This can be translated into a flat hazard function, i.e., conditional intensity, and can be also thought of as being consistent with a market that is semi-strong efficient. In such a market, public information arrives randomly and that is usually modelled with a Poisson distribution. The inter-event distribution of the waiting time of a Poisson distribution follows an exponential distribution,  P ublic −→ which exhibits a flat hazard function. Consequently, λuninf ormed ti |Fi−1   P ublic ; = 0. λuninf ormed ti |Fi−1 However, when private information, FiP rivate , arrives in the market, it instigates an information episode, Pin , which is explicitly described in the second arrow. The market participants, who possess that information, i.e., informed agents (e.g., Kyle 1985), have the incentive to act upon it before it becomes public information at time t3 . Consequently, the conditional probability of the arrival of their trades should decrease over time, especially when there they compete with other informed agents. Mathematically, this is translated into a decreasing hazard function (e.g., Gerhard    P rivate −→ λ P rivate ; < and Hautsch 2007), i.e., λinf ormed ti |Fi−1 inf ormed ti |Fi−1 0. Kalaitzoglou and Ibrahim (2013b) introduce an additional type of agent, who observes the market, extracts signals and then trades upon them until the information becomes public. These traders, i.e., fundamentals, trade on extracted fundamental information and they have a discretion on when (timing) they will

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submit their trades. This is highly in line with the discretionary liquidity traders of Admati and Pfleiderer (1988). The probability of arrival of their trades is zero when there is no information, stays at zero until informed traders appear in the market and then starts increasing when they start extracting this information. Consequently, their arrival rate should be an increasing function of time, which  P rivate (extracted) −→ mathematically can be denoted as λf undamentals ti |Fi−1   ; P rivate (extracted) λf undamental ti |Fi−1 > 0. Collectively, these approaches highlight that the use of observable information is sufficient in extracting non-price, price-related information. The immediate implication of that is private information can be extracted by observing non-price marks before this information is incorporated into prices. This is relevant to various aspects of trading practice. First, it highlights the benefit of possessing information before it is fully incorporated into prices. At the microstructure level, market imperfections are exploitable, even for a very short period of time, while information is obtained at a significant cost. This new “time dimension” of information increases the value of “real time” information, since it can increase the profitability of intraday trading strategies. Consequently, this can affect the attitude of market participants towards the timing and the cost of acquiring information. Second, market participants can now identify informed trades by simply observing past transactions. They can extract price-relevant information and can act upon it, so improving the profitability of their strategies. Third, the proposed model can be used for monitoring purposes by regulatory authorities. By identifying informed trading, further action can be taken to protect the market from “manipulation”. This can also be applied in real time to adjust the balance between market innovation and liquidity.

3.3 Multiple Marks and Multivariate The importance of economic time modelling at a UHF level is undeniable, but in several instances, the event, the arrival of which is of interest, needs to be defined in broader terms. The initial ACD modelling refers to the waiting time till the next transaction. This is a well-defined event that is defined by the execution of a market order on the opposite side of the spread. However, different types of events might be of interest in a different UHF context. For example, an HFT fund/algorithm might consider only price changes of a certain magnitude and above, or a market maker might need to trigger quote revisions for inventory management after certain levels of accumulated volume, or a limit order strategy might face a higher execution risk if a certain level of accumulated volume takes longer to get executed, etc. In all these cases, there are other characteristics, alongside duration, that need to be taken into consideration. These characteristics are called marks and they are only observed when the actual duration is observed; depending on the event at the time

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K. Iordanis

of a transaction or an order submission, etc.These marks of interest, Zi , are then accumulated from event to event, ξ (ti ) = i,0