Financial Risk Management: Management of Interest Risk from a Corporate Treasury Perspective in a Service Enterprise : Management of Interest Risk from a Corporate Treasury Perspective in a Service Enterprise [1 ed.] 9783836646185, 9783836696180
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Jana Schönborn
Financial Risk Management
Copyright © 2010. Diplomica Verlag. All rights reserved.
Management of Interest Risk from a Corporate Treasury Perspective in a Service Enterprise
Diplomica Verlag
Schönborn, Jana. Financial Risk Management: Management of Interest Risk from a Corporate Treasury Perspective in a Service Enterprise : Management of Interest Risk from a
Jana Schönborn Financial Risk Management: Management of Interest Risk from a Corporate Treasury Perspective in a Service Enterprise ISBN: 978-3-8366-4618-5 Herstellung: Diplomica® Verlag GmbH, Hamburg, 2010
Copyright © 2010. Diplomica Verlag. All rights reserved.
Dieses Werk ist urheberrechtlich geschützt. Die dadurch begründeten Rechte, insbesondere die der Übersetzung, des Nachdrucks, des Vortrags, der Entnahme von Abbildungen und Tabellen, der Funksendung, der Mikroverfilmung oder der Vervielfältigung auf anderen Wegen und der Speicherung in Datenverarbeitungsanlagen, bleiben, auch bei nur auszugsweiser Verwertung, vorbehalten. Eine Vervielfältigung dieses Werkes oder von Teilen dieses Werkes ist auch im Einzelfall nur in den Grenzen der gesetzlichen Bestimmungen des Urheberrechtsgesetzes der Bundesrepublik Deutschland in der jeweils geltenden Fassung zulässig. Sie ist grundsätzlich vergütungspflichtig. Zuwiderhandlungen unterliegen den Strafbestimmungen des Urheberrechtes. Die Wiedergabe von Gebrauchsnamen, Handelsnamen, Warenbezeichnungen usw. in diesem Werk berechtigt auch ohne besondere Kennzeichnung nicht zu der Annahme, dass solche Namen im Sinne der Warenzeichen- und Markenschutz-Gesetzgebung als frei zu betrachten wären und daher von jedermann benutzt werden dürften. Die Informationen in diesem Werk wurden mit Sorgfalt erarbeitet. Dennoch können Fehler nicht vollständig ausgeschlossen werden und der Verlag, die Autoren oder Übersetzer übernehmen keine juristische Verantwortung oder irgendeine Haftung für evtl. verbliebene fehlerhafte Angaben und deren Folgen. © Diplomica Verlag GmbH http://www.diplomica-verlag.de, Hamburg 2010
Schönborn, Jana. Financial Risk Management: Management of Interest Risk from a Corporate Treasury Perspective in a Service Enterprise : Management of Interest Risk from a
Financial Risk Management – Management of Interest Risk from a Corporate Treasury Perspective in a Service Enterprise
Copyright © 2010. Diplomica Verlag. All rights reserved.
Jana Schönborn
Schönborn, Jana. Financial Risk Management: Management of Interest Risk from a Corporate Treasury Perspective in a Service Enterprise : Management of Interest Risk from a
Copyright © 2010. Diplomica Verlag. All rights reserved.
Ji: Chinese character that is part of o both meanings, risk andd opportunity.
Schönborn, Jana. Financial Risk Management: Management of Interest Risk from a Corporate Treasury Perspective in a Service Enterprise : Management of Interest Risk from a
Table of Contents List of Figures ............................................................................................................ III List of Abbreviations ................................................................................................. IV 1. Introduction ............................................................................................................. 1 2. Essentials of Financial Risk Management in a Service Enterprise..................... 2 2.1. Why Manage Financial Risk? ............................................................................ 2 2.2. Classification of Interest Rate Risk in the Framework of Risk Management .... 3 2.3. The Financial Risk Management Cycle ............................................................. 5 2.4. Insight into the Service Sector and its Current Trends with respect to Financial Risk Management ............................................................................... 7 3. Treasury as a Central Institution of Financial Risk Management ................... 10 3.1. Corporate Treasury Risk Management and its Influencing Factors ................. 10 3.2. Financial Risk Management within the Scope of the Treasury Risk Policy .... 11 4. Quantifying Interest Rate Risk ............................................................................ 13 4.1. Understanding Interest Rate Risk ..................................................................... 13 4.2. Duration and Convexity ................................................................................... 15 4.3. Value at Risk .................................................................................................... 18 4.3.1. The Concept of Value at Risk ................................................................ 18 4.3.2. Historical Simulation.............................................................................. 21 4.3.3. Variance-Covariance-Approach ............................................................. 22 Copyright © 2010. Diplomica Verlag. All rights reserved.
4.3.4. Value at Risk of Derivatives .................................................................. 25 4.4. Cash Flow Mapping ......................................................................................... 25 4.4.1. Determining the Cash Flow Structure .................................................... 25 4.4.2. Sensitivity Mapping ............................................................................... 27 4.4.3. Variance Mapping .................................................................................. 29 4.5. Implications for a Service Enterprise ............................................................... 30
Schönborn, Jana. Financial Risk Management: Management of Interest Risk from a Corporate Treasury Perspective in a Service Enterprise : Management of Interest Risk from a
5. Interest Risk Management Techniques ............................................................... 33 5.1. Hedging ............................................................................................................ 33 5.1.1. Introduction to Hedging ......................................................................... 33 5.1.2. Symmetric Hedging Instruments ............................................................ 34 5.1.2.1. Forward Rate Agreement ........................................................... 34 5.1.2.2. Interest-Rate Future ................................................................... 35 5.1.2.3. Interest-Rate Swap ..................................................................... 36 5.1.3. Asymmetric Hedging Instruments ......................................................... 37 5.1.3.1. Option ........................................................................................ 37 5.1.3.2. Cap, Floor and Collar................................................................. 40 5.2. Implications for the Portfolio Alignment of a Service Enterprise ................... 41 5.2.1. Duration .................................................................................................. 41 5.2.2. Benchmark ............................................................................................. 43 5.2.3. VaR Limit ............................................................................................... 43 6. Conclusion .............................................................................................................. 45 7. Appendices ............................................................................................................. 47
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8. Bibliography........................................................................................................... 52
Schönborn, Jana. Financial Risk Management: Management of Interest Risk from a Corporate Treasury Perspective in a Service Enterprise : Management of Interest Risk from a
List of Figures Figure 1: Overview of the Risks Facing an Enterprise .................................................. 3 Figure 2: The Risk Management Cycle ......................................................................... 5 Figure 3: Risk-Tolerability Matrix ................................................................................. 6 Figure 4: Risk-Time Relation ...................................................................................... 11 Figure 5: Euro Area Yield Curve (Spot) ...................................................................... 14 Figure 6: Price-Interest Relation .................................................................................. 16 Figure 7: Density Function of the Normal Distribution ............................................... 19 Figure 8: Relation between the Z-Score and the Level of Confidence ........................ 20 Figure 9: Interest Rate Risk of Positive and Negative Cash Flows ............................. 26 Figure 10: Gross Value Added in Germany................................................................... 7 Figure 11: Sales Statistics of Selected Branches of the German Service Sector ........... 8 Figure 12: Overview of Derivative Instruments .......................................................... 33 Figure 13: Profit-Loss-Profile of a Long (left) and a Short (right) FRA ..................... 35 Figure 14: Intrinsic Value of an Option ....................................................................... 38 Figure 15: Profit-Loss-Profile of a Long (left) and a Short (right) Call ...................... 39 Figure 16: Profit-Loss-Chart of a Long (left) and a Short (right) Put.......................... 39 Figure 17: Put-Call-Parity ............................................................................................ 40 Figure 18: Summary of Hedging Strategies ................................................................. 41 Figure 19: Selection of a Benchmark with Optimum Interest Cost for Enterprises
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with a Debit Carryover ............................................................................... 42
Schönborn, Jana. Financial Risk Management: Management of Interest Risk from a Corporate Treasury Perspective in a Service Enterprise : Management of Interest Risk from a
List of Abbreviations AktG
Aktiengesetz (Company Law)
BilReG
Bilanzrechtsreformgesetz (Accounting Law Reform Act)
CAPM
Capital Asset Pricing Model
CFO
Chief Financial Officer
CRO
Chief Risk Officer
DAX
Deutscher Aktienindex (German Stock Index)
DCGK
Deutscher Corporate Governance Kodex (German Corporate Governance Code)
E-SOX
The European Sarbanes-Oxley Act (also 8th Company Law)
ECB
European Central Bank
EU
European Union
EUREX
European Exchange
EURIBOR
Euro Interbank Offered Rate
EWMA
Exponentially Weighted Moving Average
Fed
Federal Reserve (of the United States)
FRA
forward rate agreement
GmbH
Gesellschaft mit beschränkter Haftung (limited liability company)
GmbHG
GmbH-Gesetz (Limited Liability Company Law)
HGB
Handelsgesetzbuch (German Commercial Code)
IFRS
International Financial Reporting Standards
k
correlation coefficient
KonTraG
Gesetz zur Kontrolle und Transparenz im Unternehmensbereich (Corporate Sector Supervision and Transparency Act)
LIBOR
London Interbank Offered Rate
LIFFE
London International Financial Futures and Option Exchange
m
million
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NYSE Euronext New York Stock Exchange Euronext OTC
over-the-Counter
OECD
Organisation for Economic Co-operation and Development
P/L
profit and loss
resp.
respectively
SE
Stock Exchange
SOX Act
Sarbanes-Oxley Act
VaR
value at risk
Schönborn, Jana. Financial Risk Management: Management of Interest Risk from a Corporate Treasury Perspective in a Service Enterprise : Management of Interest Risk from a
1. Introduction The importance of a systematic risk identification, measurement and management as a management duty has increased in recent years. After risk management and interest risk management in particular was primarily relevant for banks in the past, it is a crucial competition factor for all enterprises today. Especially since the recent financial crisis treasurers are far more risk conscious and companies are reassessing their financial risk management procedures. The most important parameter for the cost of financing and the return of capital investments is the interest rate. However the interest rate is subject to fluctuations, what constitute the interest rate risk the company is exposed to 1 . With increasing volatile financial markets and global competition CFOs are focusing more and more on an efficient measurement and management of interest rate risk.2 In this context this academic paper aims to point out the risks of an adverse change in interest rates for a corporate portfolio of interest-bearing positions and show possibilities to measure and manage these risks. The 2nd and 3rd sections set the scene for interest risk management in a corporate treasury of a service enterprise by providing essential knowledge about financial risk management and giving an insight into the characteristics of a service enterprise as well as the responsibilities of a corporate treasury and the factors that influence the treasury risk management approach. In section 4 and 5 respectively follows a process-oriented instruction of how to quantify interest rate risk and how to manage it. Besides the risk measures duration and convexity (4.2), two different approaches to value at risk, the historical simulation (4.3.2) and the variance-covariance-approach (4.3.3), will be examined. The value at risk is a measure to quantify risk that allows to express the risk exposure with a single absolute figure. For the management of the interest rate risk an overview
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of possible hedging instruments to reduce interest risk exposure will be given and their different strategies examined (5.1). All approaches will be measured against their practical feasibility and for both, the quantification and the management of interest rate risk, implications for the implementation in a service enterprise will be provided (4.5; 5.2). The conclusion serves for a critical reflection of all methods being discussed.
1
The central bank sets the base rate for inter-bank lending that in turn affects the market interest rate. Important central banks are for instance the ECB for the Euro area and the Fed for the United States. 2 Sanders, 2009
1
Schönborn, Jana. Financial Risk Management: Management of Interest Risk from a Corporate Treasury Perspective in a Service Enterprise : Management of Interest Risk from a
2. Essentials of Financial Risk Management in a Service Enterprise 2.1. Why Manage Financial Risk? Centralized risk management is useful to any corporation that has exposure to financial risks.3
This statement can be backed up by many aspects a firm shall consider. The first compelling reason for a company to make a point of striving for an effective financial risk management is the comprehensive regulatory framework. After KonTraG demands regular monitoring and external reporting of the key risks since 1998, some other regulations have been passed in recent years.4 A good example is the new Basel II Accord (2007) that caused changes in the bank lending process. The relation of the total risk exposure to the equity capitalisation and the amount of working capital defines the probability of insolvency and thus influences the rating. A bad rating will lead to higher cost of borrowing or no financing at all. A prudent treasury risk management will avoid financial distress by stabilising cash flows. This results in a better capacity to serve loans and lowers the possibility of insolvency. With a good rating a company's financing options will be enhanced, not only in terms of an easier approval process but also through reduced financing cost. This is even more important in times when the risk appetite of banks is low and sourcing of finance in general becomes difficult. Thus with risk adjusted equity capitalisation calculations, the risk management defines the minimum amount of equity needed to cover possible losses.5 According to the CAPM the shareholders expect a higher return when making a more risky investment. Reducing the fluctuations of cash flows will advance the ability to plan and control. Thus predictable cash flows will not only reduce risk but also lead to less cost of unplanned financing and thus have a positive effect on the expected profit. Therefore it is a company's objective to reduce the volatility of returns in relation to the market in order to optimise shareholder value. Moreover unexpected financial Copyright © 2010. Diplomica Verlag. All rights reserved.
losses could have an adverse impact on a company’s chosen strategy. The strategy might than need to be modified, postponed or completely cancelled. Financial risk management provides transparency of the risk situation and the possibility to control such losses by weighting the expected earnings of a business decision against the risks arising with it.6 3
Jorion, 2007, x Since the legal foundation of the financial risk management is not the main focus in this paper but should also not be disregarded completely, a list of the most important regulations can be found in Appendix 1. 5 Gleißner, 2007 6 Association of Corporate Treasurers, 2009 4
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Schönborn, Jana. Financial Risk Management: Management of Interest Risk from a Corporate Treasury Perspective in a Service Enterprise : Management of Interest Risk from a
Overall it can be said, that a proactive addressing of financial risks may provide an organisation with a competitive advantage. Thus the design and implementation of an appropriate risk management system and its ongoing revision as external conditions or internal requirements change, is a core strategic tool and ensures to identify, measure and manage the firms risk exposure in an effective way.7
2.2. Classification of Interest Rate Risk in the Framework of Risk Management Since there is no consistent definition of the term risk, the understanding used in this paper should be determined as follows: “Risk can be defined as the volatility of unexpected outcomes, which can represent the value of assets, equity or earnings. Firms are exposed to various types of risks, which can be classified broadly into business and financial risks.”8 Whereas KonTraG only considers negative deviations of actual figures to the projected outcome as a threat, BilReG also includes positive ones. The latter is also reasonable from a financial point of view, since positive and negative deviations might offset. Risk management is defined as the systematic treatment of risks, including all processes involved in quantifying business and financial risks and their corresponding management.9
Risk
Strategic risk
Political risk
Financial risk
Default risk
Market risk
Interest rate risk
Equity risk
Sourcing / Sales risk
Liquidity risk
Currency risk
Corporate Governance risk
Operational risk
Commodity risk
Figure 1: Overview of the Risks Facing an Enterprise
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The main focus of this study is on interest rate risk and its respective management. Interest rate risk belongs, together with equity risk, currency risk and commodity risk to the market risk that is in turn counted among the financial risks of a firm, “[…] which relate to possible losses owing to financial market activities.”10 Wolke defines interest rate risk as market interest rate related capital risk, which can occur either as
7
Gleißner, 2007 Jorion, 2007, 3 9 Wolke, 2008 10 Jorion, 2007, 4 8
3
Schönborn, Jana. Financial Risk Management: Management of Interest Risk from a Corporate Treasury Perspective in a Service Enterprise : Management of Interest Risk from a
interest cost or return risk or as present value11 risk. It is derived from the risk of an adverse change in market interest rates and the resulting possibly negative impact on the firm’s profitability or asset value. It is particular significant for capital-intensive industries and thus for financial institutions. For a corporate, such as a service enterprise, the impact of interest rate risk depends on the amount of its assets and the value of interest rate costs to serve its liabilities.12 Another aspect of interest rate risk that is ignored by Wolke is the macro-economic interest rate exposure. This is a hidden risk resulting from the sensitivity of sales and profitability of a firm to interest rate changes. However, this impact is hard to predict and thus difficult to include in the risk quantification. For a non-financial service enterprise a direct relationship between the level of interest rates and the success of the operational business cannot be found. Therefore this risk will be disregarded in this here.13 Interest risk management is the systematic treatment of interest risks facing the enterprise. It includes all activities involved in defining an interest risk management approach, measuring the interest risk exposure and subsequently managing it with appropriate instruments. The first step is the analysis of the portfolio, the measurement of its interest rate risk and the determination of the possible change of its present value due to the expected market development. This analysis helps to identify possible adjustment needs.14 With modern interest management instruments the structure of the portfolio can be easily adapted to changed conditions. This means that interest developments do not have to be accepted, but there is the possibility of hedging interest rate risks. With respect to interest risk management a passive and an active management style can be differentiated. Passive strategies require only minimum hypotheses about the future market interest rate development and supersede a continuous portfolio Copyright © 2010. Diplomica Verlag. All rights reserved.
switching. Here one distinguishes between so-called buy-and-hold strategies, where acquired interest instruments are kept in the portfolio up to their maturity, and index fund strategies, where the portfolio shall achieve the performance of the market. An objective of passive control measures is to attain the same returns and the same risk as a selected benchmark.15 11
The present value of an interest-bearing position is the sum of its discounted cash flows. For more details see section 4.1. Wolke, 2008 Donohoe, 2003, Part 1 14 Scharpf & Luz, 2000 15 Eller, Gruber & Reif, 2002 12 13
4
Schönborn, Jana. Financial Risk Management: Management of Interest Risk from a Corporate Treasury Perspective in a Service Enterprise : Management of Interest Risk from a
The active management by contrast aims to out-perform the benchmark based on its own interest forecast 16 . According to the expected interest rate development and following strategic considerations the possibility exists to allow increased cash flows in certain maturity ranges. Since an active management causes extensive additional expenditures, a deviation from the benchmark based on the interest forecast makes only sense, if a higher profit at the same risk or less risk with the same profit can be achieved.17
2.3. The Financial Risk Management Cycle The process of financial risk management is not isolated, but rather a management philosophy and should as such be referred to in the context of the company structure and its external environment. The company should clearly state its objectives concerning risk management and align all actions aimed at identifying, quantifying, managing and reporting treasury risks to its business strategy. Furthermore, specific risks cannot be addressed in isolation from each other; the management of one risk may have an impact on another. Since strategies need to be refined as business or market requirements change, financial risk management is not a single action but a
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rather dynamic process.18
Figure 2: The Risk Management Cycle19
16
Since the core competence of a non-financial service enterprise is generally not in the field of interest risk management, the quality of an own interest rate forecast has to be challenged. As an alternative also the interest forecasts provided by banks or independent institutions, as for instance the Feri Finance AG, can be applied. 17 Eller, Gruber & Reif, 2002 18 Association of Corporate Treasurers, 2009 19 HM Treasury, 2004, 13
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Schönborn, Jana. Financial Risk Management: Management of Interest Risk from a Corporate Treasury Perspective in a Service Enterprise : Management of Interest Risk from a
The systematic and structured identification20 of all individual financial risks forms the basis for an appropriate financial risk management system. Within the scope of the risk identification the company needs to define its key risks. However there might be risks of which the company is aware but has decided not to actively manage them. Based upon the identification of the risk, the extent of it has to be quantified.21 The consideration of interacting effects of different risks is an important distinction between the examination of a single risk and a portfolio of risks. The result of the risk quantification is the basis for the following risk management. Since only the risk that is decently measured can be managed, the risk quantification has a high significance within the risk management process. The instruments to manage financial risks can be divided into measures of precaution, transfer, compensation and diversification.22 To monitor and control the measured risks on a periodic basis, limits need to be set according to the risk tolerability of the company. The result can then be illustrated in a
impact
risk matrix.23
tolerability
likelihood
Figure 3: Risk-Tolerability Matrix
The regular reporting of the progress in financial risk management and a periodical
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review of the entire process is a controlling tool that helps to refine the approach and improve strategies. Often a monthly financial risk management reporting on the outstanding financial exposure and existing hedges combined with action recommendations is prepared. This report should be easily understood at board level to allow for an appropriate decision making.24
20
Since the risk identification is already predefined by the title of this paper, the issue of risk identification will not be addressed further. 21 Association of Corporate Treasurers, 2009 22 Wolke, 2008 23 Mare, 2008 24 Association of Corporate Treasurers, 2009
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Schönborn, Jana. Financial Risk Management: Management of Interest Risk from a Corporate Treasury Perspective in a Service Enterprise : Management of Interest Risk from a
In order to achieve the objective of a company-wide consistent risk culture when addressing financial risks a risk management policy needs to be defined, the treasury policy derived, and a financial risk management programme implemented. In this regard expenditure and risk ratios are defined; permanently ex-post analysed and improved. The ex-post analysis serves as a process back-testing and at the same time functions as an early-warning-system.25
2.4. Insight into the Service Sector and its Current Trends with respect to Financial Risk Management Since the service sector is highly homogenous, a definition of the term as well as its differentiation from other business sectors can be difficult. However, in order to be aware of the special challenges of the tertiary sector one has to understand the characteristics that all services combine. First, services are marketable activities, meaning they produce a benefit that at least theoretically could be rewarded. A further distinctiveness is the intangibility of services. Although supplies might be used in the service process, the result remains of an immaterial nature. Since a service is performed on the customer or on an object provided by the customer, the service completion is not possible without the customer. Thus the customer supplies external production factors that are not in the direct sphere of influence for the service provider. Finally a service is characterised by the fact that it is completed after the agreement between buyer and seller has been made and in fact is a performance bond. Though,
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the last attribute is also true for order-oriented tangible goods.26
Primary sector
Secondary sector
Tertiary sector
(agriculture, forestry, fishing)
(industry)
(service)
Figure 4: Gross Value Added in Germany27
25
Association of Corporate Treasurers, 2009 Melzer-Ridinger & Neumann, 2008 27 Statistisches Bundesamt, 2009 26
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Schönborn, Jana. Financial Risk Management: Management of Interest Risk from a Corporate Treasury Perspective in a Service Enterprise : Management of Interest Risk from a
The commercial relevance of services is demonstrated by the increasing gross value added (see Figure 4) as well as a rising number of employees in the tertiary sector. Developed economies are characterised by a higher proportion of employees working in the service sector than in the primary and secondary sector. Germany (72.5%) is along with The United Kingdom (76.3%), Norway (75.7%), Australia (75.1%), Belgium (73.7%) and Denmark (73.3%) among the OECD economies showing the greatest employment ratio in the tertiary sector. In 1970 the quota, even in these countries, was much lower at around 50%.28 Although the service sector as a whole is growing, especially in Germany (see Figure 4), the operating cash inflows of different branches within the service sector are highly volatile (see Figure 5). Service enterprises are often facing seasonal fluctuations and are also highly dependent on the overall economic climate. Automobile trade, service and maintainance
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Figure 5: Sales Statistics of Selected Branches of the German Service Sector29 (relative change compared to prior quarter)
Opposing to the fluctuations of the operating cash inflows of a service enterprise, the out flows are characterised by a high proportion of personnel costs. These are to a
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great extent fixed costs at least in the short run. Furthermore the specifics of services, such as the lack of storability, the restricted automation possibilities, the intangibility and the resulting difficulties regarding the comparability are a difficult basis for the controlling function. Therefore the cash flows of a non-financial service enterprise are much less predictable than for instance the cash flows of a bank or a producing company.30 28
Statistisches Bundesamt, 2009 Statistisches Bundesamt, 2009 For further sales statistics on the German service sector see Appendix 2. 30 Bruhn & Stauss, 2006 29
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Schönborn, Jana. Financial Risk Management: Management of Interest Risk from a Corporate Treasury Perspective in a Service Enterprise : Management of Interest Risk from a
From a study of the financial statements of the 30 DAX-listed enterprises from the years 2003 and 2004 several statements to the trends in hedging strategies can be derived. The financial risk is in general managed by a centralised treasury department. Non-financial institutions are using derivative instruments on an increasing larger scale to hedge financial risks, but not for trading purposes. Thereby interest rate risks are after currency risks the most prevailing risks to be hedged. The most often used interest rate derivatives according to their nominal value in 2004 were swaps, options, forwards and futures. 31 This can be backed up by a survey conducted by the chair in finance and bank management of the University of Siegen in 2002, according to which 83.7% of the interviewed non-financial corporates consider the interest rate risk as relevant and manage it. Though, paradoxically only 76.7% measure the risk. 58.6% of the firms that quantify interest rate risk use scenarios of parallel yield curve32 shifts, but only 29.3% use at-risks-methods33.34 By way of example the Deutsche Post AG as a leading service enterprise for logistics shall be mentioned. Deutsche Post World Net, with its areas Brief, Express, Global Forwarding / Freight and Supply Chain / Corporate Information Solutions reported in its financial statements of 2004 total assets of EUR 153,357m and a nominal value of all hedging instruments amounting to EUR 45,870m, thereof EUR 39,058m were
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interest rate derivatives.35,36
31
Schmeisser & Hecker, 2005 For an explanation of the yield curve see section 4.1. 33 According to Schwabe, 2006 this has not changed in recent years. 34 Wiedemann, 2002 35 Schmeisser & Hecker, 2005 36 According to the annual statements of Deutsche Post World Net for 2008 the nominal value of all hedges is EUR 46.557m. 32
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Schönborn, Jana. Financial Risk Management: Management of Interest Risk from a Corporate Treasury Perspective in a Service Enterprise : Management of Interest Risk from a
3. Treasury as a Central Institution of Financial Risk Management 3.1. Corporate Treasury Risk Management and its Influencing Factors The primary role for most corporate treasurers is financial risk and profit management. In addition to the monitoring of long- and short-term liquidity risk, the management of financial market risk continues to gain in importance.37 Beside their role in risk management treasurers are also having a much wider range of functions. This includes the issues of cash forecasting, liquidity management, cash pooling, improving the working capital utilisation, implementing global collection and payment solutions and the selection of suppliers of financial services. This is all done within headcount constraints and thus forces an ever increasing effectiveness of the processes.38 Treasury management requires a very organised, disciplined and scientific approach. Since the treasury department is by definition potentially high-risk, its work has always been governed by various laws and regulations. As already mentioned in section 2.1, in addition to the internal guidelines, primarily the treasury policy, there is a range of laws on (financial) risk management.39 Regarding treasury there are for instance regulations for foreign exchange, bank relations, hedging, financial risk and intra-group financing. To give a specific example, the Sarbanes-Oxley Act demands a number of internal audit procedures, such as the four eyes principle, double signatures, the separation of front-office and back-office functions and regular conducted audit trials.40 How a treasurer approaches risk depends on the company’s risk profile, which in turn is derived from the corporate strategy. This will determine the company’s risk appetite. Is the organisation a risk taker or is it risk averse? It is crucial to identify the
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factors that constitute a threat to the company’s profits. Then the company has to decide what risks should be accepted and not managed. It also has to determine what amounts of equity capitalisation and working capital are needed to cover the existing risk exposure. Another influencing factor is the current achievement stage of the corporate. For instance if a company is about to implement a new strategy, it will be reluctant to take any risk which may endanger this undertaking. 37
Wiedemann, 2002 Donohoe, 2003, Part 1 39 Some of the most important regulations on risk management can be found in Appendix 1. 40 Masquelier, 2007 38
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Schönborn, Jana. Financial Risk Management: Management of Interest Risk from a Corporate Treasury Perspective in a Service Enterprise : Management of Interest Risk from a
Companies that are experiencing a high volatility of their cash flows and have a high financial and operational gearing will most likely be risk averse and thus pursue a conservative risk management. The attitude towards risk is also dependent on the nature of the business itself, the general volatility of the business sector, actions of the competitors and the size of financial risks.41 Based on this profile, a treasurer can determine a series of financial strategies to pursue. […] As a result, a treasurer is one of the first people to consolidate his risks and to identify their correlations. […] He identifies, quantifies, eliminates, monitors, selects and transfers risks, just like a CRO.42
3.2.
Financial Risk Management within the Scope of the Treasury Risk Policy
Although corporations are not subject to the same strict legal requirements as financial institutions, the management has to define objectives for the financial risk management and embed them into the business strategy. The treasury risk policy sets out basic principles on how to weight profit and what are the boundaries of financial risk management. It gives guidelines not only for dealing with interest rate risk, foreign exchange exposure, commodity and equity risk but also for reducing operational risk and counterparty exposure. Moreover it defines the core risks, limits for individual risks and the total risk exposure, hence the risk appetite.43 Since a firm needs time to adapt to adverse market movements the accepted risk level in the short term needs to be tightly controlled whereas the acceptable risk limit over time may
acceptable level of risk
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increase44.
time Figure 6: Risk-Time Relation
41
Association of Corporate Treasurers, 2009 Masquelier, 2007, 22 43 Association of Corporate Treasurers, 2009 44 Donohoe, 2003, Part 1 42
11
Schönborn, Jana. Financial Risk Management: Management of Interest Risk from a Corporate Treasury Perspective in a Service Enterprise : Management of Interest Risk from a
Benefits that can be accrued by developing a treasury risk policy include defining a strategy on interest rate risk and a framework for controlling and managing interest rate exposure. To decide what treasury policy is right for a company there are three key questions that need to be addressed: ¾ What is the weight of financial risk as a proportion of the firm's total risk? ¾ What is the gap between the current financial risk profile and the desired profile? ¾ What is the expertise in financial risk management? The greater the proportion of the financial risks of the total risk facing the company, the greater the need for controlling that element of the business.45 It is important, that the policy states exactly what instruments will be used for what purpose and to what limit in order to manage the defined key risks. In essence the policy always tries to strike a balance between managing risk and contributing to the financial results of the company. Since the financial risk of the firm is dynamic and ever changing an ongoing evaluation but at least an annual review of the treasury risk management policy should be considered essential in order to ensure that the policy satisfies the corporate governance requirements and has sufficient attention at board
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level.46
45 46
Donohoe, 2003, Part 2, 11 Association of Corporate Treasurers, 2009
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Schönborn, Jana. Financial Risk Management: Management of Interest Risk from a Corporate Treasury Perspective in a Service Enterprise : Management of Interest Risk from a
4. Quantifying Interest Rate Risk 4.1.
Understanding Interest Rate Risk
In order to understand interest rate risks, it is vital to analyse the factors that affect interest rates. Interest rates are made up of the real rate plus the expected rate of inflation and a risk premium. Investors demand at least the inflation rate, since the purchasing power of an asset is reduced by it. The risk premium indicates the creditworthiness of a borrower, but it may also rise due to a general increase in the risk for instance during periods of a financial market crisis. Moreover the level of market interest rates is influenced by other general economic conditions, as for instance the foreign investor demand for debt securities, the monetary policy as well as the financial and political stability.47 There are three main types of interest risk: ¾ Absolute interest rate risk, arising from changes in the level of interest rates. ¾ Yield curve risk, arising from changes in the shape of the yield curve. When the level of interest rates changes, the yield curve rarely shifts in a parallel manner, it can even show twists or humps. ¾ Basis risk, arising from mismatches between exposure and risk management instrument. The yield curve represents all spot rates respective their terms to maturity, and forms the basis for the evaluation of all interest-bearing positions. There are usually several yield curves48 within a currency area, which can move independently from each other. Since investors demand a higher return for longer lending terms, long-term rates are normally higher than short-term rates. The resulting yield curve is upward sloping and also referred to as a normal, concave yield curve. In contrast an inverse yield curve is characterised by higher spot rates at the short-end than the rates at the long-end. Copyright © 2010. Diplomica Verlag. All rights reserved.
Temporarily the short-term interest rates may be higher than the rates for longer terms caused by a rise in demand for short-term funds. As soon as the short-term interest rates are rising over a certain level, the resulting fall in demand causes the return to a normal yield curve. A flat yield curve is characterised by equally high spot-rates for all maturity ranges.49
47
Horcher 2005 E.g. the Euro area yield curve derived from AAA-rated Euro area central government bonds. 49 Obermaier, 2005 48
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Schönborn, Jana. Financial Risk Management: Management of Interest Risk from a Corporate Treasury Perspective in a Service Enterprise : Management of Interest Risk from a
Figure 7: Euro Area Yield Curve (Spot)50
Often zero bonds51 cannot be observed on the capital markets in a sufficient quality (= risk-free) or quantity to get the spot rates for all maturity ranges and derive the yield curve. Hence the yields of very good rated52 bonds for all maturity ranges are used as a calculation base. With the help of regression analysis or other mathematical methods the spot rates for discounting interest-bearing instruments can be derived and the yield curve determined.53 Basic risk is a consideration for hedging with derivatives. It arises when the contracts used to hedge interest rates have another underlying rate or another currency than the underlying to be hedged, and therefore do not perfectly match.54 According to the general practical opinion variable interest-bearing positions imply an uncertainty about the future interest expenditure and interest earnings, whereas fixed interest positions entail a reliable planning up to the final maturity. From a present value perspective the argumentation is exactly reverse. The present-value of a fixedincome security equals the discounted sum of its future cash flows, hence the interest payments and the principal repayments. The cash flows are discounted with the spot Copyright © 2010. Diplomica Verlag. All rights reserved.
rate of the respective maturity ranges. Consequently the present value depends primarily on changes of the market interest rate level and/or the yield curve.55
50
ECB, 2009 Zero bonds are bonds without regular interest payments. The issuer is only obliged to a single payment at the maturity date. The difference between the repayment and the initial payment expressed as a percentage is the zero bond rate. 52 The rating is determined by rating agencies such as Mody’s, Standard&Poors or Fitch. These agencies use different rating codes, but the code for the best rating is in all systems “AAA”. 53 Obermaier, 2005 54 Horcher, 2005 55 Dresdner Bank, 2002 51
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Schönborn, Jana. Financial Risk Management: Management of Interest Risk from a Corporate Treasury Perspective in a Service Enterprise : Management of Interest Risk from a
(4.1) PV – present value t – time unit CF – cash flow i – spot rates T - maturity
Rising interest rates bear the risk of reduced assets whereas falling interest rates constitute the risk of increased liabilities. Because money market instruments adjust to the current interest rate level on a daily basis, they are not subject to interest rate risk. The longer the fixed interest period the higher the interest rate risk. Apart from options that have an asymmetric profit-loss-profile, the chances and risks from interest rate changes are to a large extent symmetric. With the help of sensitivity measures the present value changes resulting from interest rate movements can be characterized. 56 Hence the concept of duration and convexity as measures of the sensitivity will be examined in section 4.2.
4.2.
Duration and Convexity
The duration forms the basis for many other risk measures for quantifying interest rate risk. It indicates the average length of the capital tie-up of an interest-bearing instrument. The duration according to Macaulay can be calculated with the following formula:
(4.2)
D – duration
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The duration of the entire portfolio equals the sum of the individual durations of the different maturities weighted with the corresponding present values. This connection facilitates the determination of the interest rate sensitivity not only for an individual interest-bearing position but also for an entire portfolio. For a zero bond the duration equals the maturity. The duration of a coupon bond however is shorter than the remaining time to maturity, since there are interest cash flows before the maturity date. The concept of duration facilitates the determination of the interest sensitivity.57 56 57
Wiedemann, 2008 Wilkens; 2002
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Schönborn, Jana. Financial Risk Management: Management of Interest Risk from a Corporate Treasury Perspective in a Service Enterprise : Management of Interest Risk from a
The shorter the maturity and the higher the coupon of the bond, the shorter is the duration. A long duration protects a portfolio with a net-financing position against rising interest rates, but causes higher financing costs at falling interest rates58. A short duration by contrast has the opposite impact. Here falling interest rates lead to more favourable financing conditions, while rising interest rates result in higher financing
present value
cost. This price-interest rate relation is also illustrated in Figure 8:59
Real price change
Estimated price change with modified duration
P i interest rates
Figure 8: Price-Interest Relation
Whereas the duration is measured in units of years, the modified duration indicates the relative change in the present value resulting from a change in the level of market interest rates. It is defined as the first derivative of the present value of an interestbearing position with respect to the market interest rates divided by its present value. Thus the modified duration states by what percentage the present value of an interestbearing position changes, if the level of market interest rates changes by one percentage point.60
!
! " ! "
! "
!
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Dmod – modified duration di – interest rate change
The modified duration differs from the duration by the factor
.
58
See section 6 for the application of this thought in a case study. Wilkens; 2002 60 Woke, 2008 59
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Schönborn, Jana. Financial Risk Management: Management of Interest Risk from a Corporate Treasury Perspective in a Service Enterprise : Management of Interest Risk from a
(4.3)
With the modified duration the relative change of the present value caused by a change in the level of interest rates can be calculated. The multiplication with the factor -1 represents the fact that a rise in market interest rates leads to a reduced present value and vice versa. If the interest rate changes by 100 basis points the relative change of the present value equals exactly the modified duration.61 # $ " #
(4.4)
Since the duration is only a linear approximation, large jumps of the interest rate result in significant estimation errors. Capital gains are underestimated and capital losses are overestimated. Therefore the duration is only a reliable measure for small interest rate changes. By analysing the convexity the estimation error can nearly be eliminated. It is defined as the second derivative of the present value with respect to the market interest rates.
! &
((& "
% ' "
)& ! & (4.5) C – correlation
The convexity of the entire portfolio can be determined analogue to the portfolio duration by summing up the convexity figures of the different maturities weighted with the respective present value. The change of the present value caused by a change in the level of interest rates is calculated with the help of the convexity as follows:62
# " # # & &
(4.6)
The formula shows that, the greater the convexity is the more the present value is affected by interest rate changes. The duration is a measure of sensitivity that assumes a linear connection between the Copyright © 2010. Diplomica Verlag. All rights reserved.
interest rate movements and the present value changes. If interest rates are changing more than 1%-point a better accuracy should be reached by including the mathematical derivatives of higher orders. However it must be pointed out that with the use of higher orders the accuracy advancements are becoming gradually smaller. Thus the inclusion of the 1st or 2nd derivative is sufficient for practical purposes.63
61
Wolke, 2008 Dresdner Bank, 2002 63 Wiedemann, 2008 62
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Schönborn, Jana. Financial Risk Management: Management of Interest Risk from a Corporate Treasury Perspective in a Service Enterprise : Management of Interest Risk from a
4.3.
Value at Risk
4.3.1. The Concept of Value at Risk In the traditional concepts simple interest rate scenarios form the basis for determining the interest rate risk. A basic scenario is a notional change, for instance an increase of one percent, in the level of interest rates, as it can be computed with the sensitivity measures. Another possibility is to assess the impact of the best, the worst and the expected case on the portfolio. However these scenarios are only an inadequate representation of the reality and thus their validity concerning the interest rate risk is comparatively low. This is based on the fact that these concepts make not only simplifying assumptions about parallel shifts and twists of the yield curve but are also of a subjective matter, because they are defined by the user himself. As advancement the number of scenarios can be increased. From the results of thousands of simulated scenarios frequency distributions can be derived. This refinement leads to the socalled value at risk (VaR) concepts.64 Being introduced by the American bank Morgan Stanley in 1994 after the financial disasters of the early 90s, the VaR is now a prevailing risk measure65. The treasurers of service enterprises can benefit from the experiences of the financial sector, but need to adapt the approaches to their type of business and the respective cash flow structure. Therefore this paper attempts to build on the concepts originally developed by banks and find out how they can be used by non-financial service enterprises. The VaR has been defined as the maximum loss of a portfolio during a specified holding period with a given level of confidence Į (e.g. 95%)66. The loss in value of a portfolio of interest-bearing positions is the negative deviation of the future present value (PV1) from the current present value (PV0). With different alternative market interest rates, which are determined either empirically or statistically, a distribution of
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the present value changes can be derived. Based thereupon the possible losses can be determined. The variable VaR parameters holding period, level of confidence and length of the used time series have to be defined by the enterprise before implementing the VaR concept67.68
64
Hager, 2004 Wolke, 2008 66 Jorion, 2007 67 For a more detailed instruction on how to define the variables of a VaR implementation for a service enterprise see section 4.5 and 5.2. subsequently. 68 Wiedemann, 2008 65
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Schönborn, Jana. Financial Risk Management: Management of Interest Risk from a Corporate Treasury Perspective in a Service Enterprise : Management of Interest Risk from a
For the modelling of distributions for If these trends are of temporary nature, the asymmetry should be eliminated by mirroring the data record. For this purpose not only the observed changes in value but also their opposite values are to be included (multiplication with -1). The risk assessment refers then only to the negative deviations, the so called lower partial moments.69 If the present value changes are computed based on the original present value, the VaR resulting from this is the absolute VaR. Since interest rate changes often a normal distribution is being assumed. The standard normal distribution has a mean of zero and a standard deviation of one. A random variable is normally distributed, if there is a high probability that the observed values group themselves around the expected value and only a low probability that they occur far away from it. This is for the most part true for interest rate fluctuations. However, in reality certain trends can be observed which leads to an asymmetrical distribution. the expected return stays without consideration in this approach, it makes only sense for short holding periods up to 10 days. In order to avoid distortions for longer holding periods the relative VaR should be applied. It is computed based on the arithmetic mean (expected value) of all possible present value changes. For a positive expected
propability
value the relative VaR is always larger than the absolute VaR.70
relative VaR absolute VaR
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z =(1-p)
PV0 =0
PV1 =expected return PV
Figure 9: Density Function of the Normal Distribution
69 70
Wiedemann, 2008 Wiedemann, 2008
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Schönborn, Jana. Financial Risk Management: Management of Interest Risk from a Corporate Treasury Perspective in a Service Enterprise : Management of Interest Risk from a
Of particular importance for the modelling of the risk of interest-bearing positions is the intensity of the changes in present value, the so-called volatility. It indicates the average deviation of the mean, hence the average change in value of the portfolio. A simple measure for the determination of the volatility71 is the standard deviation.72
*+
, - (./ 0
(4.7)
1
ı - standard deviation Rt – observed value changes of the risk factors µR – expected value of the value changes of the risk factors n – number of observations
The daily volatility can be converted into the volatility for longer holding periods with the following formula, which can also be applied to transform a VaR value to a longer holding period: *1(
234
56 7 *(
(4.8)
23
The product of the present value at a specific maturity and the volatility of the respective spot rate results in the present value volatility (as an absolute value). By multiplying it with the z-score73 of the standard deviation the VaR is calculated. The standard deviation of 1 signifies a confidence level of 84,14%. For other levels of confidence the standard deviation of 1 must be multiplied by the z-score according to the desired level of confidence.74 Level of confidence (one tail)
84,14%
90,0%
95%
97,5%
99,0%
99,5%
Figure 10: Relation between the Z-Score and the Level of Confidence
A regular back-testing of the VaR approach with historical data assures the statistical
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validity.75
71
If the volatility is calculated as the equally weighted average of the past changes in value that have been observed in both, times of high and times of low volatility, major divergences are smoothed and the obtained results are consequently too low in times of high volatility and too high in times of low volatility. This disadvantage can be reduced by the formula of the EWMA model, which represents short term trends in a more adequate way, because it puts a higher weight on the value changes of the more contemporary observations. The time delay factor Ȝ can lie between 0 and 1. A low Ȝ puts a higher weight on the more recent values and leads to a faster response to trends. Since this approach would complicate the risk measurement significantly, it will not be examined further in this paper, but should be mentioned because it is used by the RiskMetricsTM model. 1
< * 8 " 9 7 9 : " ;-
72
Wiedemann, 2008 73 The z-score is the number of standard deviations from the mean. 74 Wiedemann, 2008 75 Wolke, 2008
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Schönborn, Jana. Financial Risk Management: Management of Interest Risk from a Corporate Treasury Perspective in a Service Enterprise : Management of Interest Risk from a
The modelling of the distribution of the risk factors represents the biggest challenge for the VaR implementation. To determine the distribution of interest rate changes basically three approaches can be differentiated; those that are based on simulations or analytical approaches and mixed forms:76 The historical simulation is a non-parametric approach for the measurement of interest rate risks, with which the potential future value changes of the risk factors are simulated by means of actual observed historical value changes. The Monte Carlo simulation is a semi-parametric approach. The present value changes of the portfolio are simulated by random numbers considering the statistic distribution. The variance-covariance method is a parametric approach for modelling the distribution of the risk factors based on the assumption of a normal distribution. This approach facilitates an analytical calculation of the VaR.77
4.3.2. Historical Simulation The historical simulation78 investigates the risk factors based on selected historical data records instead. The historical value changes already include the correlation79 in an implicit way.80 The value changes can be computed with the difference method or with one of the quotientt methods. (1) Difference method – absolute value changes: :2=4> ? " ?( (2) Quotient method – relative value changes: :@AB>
C (CD CD
(3) Quotient method – logarithmic value changes: :B E> FGH? " FGH?( In principle these three methods are considered equally good. Only for larger interest rate fluctuations (>100bp) and longer holding periods larger differences occur. Therefore also absolute interest rate differences are often used for the modelling of stochastic interest rate processes. The differences between relative or logarithmic interest rate differences are only of marginal nature. Since the relative differences can Copyright © 2010. Diplomica Verlag. All rights reserved.
be understood intuitively, they have a more demonstrative character. However, only the logarithmic differences fulfil the criterion of independence from the absolute level.81 76
Rau-Bedrow, 2001 Wiedemann, 2008 Since the illustration of all three methods would be beyond the scope of this paper, only the historical simulation and the variance-covariance approach will be examined further. The Monte-Carlo simulation is the most capable method but by far the most elaborate one, which most likely wouldn’t suit the resources of a service enterprise. 78 See section 6 in connection with Appendix 3for the application of this approach in a case study. 79 The correlation between two market interest rates shows, to what extent the change of one market interest rate affects another market interest rate. For further explanations see section 4.3.3. 80 Hager, 2004 81 Wiedemann, 2008 77
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Schönborn, Jana. Financial Risk Management: Management of Interest Risk from a Corporate Treasury Perspective in a Service Enterprise : Management of Interest Risk from a
By adding the historically observed risk factor changes to the current value, potential interest rate scenarios with an equal probability can be produced. Through the valuation of the interest-bearing positions with the simulated market interest rates a distribution of present value changes can be derived. By adding the present values of all maturity ranges for each interest rate scenario a different portfolio present value can be calculated. With the next step the differences between the current present value (PV0) and the alternative present values are determined. This way a distribution of the present value changes is derived. The VaR is the n-smallest value of the distribution dependent upon the selected level of confidence.82 Since there is no need for an assumption about the statistical distribution, the historical simulation is a comprehensible method that can be easily implemented. Besides no statistic parameters have to be estimated, which avoids estimation errors. However, since for each scenario a revaluation of the portfolio is necessary, the historical simulation causes high computational efforts, especially if the portfolio contains options. Then for every scenario a new option price has to be determined83. Another disadvantage is the necessity of complete time series and a sufficiently large number of observations, in order to ensure the statistical validity. More over future-oriented market data is not considered and it can be problematic to derive a future risk potential from past data, particularly if exceptional developments lay in the observation period. 84 Therefore the variance-covariance-approach shall be introduced in the subsequent section.
4.3.3. Variance-Covariance-Approach Since the implementation in the RiskMetricsTM Morgan the variance-covariance-approach
86
85
model of American bank J.P.
is widespread. It is based on the
assumption that the risk factors are normally distributed and that there is a linear Copyright © 2010. Diplomica Verlag. All rights reserved.
relationship between the zero bond rate changes and the present value changes of the interest-bearing positions87. As a first step the volatilities of the individual risk factors for the given holding period need to be estimated. As it is done by the historical simulation, the volatilities of the spot rates are determined based on historical data.
82
Wiedemann, 2008 For the calculation of the option price with the Black/Scholes Model see Hull, 2009a 84 Rau-Bedrow, 2001 85 The RiskMetrics Group was spun off from J.P. Morgan in 1998 and is now a leading provider of market data about risk factors. 86 See section 6 for the application of this approach in a case study. 87 This is only approximately true for symmetric interest-bearing instruments, but not for asymmetric instruments. 83
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The VaR of a single interest-bearing position results from the multiplication of the current present value with the z-score of the desired level of confidence and the corresponding volatility of the spot rates.88 I: JKL *M
(4.9)
zCL - z-score at the given level of confidence ıHP - volatility at the given holding period
If a portfolio contains several different interest-bearing positions, the individual VaR for each maturity range have to be calculated and subsequently need to be aggregated to a portfolio VaR. The addition of the single VaR values results in the portfolio VaR without considering any diversification effects. This would imply that a completely positive correlation89 of the market interest rates is assumed. Since this is hardly ever the case in reality, assuming a complete positive correlation leads to an overestimation of the risk. The diversified VaR by contrast considers diversification effects between the risk factors.90 The correlation is a measure for the tendency of two risk factors to move together or not. It demonstrates how strong the total risk can be reduced by mixing cash flows of different maturities and is by this means a measure for the risk diversification effect. The correlation can be quantified by a coefficient k between -1 and +1. A k of +1 indicates a perfect positive correlation, which means that there are no diversification effects existing. In contrast a k of -1 indicates perfect negative correlation with opposing value changes, which means that there are maximum diversification effects. Diversification effects can also be attained when two risk factors are moving independent from each other. The corresponding correlation coefficient is zero.91 The diversified VaR incorporates the so-called portfolio effects by linking the single VaR values with one another with the help of the correlation coefficient.
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I:N +I:& I:&& < 7 I: 7 I:& 7 O>&
I:N 8I: > > I:1 7 P Q O1>
(formula for two instruments)
O>1 ? Q Q R 7 S Q T UI: 7 O 7 I: ?1
(4.10) (formula for n instruments) VaRP – value at risk of a portfolio k – correlation coefficient
88
Wiedemann, 2008 This would mean that the interest rate changes by the same magnitude in all maturity ranges, thus a parallel shift of the yield curve. 90 Wiedemann, 2008 91 Horcher, 2005 89
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Schönborn, Jana. Financial Risk Management: Management of Interest Risk from a Corporate Treasury Perspective in a Service Enterprise : Management of Interest Risk from a
The correlation can be calculated with the help of the covariance, which in turn is defined as the average of the product of the pair wise risk factor changes92.
O>V
W XY>Z
(4.11)
[Y [Z
1
\G]>V
7 :> " ;-Y 7 :V> " ;-Z 6
(4.12)
O>V - correlation between the risk factors of maturity i and j \G]>V - covariance between the risk factors of maturity i and j * ^*V - volatility of the risk factor of maturity i / j :> ^:V> - historical changes in value of the risk factor of maturity i / j ;-Y ^;-Z - expected value of the risk factor of maturity i / j
When correlations are considered in the VaR calculation, the resulting portfolio VaR is lower than the sum of the single VaRs. The lower k the larger is the diversification effect and the smaller the portfolio VaR. With k =-1, the largest netting effects occur with the resulting portfolio VaR having the lowest possible value.93 Diversification effect
_2-`YabcdYeYb`(_2-f`YabcdYeYb`
(4.13)
_2-f`YabcdYeYb`
The volatilities and covariances needed for the variance-covariance-approach have to be calculated based on historical data or they could be provided by Risk MetricsTM 94. However the variance-covariance method can be characterized as a rather simple model, but with problematic assumptions. The main issue is the assumption of normally distributed interest rate changes. Thereby extreme cases occur more often in reality than they are assumed by the normal distribution. With respect to the computational effort being put into the determination of the VaR value, the analytical
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variance-covariance-approach is more effective than the historical simulation.95
92 93
Alternatively also the approach of exponentially weighted correlations of the ghijklmnhoipkqrsltouvwluxxthlsy Alternatively one can also chose to first calculate the portfolio volatility ıP with the following formula and afterwards insert it in formula 4.9: *N +& *& && *&& < 7 & \G]>& *N +1 & *& < 7 1 1z V \G]V *& *N = 8 > > 1 7 P Q \G]1>
(formula for two instruments) (formula for n instruments)
\G]>1 ? Q Q R 7 S Q T = U 7 { 7 ?1 *1&
Wiedemann, 2008 In addition to Risk MetricsTM, some data is also provided by Reuters, Telerate, Bloomberg, banks and brokers. 95 Dresdner Bank, 2002 94
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Schönborn, Jana. Financial Risk Management: Management of Interest Risk from a Corporate Treasury Perspective in a Service Enterprise : Management of Interest Risk from a
4.3.4. Value at Risk of Derivatives Derivatives can be classified as symmetric or asymmetric according to their profitloss-profile. Independent of the applied risk measurement approach the determination of the risk for symmetrical interest rate derivatives is always based on the same principle. The instruments are fractionalised into their cash flow equivalents of different maturity ranges. Then the VaR can be determined as described for nonderivative interest-bearing instruments.96 In order to compute the VaR, for interest-bearing instruments with option rights, the so-called asymmetrical financial instruments, a delta must be considered. The delta of an option expresses the dependence of the option price on the underlying asset. The delta is computed as the first derivative of the option price function with respect to the value of the underlying asset. The delta of a call is between 0 and 1 and that of a put between 0 and -1. The delta of options that are afar out the money is 0. If the option is in the money, the delta of a call approaches 1 and that of a put approaches -1. The delta normal approach adjusts the VaR of the option by its delta. However, since the delta is not static but ever changing this method often leads to a wrong estimation the risk. To eliminate this estimation error the delta-gamma approach can be applied. This approach considers the convexity the option price curve. The gamma is computed as the second derivative of the price function with respect to the value of the underlying asset. Thus the delta-gamma approach considers the change of the delta resulting from changes in the value of the underlying asset. However this approximation still leads to estimation errors when the remaining time to maturity approaches zero and/or the option is clearly in the money97.98
4.4.
Cash Flow Mapping
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4.4.1. Determining the Cash Flow Structure In order to quantify the interest rate risk of a portfolio of interest-bearing positions, first of all the assets and liabilities will be split into a portfolio of different individual cash flows. The resulting cash flow structure points out exactly, which redemption and interest payments become due at what point in time. Through the netting of positive
96
Scharpf & Luz, 2000 The VaR could also be calculated with the Cornish Fisher expansion, though this considerably increases the complexity. For the application of the Cornish Fisher expansion see Hull, 2009b 98 Hager, 2004 97
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Schönborn, Jana. Financial Risk Management: Management of Interest Risk from a Corporate Treasury Perspective in a Service Enterprise : Management of Interest Risk from a
and negative cash flows99 with identical maturities the sum-cash-flow can be derived. The sum-cash-flow can be discounted with the spot rates for each maturity range (see formula 4.1). This cash flow figure in present value terms constitutes the key factor of the interest risk management.100 By knowing the cash flow structure of the entire interest-bearing positions it is possible to analyse what interest rate developments lead to high losses and what to large profits for the company. Assuming a net-financing position, the negative portfolio value increases with falling market interest rates. The longer the duration of the cash flows, the stronger is the effect of interest rate changes on the present value of the portfolio. However it needs to be considered that an interest rate change generally does not occur in all maturity ranges in the same altitude and at the same
present value
time.101
The longer the duration, the higher the risk/opportunity
time
Figure 11: Interest Rate Risk of Positive and Negative Cash Flows
To interpret the cash flow structure and analyse its sensitivity to interest rate changes it is generally advantageous to group the cash flows and thereby reduce the total number of cash flow dates. Without simplifying measures it is in practice hardly possible to measure the interest rate risks of the entire portfolio with its multitude of cash flows. Moreover the subsequent management of the risk of such a detailed sumcash-flow would be very unpractical and cost-intensive.102
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If for simplifying reasons the risk factor data provided by RiskMetricsTM shall be applied in the risk measurement process, the cash flows need to be mapped to the dates used by this model. The volatilities and correlations of the zero bond rates are published for 14 different maturity dates103 and a holding period of one and ten days. 99
In this respect it is of no consequence whether the cash flows are working capital or fixed capital related, since for the measurement of the interest rate risk commercial law is now applicable. 100 Wiedemann & Hager, 2004 101 Wiedemann, 2009 102 Wiedemann, 2008 A further objective of cash flow mapping is the achievement of a favourable effect of the interest risk management activities on the firm’s income statement. 103 Precisely these are the maturities of 1 month, 3 months, 6 months, 1 year, 2 years until 5 years, 7 years, 9 years, 10 years, 15 years, 20 years and 30 years.
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Schönborn, Jana. Financial Risk Management: Management of Interest Risk from a Corporate Treasury Perspective in a Service Enterprise : Management of Interest Risk from a
As an important precondition for the mapping of cash flows the original cash flow and the cash flow after mapping have to equal each other to a large extent in terms of their present value and their response to interest rate changes. For the technique of cash flow mapping sensitivity-oriented approaches and those methods, that incorporate the volatility as well as the correlations of the spot rates, can be differentiated. In the following sections the sensitivity mapping and the variance mapping will be introduced104.105
4.4.2. Sensitivity Mapping In order to fulfil the requirement of an identical reaction to interest rates changes the cash flow after mapping has to be construed in such a way that its interest induced present value sensitivities are equal to those of the original cash flow. Deviations are caused by the conception of the model. On the one hand a completely positive correlation of the spot rates is assumed; on the other hand the allocation of the cash flows to the payment dates takes place linear relating to the maturity specific durations. This implicitly also assumes a linear relationship between the durations and the volatility.106 The first method for cash flow mapping being introduced is the duration mapping. It allocates the cash flows that do not have one of the desired standard maturities to a neighbouring standard maturity date based on the modified duration. The two conditions of identical present values and modified durations (in the following only referred to as duration or abbreviated D) of the original cash flow and the cash flow after mapping, are leading to a mathematical system with two equations: & & &
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Through rewriting the equations above, the following present value formulas for payment date 1 and payment date 2 & can be obtained:
| (| | (| | (|
& | (|
104
See section 6 for the application of these approaches in a case study. Wiedemann, 2008 106 Wiedemann, 2008 105
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Schönborn, Jana. Financial Risk Management: Management of Interest Risk from a Corporate Treasury Perspective in a Service Enterprise : Management of Interest Risk from a
(4.14) (4.15)
These equations facilitate the splitting of individual cash flows or the entire sum-cashflow into two defined maturity ranges. The mapping of single cash flows allows the flexible segmentation of any individual cash flow independent from other cash flows into any two maturities. Thus the sum-cash-flow can be mapped into any desired number of payment dates. The only restriction regarding the aggregation in the sensitivity concept with the first derivation is the minimum number of two payment dates.107 In contrast to the duration mapping, the convexity mapping considers the convex relationship between interest rate and maturity. This facilitates a more precise estimation of the opportunity and risk potential resulting from interest rate changes. As for the duration mapping, also for the convexity mapping the condition that it must be ensured that the risk potential of the portfolio remains the same must hold true. In addition to the already known requirements of an identical present value and modified duration a third condition arises. In addition the cash flow after mapping has to have the same convexity as the original cash flow. This leads to the following set of equations: & } & & } } & & } } The conversion of the system of equations to PV1, PV2 and PV3 allows to allocate any cash flow into three defined maturity ranges:
&
K |~ (| K | (|~ K~ | (| K |~ (| K | (|~ K~ | (| K |~ (| K | (|~ K~ | (| K | (|~ K |~ (| K~ | (|
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} " " &
(4.16) (4.17) (4.18)
Like the duration mapping, the convexity mapping facilitates the segmentation of the portfolio cash flow into any desired maturity ranges. Both methods attempt to achieve the condition that the cash flow after mapping should have the same response to interest rate changes as the original cash flow by introducing the condition of equal interest induced present value sensitivities. Thereby the present value sensitivities of the different maturity ranges are only related to the respective maturity specific 107
Wiedemann, 2008
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Schönborn, Jana. Financial Risk Management: Management of Interest Risk from a Corporate Treasury Perspective in a Service Enterprise : Management of Interest Risk from a
interest rate fluctuations. Hence correlations, other than a complete positive correlation, between the market interest rates are disregarded. As a consequence the sensitivity oriented approaches lead only to a reliable cash flow structure when the market interest rates are highly positive correlated within the examined maturity ranges. Further deviations are caused by assuming a linear relationship between the maturity specific durations and the respective volatilities. Therefore in the following section an entire different approach, the variance mapping, will be introduced.108
4.4.3. Variance Mapping The variance mapping was developed by J.P. Morgan and aims at maximizing the accuracy of the risk measurement. In contrast to the sensitivity oriented approaches the variance mapping considers the volatilities and correlations of the spot rates of the different maturities.109 From the conditions of every mapping, identical present value and risk, the following two equations can be derived: & I: +I:& I:&& < 7 I: 7 I:& 7 O>& *
(4.19)
In addition the following equation ensures that the sign of the cash flow figures after mapping is identical with the sign of the original cash flow figures: und & "
(0x1)
(4.20)
x - weighting factor
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Through inserting and transforming of the equations the following equation arises: *& & *& " & *&& < " O * *& *&
/
*&&
*& – variance of the original cash flow - variance of the cash flows with the maturity 1 / 2
With the following transformation a quadratic equation is formed: *& *&& "< O * *& & < "*&& O * *& *&& " *& (4.21)
108 109
Wiedemann, 2008 Wiedemann, 2008
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Schönborn, Jana. Financial Risk Management: Management of Interest Risk from a Corporate Treasury Perspective in a Service Enterprise : Management of Interest Risk from a
To segment a cash flow, the first step is to form the quadratic equation for the chosen payment dates. With the resulting values for the coefficients a, b and c the weighting factor x can be calculated, whereas x is only true for 0x1. ax2+bx+c=0 ĺ
>&
(=5= (727W &72
0x1
Finally the present value of the original cash flow has to be multiplied with the weighting factor x to ascertain the first cash flow and with (1-x) to calculate the second cash flow (see 4.20). The variance mapping sets narrow boundaries for the structuring of the cash flow profile. A cash flow with maturity t can not be allocated solely to longer maturities (tt1, tt2) or shorter maturities t1 and t2 (t1t, t2t), but has to be within the two newly-arranged maturity ranges (t1tt2). Thus the simplification of the cash flow to only very few payment dates is not possible.110
4.5.
Implications for a Service Enterprise
Before the implementation of the VaR concept as a risk management tool, a set of decisions related to the VaR parameters holding period, level of confidence and length of the used time series has to be made.111 Since the interest risk management process for a service enterprise is not yet described by literature, this section tries to derive some implications for service enterprises based on their specific business model. When deciding about the planning horizon, the difficulties for service enterprises regarding the cash forecast, as already discussed in section 2.4, need to be considered. The management of the interest rate risk makes only sense if reliable cash forecast data is available. Thus the planning horizon should only go as far into the future as
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there is a sufficient planning reliability. Whereas banks can easily plan their cash flows ten years into the future, service corporates might choose a shorter time period. For implementing the VaR concept first a holding period has to be defined. The longer the selected period, the larger are the possible present value changes between the current present value and the expected future present value at the planning horizon.
110 111
Wiedemann, 2008 For banks these parameters are defined by Basel II as follows: 99% level of confidence, 10 day holding period based historical data that shall go back at least a year.
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Schönborn, Jana. Financial Risk Management: Management of Interest Risk from a Corporate Treasury Perspective in a Service Enterprise : Management of Interest Risk from a
The optimum holding period depends on factors such as the degree of competitiveness in the market, the length of sales and payment cycle, the flexibility in the companies cost base, regulations and its adoptability in responding to changes. For instance if the decision process for an unplanned loan redemption or the buying of a hedging instrument takes 10 days, the VaR calculation could be based on a respective holding period. Banks compute the VaR generally for a time horizon of one day (overnight VaR). This results in the smallest risk, while an extension of the holding period leads to higher VaR values. 112 If the portfolio contains only marketable interest-bearing instruments, a holding period of one day is reasonable. But if there are loans without extraordinary termination rights in the portfolio the holding period needs to be accordingly longer. By all means the optimal time horizon should leave enough time, to adapt to an adverse movement in interest rates or new cash requirements. Also the level of confidence has an effect on the resulting risk value. There is no uniform standard regarding the level of confidence, but it usually lies between 95% and 99%. The higher the percentage the higher is the resulting VaR value. However a low level of confidence does not necessarily indicate a higher risk tolerance, since it could be balanced by tighter risk limits. A service company could also choose to implement a traffic-light system113, where the exceeding of the 95% VaR-limit turns on the yellow light and the exceeding of the 99% VaR-limit turns on the red light. In any case the company should be able to bear the defined VaR-limit. Thus it should not exceed a certain percentage of the projected net sales. The VaR-limit has than to be chosen according to the risk appetite of the management.114 When selecting an optimal time range it must be recognised that values that lie too far in the past might not be relevant for the risk measurement. However if the time series is to short, the question arises whether the number of regarded values is representative. At the same time the estimation error increases with fewer samples115
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The fundamental decision when implementing the VaR concept is the method used to determine the VaR. To decide about the right method the accrued advantages and disadvantages shall be summarised. In the historical simulation no assumptions about statistic parameters have to be made. Thus there are no estimation errors possible which constitute an advantage over the variance-covariance-approach.
112
Donohoe, 2003, Part 1, 2 A colour-coded system where green is the signal that risk measures are within the defined limits, amber is a warning signal and red symbolises that urgent action is required. 114 Wiedemann, 2008 115 Hager, 2004 113
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On the other hand the variance-covariance-approach facilitates an analytical calculation of the VaR which means less computational efforts for the implementation. However a drawback for both methods is the fact, that future-oriented market data is disregarded in the calculation. Furthermore both methods are not suited for portfolios with a high proportion of options. The historical simulation requires a re-valuation of the options for each scenario.116 The best possible way for computing the option price in the variance-covarianceapproach is the delta-gamma method, which still leads to estimation errors when the remaining time to maturity approaches zero and/or the option is clearly in the money. Assuming that a more precise method such as the Monte Carlo simulation is igonored by a service enterprise because of its complexity, the decision between the two methods is mainly based on the general preference of a parametric or a non-parametric method. In any case the chosen approach should be complemented by stress test scenarios that consider the effect of some hypothetical scenario, e.g. high loss or low probability scenario, applied to the portfolio. The basic assumptions of the scenario should be agreed by the management.117 Since there are typically tight personnel constraints in the treasury department and interest risk management in a service enterprise has not as a high status as for instance in a bank, where it is also governed by even more regulations, an effective risk management has to be attempted. The mapping of cash flows is an instrument to simplify the cash flow and thereby reduce the effort to manage the risk. When it comes to the method of cash flow mapping it is a question how much effort the company wants to put into their interest risk management. The variance mapping is the most complicated of the three methods being discussed, but also the most precise one. When deciding between the duration mapping and the convexity mapping, one has to consider that the duration mapping has a significant higher estimation error
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since it ignores the convexity of the present value changes. On the other hand the increase in the complexity that comes with the convexity mapping can be nearly overruled with today’s standard in technology.118
116
Rau-Bedrow, 2001 Rau-Bedrow, 2001 118 See section 4.4.2 and 4.4.3. 117
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5. Interest Risk Management Techniques 5.1.
Hedging
5.1.1. Introduction to Hedging After having discussed how to quantify interest rate risk, this section examines the possibilities for reducing the risk with the help of interest rate hedging instruments. Interest rate derivatives are interest instruments deriving its value from an underlying instrument (e.g. LIBOR, EURIBOR). Derivatives entitle the buyer to purchase or sale an underlying instrument at an agreed price on a future date.119 They are either traded over future exchanges or directly between financial institutions and enterprises (= over-the-Counter). Exchange traded instruments generally possess a higher liquidity, a stronger standardisation and a permanent price fixing by the clearinghouse. Hedging strategies attempt to protect an existing or planned underlying (= hedged item) against changes in value (= fair-value-hedge) or changing cash flows (= cash-flow-hedge) caused by market price changes120.121 For an optimal hedge basis risks should be avoided by matching the reference interest rate with the underlying position. The choice of the maturity range depends largely on the structure of the assets and liabilities that need to be protected against interest rate risk and should widely match their maturity.122 The overview below shows a possibility to classify interest risk instruments according to their settlement date, subject-matter and place of contract conclusion.
Derivatives
Symmetric
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OTC
Asymmetric
SE FRA
OTC
SE Cap
Future
Options
Floor
Swap
Collar Swaption Figure 12: Overview of Derivative Instruments
119
Hull, 2009a Opposed to this, trading strategies attempt to gain short term profits by systematically taking risk through financial derivatives. Schmeisser & Hecker, 2005 122 Schmidt, 2006 See also ‘basis risk’ discussed in section 4.1. 120 121
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Schönborn, Jana. Financial Risk Management: Management of Interest Risk from a Corporate Treasury Perspective in a Service Enterprise : Management of Interest Risk from a
Due to the leverage effect of derivatives, the relative change in the value of the underlying results in a higher effect on the price of the derivative. This causes not only low transaction costs but also a difficult risk assessment. Hence a cautious monitoring of derivative risks is essential. 123 Depending on the legal accounting regulation applied by the company, derivative instruments are either excluded or included in the legal reporting124.
5.1.2. Symmetric Hedging Instruments 5.1.2.1 Forward Rate Agreement A FRA 125 is an agreement between two contracting parties to exchange a defined interest rate (= FRA-rate) and an as yet unknown variable reference rate of a specified maturity for a certain time range in the future126. The interest payment is computed, based on an agreed notional principal. The buyer pays the fixed interest amount to the seller, who in return pays variable, whereas in reality only a settlement payment is made. If the reference rate at the beginning of the contract term (= start date) is higher, the buyer receives a settlement amount. If the reference rate is lower, the buyer pays the seller. The duration of a FRA is made up of the forward term prior to the beginning of the FRA and the contract term covered by the FRA.127 The settlement amount can be computed as follows128: lmmtlqlvmuqrvm %
D D D ~
D ~
(5.1)
FRA rates are determined by the yield curve. The calculation of the FRA-rate is based on the total-return-approach. If an investor would have the choice to decide today either to invest its money for one year or to invest it first for half a year and then again for half a year, he/she would expect to receive the same return for both possibilities. If
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the compound interest rate effect is ignored, the following equation can be derived:129 FRA-rate h( ¡
£¤¥D ~ ¦D ¢¦D ~
¢£¤¥D
§ " ¨ «¬
}©ª
D
123
(5.2)
Jorion, 2007 In contrast to the HGB for instance IFRS demands the inclusion of derivatives along with comprehensive comments. See section 6 for the use of a FRA in a case study. 126 From this agreement a counterparty risk for both contracting parties arises. 127 Wiedemann, 2008 128 Since the settlement takes place already at the end of the forward term, but the term in the numerator calculates the settlement payment at the end of the total duration, it has to be discounted. 129 Dresdner Bank, 2002 124 125
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Schönborn, Jana. Financial Risk Management: Management of Interest Risk from a Corporate Treasury Perspective in a Service Enterprise : Management of Interest Risk from a
profit
profit in the money in the money
FRA-rate
FRA-rate reference rate
reference rate
out the money
out the money
loss
loss
Figure 13: Profit-Loss-Profile of a Long (left) and a Short (right) FRA
For the risk assessment a FRA can be construed synthetically by combining a fixed rate bond that is due on the effective date and a floating rate note that is due on the termination date. The bond represents the long position of the FRA and the floating .
rate note the short position.130 Since the values of the long and the short positions move in the opposite directions if the interest rates are completely positive correlated, the undiversified VaR of an FRA is lower than its diversified VaR. A correlation of k equal to 1 results in the lowest risk and k equal to -1 in the highest possible risk. Upon conclusion of the contract the present value of the FRA is equal to zero, because it was contracted at the current market conditions (= at-the-market).131 The aim of a FRA is to fix already today an interest rate for variable interest-bearing assets or liabilities, which comes only into effect at a future date. Thus a FRA facilitates the protection against an adverse change in interest rates. However at the same time the opportunity to participate in a possible positive interest rate development is abandoned. The purchase of a FRA secures existing or planned assets against interest rate reductions, whereas the sale of a FRA secures existing or planned
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liabilities against interest rate increases.132
5.1.2.2 Future Futures are a further development of the forward-contracts. Thus they have the same profit-loss-profile 133 . A Future is a standardised forward contract and as such marketable. The integral parts of the contract, such as the underlying instrument, the contract size, the delivery date and other terms of payment and delivery are not 130
Eller, 1994 Wiedemann, 2008 Dresdner Bank, 2002 133 Due to the daily settlement (marking-to-market) and the initial margin that has to be paid by all market participants, the counterparty risk can be disregarded here. 131 132
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Schönborn, Jana. Financial Risk Management: Management of Interest Risk from a Corporate Treasury Perspective in a Service Enterprise : Management of Interest Risk from a
individually negotiable, but determined by the respective futures exchange134. Because of the high standardisation the transaction costs are declining. In contrast to a FRA a future does not fix an interest rate, but the price resulting from the interest rate. Thus an interest rate future is in the end the purchase or sale of a standardised bond at a future date. 135 Futures are generally not fulfilled prematurely, but closed out with a counter trade before maturity (= closing). Instead of a physical delivery often a cash settlement takes place at the due date.136 The purchase of a future (= short-future) hedges assets against falling interest rates whereas its sale (= long-future) hedges liabilities against rising interest rates. Futures put an enterprise in a position to lock in a price or rate for a future date. This means also to forfeit the possibility of taking part in interest rate chances.137
5.1.2.3 Interest-Rate Swap With a swap the counterparties commit themselves to exchange one series of cash flows for another series of cash flows at a specified point in time138. In essence the interest rate swap is a strip of consecutive FRAs, hence it has at the payment dates the same profit-loss-profile as a FRA. An interest-rate swap is an agreement to exchange interest rates. A receiver-swap 139 protects against falling interest rates, the buyer receives a fixed interest amount and pays a variable reference rate. The hedging effect of a payer-swap140 is the other way around, the buyer receives variable and pays fixed. Thereby it can for instance protect a liability with a variable interest rate against rising market interest rates. There are many further swap variations, for instance the index swap141 that changes one floating interest rate for another one, the forward-swap with a different start-time or the amortising, step-up- or step-down-swap with a changing nominal amount.142 For valuing swaps, they can also be considered as a long (/short) position in a fixed Copyright © 2010. Diplomica Verlag. All rights reserved.
rate bond combined with an equivalent short (/long) position in a floating rate note. In contrast to the cash flows resulting from the fixed rate bond, the variable cash flows are only in the first year a secure payment. Since the subsequent interest payments are 134
The major future exchanges in Europe are the LIFFE in London (since 2002 belonging to the NYSE Euronext) and the EUREX in Frankfurt. 135 Eller, 1994 136 Schmeisser & Hecker, 2005 137 Eller, 1994 138 Due to several payment dates the counterparty risk is lowered. 139 Also fixed-to-floating or plain vanilla swap. 140 Also floating-to-variable-interest-rate-swap. 141 Also floating-to-floating-interest-rate-swap. 142 Dresdner Bank, 2002
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Schönborn, Jana. Financial Risk Management: Management of Interest Risk from a Corporate Treasury Perspective in a Service Enterprise : Management of Interest Risk from a
adjusted to the agreed reference rate at the agreed date, only the present value of the first year is subject to interest rate risk. From the cash flows resulting from the long and the short position the VaR can be calculated.143 The swap market is working at a high pace and trades can be positioned very fast. This is an advantage for instance if an enterprise expects rising interest rates and has a financing need. Whereas the contracting of a fixed interest loan with a bank would need a longer lead time, a swap can fix the interest rate without loosing time.144
5.1.3. Asymmetric Hedging Instruments 5.1.3.1 Option An option is an agreement between two contracting parties, according to which the seller of the option grants the right to the buyer to buy (= call) or sell (= put), an underlying interest instrument at a defined strike-price within a certain period (= American option) or at a certain expiration date (= European option). For the buyer the risk is limited to the option premium payment, whereas his profit potential is theoretically unlimited. For the seller the profit potential is limited to the option premium amount and he has to bear the option writer risk. Assuming liquid markets both, the buyer and the option writer, unless the option is exercised, can close out the contract. The optional right expires if it is not exercised up to the date of maturity. The option price is composed of the intrinsic value and the time value. The intrinsic value of an option is the difference between the strike price and the current price of the underlying (see Figure 14). The time value represents the amount that market participants pay in anticipation of market price changes of the underlying. It approaches zero at the maturity date. 145 The choice of the strike-price depends as for all asymmetric hedging instruments not Copyright © 2010. Diplomica Verlag. All rights reserved.
only on the expectation about the interest rate development, but also on how strong the business profit is affected by rising or falling interest rates and how much the enterprise is willing to spend on the interest rate hedging.146
143
Wiedemann, 2008 Dresdner Bank, 2002 145 Schmeisser & Hecker, 2005 146 Dresdner Bank, 2002 144
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Schönborn, Jana. Financial Risk Management: Management of Interest Risk from a Corporate Treasury Perspective in a Service Enterprise : Management of Interest Risk from a
value
at the money
out of money
in the money
time value
intrinsic value
Interest rate Figure 14: Intrinsic Value of an Option
A swaption represents a special form, where the buyer has the option to enter in a swap contract. One differentiates between a payer-swaption, where the buyer pays the fixed interest amount and a receiver-swaption where the buyer receives the fixed interest amount.147 Depending upon the expectation about the interest rate development four basic strategies can be differentiated. When expecting falling interest rates the strategy of a long-call can be pursued. If the interest rates are falling the price of the underlying rises. Once the current market price lies over the strike-price, the buyer will exercise his right. However the break even point is only reached when the price rises high enough so that the option premium is won. When expecting a stagnating interest rate development or only slightly increasing interest rates a short-call position would be an alternative to consider. If the interest rates rise marginal, the price of the underlying falls slightly. If the price of the underlying is below the strike-price, the buyer will not exercise his right, since he can buy the interest instrument at the spot market for a cheaper price. If however the price of the underlying is rising above the strike-price, the seller has the obligation to Copyright © 2010. Diplomica Verlag. All rights reserved.
deliver at the agreed price.148 If rising interest rates are expected a long-put strategy can be favourable. When the interest rates are rising, the price of the underlying goes down. If the current price of the underlying is below the strike-price, the option owner can sell the paper to the option writer for a higher price than he has to pay for it at the spot market. Since the price cannot go below zero, the profit potential is theoretically limited. 147 148
Hull, 2009a Schmeisser & Hecker, 2005
38
Schönborn, Jana. Financial Risk Management: Management of Interest Risk from a Corporate Treasury Perspective in a Service Enterprise : Management of Interest Risk from a
profit
profit
break-even strike
in the money
in the money
underlying value
underlying value
strike out the money
break-even out the money loss
loss
Figure 15: Profit-Loss-Profile of a Long (left) and a Short (right) Call
With the expectation of stagnating or slightly falling interest rates a short-put position can be pursued. If the interest rates are slightly falling, the price of the underlying goes up slightly. If the expectation is met, the buyer will not exercise his right, since he can sell the underlying instrument at the spot market for a higher price. If however the price of the underlying falls below the strike-price, the seller has to buy the underlying at the agreed price.149 profit
profit
break-even strike
in the money
in the money
strike break-even out the money
out the money
loss
loss
Figure 16: Profit-Loss-Chart of a Long (left) and a Short (right) Put
Important in conjunction with options is that they only at first sight differ fundamentally from other interest instruments. Just as futures and swaps, options can
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be construed with a combination of forwards and bonds. A portfolio with a long-call and a short-put with an equal strike and maturity based on the same underlying has the same profit-loss-profile as a long-forward on the same underlying. With the same approach a short-forward is construed by combining a long-put and a short-call position with an equal strike and maturity based on the same underlying. This socalled put-call-parity shows the connection between symmetrical and asymmetrical instruments.150 149 150
Schmeisser & Hecker, 2005 Eller, 1994
39
Schönborn, Jana. Financial Risk Management: Management of Interest Risk from a Corporate Treasury Perspective in a Service Enterprise : Management of Interest Risk from a
Long Call
Long Forward
Short Put
in the money
in the money
in the money
+ out the money
=
out the money
Long Put
out the money
Short Forward
Short Call
+
in the money
in the money
out the money
=
out the money
in the money
out the money
Figure 17: Put-Call-Parity
5.1.3.2 Cap, Floor and Collar Caps, floors, and collars are options on short term interest rates that can also be referred to as interest ceiling instruments. Whereas a cap limits a variable reference rate with a maximum rate and a floor with a minimum rate, a collar limits the interest rate in both directions (cap and floor). A cap is an agreement between the seller and the buyer where the seller pays a settlement amount if the interest rate rises above a defined strike. Thus a long-cap position is suitable for hedging the interest rate risk of liabilities at a variable interest rate, when rising interest rates are expected. Floors represent the counterpart to caps. Here the seller pays a settlement amount to the buyer, if the variable interest rate falls below the strike. Hence a long-floor position is suitable for hedging the interest rate risk of assets at a variable interest rate, Copyright © 2010. Diplomica Verlag. All rights reserved.
when falling market interest rates are expected.151 ®¯°±±¯²¯³° ´µ¶ ·¸¹³º¹¶µ±
®¯°±±¯²¯³° ű¾¾¸ ·¸¹³º¹¶µ±
151
¸¯»¯¸¯³º¯¸µ°¯(¼°¸¹½¯º¾³°¸µº°¹³¿ÀµÁ¼ ÂÃÄ
¼°¸¹½¯ " ¸¯»¯¸¯³º¯¸µ°¯º¾³°¸µº°¹³¿ÀµÁ¼ ÂÃÄ
Hull, 2009a
40
Schönborn, Jana. Financial Risk Management: Management of Interest Risk from a Corporate Treasury Perspective in a Service Enterprise : Management of Interest Risk from a
(5.3) (5.4)
Caps and floors can be understood as portfolios of several interest options. From the buyer’s point of view an unlimited opportunity comes at a limited risk amounting to the premium payment he has to pay at the beginning. Thus in contrast to swaps and FRAs these hedging instruments facilitate a protection for variable interest rates, without having to forfeit variable interest rate opportunities. In addition they are flexible regarding the amount of the interest hedging cost and the hedging range. The purchase of a collar is equal to the combination of a long-cap and a short-floor. With a collar the buyer can fix an interest rate range, which however also limits the interest chances. With a collar the cost of the hedging can be reduced. In the special case of a zero-cost-collar no premium has to be paid at all. The application possibilities are however limited, since the interest rate ceiling is usually very small.152 The following illustration summarises the basic hedging strategies that can be pursued with derivatives: Assets
Liabilities
short-term
long-term
short-term
long-term
Interest rate
floating rate
fixed rate
floating rate
fixed rate
Interest risk (=expectation)
falling interest rates
rising interest rates
rising interest rates
falling interest rates
Decision: Hedging
Change to fixed rate / duration extension
Change to floating rate / duration shortening
Change to fixed rate / duration extension
Change to floating rate / duration shortening
Hedging instrument
FRA
sell
buy
buy
sell
Future
buy
sell
sell
buy
Swap
pay floating rate, receive fixed rate
pay fixed rate, receive floating rate
pay fixed rate, receive floating rate
pay floating rate, receive fixed rate
Cap
sell*
buy
buy
sell*
Floor
buy
sell*
sell*
buy
P/L
increased earnings
reduced financing costs
* As long as there is not a exact contrary deal, a option writer position constitutes not a pure hedging strategy.
Figure 18: Summary of Hedging Strategies153
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5.2.
Implications for the Portfolio Alignment of a Service Enterprise
5.2.1. Duration To achieve an optimal risk-return-profile the first step is to analyse the actual situation regarding the financing expenditure and the volatility of the present value. As to the term of the interest rate fixing there are basically two extreme alternatives possible: a revolving interest rate adjustment based on a short term key interest rate and a longterm interest rate fixing. 152 153
Dresdner Bank, 2002 Adapted from Dresdner Bank, 2002
41
Schönborn, Jana. Financial Risk Management: Management of Interest Risk from a Corporate Treasury Perspective in a Service Enterprise : Management of Interest Risk from a
amount of interest cost
volatility of interest cost
Optimum ?
duration
Figure 19: Selection of a Benchmark with Optimum Interest Cost for Enterprises with a Debit Carryover154
Assuming a normal yield curve the revolving interest rate adjustment causes the lowest interest expenditure (at least at first), but also the highest volatility of the interest cost. At a fixed interest rate the interest costs are higher, however at the same time the interest rate fluctuations are lower. With regard to external reporting for an enterprise both is of importance, the interest expenditure and its volatility. For the internal management the present value is decisive. From a present value point of view it can be said, that the longer the fixed interest rate term the higher is the interest rate risk. By knowing the cash flow structure of the interest portfolio systematic measures can be applied to reduce the interest rate risk within certain maturity ranges. Since a long duration protects a portfolio with a debit carry-over against rising interest, the duration should be extended if rising interest rates are expected by the management. Contrary the duration should be shortened if falling interest rates are expected. Interest rate derivatives are particularly appropriate to change the duration since the underlying balance sheet item is not changed.155 Under a normal yield curve, the decision for the ratio of variable interest-bearing and fix-rated positions, is one between a high volatility of interest rate cost at lower current interest rates and a low volatility of interest rate cost at higher current interest rates. Thus it is a question of the interest rate expectation, the risk appetite and the cost Copyright © 2010. Diplomica Verlag. All rights reserved.
the company is willing to bear for the hedging of their interest risk. This question every company has to answer individually, independent from the type of business it is operating in. However based on the specific cash flow structure of a service enterprise discussed in section 2.4 it can be said that it is difficult to project the cash inflows too far into the future. Together with a high proportion of fixed costs this results in narrow constraints for the projection of financing needs. The maturity of fix-rated loans should only be as long as there is a reliable cash flow forecast available. 154 155
Wiedemann & Hager, 2004 Dresdner Bank, 2002
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5.2.2. Benchmark The strategic alignment of the interest portfolio of an enterprise according to cost and profit respective risk considerations requires not only a regular analysis of the actual situation but also a suitable benchmark and a limit system. The selection of a benchmark requires some considerations. Unlike banks, which are usually characterised by an asset carryover, the interest portfolio of an enterprise more likely shows a higher amount of liabilities than assets. Thus they rarely have investment requirements, but rather financing needs. Therefore the benchmarks designed for banks, as for instance the ten years moving average, cannot be applied by enterprises and an appropriate benchmark has to be developed for their net financing position. The benchmark has to be selected according to individual criteria, since it reflects the risk and return approach of the enterprise. Generally the portfolio is compared to the benchmark on a monthly basis.156 Taking into account the specific issues of cash flow forecasting in a service enterprise discussed in section 2.4, the planning horizon of the benchmark should only go as far into the future as a reliable forecast can be provided. The investment into moving averages applied by banks however can also be assigned to the net financing cash flows of service enterprises. Thereby a situation can be achieved where a twist in the yield curve leads to an increase of the present values at the short end and a decrease of the present values at the long end or the other way around. In this way the effects of changes in the shape of the yield curve can be smoothed. 5.2.3. VaR Limit For quantifying the potential loss the VaR concept based on an analytic approach or simulation based methods, as presented in chapter 4.3, can be applied. If a negative portfolio present value is assumed, a rise in the level of interest rates represents a
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chance, because then the change in the present value is positive. Contrary the risk lies in falling interest rates and the resulting negative present value changes.157 A continuous monitoring of the risk situation can be implemented by defining a limit system. Thereby the VaR, the maximum interest portfolio loss which cannot be exceeded with a given probability, can be limited and the possibility of high losses can be reduced. An absolute limit value would stay constant if the present value of the portfolio changes. If the limit is quoted as a percentage it adapts automatically to 156 157
Wiedemann & Hager, 2004 Wiedemann & Hager, 2004
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increases or decreases in the present value, since a proportional limit expands with an increasing present value and downsizes with a falling present value. The VaR has to be limited in accordance with the risk tolerance and the risk-bearing capacity of the enterprise. It is hard to establish a correct maximum VaR limit. A rule of thumb is that the VaR over a financial year should not exceed the amount that can be generated through net earnings during the same time period. A prudent VaR limit could be around 20 to 30 percent of net earnings. Another possibility is to build up reserves for possible interest losses und define these as the VaR limit. In order to set up a compelling risk limit it is necessary to determine the variable parameters included in the calculation of the VaR. It should be defined for what level of confidence, what holding period and for what maturity range the VaR is computed. Eventually the definition of the risk limit requires a business decision.158 After the actual situation of the portfolio has been analysed regarding financing expenditure, cash-flow structure, current VaR and the firm specific limits a complete estimation of the risk situation can take place. Since effective risk management requires escalation processes, it must be immediately brought to manager’s attention if the VaR limit is exceeded or the deviation from the benchmark exceeds a certain amount or percentage. Furthermore appropriate risk measures have to be planned in order to keep the interest risk exposure within the given limits. The framework for
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these measures is mandated by the treasury risk policy.159
158 159
Donohoe, 2003, Part 1 Association of Corporate Treasurers, 2009
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6. Conclusion The various reasons for financial risk management have been highlighted already in the first section as well as in section 2.1. Thus the question that arises is not if financial risks and in particular interest rate risk shall be managed, it is rather how this management shall be undertaken and how the process can be adapted to meet the special needs and constraints of a service enterprise. As Jorion puts it “For industrial corporations, exposure to financial risks can be optimized carefully so that firms can concentrate on what they do best – manage their business risks.”160 This constitutes the main difference of non-financial service enterprises to financial institutions. Whereas the primary function of the latter is the active management of financial risks, non-financial service enterprises have their key expertise in other areas. Hence, the approaches of banks towards risks management cannot, as already mentioned in section 4.5 and 5.2, be imposed on service corporates. However, service enterprises can and should build on the expertise of the pioneers in risk management. From my point of view, in search of an adequate risk management approach for a service enterprise, one should stick to the rule: as simple as possible and as extensive as necessary. When the number of cash flows of the company exceeds a certain amount, the mapping of cash flows should be considered as an instrument to simplify the cash flow structure in order to keep the effort to manage the risk at a low level. As explained in section 4.4.2 and 4.5, the convexity mapping is the most flexible method of the three approaches being discussed and is with today’s technology standard also easy to implement. The VaR is the risk measure that is primarily relevant for the risk estimation, defining a risk level for a specified time horizon and the reporting of a risk ratio to the
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management. One of its most important advantages over the traditional scenario methods is that it is not affected by a subjective opinion. Furthermore it allows the comparison of different risk types and the consolidation of the risk the firm is exposed to. By linking the VaR with return measures, a risk adjusted return management is facilitated (= return on risk adjusted capital). However, since the VaR value depends not only on the used variables, such as the holding period and the level of confidence being chosen, but also on the data input for correlations and volatilities, the accuracy depends highly on the quality of this data. 160
Jorion, 2007, 4
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After all the VaR concept is as every model a balancing act between complexity and accuracy. The analytical concepts, as for instance the variance-covariance-approach, assume a normal distribution of the risk factors to simplify the model. The simulation based approaches, as for instance the historical simulation, do without statistical assumptions and thereby eliminate the model risk but are by definition limited to a finite number of scenarios. With regard to the specific characteristics of service enterprises I would classify the historical simulation as an approach that causes too much effort which needs to be put into the preparation of a sufficient large data base and the permanent revaluation of the portfolio for each scenario. In addition the approach is past-oriented; since a future risk potential shall be derived from it, this can be problematic. By contrast the computation of the VaR with the variance-covariance approach is more effective and still comprehensible. Since the market interest rate changes don’t generally follow a normal distribution, this method shall be combined with stress test scenarios, in particular in times of high volatility in the financial markets. A pitfall of the variance-covariance approach is that in its original conception it is not tailored for portfolios with a high proportion of options and other derivatives. Since most service enterprises use derivatives only for hedging purposes (see section 2.4), the significance of this disadvantage is reduced. However, if the use of derivatives increases, more complex methods of risk measurement have to be considered. As to the management of the risk exposure basically all methods being examined in section 5 are sufficient. The hedging instruments shall be chosen according to the volume of the interest risk exposure of the company, its interest rate expectation, its risk appetite and the cost it is willing to bear for the interest risk hedging. One should always aim at striking a balance between the effort being put into risk management and the value for money being offered by it.
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As to the overall interest risk management process in a service company, I would in case of doubt opt for a more simple approach, where a sufficient quality of the data input can be assured as and if needed with the help of external risk metrics providers. A further challenge for the management of financial risks will be the consolidation of all risks and its subsequent integration in the company-wide risk management.
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7. Appendices Appendix 1: Regulatory Framework for Risk Management Sarbanes-Oxley Act (SOX) - Signed into law in July 2002 in the USA - The law is applicable for all US-noted enterprises - Sec 302 obliges the CFO and the CEO to testify the quarter and annual reports and thereby notably increases their governance role relating to the financial reports - Sec 404 demands the implementation of an internal control mechanism for financial accounting - E-Sox: the European Sarbanes-Oxley Act
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Risk reporting according to IFRS - The EU regulation EC 1606/2002 on IAS requires that all companies listed on a regulated exchange in a member state have to prepare their consolidated accounts under IFRS (for accounting periods starting on or after 01/01/2005 - IFRS demands a comprehensive risk reporting both in the financials part (unscheduled depreciations, provisions) and verbal in the management report - IAS 32 and IFRS 7 require detailed information about the cash flows resulting from financial innovations (amount, temporal structure, risks) - IAS 39 includes provisions for the fair-value of financial instruments EU Directives - Prospectus Directive o The original proposal of the European Commission was adopted by the European Council in May 2001 o The directive aims to harmonise the prospectus requirements (approval, publication) for the public offering of securities - Market abuse directive o The directive includes regulations on insider dealing and market manipulation in the EU - Basel II (2006/48/EG und 2006/49/EG) o Put into force as from 01/01/2007 o The accord institutes a more risk aware approach to the measurement of the capital adequacy by banks and securities firms (e.g. loan capital treatment according to borrower rating, greater netting possibilities) o It will also have some impact on treasurer’s dealings with financial institutions Accounting Law Reform Act (BilReG) - Put into force as from 31/12/2004 - Sec 289 (1) s. 4 HGB contains new forecast reporting obligations for corporations; as for instance the evaluation of the prospective enterprise development and the description of the underlying assumptions - The objective is to achieve an enhanced transparency and traceability of forecast planning 47
Schönborn, Jana. Financial Risk Management: Management of Interest Risk from a Corporate Treasury Perspective in a Service Enterprise : Management of Interest Risk from a
- The act promotes the development of an integrated enterprise risk management system (integrated chance and risk management) which is the = basic requirement for value-oriented management German accounting standard No. 5 and 15 - No. 5 incorporates concrete principles for the external risk reporting: - Statement on the risk management system, definition of the risk fields, description of the individual risks, quantification of the risks, description of the risk management instruments - No. 15: is based on BilReg and demands the incorporation of chances and underlying assumptions into the forecast report - These standards are applicable for companies that report under HGB and IFRS The German Corporate Governance Code (DCGK) - Passed 26/02/2002 - The objective is to attain a transparent German corporate governance system and encourage the believe of the stakeholder in a responsible management - The code regulates rights and obligations of the shareholders, the supervisory board and the executive board (e.g. the executive board has to provide an appropriate risk management and controlling)
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Corporate Sector Supervision and Transparency Act (KonTraG) - Passed 06/03/1998 by the German Bundestag, put into force as from 01/05/1998 - Augments the AktG (Sec 91 (2) AktG) and the GmbHG (Sec 43 GmbHG) - stipulates an early-warning system and regulates the responsibility of the executive board to implement an appropriate risk management system as well as a suitable internal revision - The objective is an early recognition of endangering developments and assurance of the business continuity - The law is only applicable for public companies, but has also effects on other types of business ownership, most notably for limited liability companies (GmbHs)
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Appendix 2: Extract from “Der Dienstleistungssektor – Wirtschaftsmotor in Deutschland - Ausgewählte Ergebnisse von 2003 bis 2008”
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published by the Statistisches Bundesamt, 2009
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8. Bibliography Books Association of Corporate Treasurers. (2009). The International Treasurer's Handbook (19 ed.). London. Bruhn, M., & Stauss, B. (2006). Forum Dienstleistungsmanagement: Dienstleistungscontrolling (1 ed.). Wiesbaden. Dresdner Bank. (2002). Zinsmanagement (1 ed.). Dresden. Eller, R., Gruber, W., & Reif, M. (2002). Handbuch des Risikomanagements (2 ed.). Stuttgart. Eller, R. (1994). Zins- und Währungsrisiken optimal managen (1 ed.). Wiesbaden. Horcher, K. A. (2005). Essentials of financial risk management (1 ed.). New Jersey. Hull, J. (2009a). Optionen, Futures und andere Derivate (7 ed.). München. Jorion, P. (2007). Value at Risk: The New Benchmark for Managing Financial Risk (3 ed.). New York. Melzer-Ridinger, R., & Neumann, A. (2008). Dienstleistung und Produktion (1 ed.). Heidelberg. Metzler, L. (2004). Risikoaggregation im industriellen Controlling (1 ed.). Köln. Scharpf, P., & Luz, G. (2000). Risikomanagement, Bilanzierung und Aufsicht von Finanzderivaten (2 ed.). Stuttgart.
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Schmeisser, W., & Hecker, T. (2005). Strategien von Futures und Options (1 ed.). München. Schmidt, M. (2006). Derivative Finanzinstrumente – Eine anwendungsorientierte Einführung (3 ed.). Stuttgart. Wiedemann, A. (2009). Financial Engineering – Bewertung von Finanzinstrumenten (5 ed.). Frankfurt a.M.
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Wiedemann, A. (2008). Risikotriade Zins-, Kredit- und operationelle Risiken (1. ed.). Frankfurt a.M. Wilkens, M. (2002). Wertpapiermanagement (5 ed.). Göttingen. Woke, T. (2008). Risikomanagement (2 ed.). Bad Langensalza.
Journals Mare, E. (2008). Special report. Market Risk: A brief discussion. TMI - Treasury Management International, 43-45. Masquelier, F. (2007). Treasury Risk Management: A Model for ERM? TMI Treasury Management International (159), 21-24. Sanders, H. (2009). Trimming the Sails: the 2009 Risk Agenda. TMI - Treasury Management International (172), 4-8. Schwabe, J. (2006). Value-at-Risk: Zun innovativ 200 jahre nach Gauß? Finance (Special ed.), 6-8. Wiedemann, A., & Hager, P. (2004, November). Zinsrisikomanagement in Unternehmen: Die Entdeckung einer neuen Risikokategorie? Finanzbetrieb, 725729.
Internet Resources Donohoe, C. (2003, August 12). Treasury Risk, The Roadmap - Part One. Retrieved
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June 24, 2009, from http://www.gtnews.com/article/5114.cfm Donohoe, C. (2003, September 2). Treasury Risk, The Roadmap - Part Two. Retrieved June 24, 2009, from http://www.gtnews.com/article/5143.cfm ECB. (2009). Euro area yield curve. Retrieved November 02, 2009, from http://www.ecb.int/stats/money/yc/html/index.en.html
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Gleißner, W., & Berger, T. (2007). Einfach lernen! Risikomanagement. Retrieved November 02, 2009, from http://www.chemieonline.de/bibliothek/buecher_download.php gtnews. (2003, May 20). Devising a Treasury Policy. Retrieved June 24, 2009, from http://www.gtnews.com/article/5003.cfm Hager, P. (2004). Risk Net. Retrieved November 02, 2009, from http://www.risknet.de/fileadmin/template_risknet/images_content/Methoden/VaR -Verfahren_RiskNET.pdf HM Treasury. (2004). The Orange Book. Management of Risk – Principles and Concepts. Retrieved November 02, 2009, from http://www.hmtreasury.gov.uk/orange_book.htm Hull, J. (2009b). Technical Note No. 10* - Options, Futures, and Other Derivatives, Seventh Edition. Retrieved November 20, 2009, from http://www.rotman.utoronto.ca/~hull/TechnicalNotes/TechnicalNote10.pdf Obermaier, R. (2005). Unternehmensbewertung, Basiszinssatz und Zinsstruktur: Kapitalmarktorientierte Bestimmung des risikolosen Basiszinssatzes bei nichtflacher Zinsstruktur. Retrieved November 10, 2009, from http://epub.uniregensburg.de/4530/ Rau-Bredow, H. (2001). Überwachung von Marktpreisrisiken durch Value at Risk. Retrieved October 27, 2009, from http://www.econbiz.de/archiv/wue/uwue/ bank/ueberwachung_marktpreisrisiken.pdf Statistisches Bundesamt. (2009). Retrieved November 20, 2009, from Der Dienstleistungssektor: Wirtschaftsmotor in Deutschland, Ausgewählte Ergebnisse
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von 2003 bis 2008: http://www.destatis.de/jetspeed/portal/cms/Sites/destatis/ Internet/DE/Navigation/Statistiken/DienstleistungenFinanzdienstleistungen/Dienst leistungenFinanzdienstleistungen.psml Wiedemann, A. (2002). Messung und Steuerung von Risiken im Rahmen des industriellen Treasury-Managements. Retrieved October 12, 2009, from http://www.ccfb.info/fileadmin/media/corporate_risk/Industrielles_TreasuryManagement.pdf
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