Bank Management and Control: Strategy, Pricing, Capital and Risk Management [2nd ed.] 9783030428655, 9783030428662

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Management for Professionals

Johannes Wernz

Bank Management and Control Strategy, Pricing, Capital and Risk Management Second Edition

Management for Professionals

The Springer series Management for Professionals comprises high-level business and management books for executives. The authors are experienced business professionals and renowned professors who combine scientific background, best practice, and entrepreneurial vision to provide powerful insights into how to achieve business excellence.

More information about this series at http://www.springer.com/series/10101

Johannes Wernz

Bank Management and Control Strategy, Pricing, Capital and Risk Management Second Edition

Johannes Wernz Zurich, Switzerland

ISSN 2192-8096 ISSN 2192-810X (electronic) Management for Professionals ISBN 978-3-030-42865-5 ISBN 978-3-030-42866-2 (eBook) https://doi.org/10.1007/978-3-030-42866-2 © Springer Nature Switzerland AG 2020 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors, and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, expressed or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. This Springer imprint is published by the registered company Springer Nature Switzerland AG. The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland

Preface

This is the second edition of Bank Management and Control (2020 edition). This book focuses on bank management and control in terms of strategy, pricing, capital (return on equity) and risk management—in the context of the recent regulatory and macroeconomic developments. Only recently last adjustments were made to the Basel III rules and their national implementations—with important implications for banks, customers and economy. The political and macroeconomic situation changed considerably in the last few years, too. Banks are heavily affected by the following macroeconomic and regulatory developments: • On the one hand, interest rates in different jurisdictions are very low or even negative (like in Switzerland, Germany, Japan); generally interest rates are low (European Union, USA, etc.). This situation got even more pronounced with the coronavirus crisis. • For mortgage loans and other loans, margins decrease due to the interest rate situation. • On the other hand, public and private debt increases massively (e.g. in the USA, in many countries of the European Union and in China). This situation got even more pronounced with the coronavirus crisis. • House prices rise significantly in many jurisdictions. • Basel III became effective in 2019 (for some important elements, it stipulates the implementation date January 2022). There is a lot of pressure on business • Due to low or negative interest rates • Due to tighter capital

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Preface

Additional developments have implications, too. Amongst others: • • • • • •

Coronavirus crisis in 2020 Conflicts in different parts of the world (like in the Middle East) Alienation of the USA-Europe Disputes between the USA and China Brexit (implications for different countries and sectors) The climate change discussion, potentially disrupting some industries

The regulations trigger certain additional things: Resolution and recovery plans (RRPs) are required and must be ready for brisk execution, including potential splitting-up of the business and cutting-off of portfolios; the RRPs had and have implications for the legal entity structure of certain banks (e.g. re-establishment of a core division). Zurich, Switzerland

Johannes Wernz

Short History

Within the last several years (mainly after the global financial crisis), the banking industry and the regulations have changed significantly. The following had and has bigger implications: • The implementation of Basel II in 2006 (with implications on capital and business) • The economic and financial crisis that started with the mortgage bubble in the USA and spread to Europe and other parts of the world in 2007 and 2008 • The implementation of Basel III (and intermediate steps like Basel 2.5)—as shortcomings of Basel II were observed during the economic and financial crisis. Basel III became fully effective on 1 January 2019 for those countries that have adopted Basel III • Low or even negative interest rates • Increasing public and private debt in many jurisdictions • Coronavirus crisis The main topics of this book are management and steering, pricing, capital planning and capital optimization and the implications and implementation of Basel III. Bank management, strategy, pricing, capital planning and risk management are challenged within the perimeters of Basel III. There are and will be shifts in strategy for many banks due to the new regulatory requirements. Within the economic and financial crisis (starting in 2007), several banks were affected heavily. Within the coronavirus crisis (2020) pressure came back. • The US Bank Lehman Brothers crashed in 2008. • In the United Kingdom, the Halifax Bank of Scotland (HBOS)—a merger of Halifax plc and the Bank of Scotland—faced big issues; a merger of HBOS and Lloyds TSB under the new name Lloyds Banking Group resulted. • The Royal Bank of Scotland (RBS) faced big issues. • Banks like Dexia in Belgium or Depfa in Ireland were affected.

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Short History

• HRE of Munich/Germany purchased Depfa, and shortly after the purchase, the economic and financial crisis hit and resulted in massive problems for HRE. HRE could only be saved with the help of the German government and thus German taxpayers. • Many of Germany’s Landesbanken completely underestimated the risks associated with securitized products (such as CDOs) and faced significant trouble beginning in 2007. The Landesbank of North Rhine-Westphalia, the Düsseldorf-based WestLB, was particularly hard hit. • During the crisis of 2007 and, in the subsequent years, UBS requested help from the Swiss state and the Swiss National Bank (SNB). UBS had underestimated the risks associated with securitized products (CDOs) and faced huge losses. • IKB, a Düsseldorf-based bank (associated with the German state), invested massively in securitized products from the USA and faced massive losses. If one bank faces a problem, many other banks are also affected. In the financial crisis regulators faced a situation in which regulatory requirements were deemed to be insufficient. As a result, regulatory requirements were adjusted (Basel 2.5 and Basel III). Depending on the business model of a bank, adopting the new regulatory requirements had and will have significant implications for the bank’s capital allocation. The risk/return management of most banks is affected strongly.

Motivation and Goal

Regulatory requirements for capital do have a huge influence on the return, and risk modelling has a significant influence on the capital requirement and pricing for the corresponding business segment. Risk modelling, therefore, has an impact on the return of equity (RoE) of the corresponding business segment. It is part of the philosophy (since Basel II, re-emphasized with Basel III) that incentives are provided for a good and granular risk management. The improvement of risk management and the increase of granularity within risk management are often rewarded with lower capital charges. The book shows many relevant focus areas with potential rewards (including the technical details). This book provides a systematic in-depth overview of all areas that are relevant to the management of risk and return and therefore to banks’ strategy. The discussed topics are embedded in the context of the regulatory requirements of Basel III and the national implementations (e.g. Eigenmittelverordnung in Switzerland, Capital Requirements Regulation in the European Union, etc.). This book often focuses on the advanced approaches within Basel III, as the advanced approaches provide most opportunities for improving risk management and thus provide leeway for strategic considerations. An overview of Basel III—the regulatory rules specifying the requirements for capital and reporting on risks—is given. The national implementations are discussed to some extent, too. The philosophy of Basel III is carved out and important details are emphasized. Terms like “Basel III”, “Basel”, the “Basel Rules” and the “Basel Accord” are used synonymously in this book.

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Acknowledgments

I would like to thank my colleagues and friends for great discussions and insightful comments. Particularly, I would like to thank • • • • • • • • • • • • • • • • • • • • • • • • •

Alessandro Lana Dr. Tamás Mayer Dr. Friedrich Hoheneck Max Schieler Dr. Janusz Milek Barbara Marin Stefan Herschel Dominique Rohr Ebed Mwandembe Dr. Pratibha Vikas Dr. Irina Singer Dr. Giovanni Cesari Dr. Jörg Behrens David Kang Olaf Schmid Volker Langner Dr. Michael Hügler Andreas Dierolf Gunter Schmid Nicola Lambiase Peter Schmid Roland Schmid Daniel Niehus Dr. Marc Ryser Bruno Oppliger Psalm 136:1—O give thanks unto the LORD; for he is good.

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Contents

1

Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1

2

Bank Management and Steering . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1 Strategy Planning: Iterative Process . . . . . . . . . . . . . . . . . . . . . 2.1.1 Process of Planning . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1.2 Capital Allocation . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2 Strategy Planning: Tools . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2.1 EaR/CaR: Overall Aggregation . . . . . . . . . . . . . . . . . . 2.2.2 Scenario-Based Assessment/Stress Testing . . . . . . . . . . 2.3 Capital Optimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . .

3 3 3 8 9 9 13 23

3

Banks and the Regulatory and Economic Environment . . . . . . . . . 3.1 Economic and Political Aspects . . . . . . . . . . . . . . . . . . . . . . . . 3.2 Types of Banks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3 Banks in Different Legislations . . . . . . . . . . . . . . . . . . . . . . . . 3.4 Role of the Banks’ Credit Rating . . . . . . . . . . . . . . . . . . . . . . . 3.5 Role of Rating Agencies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.6 Role of the International Swaps and Derivatives Association (ISDA) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.7 Regulatory Environment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.7.1 BIS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.7.2 BIS and the Great Depression: History in a Nutshell . . . 3.8 Basel III . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.8.1 Basel III: Philosophy and Evolvement . . . . . . . . . . . . . 3.8.2 Basel III: Timeline and Implementation Status . . . . . . . 3.8.3 Basel III: Some Spotlights . . . . . . . . . . . . . . . . . . . . . 3.8.4 Basel III: Capital Ratio . . . . . . . . . . . . . . . . . . . . . . . . 3.8.5 Basel III: Output Floor . . . . . . . . . . . . . . . . . . . . . . . . 3.9 Issue Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . .

25 25 26 27 27 28

. . . . . . . . . . .

28 29 29 29 30 30 32 32 34 34 35

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Contents

3.10

Issue Complexity and Risk Identification . . . . . . . . . . . . . . . . . . 3.10.1 Sale and Leaseback Transactions . . . . . . . . . . . . . . . . . . 3.10.2 Securitization and Subprime . . . . . . . . . . . . . . . . . . . . .

36 36 36

4

Risk Modeling and Capital: Credit Risk (Loans) . . . . . . . . . . . . . . . 4.1 Pricing and Expected Loss . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1.1 Adverse Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1.2 Risk Adjusted Pricing and RoE . . . . . . . . . . . . . . . . . . . 4.2 Loan Loss Provisioning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3 Capital: Relevant Points . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3.1 Default Definition . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3.2 Maturity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3.3 Granularity of Rating Engines . . . . . . . . . . . . . . . . . . . . 4.3.4 Classification of Exposures as Retail or Corporate . . . . . 4.3.5 Recent Bubbles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3.6 Missing Values . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.4 PD-Rating Tools, LGD Tools, and EAD Estimations . . . . . . . . . . 4.5 Advanced Regulatory Approaches . . . . . . . . . . . . . . . . . . . . . . . 4.6 Rating Tools (PD Models) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.6.1 Development of Rating Tools . . . . . . . . . . . . . . . . . . . . 4.6.2 Calibration of the Rating Tools . . . . . . . . . . . . . . . . . . . 4.6.3 Example of a Corporate Rating Tool . . . . . . . . . . . . . . . 4.7 LGD Models (LGD Tools) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.7.1 LGD Tool for Vehicles/Machinery . . . . . . . . . . . . . . . . 4.7.2 LGD Tool for Mortgages . . . . . . . . . . . . . . . . . . . . . . . 4.8 Backtesting Within Credit Risk . . . . . . . . . . . . . . . . . . . . . . . . . 4.8.1 Backtesting Versus Validation . . . . . . . . . . . . . . . . . . . 4.8.2 Backtesting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.8.3 Backtesting Framework PD . . . . . . . . . . . . . . . . . . . . . 4.8.4 Backtesting Framework LGD . . . . . . . . . . . . . . . . . . . .

39 39 40 41 42 42 43 44 46 47 49 50 51 51 52 52 55 57 58 60 62 65 65 65 66 68

5

Risk Modeling and Capital: Counterparty Credit Risk (“EPE” and “CVA”) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.1 Cash Flows, Exposure, Pricing, and Capital . . . . . . . . . . . . . . . 5.1.1 “EPE” Capital Modeling/Capital Charge . . . . . . . . . . . 5.1.2 CVA Capital Charge . . . . . . . . . . . . . . . . . . . . . . . . . 5.2 Wrong Way Risk . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. . . . .

71 71 72 74 76

6

Risk Modeling and Capital: Credit Risk (Securitizations) . . . . . . . . . 6.1 Basel III Approaches: Securitization-Related Capital . . . . . . . . . . 6.2 History: Financial Crisis of 2007 . . . . . . . . . . . . . . . . . . . . . . . .

79 79 80

7

Risk Modeling and Capital: Market Risk . . . . . . . . . . . . . . . . . . . . 7.1 Pricing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.2 Capital: Internal Models Approach . . . . . . . . . . . . . . . . . . . . . . 7.3 P&L Attribution Testing: Internal Models Approach . . . . . . . . . 7.4 Capital: Standardized Approach . . . . . . . . . . . . . . . . . . . . . . . .

81 81 81 83 83

. . . . .

Contents

7.5 7.6

7.7 8

9

xv

History: Basel 2.5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Exposure Modeling (Pricing and Capital): Interest Rate Derivatives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.6.1 Monte Carlo Simulation . . . . . . . . . . . . . . . . . . . . . . . 7.6.2 Market Data: Caps . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.6.3 Fitting of Volatility Curves to the Data . . . . . . . . . . . . 7.6.4 Correlations: Setting . . . . . . . . . . . . . . . . . . . . . . . . . . 7.6.5 Longstaff–Schwartz Regression . . . . . . . . . . . . . . . . . Backtesting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Risk Modeling and Capital: Operational Risk . . . . . . . . . . . . . . . . . 8.1 Standardized Measurement Approach . . . . . . . . . . . . . . . . . . . . 8.1.1 Business Indicator Component of the SMA . . . . . . . . . 8.1.2 Loss Component (ILM) of the SMA . . . . . . . . . . . . . . 8.1.3 Loss Event Taxonomy (Categories) for SMA (and Other Approaches) . . . . . . . . . . . . . . . . . . . . . . . 8.2 AMA Model (Pillar II): Modeling and Simulation . . . . . . . . . . . 8.3 Internal Data/External Data . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.4 Controls . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.5 Cost/Benefit Considerations for Controls . . . . . . . . . . . . . . . . . 8.6 Backtesting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

.

84

. . . . . . .

85 85 86 86 87 87 88

. . . .

89 89 90 90

. . . . . .

90 93 101 102 103 104

Risk Modeling: Asset Liability Management . . . . . . . . . . . . . . . . . . . 105 9.1 Liquidity Coverage Ratio . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105 9.2 Net Stable Funding Ratio . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106

Appendix A: A-IRB Formulas for the Derivation of Capital . . . . . . . . . A.1 Residential Mortgage Exposure . . . . . . . . . . . . . . . . . . . . . . . . . . A.2 Qualifying Revolving Retail Exposures . . . . . . . . . . . . . . . . . . . . A.3 Other Retail . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A.4 Corporates and Bank Exposures . . . . . . . . . . . . . . . . . . . . . . . . . A.5 Big Banks and Financial Institutions . . . . . . . . . . . . . . . . . . . . . . A.6 Corporate: SME . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . .

109 109 110 110 110 111 111

Appendix B: Credit Portfolio Modeling . . . . . . . . . . . . . . . . . . . . . . . . . 113 Appendix C: Country Risk/Issuer Risk . . . . . . . . . . . . . . . . . . . . . . . . . . 115 Appendix D: Settlement Risk . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117 Appendix E: Historical Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119 Appendix F: Specialized Lending/Project Finance . . . . . . . . . . . . . . . . . 123 Abbreviations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125 Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129 Glossary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131

Chapter 1

Outline

This book is divided into the following chapters: Chapter 2 deals with all topics relevant for bank management and steering, for strategy, and especially for the riskreturn management. In this chapter, business models are discussed. In Chap. 3 the economic and political situation is discussed; the regulatory framework and the development of the philosophy within the Basel Accords, specifically Basel III, are presented. Chapters 4–6 deal with Credit Risk (loans) and Counterparty Credit Risk (derivatives). Risk and return relevant topics such as risk-adjusted pricing and the underlying parameters are illustrated. Risk models are presented. Chapter 7 deals with Market Risk, whereas Chap. 8 deals with Operational Risk. In Chap. 9 Asset Liability Management is discussed. Relevant topics (such as capital optimization) are discussed in greater detail, and the important points regarding risk-adjusted pricing are addressed in various sections throughout the book. Bank management and risk-return management are the main topics of this book. Areas/topics that have an impact on risk-return management are therefore highlighted in gray boxes (light gray) embedded within the sections. Regarding Capital and Capital Optimization this means. . . Bank management and risk-return management are heavily influenced by the regulatory requirements and thus by the changes to the required capital. The other recurring topic in this book: the Basel Accords (Basel III). Topics related to Basel III are highlighted and outlined in dark gray boxes embedded in the sections. The significant Basel III changes in that area are/mean. . .

© Springer Nature Switzerland AG 2020 J. Wernz, Bank Management and Control, Management for Professionals, https://doi.org/10.1007/978-3-030-42866-2_1

1

2

1

Outline

The sample bank described in this book is typically found in locations like London, New York, Zurich, or Frankfurt. The illustrative bank is a major fullservice bank; on the one hand, it has strong roots in the domestic retail and corporate loans area (mortgages, consumer loans, loans to SME and big corporations, specialized lending), and on the other hand, it also has a strong investment bank division and a significant wealth management division. All presented balance sheet figures, risk weighted assets (RWA), and capital figures are realistic vis-à-vis banks based in London, New York, Zurich, or Frankfurt. The regulatory capital is calculated/shown according to Basel III. Assessments are made according to the discussed macroeconomic scenarios.

Chapter 2

Bank Management and Steering

2.1

Strategy Planning: Iterative Process

Appetite, risk appetite—how much of it, with what consequences, with what impact on the strategy and on the volatility of earnings? This is a fundamental question in bank management. Managers are often tempted by high profits; especially when there are new products on the market that promise high profits, the buying pressure is great; one wants to participate. Often, the volatility of earnings is disregarded. Risk and return are, however, almost always coupled. How much volatility of earnings (and therefore the probability of a total loss) can one tolerate? Often one chooses a mix. For example, one decides to allocate 60% of the capital to the investment banking division (with the hope of higher returns) and one allocates 40% of capital to the domestic division—especially retail—hoping for stable (though lower) returns. Retail business—for example, mortgage and consumer loans—generally offers a lower return, but there is lower volatility of the results, the results are more stable. The total return and the overall volatility of the distribution result from the mix (in this example, 60/40).

2.1.1

Process of Planning

Usually, at least once a year, an intense review of the strategy takes place. Decisions of the past are challenged. Decisions for the future are made. To ensure that such a process does not produce erroneous decisions, the process should take place according to defined rules. Tools should be made available to assess the potential strategies associated with the risk appetite, and also to assess the consequences of the strategies (Fig. 2.1).

© Springer Nature Switzerland AG 2020 J. Wernz, Bank Management and Control, Management for Professionals, https://doi.org/10.1007/978-3-030-42866-2_2

3

4

2 Bank Management and Steering 1. Define Risk Appetite and RoE 7. Modify RoE

2. Define Strategy 8. Modify Strategy

3. Determine Earnings and EaR/CaR for the (new) Strategy

6. Accept Strategy

5. If EaR and CaR are within their Capacities 6., else 7.

4. Determine Capacities for the Strategy

Fig. 2.1 Iterative process of the strategy planning

The senior management decides which return on equity and thus which volatility of the profits is desirable. One bank might decide that a stable return on equity of 5% is sufficient. A more aggressive bank possibly decides for a return on equity of 10% (facing higher volatility though). The bigger risk appetite and thus higher return are associated with higher volatility. It may be that in 1 year 10% can be achieved, while the return in the next year goes down or is negative even. Whatever the decision, the risk appetite needs to be translated into a strategy. In the first case of the example, the bank probably strengthens the domestic business, the lending to small and medium enterprises (SMEs)—a focus on Credit Risk; in the second case, the bank probably tends toward riskier investments (Market Risk). The strategy has implications for many parts of the bank. Finance, treasury, and risk should be involved in the planning process. To determine whether the chosen strategy can provide the required return (with sufficient probability), risks should be assessed with an overall tool. This tool considers all divisions/desks, regions and categories of risk. The corresponding Value at Risk (VaR) and Expected Shortfall (ES) are calculated by aggregating all these pieces and bits. The VaR (and ES) is always calculated for a given quantile (“probability”). To each considered quantile a risk capacity is assigned. The resulting rules are explained in detail below. It makes sense to choose one quantile of the overall VaR that assesses the threats to revenues, and another quantile that assesses the threat to capital. The following measures result from these considerations:

2.1 Strategy Planning: Iterative Process

5

• The “earnings at risk” (EaR) are calculated at a quantile of 95%. The meaning of this definition of EaR is that the calculated risks at this quantile manifest once in 20 years. • The “capital at risk” (CaR) is calculated at a quantile of 99.9%, which corresponds to the “regulatory measure” (the Basel measures represent a quantile of 99.9%). The meaning of this definition of CaR is that the calculated risks at this quantile manifest once in 1000 years. To each of the defined risk measures a capacity is assigned. Capacity1 is associated with the measure earnings at risk (earnings at risk are calculated at a confidence level of 95%). Capacity1 ¼ Income before tax including bonuses and dividends The condition is as follows: Capacity1 > Earnings at risk This condition implies that losses erasing dividends and/or bonuses should occur only once in 20 years at the maximum. Capacity2 is assigned to the measure capital at risk (capital at risk is calculated at a confidence level of 99.9%). Capacity2 ¼ Capacity1 plus capital The condition is as follows: Capacity2 > Capital at risk This condition implies that losses erasing the capital and leading to bankruptcy should occur only once in 1000 years. Besides the above requirements, the regulatory requirement is always: there must be enough capital to satisfy the following: capital/RWA > x. For example, in Switzerland in 2020 for “going concern” (major banks) this means capital/ RWA > 14.3%. With the help of earnings at risk and capital at risk and their corresponding capacities, the following example could result: • With the strategy to increase loans for SME, the return on equity (RoE) can be reached within 19 of 20 years. This is a result of the comparison of EaR and the corresponding Capacity1 (see Fig. 2.2). • With this strategy total losses occur less than once in 1000 years. This is a result of the comparison of CaR and the corresponding Capacity2 (see Fig. 2.3). The decision of senior management in this example would presumably be to implement the discussed strategy.

6

2 Bank Management and Steering

Capacity1 > EaR 12 10 8 6 4 2

Bonuses 3 5

Dividend and Recapitalization 3

0

Capacity1

EaR

Fig. 2.2 Capacity1 vs. EaR—in this case acceptability of risks is given

Capacity2 > CaR 40 35 30

Earnings 6

25 20 15

Capital 27.7 21

10 5 0

Capacity2

CaR

Fig. 2.3 Capacity2 vs. CaR—in this case acceptability of risks is given

On the other hand, perhaps, the following example (for another strategy) resulted: • The strategy to increase riskier investments implies that the desired RoE can only be reached in 12 of 20 years (see Fig. 2.4). • Besides, total losses occur five times within 1000 years (see Fig. 2.5).

2.1 Strategy Planning: Iterative Process

7

Capacity1 < EaR 12 10 8 6

Bonuses 4 10

4 2

Dividend and Recapitalization 4

0

Capacity1

EaR

Fig. 2.4 Capacity1 vs. EaR—in this case acceptability of risks is not given

Capacity2 < CaR 40 35 30

Earnings 8

25 20 15

39 Capital 27.7

10 5 0

Capacity2

CaR

Fig. 2.5 Capacity2 vs. CaR—in this case acceptability of risks is not given

Compared to the first discussed strategy, potentially higher revenues result (also both capacity measures are increased). On the other hand, risk is increased so much that the EaR are bigger than Capacity1 and the CaR is bigger than Capacity2. This strategy should not be implemented.

8

2.1.2

2 Bank Management and Steering

Capital Allocation

In the above discussed example, the first strategy can be implemented. The capital has to be allocated to the investment bank division and to the domestic division of the bank. Table 2.1 shows the overall regulatory capital for the bank according to Basel III. The desired yields are: • 10% for the investment bank division—to compensate for the higher risks—and • 5% for the domestic division of the bank The allocation of the capital and the volatility of the results are shown in Table 2.2. There is a total of 17.7 billion for Credit Risk of which 8 billion are allocated to the domestic division of the bank (mainly mortgage loans, loans to SMEs and big corporations) and 9.7 billion are allocated to the investment bank division (big loans to multinationals, Credit Risk in derivatives trading (see Chap. 5) and securitization). There is a total of 4 billion for market risk. Of this amount 3.3 billion are allocated to the investment bank division and 0.7 billion to the domestic division of the bank. The Operational Risk (OpRisk) capital of 6 billion is distributed in the following way: 4 billion are allocated to the investment bank division and 2 billion to the domestic division of the bank. Thus, a total of 10.7 billion results for the domestic division of the bank and a total of 17 billion results for the investment bank division (see Table 2.2).

Table 2.1 Capital (billion US$)—example according to Basel III

Credit Risk Loans Counterparty Credit Risk Securities Market Risk Operational Risk Total

Basel III capital in bn US$ 17.7

Thereof 12.7 3.5 1.5

4 6 27.7

Table 2.2 Yield and volatility of the results Domestic division Investment bank division Bank overall

Capital 10.7 17.0 27.7

Yield 5% 10% 8%

Volatility of the results 15% 65% 45%

2.2 Strategy Planning: Tools

2.2

9

Strategy Planning: Tools

With the help of tools like: • The overall VaR measures EaR and CaR and • The overall stress testing (see below) the desired strategy is challenged and then assessed whether it holds from the earnings and capital point of view.

2.2.1

EaR/CaR: Overall Aggregation

Using overall measures like EaR and CaR it can be determined which loss amount can occur for the desired/chosen strategy. Each risk (type) is considered and aggregated. Correlations between different risks are a key element within the process of aggregation. In Table 2.3 typical Risk Weighted Assets (RWA) of a big bank as of the year 2020 are shown. These figures need to be provided in a Pillar 3-Report—as required for the Internal Capital Adequacy and Assessment Process (ICAAP). The total of the risk weighted assets (RWA) implies a capital of 27.7 billion (corresponding to 8% of the RWA).

2.2.1.1

Internal Modeling of EaR/CaR

The measures EaR and CaR are calculated with the help of an overall VaR simulation. The risks are partly influenced (“triggered”) by each other. An example of these dependencies (or correlations) is provided in Table 2.4. The correlations are determined with the help of correlation analyses (taking into account correlations between default rates and stock prices for example). For the correlation of 25% between Credit Risk and Market Risk an Inverse Clayton Copula with a theta of 2/3—like shown in Fig. 2.6—results. Values for the CaR as shown in Table 2.5 might result. Table 2.3 Part of an ICAAP report ICAAP 2020 Credit Risk Loans Counterparty Credit Risk Securities Market Risk Operational Risk Total

Basel III RWA in billions 221.25

Thereof 158.75 43.75 18.75

50 75 346.25

10

2 Bank Management and Steering

Table 2.4 Correlations between risks

Credit Risk Credit Risk Market Risk OpRisk

Fig. 2.6 Inverse Clayton copula for low correlation (plotted with R)—also compare to Fig. 8.2

Market Risk 25%

OpRisk 35% 35%

Inverse Clayton Copula - Theta=2/3 1.00

risk factor 2

0.75

0.50

0.25

0.00 0.00

0.25

0.50 risk factor 1

0.75

1.00

Table 2.5 Basel III capital vs. internal capital model results Credit Risk Loans Credit Risk Trading Credit Risk Securitization Market Risk Operational Risk Other risks (Pension Risk, Tax Risk. . .) Sum Considering diversification

2.2.1.2

Basel III capital 12.7 3.5 1.5 4 6 0 27.7 27.7

CaR (internal capital model) 6 2.5 1.5 3 4 9 26 21

Overall Simulation

Within the overall simulation all kinds of risks are included. The relevant risks depend on each other as outlined in Table 2.4 (Fig. 2.7). For lower correlations there is more diversification benefit. Figure 2.8 shows the mechanisms of correlation. On the left side there is no correlation (correlation ¼ 0). The value of the second risk factor (for example, stock

2.2 Strategy Planning: Tools

11

Risks

Credit Risk

Market Risk

Gains/Losses Defaults

Monte Carlo Simulation

Price Developments Inputs: Gains/Losses, Copulas/Correlations ...

...

Fig. 2.7 Monte Carlo simulation and its inputs Correlation = 0

Actual Correlation

Correlation = 1

RF 1

RF 2

Fig. 2.8 Dependency of the risk factors (RF), transmitted by the correlations

prices within market risk) is independent of the value of the first risk factor (for example, a default rate within Credit Risk). In the middle and on the right side the value of the first risk factor influences the value of the second. Mathematically this corresponds to a convolution. The comparison is discussed in detail in Sect. 2.2.1.3.

12

2 Bank Management and Steering

2.2.1.3

Comparison of Internal Modeling (pillar 2) and Basel III (pillar 1)

The example provided in Table 2.5 shows the differences that might occur between the regulatory requirements according to Basel III (pillar 1) and the internal assessment, calculated with the help of CaR (pillar 2). The main reasons for the differences are discussed hereafter. From a Pillar 2 point of view the resulting 21 billion are sufficient (Table 2.5), as these 21 billion are less than Capacity2 (in our example Capacity2 is 33.7 billion; see also Fig. 2.3). All risks are considered; therefore, the requirements of Pillar 2 are fulfilled`. Due to the diversification benefit (that is acknowledged within the internal model, as opposed to Basel) the overall capital (21 billion) is less than the sum (26 billion). For Credit Risk the capital charge is also quite different. The reason lies within the correlation assumptions (see below). The equity capital that is needed for Credit Risk is determined with the help of the following parameters: • • • • • •

Exposure at Default (EAD) Probability of Default (PD) Loss Given Default (LGD) Maturity Business volume The correlations between obligors

Formulas are provided in Appendix A. In the Basel formulas predefined values for the correlations are implemented, there is a “hard coding” of these correlations. According to many papers written on the topic, these correlations are very high and thus quite conservative—at least for few regions and industrial sectors (see Table 2.6). On the other hand, during the credit crunch in the United States (beginning in 2007), even higher correlations were observed—at least for the sub-prime loans. Table 2.6 Asset correlation according to different sources Paper of Moody’s KMV (2008) Jakubik (2006) Dietsch and Petey (2004) Hamerle et al. (2003) Frey et al. (2001) Gordy (2000) Cespedes (2000)

Data Moody’s KMV 1981–2006 Bank of Finland 1988–2003 Coface 1994–2001 Standard and Poor’s 1982–1999 UBS Standard and Poor’s Moody’s Investor Service

Correlation 7.87–29.98% 5.7% 0.12–10.72% 0.4–6.04% 2.6–9.21% 1.5–12.5% 10%

Jakubik (2006) Working paper, Institute of Economic Studies in Prague Dietsch and Petey (2004) A comparative analysis, Journal of Banking & Finance Hamerle (2003) Benchmark asset correlations, Risk Frey et al. (2001) Copulas and credit models Gordy (2000) A comparative anatomy of credit risk models, Journal of Banking & Finance Cespedes (2000) Asset correlations, Moody’s Investor Service

2.2 Strategy Planning: Tools

13

Table 2.7 Basel III capital vs. capital according to internal credit portfolio models (Switzerland) Rho (correlation) Capital at risk Credit Risk (99.9%)

Basel III 12–24% X CHF

Bank 1 About 8% About 1/2  X CHF

Bank 2 About 5% About 1/3  X CHF

Table 2.8 EaR and CaR Credit Risk Loans Credit Risk Trading Credit Risk Securitization Market Risk Operational Risk Other risks (Pension Risk. . .) Sum Considering diversification

EaR (internal model) 1.5 0.6 0.4 0.8 1 2.5 6.8 5

CaR (internal model) 6 2.5 1.5 3 4 9 26 21

Analyses of time series for Switzerland led to the conclusion that the correlations could be of the magnitude as shown in Table 2.7. Values in this table are used in internal credit portfolio models (see Appendix B). Table 2.7 also shows the resulting capital charge according to Basel and according to the internal model of these banks. A comparison between the EaR and the CaR values is provided in Table 2.8.

2.2.2

Scenario-Based Assessment/Stress Testing

With the help of scenario-based assessments (SBA) and stress testing, firms can assess the upside potential and the downside risk of their overall business—for different future developments. The advantage of scenario-based assessments and stress testing is that these tools are not that much “restricted” by historical developments. These tools are expert based and forward looking (historical data are used as inspiration though). Ideally the previously discussed tools like EaR and CaR and the scenario-based assessments and stress testing are done in “parallel,” meaning that there is a mutual benchmark of the respective results. As mentioned, for scenario-based assessments and stress testing there is no restriction due to missing or biased historical data. There is no a priori restriction. Also, outside the box thinking can be reflected within the scenarios. One, nevertheless, should consider certain causes and effects that have to be reflected in modeling the scenarios. As an example, one can assume that rising unemployment within a country or region causes increasing default rates within that country or region. There are quite some of these causes and effects that should be considered in the modeling process.

14

2 Bank Management and Steering

Two scenarios are provided in detail: a recession scenario and a stagflation scenario. By analyzing EaR, CaR, scenario-based assessments and stress testing results, the strategy of the bank is challenged. Different banks put different emphasis on certain scenarios. The scenarios provided in this chapter are modeled for major full-service banks; nevertheless, others can use the relevant parts of these scenarios. For major full-service banks, it is important to have holistic parameter sets covering countries and regions worldwide and covering the whole spectrum of risk parameters such as: • • • • • • • •

Gross Domestic Product (GDP) Stock Prices Interest Rates (IR) Default Rates Spreads of Credit Default Swaps (CDS) Unemployment Rates Inflation Commodity Prices (Oil, Gold...)

The different locations/units and divisions apply the relevant parameters and report back their specific results—in terms of P&L impact and capital consumption (see Fig. 2.11). Concentrations that are not material on a business unit/divisional level might get material on group level. One big opportunity of the scenario-based assessments and stress testing is the holistic view it can provide. With the help of the SBA one is able to identify possible concentrations or wrong way risks at a group level (see Sect. 5.2 about wrong way risk). It might be that there are concentrations that were not previously identified. For example, different divisions or subsidiaries might hold stock in the same regions of the world (there might be a concentration on a group level). Another example for a concentration could be that the domestic division provided many loans in one region whereas the investment bank division sold many CDS on firms in this region. There are primary parameters in these scenarios such as GDP, stock prices, and interest rates (these primary parameters are provided by the experts and economists). And then there are secondary, derived parameters, which are derived from the primary ones with the help of models and regressions. There are IR/FX models and regressions of the GDP vs. PD for example. In Tables 2.9 and 2.10 the primary and secondary parameters of the recession scenario are provided for three subsequent years. The recession scenario is motivated by the following assumptions: • There is a recession in the United States. • The recession spills over to Europe. In Europe the ever-increasing sovereign debts become critical, several banks go down.

2.2 Strategy Planning: Tools

15

Table 2.9 Primary set of parameters of the recession scenario Year 1 Development GDP in % USA 0.9 UK 0.2 Japan 0.6 China 9.0 Germany 1.3 France 0.7 Italy 0.8 Eurozone 1 1.0 Eurozone 2 0.1 Switzerland 1.4 Russia 2.5 Turkey 0.6 Brazil 2.3 India 6.1 World 2.4 Development stock markets in % USA 45.5 UK 43.1 Japan 45.6 China 17.0 Germany 40.5 France 39.7 Italy 40.9 Eurozone 1 40.7 Eurozone 2 44.0 Switzerland 29.1 Russia 49.4 Turkey 47.0 Brazil 12.3 India 23.6 World 34.8 Interest 3M libor in % US$ 0.5 GBP 0.2 JPY 0.2 CNY 3.0 EUR 0.5 CHF 0.8 RUB 5.1 TRL 8.1 BRL 4.5 INR 5.9

Year 2

Year 3

3.0 4.9 5.4 5.1 4.9 4.0 3.9 4.8 6.5 1.7 6.5 5.3 0.4 5.9 0.6

0.1 0.1 0.5 3.9 0.3 0.5 0.2 0.1 0.4 0.6 1.3 3.0 3.2 6.4 2.5

25.3 20.6 23.3 5.5 23.5 22.7 23.3 24.0 25.3 14.4 35.5 35.0 41.5 12.7 24.2

23.7 20.8 22.7 14.5 19.5 20.3 19.9 20.2 23.2 10.6 16.2 23.4 6.7 12.9 17.7

0.2 0.6 0.4 2.5 0.8 1.0 3.1 7.1 4.2 5.0

0.1 0.8 0.4 2.5 1.0 1.3 1.2 6.8 4.1 5.1

16

2 Bank Management and Steering

Table 2.10 Secondary set of parameters of the recession scenario Year 1 Oil US$/barrel 80 Gold US$/ounce 1900 CDS spreads sovereigns (5 years) in bp USA 150 UK 100 Japan 150 China 150 Germany 100 France 200 Italy 600 Eurozone 1 130 Eurozone 2 900 Switzerland 60 Russia 250 Turkey 560 Brazil 150 India 180 World 250 Unemployment in % USA 10.0 UK 8.1 Japan 5.1 China 4.1 Germany 8.0 France 9.2 Italy 8.3 Eurozone 1 8.1 Eurozone 2 12.8 Switzerland 2.6 Russia 8.0 Turkey 13.5 Brazil 6.5 India 7.5 World 9.1 Development house prices in % USA 20.5 UK 12.3 Japan 3.4 China 2.5 Germany 12.7 France 2.1 Italy 3.5

Year 2 70 2100

Year 3 50 2350

250 200 190 160 160 330 850 180 1100 70 350 610 150 180 280

260 220 190 160 170 340 900 190 1150 80 360 620 160 180 290

13.5 9.5 5.5 4.1 9.4 10.9 9.6 9.5 16.0 3.4 10.1 15.5 6.6 7.6 9.3

14.0 10.1 6.0 4.2 9.9 11.3 10.7 10.1 16.3 4.1 10.9 14.0 7.0 8.0 9.5

13.4 7.5 1.0 2.6 10.8 12.0 5.5

4.5 0.1 1.2 2.7 1.1 3.0 0.0 (continued)

2.2 Strategy Planning: Tools

17

Table 2.10 (continued) Eurozone 1 Eurozone 2 Switzerland Russia Turkey Brazil India World Default rates in % USA UK Japan China Germany France Italy Eurozone 1 Eurozone 2 Switzerland Russia Turkey Brazil India World FX rates EUR/US$ EUR/GBP EUR/JPY EUR/CNY EUR/CHF EUR/RUB EUR/TRL EUR/BRL EUR/INR Inflation in % USA UK Japan China Germany France Italy

Year 1 2.5 20.0 4.8 10.2 2.0 0.1 4.5 2.4

Year 2 3.5 13.3 2.1 2.3 3.7 0.1 3.2 2.2

Year 3 4.6 5.6 2.5 2.3 2.6 0.3 4.7 1.7

5.5 4.6 1.1 1.2 2.5 2.7 2.8 2.7 3.5 1.0 4.3 2.5 3.1 1.1 3.4

13.7 12.3 4.5 2.5 8.0 8.2 8.1 8.2 10.5 1.5 8.8 6.6 3.5 1.8 5.5

14.0 12.9 4.0 2.6 8.5 8.9 8.7 9.9 10.3 1.8 8.7 6.1 4.0 2.3 5.7

1.10 0.85 122 8.03 1.10 70.2 7.02 4.50 80

1.10 0.84 113 8.12 1.05 70.0 7.45 4.22 78

1.09 0.78 107 8.30 1.01 65.5 7.83 4.04 76

4.0 3.7 0.2 6.0 2.7 2.6 3.3

0.3 0.2 1.1 5.0 0.8 0.6 0.9

2.2 2.3 1.2 5.3 2.1 1.7 2.3 (continued)

18

2 Bank Management and Steering

Table 2.10 (continued) Eurozone 1 Eurozone 2 Switzerland Russia Turkey Brazil India World

Year 1 2.8 3.3 2.3 8.0 7.5 6.9 8.9 5.1

Year 2 0.9 0.9 0.3 4.1 4.2 6.1 9.0 3.7

Year 3 2.3 2.1 1.5 3.9 4.0 6.1 8.7 4.0

•GDP •Stock Prices •Interest Rates Macroeconomic Set of Assumpons

•IR/FX Model •Regression Analyses Model

Derived Measures

•Sovereign Bonds (Spreads) •Inflaon •Unemployment, Default Rates •FX Rates •Commodity Prices: Oil, Gold...

Fig. 2.9 Process of the determination of parameters within the recession scenario

The holistic parameter set consists of the primary parameters (Table 2.9) and the secondary ones (Table 2.10) derived from the primary parameters with the help of the models and regressions (shown in Fig. 2.9). In Tables 2.11 and 2.12 the primary and secondary parameters of the stagflation scenario are provided for three subsequent years. The stagflation scenario is motivated by the following assumptions: • The debt crisis in the United States, Europe, and China intensifies. • Economy stagnates. • There is significantly increased inflation (house prices etc.).

2.2 Strategy Planning: Tools

19

Table 2.11 Primary set of parameters of the stagflation scenario Year 1 Development GDP in % USA 1.0 UK 1.3 Japan 1.7 China 8.0 Germany 1.0 France 1.2 Italy 1.5 Eurozone 1 1.0 Eurozone 2 1.5 Switzerland 1.0 Russia 3.1 Turkey 2.6 Brazil 3.1 India 5.9 World 2.5 Inflation in % USA 4.0 UK 3.7 Japan 0.2 China 6.0 Germany 2.7 France 2.6 Italy 3.3 Eurozone 1 2.8 Eurozone 2 3.3 Switzerland 2.3 Russia 8.0 Turkey 7.5 Brazil 6.9 India 8.9 World 5.1 Development stock markets in % USA 2.0 UK 1.5 Japan 2.5 China 5.0 Germany 2.1 France 2.0 Italy 2.0 Eurozone 1 2.0 Eurozone 2 2.0 Switzerland 2.6 Russia 4.0 Turkey 4.0 Brazil 5.0 India 4.9 World 1.5

Year 2

Year 3

0.5 0.8 1.5 7.1 0.4 0.3 0.5 0.4 0.5 0.4 3.3 1.8 2.0 5.2 1.8

0.2 0.4 1.5 7.0 0.2 0.3 0.2 0.2 0.2 0.3 2.5 1.0 1.5 5.1 1.5

7.6 7.0 6.4 7.1 6.8 6.5 7.6 6.4 7.4 5.7 10.9 11.4 7.5 9.2 10.0

11.0 9.5 9.0 7.1 9.3 9.1 12.2 9.0 12.0 8.2 13.8 13.6 7.8 9.2 12.0

0.3 0.2 0.0 3.0 0.7 0.3 0.3 0.2 0.3 1.1 2.0 2.4 2.3 2.9 0.5

6.7 6.1 7.6 8.1 5.4 5.4 5.6 4.9 6.7 5.4 6.7 6.7 5.6 5.4 5.0

20

2 Bank Management and Steering

Table 2.12 Secondary set of parameters of the stagflation scenario Year 1 Oil US$/barrel 100 Gold US$/ounce 1900 Interest 3M libor in % US$ 1.5 GBP 1.0 JPY 0.3 CNY 6.0 EUR 0.5 CHF 0.8 RUB 6.2 TRL 10.5 BRL 5.5 INR 5.9 CDS spreads sovereigns (5 years) in bp USA 150 UK 100 Japan 150 China 150 Germany 100 France 200 Italy 600 Eurozone 1 130 Eurozone 2 900 Switzerland 60 Russia 250 Turkey 360 Brazil 150 India 180 World 250 Unemployment in % USA 10.0 UK 8.1 Japan 5.1 China 4.1 Germany 8.0 France 9.2 Italy 8.3 Eurozone 1 8.1 Eurozone 2 12.8 Switzerland 2.6 Russia 8.0 Turkey 13.1 Brazil 6.5 India 7.5

Year 2

Year 3

120 2300

140 2700

6.0 4.8 4.5 7.8 3.3 3.1 7.4 15.5 5.0 8.0

9.7 8.9 8.7 8.6 7.1 6.8 10.2 19.3 4.7 8.2

180 140 160 160 130 250 680 150 980 60 300 380 150 180 250

200 160 160 160 150 260 720 160 1000 70 310 380 160 180 260

10.5 8.2 5.5 4.1 8.2 9.4 9.3 8.3 14.4 2.9 8.1 13.1 6.6 7.6

11.5 9.1 5.6 4.0 8.9 9.9 9.7 9.1 13.9 3.3 9.3 14.1 6.5 7.5

(continued)

2.2 Strategy Planning: Tools

21

Table 2.12 (continued) World Development house prices in % USA UK Japan China Germany France Italy Eurozone 1 Eurozone 2 Switzerland Russia Turkey Brazil India World Default rates in % USA UK Japan China Germany France Italy Eurozone 1 Eurozone 2 Switzerland Russia Turkey Brazil India World FX rates EUR/US$ EUR/GBP EUR/JPY EUR/CNY EUR/CHF EUR/RUB EUR/TRL EUR/BRL EUR/INR

Year 1

Year 2

Year 3

9.1

9.1

9.2

4.5 5.3 3.4 8.5 7.7 3.1 3.5 3.6 2.9 4.8 5.2 5.0 5.1 8.5 5.0

6.7 7.8 4.0 8.6 10.5 5.0 5.6 6.5 5.2 7.1 5.5 5.7 6.1 8.2 7.2

13.5 12.7 7.2 9.3 16.2 10.7 10.2 12.8 11.2 8.5 7.9 6.6 6.3 9.7 9.8

5.5 4.6 1.1 1.2 2.5 2.7 2.8 2.7 3.0 1.0 4.3 2.5 3.1 1.1 3.4

7.0 6.1 1.5 1.8 3.5 3.9 4.1 3.6 3.8 1.3 5.8 3.3 3.5 1.7 3.9

9.1 7.8 3.0 2.0 4.6 5.1 4.9 4.8 5.4 1.4 6.1 3.6 3.7 1.9 4.1

1.10 0.85 122 8.03 1.10 70.2 7.02 4.50 80

1.13 0.86 120 7.94 1.07 70.2 7.01 4.35 78

1.17 0.86 121 7.72 1.05 72.6 6.88 4.12 76

22

2 Bank Management and Steering

•GDP •Inflaon •Stock Prices Macroeconomic Set of Assumpons

Model

Derived Measures

•IR/FX Model •Regression Analyses

•Sovereign Bonds (Spreads) •Interest Rates •Unemployment, Default Rates •FX Rates •Commodity Prices: Oil, Gold...

Fig. 2.10 Process of the determination of parameters within the stagflation scenario

The holistic parameter set consists of the primary parameters (Table 2.11) and the secondary ones (Table 2.12) derived from the primary parameters with the help of the models and regressions (shown in Fig. 2.10). Within the stagflation scenario inflation is a primary parameter (which is not the case for the recession scenario). In a first step, the parameter sets are provided for each division/desk of the bank. Within the divisions and desks the stressed exposures/capital consumptions/revenues are determined. In a second step, the aggregation is done on a group level (see Fig. 2.11). For inspiration (potential scenarios), past crises should also be considered (see Appendix E). Scenarios should be prioritized according to their probability. Table 2.13 shows an example of stress testing values compared to Basel III values.

2.3 Capital Optimization

23

Definition of Scenarios

Parameters provided to the Divisions (IR, FX... to the Investment Bank Division; PDs and house prices to the Domestic Division; IR, FX, own spread... to Treasury/Finance)

Calculations within the Divisions/Desks

Aggregation on Group Level

Fig. 2.11 Subsequent steps within scenario-based assessments and stress testing Table 2.13 Results of stress testing (in terms of capital) compared to the Basel III requirements

2.3

Credit Risk Loans Credit Risk Trading Credit Risk Securitization Market Risk Operational Risk Other risks (Pension Risk. . .) Sum Considering diversification

Basel III 12.7 3.5 1.5 4 6 0 27.7 27.7

Stress testing 8 3.5 4 8 7 10 40.5 33

Capital Optimization

There is a strong motivation for capital optimization; an increased return on equity (RoE) is the key motivation. This increase is often possible because better/advanced risk management (and thus risk awareness) is rewarded (by the regulations/ regulator). In the following chapters many points regarding capital optimization are discussed. The important and material points are highlighted in a box. These points can be used as a “checklist.” Whenever important points regarding capital and thus the return on equity are discussed, they are highlighted by a light gray box—summarizing key messages. Regarding capital this means. . .

Chapter 3

Banks and the Regulatory and Economic Environment

3.1

Economic and Political Aspects

Banks serving as an interface between investors and borrowers are important for the economy. Banks provide loans and enable private and commercial investment and growth. Most people buying a house or a flat need a loan. Also, most companies can handle larger investments only through loans. Lending and the associated risk assessments are key tasks of the banks’ business. Money from savers, investors, and from central banks is provided to economy. Thus, it is important that the bank can borrow enough money from the central bank, from other commercial banks and from savers and that this supply is not interrupted—as it can happen in times of a crisis. For the depositors it is crucial that their money is not lost—even in times of a crisis. Confidence in the system—avoiding massive withdrawing of creditors’ money—is an important element. The failure of a bank can trigger a domino effect in the banking world. When banks mistrust each other and reduce lending, the wider economy is also affected. For many countries it is a huge dilemma of what to do in such a crisis, especially for countries and economies in which the banking sector plays a dominant role. The big banks are just too big; they are “too big to fail.” One consequence is the regulatory request that big banks (Global Systemically Important Banks, G-SIBs) must be providing living wills and resolution and recovery planning (see Sect. 3.8.3). The economic and financial crisis of the recent years took place against the background of past political, technological, and economic developments and regulatory decisions. These are the following: • In 1986, the British Prime Minister Margaret Thatcher liberalized stock trading. The legislative package was subsequently referred to as the “Big Bang.” Stock trading became easy and cheap. • U.S. president Bill Clinton repealed the Glass-Steagall Act in 1999. This law from the 1930s (which was enacted after the Great Depression) prohibited banks from doing traditional lending and investment banking at the same time. © Springer Nature Switzerland AG 2020 J. Wernz, Bank Management and Control, Management for Professionals, https://doi.org/10.1007/978-3-030-42866-2_3

25

26

3 Banks and the Regulatory and Economic Environment

• The SEC (the U.S. Securities and Exchange Commission) in 2001 lowered the minimum tradable amount of 16 cents to 1 cent. After which high-speed trading was reinforced. • In 2005, the German government passed a law that allowed corporations to sell their shares of other corporations tax free. The mutual interdependences of the so-called “Germany Inc.” were repealed thus increasing pressure for some firms. • In 2005, stock exchanges in the United States introduced e-trading. All these developments must be seen in the context of deregulation and globalization starting in the 1980s. These developments were accompanied by fast technological changes.

3.2

Types of Banks

In Germany and Switzerland there are many banks that operate almost exclusively within saving and lending; for example, the district savings banks and the local cooperative banks. There are many special banks and numerous car banks. In Switzerland, a Cantonal Bank (Kantonalbank) is assigned to each Canton. The thrifts (Bausparkassen) in Germany play a major role in mortgage financing. Investment banks are active in mergers and acquisitions (M&A); they bring together investors and borrowers, and they support companies with initial public offerings (IPOs). Moreover, they are market makers in the pricing of products. They are active in proprietary trading; they do investments in promising businesses. Some investment banks are (or were) Goldman Sachs, Merrill Lynch, Morgan Stanley, Lehman Brothers, Bear Stearns, and Salomon Brothers. Some of the investment banks went bankrupt, some transformed, and some gave up their status as an investment bank. Banks that are active in both the lending business (often in their domestic market) and investment banking are considered major full-service banks: • In the United Kingdom, HSBC and Barclays are prominent full-service banks. • In the United States, one thinks of Bank of America for example. • In China, Industrial and Commercial Bank of China and China Construction Bank come to mind. • In Switzerland, UBS and Credit Suisse are the two dominant banks. They are active in asset management, domestic and international lending (mortgages and corporate) and, of course, investment banking. • In France, BNP Paribas, Credit Agricole and Société Générale are prominent fullservice banks. • In Germany, the Deutsche Bank is a major full-service bank. The Deutsche is strong in the lending business for large corporate customers, it is also strong in retail banking (especially since the purchase of Postbank) and it is active in investment banking. • In Italy, UniCredit is a major full-service bank.

3.4 Role of the Banks’ Credit Rating

3.3

27

Banks in Different Legislations

In Switzerland, as per 2020 the two “global systemically important banks” are UBS and Credit Suisse. Due to their size and economic significance these banks play a very important role. Besides these two, there are a some other big and medium-sized banks that also play an important role. There are the cantonal banks, some of which have sovereign guarantees provided by their cantons. In more rural areas the Raiffeisen Bank plays a big role. The regulatory capital ratios that are applied to banks in Switzerland are different from the ones that are applicable in other countries (see Sect. 3.8.4). All in all, the German economy and private households survived the economic and financial crisis of 2007 and subsequent years quite well. This is partly due to the structure of the German banking sector and the structure of the German real economy. Typical German banks are the cooperative banks with their cooperative structure. The capital of the partners and the deposits of the savers create a solid regional base for lending. Many Germans still have a regional savings bank as their main bank. In German banking neither big banking corporations nor private banks play a dominant role. Financing through loans is of great significance in Germany. This is different in the Anglo-Saxon countries, where funding from the capital market is much more significant. In the United States loans from banks have a 15% share in funding, in Germany the share is about 50%. The main problems German banks faced in the crisis of 2007 and subsequent years were their investments in CDO transactions and in some cases short-term funding and long-term lending.

3.4

Role of the Banks’ Credit Rating

The banks’ credit rating is of increasing importance. Its influence on the trust of customers and depositors and generally on the refinancing, especially on refinancing in the interbank market, is enormous. The rating agencies weigh the capital (the capital ratio) of the bank quite heavily when they determine the rating of the bank. The strategy, governance, management, and reputation of the bank are considered too. Nevertheless, the impact of capital on the rating is quite dominant. Capital has a significant impact on the rating and thus on refinancing and trust.

28

3.5

3 Banks and the Regulatory and Economic Environment

Role of Rating Agencies

The rating agencies have gained great importance in the Basel III world (already with Basel II). The external ratings, which banks receive from the rating agencies, are essential for many banks, if they have no internal tools for determining credit ratings. In addition, many legislatives, for example, tie pension funds to guidelines on investment that are ratings influenced. Particularly when investing in sovereign bonds (see Appendix C) the—mostly external—ratings are crucial. In the economic and financial crisis, the rating agencies rated tranches of securitizations way too good. Many European banks did not have their own assessment of the situation in the United States. The local lending practice in the United States (“subprime”) was alien or unknown to many Europeans. In assessing securitization tranches, the rating agencies generated excellent earnings in the early years of the new century. According to Michael Lewis, the models used by the rating agencies were rather rudimentary and ignored important aspects. It happened that tranches of securitizations, which were almost exclusively based on subprime loans, received very good ratings or even top ratings by the rating agencies. A more independent setup could be a rating agency that is associated with a “neutral” organization, which could be the Bank for International Settlements (BIS) in Basel for example.

3.6

Role of the International Swaps and Derivatives Association (ISDA)

The global volume of credit default swaps (CDS) is enormous. The CDS are usually effective hedging instruments, but their global volume goes far beyond hedging purposes. A credit default swap works like an “insurance policy,” the protection buyer pays premiums to the insurer in order to protect himself against the default of a reference entity (a company or a state). In the case of the default of this reference entity, the insurer pays the hedged amount to the policyholder. The main question regarding the “insurance” payments being provided or not is whether there is a default or not. Naturally a conflict of opinion can arise among the parties. The International Swaps and Derivatives Association (ISDA) acts as a court of arbitration. The ISDA is home to five committees, each responsible for a specific region of the world. Each committee consists of 15 members, who are entitled to vote (ten “sell-side” and five “buy-side” market participants). The committee provides binding decisions, whether an event is seen as default. According to the ISDA, a default is given in case of an insolvency of the reference entity, in case of the nonpayment by the reference entity and further if debt restructuring of the reference entity is given. In 2012 the ISDA classified the restructuring of Greek debts as a default. Argentina was declared in default in 2014 and Venezuela was declared in default in 2017.

3.7 Regulatory Environment

3.7 3.7.1

29

Regulatory Environment BIS

The Bank for International Settlements (BIS) is the organization of central banks. The BIS was formed during the Great Depression (see Appendix E) in 1930. The main participants in its establishment were Montagu Norman, the Governor of the Bank of England and his German colleague Hjalmar Schacht.1 The Bank’s original purpose was to facilitate reparation payments (imposed on Germany by the Treaty of Versailles). The BIS provided the Basel Committee on Banking Supervision with its 17-member secretariat, and with it has played a major role in establishing the Basel Capital Accords (see Sect. 3.8.1).

3.7.2

BIS and the Great Depression: History in a Nutshell

The main central banks of the 1920s had their currencies tied to gold (as before World War I), thus there have been fixed foreign exchange rates (FX rates) among those countries. The French central bank had fixed the FX rate of the Franc in such a way that the Franc was undervalued. This brought France a competitive advantage during the hard times of the Great Depression. After World War I the biggest gold reserves were held by the United States and France. The United States accumulated gold as they had lent much money to the United Kingdom and France (as war loans). Germany faced high reparation payments imposed on it by the Treaty of Versailles. In Germany a hyperinflation took place in the early 1920s. Afterwards the Governor of the Reichsbank, Hjalmar Schacht, did everything to avoid inflation. The reparation payments were mainly to the United Kingdom and France. These countries (the United Kingdom and France) had to pay back the huge war loans to the United States. Before the bubble in the U.S. stock market started, U.S banks provided many loans to Germany. As everybody was drawn to the U.S. stock market, the loans provided to Germany dried out and Germany faced a recession. In 1929 the bubble burst and there was a chain reaction in the United States. Loans defaulted, banks crashed, unemployment rose, and there was the depression. Also, many European banks crashed—like the Creditanstalt in Austria and the Danatbank in Germany. To facilitate the rest of the reparation payments imposed on Germany, in 1930 the BIS was founded. In the end Germany paid much less money in reparations than originally intended.

1

See Lords of Finance, Liaquat Ahamed, 2009.

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3 Banks and the Regulatory and Economic Environment

3.8 3.8.1

Basel III Basel III: Philosophy and Evolvement

The main changes of Basel III (as compared to Basel 2.5 and Basel II) are to be found in: • Overall capital and leverage ratios • Output floors (50% in 2022, subsequently increased to 72.5% in 2027) • Capital requirements for Counterparty Credit Risk—like the CVA capital charge (changes kick in 2022) • Capital requirements for securitization • Capital requirements for Market Risk (major changes kick in 2022) • Capital requirements for Operational Risk and (change of paradigm kicks in 2022) • Asset liability management (refinancing and liquidity related points) Details and implications of the changes are being discussed in subsequent sections and chapters. Basel III seeks to address the following main issues: • • • • •

Raising the quality, consistency, and transparency of the capital base Enhancing risk coverage Addressing systemic risk and interconnectedness Reducing procyclicality and promoting countercyclical buffers Supplementing the risk-based capital requirement with a leverage ratio

In this book relevant implications of Basel III are highlighted and summarized in the corresponding dark gray boxes. Basel III has impacts on. . . Already with Basel 2.5 there were changes for the Market Risk capital requirements, with Basel III other changes followed (see Chap. 7 on Market Risk). One striking change in the context of Basel 2.5 was the significant increase in capital requirements for Market Risk—driven by the experience of the economic and financial crisis of 2007 and the subsequent years. In the financial crisis, the capital requirements for Market Risk were generally assessed as being too low to absorb the losses. Under Basel II the 10-day Value at Risk (VaR) at a 99% quantile determined the regulatory equity. With Basel 2.5 this value was supplemented by additional summands: • By a stressed VaR • By the incremental risk charge (IRC) • By a comprehensive risk measure (CRM)

3.8 Basel III Table 3.1 Risk weights and capital quota

31 Risk weight (%) 50 100 150

Capital quota (%) 4 8 12

The IRC took into account the migration and default risks, the CRM took into account correlation risks within securitizations. In most legislations the rules of Basel 2.5 were enforced in 2011 or 2012. With Basel III a more stringent approach for Market Risk is to be implemented (see Chap. 7 on Market Risk). The basic idea of Basel (already with Basel II) is that banks quantify their risks more precisely and then the results determine the adequate required capital. The required capital should correspond to the risk. The idea is that the capital in most cases (usually in “999 of 1000” cases) is sufficient to protect the bank from an insolvency in the event of a crisis. With Basel II “new” risks, which were not taken into account under Basel I, became relevant. Operational Risk (OpRisk) has been classified as critical under Basel II and needs to be taken into account since then. Credit Risk, Market Risk, and OpRisk since then form the “first pillar” of the Basel Accords. The “second pillar” of Basel highlights adequate internal assessments of the overall risks a bank faces. In addition to the risks covered within the first pillar, other risks like pension risk or goodwill risk need to be covered in the second pillar. The “third pillar” of Basel stresses the importance of holistic reporting of the risk and capital structure of the bank. Since Basel II, 8% of the measure “risk-weighted assets” (RWA) determine the regulatory capital. The RWA are calculated as exposure multiplied by a risk weight. How the risk weight is calculated is discussed in detail in the following chapters. As a rule of thumb a risk weight of 100% corresponds to the Basel I world, whereas a higher risk weight leads to higher capital and a lower risk weight accordingly leads to lower capital (see Table 3.1). In the Basel Accords there are different approaches to determine the risk weights. For example, in Credit Risk there is the Standardized Approach, in which risk weights are dependent on external ratings. Then there is the Internal Ratings-Based Approach, in which risk weights are dependent on internal ratings. The implementation and maintenance of the Internal Ratings-Based Approach is more complex and costly (in terms of resources and systems). Nevertheless, the additional effort is rewarded. The implementation of the Basel rules into national laws is accomplished for example through the Eigenmittelverordnung in Switzerland and through the Capital Requirements Regulation in the European Union. Detailed specifications usually are done by papers provided by the national regulators (like the Rundschreiben in Switzerland). The differences between the various national implementations are small, although in some countries there are specific “hot topics.” For example, in the United Kingdom, the issue point-in-time versus through-the-cycle calibration of the ratings (see Sect. 4.6.2.2) is of much bigger interest than in Central Europe.

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3 Banks and the Regulatory and Economic Environment

A key requirement of the second pillar of Basel III (Pillar 2) is the comprehensive risk management of all risks (including those risks that are not mentioned in Pillar 1, such as pension risk). The most material risks (except the “core risks” Credit Risk, Market Risk, and Operational Risk) are for example pension risk, tax risk, and liquidity risk. Depending on the business, risks such as goodwill risks, legal risks, reputation risks, and various concentration risks can also be important. A full consideration of all risks is an essential part of bank management. Consistent scenario-based assessments and stress testing provide a good assessment of the bank’s situation.

3.8.2

Basel III: Timeline and Implementation Status

According to the Financial Stability Institute, as of 2020 around 60 countries have implemented Basel III (at least to some extend). Some other 40 countries are still under Basel I or Basel II. By 2022 some main changes of Basel III kick in (in Credit Risk and Counterparty Credit Risk, Market Risk and Operational Risk, as well regarding the output floor). By 2022 some main changes of Basel III kick in.

3.8.3

Basel III: Some Spotlights

To achieve a higher quality of the capital base there are increased capital ratios (see Sect. 3.8.4) and there are leverage ratios set out by Basel III. One bigger innovation of Basel III is the demand for the consideration of stressed risk factors in calculating Counterparty Credit Risk (see Chap. 5). In addition, CVA capital charges have been implemented (see Chap. 5). To reduce systemic risk in the banking sector, within Basel III an incentive was created for banks to settle their transactions via a central counterparty (CCP) like “Continuous Linked Settlement” (CLS). In this case the capital charge for the transactions is much lower than it would be otherwise (see Appendix D). After the economic and financial crises of 2007 and of the subsequent years the wish for “resolution and recovery planning” (RRP) came up. If there is a possible bankruptcy of a bank, important parts of the bank (like the domestic division with its deposits of the customers) shall be split off to keep going. How this splitting would be handled must be detailed in a “living will” (resolution and recovery planning). The introduction of a countercyclical capital buffer is one of the countercyclical elements of Basel III. This buffer can be activated by the national banks or

3.8 Basel III

33

regulators, for example when they come to the conclusion that there might be bubble. The first country to activate a countercyclical buffer was Switzerland. In 2013 the Swiss Government together with the Swiss National Bank (SNB) activated a “sectoral countercyclical capital buffer” (sectoral CCyB) for mortgage loans. In the area of liquidity risk there were new standards in Basel III. First, the measure liquidity coverage ratio (LCR) was introduced. It is meant to demonstrate the ability to pay back liabilities within a time horizon of 30 days. Second, the measure Net Stable Funding Ratio (NSFR) was introduced. It is meant to demonstrate that there is no bigger asset mismatch (see Chap. 9). After the economic and financial crises of 2007 and the subsequent years the topic of living wills for banks was introduced. Parts of a bank that are deemed to be of relevance for the whole banking system and/or for customers like depositors shall be kept alive even in the event of crises, whereas other parts of the bank can be split off or even shut down. Banks in scope have to create resolution and recovery planning (RRP), which outlines the procedure. These RRPs have to address how the remaining parts of the bank are provided with enough liquidity and capital. If the regulator deems this planning as effective, the regulator grants an easing of capital. If the regulator deems the resolution and recovery planning of the bank as effective, the regulator grants an easing of capital. Capital planning and capital allocation (as prominently discussed in this book) are of crucial importance for living wills. Capital allocation to certain remaining parts of the bank is one main concern in the resolution and recovery planning. If there is a shortfall of capital in a division of the bank, this might be a trigger for the resolution and recovery planning to be executed. Basel III sets emphasis on the topic of living wills. Banks have to provide a stringent resolution and recovery planning. Capital is allocated to the bank’s divisions according to the strategy and regulatory requirements (see Sect. 2.1.2). For example, part of the capital is allocated to the domestic division of the bank, the other part of the capital is allocated to the investment bank division. If there is a limit excess due to losses created by, for example, the trading activity of the investment bank—meaning too much of the allocated capital is being consumed—, the investment bank is split off according to the resolution and recovery planning.

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3 Banks and the Regulatory and Economic Environment

Table 3.2 Capital ratios according to Basel III Minimum common equity tier 1 (%) 4.5

3.8.4

Capital conservation buffer (%) 2.5

Additional tier 1 and tier 2 capital (%) 3.5

Overall ratio (%) 10.5

Basel III: Capital Ratio

Since 2019, according to Basel III the minimum common equity tier 1 (CET1) requirement is 4.5% (of the RWA). In addition, a 2.5% CET1 capital conservation buffer is required. In addition to the CET1 requirements, there is also a requirement for 1.5% of additional tier 1 capital and 2% of tier 2 capital: • Tier 1 capital is the bank’s core capital; tier 1 capital includes the bank’s shareholders’ equity and retained earnings. • Tier 2 capital is the bank’s supplementary capital: undisclosed reserves, subordinated term debts, hybrid financial products, and others. The Financial Stability Board (FSB) decides on systemic importance. A progressive buffer between 1 and 2.5% is an additional capital requirement for global systemically important banks (G-SIBs). The implementation of Basel III in Switzerland goes beyond the Basel III minimum standards. As of 2020 this leads to an overall ratio of 14.3%2 for a global systemically important bank (as compared to Table 3.2).

3.8.5

Basel III: Output Floor

The output floor is a new element of Basel III. It is meant for banks that use advanced approaches. Though it is an essential part of the philosophy since Basel II that good risk management “gets rewarded” (capital wise), under Basel III these “rewards” are getting floored. Banks that have the approval for the use of advanced approaches: • Calculate their risk capital according to these advanced approaches, then • Compare the aggregated result with the aggregated value of the standardized approaches, • Apply the floor. The resulting minimum capital is the floor times the aggregated capital (calculated with the help of the standardized approaches). The output floor kicks in 2022, its initial value being 50%, then the floor is subsequently increased to 72.5% (in 2027) (Table 3.3).

2

Eidgenössisches Finanzdepartement EFD, Regulierungsfolgenabschätzung, 2015.

3.9 Issue Overview Table 3.3 Output floor

35 January 1st of 2022 2023 2024 2025 2026 2027

Output floor (%) 50 55 60 65 70 72.5

The output floor gets activated in 2022 (floor: 50%). By 2027 its final value of 72.5% is reached. The aggregated capital value (calculated with the help of the advanced approaches) need to be compared to the aggregated outputs of the standardized approaches, like: • Credit Risk: Standardized approach for credit risk • Counterparty Credit Risk: Standardized approach for measuring counterparty credit risk (SA-CCR) • Regulatory CVA Capital: Standardized approach for CVA (SA-CVA), Basic Approach (BA-CVA) or 100% of a bank’s counterparty credit risk capital requirement (depending on which approach the bank uses for CVA risk) • Securitization: External ratings-based approach (SEC-ERBA), standardized approach (SEC-SA) or a risk-weight of 1250% • Market Risk: Standardized approach for market risk. The SEC-ERBA, SEC-SA or a risk-weight of 1250% must also be used when determining the default risk charge component for securitizations held in the trading book • Operational Risk: SMA (as there is only the SMA) Aggregated results of the advanced approaches always need to be compared to the potential results of the standardized approaches (parallel calculations).

3.9

Issue Overview

In almost every organization there is an issue regarding the overview. Missing overview can lead to inefficiencies and sometimes even to dysfunctions. Many issues arise at the interfaces between topics and divisions.

36

3.10

3 Banks and the Regulatory and Economic Environment

Issue Complexity and Risk Identification

Whenever complexity increases, potential issues can arise. Often poor judgment is a consequence of too complex setups. Instead of questioning complex products and structures, problems sometimes are ignored—consciously or unconsciously. As examples the sale and leaseback transactions of the 1990s and the securitizations of the early 2000s are discussed in this section.

3.10.1 Sale and Leaseback Transactions In the 1990s and the early 2000s sale and leaseback transactions were quite popular. Often the public sector of European countries was involved. Public transportation, infrastructure, and supply chain management firms signed up. Institutions and firms were motivated by the instantaneous increase of liquidity that resulted for them through the transaction. The transactions were designed in a way that a tax advantage in the United States was used and “split” between the U.S.-based originator of the transaction and the Europe-based firm. The increase of liquidity plus the incentive created by the tax advantage in the United States motivated many firms to become involved in these transactions. Little or no attention was paid to the risks that were involved. Often these transactions even violated the law of the involved institutions’ countries. For example, the German public sector by law was only allowed to sign contracts that were written in German, but the contracts of the sale and leaseback transactions often were provided in English only. There was enormous complexity of these sale and leaseback transactions. The contracts often were few hundred pages in volume; this alone illustrates the complexity of these transactions. Brass plates indicating the new owner and lease provider in the United States could be seen in many Swiss trains in the 1990s, be it the trains of the national railway corporation SBB or of local train corporations like the famous RhB (running the Glacier and the Bernina-Express in the Alp Mountains). In Germany a broad spectrum of institutions was involved in sale and leaseback transactions. Few examples were hospitals, clarification plants, and water supply firms like the big “Bodenseewasserversorgung” in the southern part of Germany. It is well known that the “Bodenseewasserversorgung” repurchased all its equipment to date. In doing this, the firm faced big losses, which were rolled over to the customers. The customers were paying higher prices for their water supplies afterwards.

3.10.2 Securitization and Subprime In the 2000s the business of providing subprime loans was in full swing in the United States. Companies like Countrywide Financial provided loans to the poorer

3.10

Issue Complexity and Risk Identification

37

U.S. citizens who wanted to finance their dream of owning a home. These people were provided with mortgages with comparably high interest rates of 7%, for example. The interest rates were fixed for only 2 years, afterwards the rates jumped to, for example, 12%. Often the customers could not afford these higher levels. The hope of these people (and often the selling point of the loans) was that the value of their homes would continue to increase. Companies like Countrywide borrowed the money from the big banks and provided subprime mortgages. Once the contracts were signed, these firms sold the contracts to banks, earning significant profits. In contrast to this practice in the United States in most parts of central Europe, like Switzerland and Germany, such loans would not have been provided due to the regulation regarding the acceptance of collateral and the minimum of available equity the lenders must provide. The big U.S. banks like Lehman Brothers, Bear Stearns, Goldman Sachs, Merrill Lynch, Morgan Stanley, JPMorgan, Citigroup, or the Bank of America bought mortgages that companies like Countrywide provided and issued these mortgage loans as bonds. They were competing with government-sponsored enterprises like Fannie Mae and Freddie Mac. Salomon Brothers and others started trading with Mortgage-Backed Securities (MBS) in the 1980s. In the early 2000s the standards for obtaining loans were lowered drastically. To make these mortgage loans more attractive for the poorer customers “teaser rates” and/or negative amortization were provided. The bonds created with the help of the underlying mortgages did not have a good rating. But then products like CDOs were invented. The investor could choose between different tranches. On the one hand, there were tranches having a very good rating. These tranches were supposed to bear very low risk (supposedly like government bonds, but paying higher interest rates than government bonds). On the other hand, there were the tranches with a worse rating and thus paying quite high interest rates. The products were constructed such that if the defaulting mortgage loans exceeded a certain level the junior tranches (the worse ones) would become worthless. The better tranches would become worthless only later, when the defaults exceeded an even higher level. The attractive thing about the good tranches was that they were considered as almost risk free (such as government bonds). Korean and Japanese funds, in particular, and “investors from Düsseldorf” liked these features. The good ratings provided by the rating agencies were tempting for these investors. Assessments and ratings are the rating agencies’ job. Nevertheless, according to author Michael Lewis,3 the rating agencies were not capable of getting granular data from the originating banks. And they did not have advanced models like the originating banks to validate the risk of the products and the underlying collateral. The assumption of the agencies was that house prices would evolve steadily. The possibility of a decrease in prices and thus of increasing defaults was neglected.

3

The Big Short, Michael Lewis, 2010.

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3 Banks and the Regulatory and Economic Environment

As correlation between the customers (of the mortgage loans) is a main risk driver of these products, securitization trading is also called correlation trading. The rating agencies’ assumption was a correlation of about 30%. This proved to be far too low. Almost all of the customers of these subprime loans were dependent on increasing house prices (see the above discussed terms of the loans). Thus, the correlation induced by the adverse house price development was rather 80–90% in reality. According to author Michael Lewis “Idiots from Düsseldorf” was a standard term on Wall Street. Those “Idiots from Düsseldorf,” meaning some German bankers, purchased the tranches of the CDOs even when no other buyers could be found. With sale and leaseback transactions and with securitization complexity is quite high, and the contracts are quite big. For most of these transactions due diligence (assessing the risks) is quite complicated and it is time consuming. Often bespoken validations are necessary, as cash flows of the tranches have to be modeled and simulated thoroughly. The mean annualized default rates of the subprime loans tended to be about 4% in the good times (in the early 2000s). The tranches rated BBB, for example, were constructed in a way that they would default when a moderate decline of house prices would induce default rates of about 7 or 8%. The better rated tranches (for example AAA) were constructed such that default would occur when the underlying loans faced default rates of about 15%. In the early 2000s, only few foresaw a decline in housing prices; default rates of the underlying subprime loans of 7% (BBB) or even 15% (AAA) were deemed highly improbable. The reality was different: in 2006 and subsequent years, between 30 and 40% of the underlying loans defaulted.

Chapter 4

Risk Modeling and Capital: Credit Risk (Loans)

All the relevant measures (expected losses and provisions, economic capital, regulatory capital, and interest for pricing) can be derived from one or two handful of parameters (discussed in the following sections).

4.1

Pricing and Expected Loss

The interest is calculated such that: • • • •

Cost of refinancing Internal costs Losses due to defaults (usually referred to as “expected loss”) and The margin (“cost of capital,” interest on the capital according to desired Return on Equity)

for this portfolio (or part of the portfolio) are covered. Whereas the cost of refinancing and the internal costs are considered straightforward here, we have a closer look at the expected loss component and the cost of capital component (margin): • Expected loss component: statistically each year a certain fraction of customers defaults, creating a loss amount, the expected loss (EL), calculated as EL ¼ PD  LGD1 [probability of default (PD) times the loss given default (LGD)]. As long as the expected loss, which the bank prices into the interest, is as predicted, the return on equity is as desired. If the realized loss is bigger than the EL, the return on equity is less than desired, however. For example, the return on equity might be 8% instead of the desired 11%. On the other hand, if the 1 The LGD is 100% if there are no recoveries and 0% if there is a security (mortgage) covering the whole loss amount; depending on the recoveries, the LGD is in between 0 and 100%.

© Springer Nature Switzerland AG 2020 J. Wernz, Bank Management and Control, Management for Professionals, https://doi.org/10.1007/978-3-030-42866-2_4

39

40

4 Risk Modeling and Capital: Credit Risk (Loans)

expected loss is lower than predicted, the return on equity is higher than desired. The expected loss can be calculated either as percentage (and thus be translated into the interest rate straightforwardly) or it can be calculated in terms of money by multiplying PD, LGD, and the exposure at default (EAD). • Cost of capital component (margin): the RoE-dependent margin is calculated as follows: Percentage points margin ¼ RoE  risk weight ðRWÞ=12:5 The risk weights for the loans/customers are being discussed below. There is an increased tendency that banks implement risk adjusted pricing (see below). Risk adjusted means that specific risk is priced into the interest as granular as possible. This leads to a bespoken interest depending on the expected loss (risk parameters PD and LGD) and on the capital charge. The price is not calculated for the whole portfolio any longer but for buckets with “similar risk.” In other words: the “mutual insurance” is not done for the whole pool of customers any longer but rather for customers with similar expected loss estimations: • Customers with lower expected loss pay lower interest rates • Customers with higher expected loss pay higher interest rates All in all, there is much more differentiation in interest rates these days. In Sect. 4.1.1 adverse selection is discussed. If a bank does not do risk adjusted pricing and its competitors do, adverse selection can have problematic implications for the bank.

4.1.1

Adverse Selection

The more banks do risk adjusted pricing, the more there is a potential problem of adverse selection for the remaining banks. Adverse selection means that there is an accumulation of riskier than expected customers at a certain bank. As an example, we consider two banks. One of these (the first one) offers an interest rate of 5% for all the customers (for financing cars for example). The interest is not differentiated according to risk grades. The other bank (the second one) offers customers with a good expected loss risk grade interest of 4.5% and customers with a worse expected loss risk grade interest of 5.4%. Customers compare offers from different banks (and even from insurance companies that provide banking products). The better customers presumably move to the second bank. The worse customers go to the first bank. The second bank is able to realize its desired return on equity, whereas the first one is not able to do so.

4.1 Pricing and Expected Loss

4.1.2

41

Risk Adjusted Pricing and RoE

There are several components of the interest rate: • • • •

Refinancing costs Internal costs Expected loss RoE-dependent margin The RoE-dependent margin is calculated as follows: Percentage points margin ¼ RoE  risk weight ðRWÞ=12:5

In the following, an LGD of 30% and increasing PDs of 0.1%, 0.5%, 1%, 2%, and 5% are assumed (Fig. 4.1). If the desired return is 12%, the interest rates as provided in Fig. 4.2 result (per risk grade)—under the assumption of refinancing costs of 1% (as an illustrative example, though as of 2020 in Europe 0% refinancing cost is closer to reality) and internal costs of 0.4%.

PD

Probability of Default

6.0% 5.0% 4.0% 3.0%

PD

2.0% 1.0% 0.0% 1

2

3

Rating Grade Fig. 4.1 PD of the different rating grades

4

5

42

4 Risk Modeling and Capital: Credit Risk (Loans)

4 3.5 3 2.5

Margin Expected Loss

2

Internal Costs 1.5

Refinancing

1 0.5 0 1

2

3

4

5

Fig. 4.2 Resulting risk adjusted interest rates

4.2

Loan Loss Provisioning

According to IFRS 9 the expected loss needs to be accounted for as allowance. The allowance equals the sum of all the single expected losses of the customers. Bad debt provisions are calculated considering the LGD for defaulted assets and thus the EL for defaulted assets.

4.3

Capital: Relevant Points

The regulatory capital charge that has to be held by the bank within the advanced approaches of Basel III—the Internal Rating Based Approaches—is calculated with the help of formulas as provided in Appendix A. In these formulas a confidence level of 99.9% is given. The Expected Loss (PD times LGD) is subtracted as this should be covered by the previously discussed general allowances. Definition and parameters influencing the resulting value are discussed in the following. The regulatory formula for the capital and the risk weighted assets (RWA) for loans is as follows: Capital ¼ K  EAD, or in terms of risk weighted assets RWA ¼ 12:5  K  EAD: The discussed risk weight RW is calculated as 12.5  K, RWA ¼ RW  EAD.

4.3 Capital: Relevant Points

43

For Small and Medium Enterprises (SME), the factor K is calculated in the following way. For other customers (corporates, retail etc.) it is similar (see all the formulas in Appendix A). The factor K is depending on the probability of default (PD), the loss given default (LGD) and the maturity (M ) in the following way: pffiffiffi     R  Gð0:999Þ GðPDÞ 1 þ ðM  2:5Þ  b pffiffiffiffiffiffiffiffiffiffiffiffi K ¼ LGD  N pffiffiffiffiffiffiffiffiffiffiffiffi þ ,  PD  LGD  1  1:5  b 1R 1R R ¼ 0:12 

1  exp ð50  PDÞ 1  exp ð50  PDÞ þ 0:24  0:24   0:04 1  exp ð50Þ 1  exp ð50Þ

 ð1  ðS  5Þ=45Þ  0:12 þ 0:12  exp ð50  PDÞ  0:04  ð1  ðS  5Þ=45Þ, b ¼ ð0:11852  0:05478  ln ðPDÞÞ2 : The parameter R represents correlation. The sales component S for SME is meant to be in between EUR 5 and 50 million. N(x) means the cumulative distribution function of a random variable according to a standardized normal distribution; G(z) means the inverse cumulative distribution function of a random variable according to a standardized normal distribution. Special emphasis should be put on the correlation parameter R. For big corporations this parameter ranges from 12% up to 24%. These values should be compared to the correlations given within Sects. 2.2.1.3 and 3.10.2. With Basel III the correlation parameter for big banks is increased by 25% (multiplier 1.25).

4.3.1

Default Definition

There are several ways of implementing and executing the default definition. Though a definition is given in the Basel Accords, one is allowed to use a stricter definition.2 The Basel default definition is as follows (Paragraph 220 and 221 of Basel III/Paragraph 452 and 453 of Basel II)—see Sect. 4.6.1.1. A default is considered to have occurred with regard to a particular obligor when either or both of the two following events have taken place: • The bank considers that the obligor is unlikely to pay its credit obligations to the banking group in full, without recourse by the bank to actions such as realizing security (if held).

2

The possibilities for a less strict default definition are limited according to the Basel rules.

44

4 Risk Modeling and Capital: Credit Risk (Loans)

• The obligor is past due more than 90 days on any material credit obligation to the banking group. Overdrafts will be considered as being past due once the customer has breached an advised limit or been advised of a limit smaller than current outstandings. If one chooses a stricter default definition instead, on the one hand, higher PD values result (as there are many defaults that recover when payments are continued). On the other hand, lower LGD values result, as all the recovered customers (continuing to pay back) do have LGD values of 0%. When the default definition is less strict, it is the other way around: lower PD values and higher LGD values result: • The expected loss is the same for the different definitions. • The resulting capital for Credit Risk, as calculated by the Basel formulas (see Appendix A), can differ significantly. This (according to Sect. 4.1.2) can have an influence on pricing as well. The chosen default definition has a significant impact on capital.

4.3.2

Maturity

There are still many banks that do not calculate differentiated values for the maturity M. More capital has to be held by the banks then. The formula for the maturity is as follows: PT t¼1 CFt  t M¼ P : T t¼1 CFt It might look cumbersome on first sight; nevertheless, this formula can be simplified. For usual loans the following simple version results: M¼

remaining time to maturity : 2

Now it is very handy and can be implemented quickly. If the calculation for M is not implemented, a default value of 2.5 for M needs to be used. Compared to this default value of 2.5, the capital is significantly reduced when implementing the handy formula. In Table 4.1 the values are provided for a corporate portfolio in which the remaining time to maturity of the loans is 3 years and for a corporate portfolio in which the remaining time to maturity of the loans is 4 years. As parameters a PD value of 1% and an LGD value of 30% have been assumed.

4.3 Capital: Relevant Points

45

Table 4.1 Effect on capital due to consideration of the details of the maturity parameter M Portfolio with a remaining time to maturity of the loans of 3 years 7%

Portfolio with a remaining time to maturity of the loans of 4 years 15%

If the above formula for M is considered—instead of the default value of 2.5— the capital is reduced considerably. The simplified formula for M is justified as follows: PT t¼1 M¼ P T

CFt  t

t¼1 CFt

:

For usual loans the cash flows paid by the customers remain constant over the months CFt ¼ a: The remaining time to maturity of the loans is T (in years, months or in days). With the help of the Gauss formula one gets PT t¼1 M¼ P T

CFt  t

t¼1 CFt

¼

a  T ðT þ 1Þ=2 ¼ ðT þ 1Þ=2: aT

When increasing the number of intervals (granularity), the following formula results: M¼

remaining time to maturity : 2

Similar considerations can be done for loans with en-bloc payments. If the cash flow on the final due date (en-bloc payment) equals x% of the total sum, then with the other monthly cash flows of a and the remaining time to maturity of T the following results PT a  T ðT  1Þ=2 þ x=ð100  xÞ  a  T ðT  1Þ 100 þ x t¼1 CFt  t M¼ P T: ¼ ¼ T 200 a  100=ð100  xÞ  ðT  1Þ CF t t¼1 In Table 4.2 few examples are given. In implementing the above formulas, the discussed reductions of capital can be achieved.

46

4 Risk Modeling and Capital: Credit Risk (Loans)

Table 4.2 Maturity parameter M for loans with en-bloc payments (en-bloc payments are typical for several loan types in Central Europe)

En-bloc payment 10% 20% 30% 40% 50%

M 11/20  T ¼ 0.55  T 12/20  T ¼ 0.6  T 13/20  T ¼ 0.65  T 14/20  T ¼ 0.7  T 15/20  T ¼ 0.75  T

12.00%

Probability of Default

10.00% 8.00% 6.00% 4.00% 2.00% 0.00% A

B

C

D

E

F

G

Rating Grade Fig. 4.3 PD of the different rating grades

4.3.3

Granularity of Rating Engines

A rating tool determining the PDs of the customers distributes the customers over several rating grades. Customers with very good credit ratings have very low risk of default. Customers with worse credit ratings have higher risk of default. In the past many western countries (states) for example had very good credit ratings. The granularity of the rating tool (or to put it differently the number of rating grades of a rating tool) influences the capital that has to be held. The less granular the tool, the more capital has to be held. On the other hand, the more rating grades there are, backtesting and calibration become more difficult. For backtesting purposes a clustering of rating grades can be useful. With the help of the following examples the influence of granularity is demonstrated. The first case is less granular with rating grades ranging from “A” to “G” (Fig. 4.3; Table 4.3). In the second case there are three times as many rating grades. There are rating grades ranging from “A+” to “G” (Fig. 4.4; Table 4.4). The capital values of Table 4.5 result.

4.3 Capital: Relevant Points Table 4.3 PD of the different rating grades

47 Rating grade A B C D E F G

PD 0.03% 0.10% 0.30% 1% 2% 5% 10%

14.00%

Probability of Default

12.00% 10.00% 8.00% 6.00% 4.00% 2.00% 0.00% A+ A A- B+ B B- C+ C C- D+ D D- E+ E E- F+ F F- G+ G G-

Rating Grade Fig. 4.4 PD of the different rating grades

The granularity of the rating tool has some influence on the capital.

4.3.4

Classification of Exposures as Retail or Corporate

The definition of retail exposure according to Basel (Basel II, Paragraph 231) is as follows: “An exposure is categorized as a retail exposure if it meets all of the following criteria: • Exposures to individuals—such as revolving credits and lines of credit (e.g. credit cards, overdrafts, and retail facilities secured by financial instruments) as well as personal term loans and leases (e.g. installment loans, auto loans and leases,

48 Table 4.4 PD of the different rating grades

4 Risk Modeling and Capital: Credit Risk (Loans) Rating grade A+ A A B+ B B C+ C C D+ D D E+ E E F+ F F G+ G G

PD 0.02% 0.03% 0.04% 0.06% 0.10% 0.14% 0.19% 0.30% 0.41% 0.70% 1.00% 1.30% 1.60% 2.00% 2.40% 3.60% 5.00% 6.40% 8.00% 10.00% 12.00%

Table 4.5 Capital for different granularities of the approaches Capital for the less granular tool (7 grades) 100%

Capital for the more granular tool (21 grades) 99.4%

student and educational loans, personal finance, and other exposures with similar characteristics)—are generally eligible for retail treatment regardless of exposure size, although supervisors may wish to establish exposure thresholds to distinguish between retail and corporate exposures. • Residential mortgage loans (including first and subsequent liens, term loans and revolving home equity lines of credit) are eligible for retail treatment regardless of exposure size so long as the credit is extended to an individual that is an owneroccupier of the property (with the understanding that supervisors exercise reasonable flexibility regarding buildings containing only a few rental units—otherwise they are treated as corporate). Loans secured by a single or small number of condominium or co-operative residential housing units in a single building or complex also fall within the scope of the residential mortgage category. National supervisors may set limits on the maximum number of housing units per exposure. • Loans extended to small businesses and managed as retail exposures are eligible for retail treatment provided the total exposure of the banking group to a small

4.3 Capital: Relevant Points

49

business borrower (on a consolidated basis where applicable) is less than 1 million euros. Small business loans extended through or guaranteed by an individual are subject to the same exposure threshold. • It is expected that supervisors provide flexibility in the practical application of such thresholds such that banks are not forced to develop extensive new information systems simply for the purpose of ensuring perfect compliance. It is, however, important for supervisors to ensure that such flexibility (and the implied acceptance of exposure amounts in excess of the thresholds that are not treated as violations) is not being abused.” The section about “Loans extended to small businesses. . .” is important. For example: a truck for a small enterprise is financed. If the retail classification (instead of the corporate classification) can be used, the capital of the bank can be about 25% lower. The classification of exposures as retail or corporate has a significant influence on capital.

4.3.5

Recent Bubbles

Around the year 2000 mortgage loans boomed in the United States. There was no stringent assessment of the creditworthiness of the customers (as it is practiced in Central Europe). Many loans—later known as subprime loans—were provided. Many banks were very aggressive in providing these mortgage loans. A housing bubble resulted. These loans were repackaged as RMBS transactions and sold to Europe and other places. In Ireland, banks were also quite aggressive in providing doubtful loans. In the 1990s and 2000s the mortgage business boomed. The Irish took loans and bought houses, apartments, cars, and consumer goods. Figure 4.5 shows the development of house prices in Ireland in those years. Hungary (in the 1990s and 2000s) is another example. Many banks, especially Austrian banks, expanded their business into Eastern Europe. Most loans provided in Hungary were loans on a CHF basis. The low interest rates (CHF) were attractive for customers. Loans were provided at an FX rate of 140 Forint per CHF. Beginning in 2007, FX rates moved to about 240 Forint per CHF. Many customers could not afford the payments for their loans any longer. The newly elected Hungarian government in 2010 made the decision that the Hungarian customers could pay back the loans for 180 Forint per CHF, with the difference to be made up by the affected banks. The reasoning behind this decision was that the banks allegedly did not tell the customers about all the risks involved (see Chap. 8 for a discussion about

50

4 Risk Modeling and Capital: Credit Risk (Loans) 500’000

400’000

300’000

200’000

100’000

0 1995

2000

2005

New House Price National

2010

2015

2020

New House Price Dublin

Fig. 4.5 Development of house prices (in Euro) in Ireland overall and in Dublin (Source: Department of the Environment, Community and Local Government, www.environ.ie)

Operational Risks like conduct risks). Many banks lost money and sought legal action. It is up to the national banks and the national regulators to identify critical developments (like bubbles). At least since 2011 the Swiss National Bank (SNB) highlighted a potential bubble regarding house and apartment prices. In 2013 the Swiss Government together with the SNB activated a Basel III “sectoral countercyclical capital buffer” (sectoral CCyB) for mortgage loans. As of 2020 the sectoral CCyB remains at 2%. As of 2020 there might be a bubble in quite some countries (as the interest rates are low, and in some places even negative). Germany and Switzerland are amongst these countries.

4.3.6

Missing Values

Banks tended to use quite conservative proxies for missing values. When, for example, in the annual re-rating of customers the customer’s zip code was missing in the data set, the attribute zip code was rated with the worst possible value. The same held true for the rating of ratios in balance sheet analyses. When a certain ratio could not be calculated, the ratio was rated with the worst possible value. This kind of handling is conservative. Statistics often show that this handling is too conservative. Often it is justified to use a quantile of 75%, for example. In terms of capital the difference is few percent. In the Basel Accords missing values are often not rated too conservatively. Often a quantile of about 75% is assumed. By not using the worst rating—but still assuming a prudent proxy—for the missing value, one can reduce capital by about 10% (on average).

4.5 Advanced Regulatory Approaches

51

The assessment of missing values has a significant influence on capital.

4.4

PD-Rating Tools, LGD Tools, and EAD Estimations

The two parameters: • Probability of default (PD) and • Loss given default (LGD) are equally important for: • Pricing and • Capital In terms of dollar amounts, the Exposure at Default (EAD) is important, too (but often straightforward). Tools (models) for the determination of PD and LGD are discussed below. It is important that all the features that are relevant for both parameters (like default definition etc.) are consistently defined in the modular tools for PD and LGD estimation.3 In the past, many banks put much more effort into the implementation of PD tools than into the implementation of LGD tools. Often LGD tools work only on a pool level (as a kind of “sophisticated average value”), but not on customer level, which is a problem for pricing purposes. This is also a problem for the portfolio management, as adverse selection can be a consequence (see also Sect. 4.1.1). In the following, best practice PD and LGD tools are being discussed.

4.5

Advanced Regulatory Approaches

Under Basel III there is the Standardized Approach (SA) and there are the two advanced approaches [Advanced Internal Ratings-Based Approach (A-IRBA) and Foundation Internal Ratings-Based Approach (F-IRBA)]: • The PD and the LGD need to be own estimates for the A-IRBA. • The PD needs to be an own estimate for the F-IRBA.

3

Some banks experienced the problem that PDs determined by the rating tools and LGDs coming from the LGD tools did not match correctly (as PD tools and LGD tools had a different classification of exposures, for example). When it comes to pricing (see Sect. 4.1.2) this is quite a problem.

52

4 Risk Modeling and Capital: Credit Risk (Loans)

4.6

Rating Tools (PD Models)

The creditworthiness—reflected in the credit rating of a customer—is estimated with the help of a rating tool. Thus, the probability of default (PD) is determined. These assessments are performed when the customer approaches the bank (loan request) and on a continuous basis (each year).

4.6.1

Development of Rating Tools

4.6.1.1

Good/Bad Definition

Two main things/goals are important for the rating tool: • Good discriminatory power, classification of good and bad customers. • Stability/calibration of the estimations; it is imperative that the estimations of the PD and the realization of the default rates match well. This is important for the pricing and thus for the portfolio management. For the development of the tool it is crucial that these two goals can be achieved: • The measure discriminatory power (or Gini coefficient) helps assess how well the tool is able to estimate whether someone has a good or bad creditworthiness. The higher the value of the discriminatory power, the better the ability to distinguish between good and bad creditworthiness. Customers are being classified and provided with risk grades—according to their creditworthiness. • This stability is assessed with the help of backtesting (see Sect. 4.8). Now the bank has a good basis for decisions like: “should someone with rather bad creditworthiness be rejected (to avoid losses for the bank) or does this customer have to pay more interest (pricing)?” The graphical representation of the Gini coefficient is done in the following way. The x-axis represents the cumulated ratio of all the observations (in this case all the customers), whereas the y-axis represents the cumulated ratio of the observations having specific characteristics—in this case the ones that are being defaulted. In Fig. 4.6 in the worst grade there are about 10% of the customers and 50% of the defaults. In the two worst grades there are about 20% of the customers and about 70% of the defaults. The ratio of the area between curve and bisecting line and the best possible area (indicated by the dotted line in Fig. 4.6) is called the Gini coefficient. It has been argued that a perfect rating tool would classify all the future defaults within a default grade and all the others within non-default grades. Losses should be avoided; therefore, it makes sense to build a rating tool according to the following good/bad definition: economic loss vs. no economic loss. From an economic point of view this good/bad definition is more relevant than the good/bad definition according to Basel (Basel II, Basel III).

4.6 Rating Tools (PD Models) Fig. 4.6 Graphical representation of the discriminatory power (“Gini coefficient”)

53

Power Curve 100%

75%

50%

25%

0% 0%

25%

50%

70.01%

75%

100%

Optimal

Nevertheless, in the end the calibration of the rating tool has to be done according to the Basel definitions. Having said this, the following two steps should be done: 1. Development of the tool according to the good/bad definition economic loss/no economic loss or significant economic loss/no significant economic loss 2. Calibration of the tool according to the Basel II default definition The Basel default definition is as follows (Paragraph 220 and 221 of Basel III and Paragraph 452 and 453 of Basel II): A default is considered to have occurred with regard to a particular obligor when either or both of the two following events have taken place. • The bank considers that the obligor is unlikely to pay its credit obligations to the banking group in full, without recourse by the bank to actions such as realizing security (if held). • The obligor is past due more than 90 days on any material credit obligation to the banking group. Overdrafts will be considered as being past due once the customer has breached an advised limit or been advised of a limit smaller than current outstandings. The elements to be taken as indications of unlikeliness to pay include: • The bank puts the credit obligation on non-accrued status.

54

4 Risk Modeling and Capital: Credit Risk (Loans)

• The bank makes a charge-off or account-specific provision resulting from a significant perceived decline in credit quality subsequent to the bank taking on the exposure. • The bank sells the credit obligation at a material credit-related economic loss. • The bank consents to a distressed restructuring of the credit obligation where this is likely to result in a diminished financial obligation caused by the material forgiveness, or postponement, of principal, interest or (where relevant) fees. • The bank has filed for the obligor’s bankruptcy or a similar order in respect of the obligor’s credit obligation to the banking group. • The obligor has sought or has been placed in bankruptcy or similar protection where this would avoid or delay repayment of the credit obligation to the banking group.

4.6.1.2

Design of the Tools

The previously discussed points about the design of the tools hold true for all kinds of rating tools, like: • Rating tools to assess retail customers • Rating tools for the assessment of (big) corporates (balance sheets etc.)

4.6.1.3

Splitting of Data: Training and Test Group

In developing the tool an effect usually referred to as “overfitting” has to be avoided. To avoid overfitting, it is best to split the data into two parts: • One part being the training group • The other part being the test group Future stability is to be expected when the results like the Gini coefficient and the PDs per grade are comparable between training group and test group. In this case there is no overfitting. The testing (test group) is particularly important for tools based on a neural network (overfitting is a big topic for neural networks), but it is also important for our approach.

4.6 Rating Tools (PD Models)

55

4.6.2

Calibration of the Rating Tools

4.6.2.1

Impacts of the Default Definition

The Basel formulas determining the Credit Risk-related risk weights and the capital have the risk parameters Probability of Default (PD) and Loss Given Default (LGD) as their main inputs. As discussed previously, more rigor of the default definition is possible (more rigor than Basel expects). The default definition has an impact on PD and LGD and the capital (but not on the expected loss). Table 4.6 shows the values for a PD of 1% and an LGD of 30%, the maturity parameter M is set to 2.5. The rigor of the default definition has a significant impact on the capital.

4.6.2.2

Rating Philosophy: Calibration Point in Time Versus Through the Cycle

Regulators in the United Kingdom mainly, but increasingly also in Central Europe and other parts of the world, are discussing Point in Time (PIT) vs. Through the Cycle (TTC) calibration. Calibration is done in the following way: Calibration of the PD ¼ ð1  cyclicalityÞ  CT þ cyclicality  default rate The Central Tendency (CT) is the long-term average of the default rates observed in the last several years. As an example, the default rates develop like a sine wave around the central tendency (Fig. 4.7). In this example, one period lasts 8 years. The central tendency in this example is 2%. In this example the cycle starts with an average default rate of 2% and an upcoming boom phase. In the second year, the average default rate decreases to 1.5% (due to the positive economic effects of the boom period). Then the economy cools down, consequently in the fourth year the default rate is back to the level of Table 4.6 Effect on capital due to different default definitions (increased recovery rate due to more rigor of the default definition)

10% increased recovery rate 20% increased recovery rate 30% increased recovery rate

PD 1% 1.1% 1.2% 1.3%

LGD 30% 27.27% 25% 23.08%

EL 0.3% 0.3% 0.3% 0.3%

Capital X 6% 12% 16%

56

4 Risk Modeling and Capital: Credit Risk (Loans) 3.0%

Default Rate

2.5% 2.0% 1.5% 1.0% 0.5% 0.0% 0

1

2

3

4

5

6

7

8

Years Fig. 4.7 Default rate over the years

2%. In the following recession, average default rates increase to 2.5%. With the economy back on track in the eighth year default rates are down to the average level of 2% again. Default rate always means the latest default rate (for example the one within the last year). The remaining input of the above formula is the cyclicality. The cyclicality defines whether the calibration is done according to the PIT or according to the TTC thinking. A cyclicality of 100% means that the calibration of PDs is performed according to the latest default rates (e.g., the ones of the last year); this would be the PIT calibration. On the other hand, a cyclicality setting of 0% stands for a calibration according to the long-time average (TTC). Generally, the lower the cyclicality is set the more the calibration is dampened according to the long-term average and the less it is done according to recent default rates. The advantage of a TTC calibration is “to take cyclical volatility out of the estimation” (see below). As the Bank of England stated4: “Regulators have coined the term ‘rating philosophy’ to describe where a rating system sits on the spectrum between the stylized extremes of: (a) Point in Time (PiT): in which firms seek to explicitly estimate default risk over a fixed period, typically 1 year. A consequence of the use of such an approach is that the increase in default risk in a downturn results in a general tendency for migration to lower grades. When combined with the fixed estimate of the long-run default rate for the grade, the result is a higher IRB capital requirement; and (b) Through The Cycle (TTC): in which firms seek to take cyclical volatility out of the estimation of default risk, by assessing a borrower’s performance

4 Bank of England: Consultation Paper, CP4/13, “Credit Risk: Internal Ratings Based Approaches,” March 2013.

4.6 Rating Tools (PD Models)

57

across the business cycle. Such ratings do not therefore react to changes in the cycle when it occurs, so there is no consequent volatility in capital requirements.”

4.6.3

Example of a Corporate Rating Tool

Relevant information is being extracted from: • The balance sheets • Additional sources In the database the following information is connected within data sets: • Balance sheets and derived quantitative measures • Other information (e.g., management assessment etc.) • Default status (and potentially historical defaults) The resulting data sets (including all relevant information) are split into a training group and into a test group, for example 60/40 (Fig. 4.8). Relevant ratios are being calculated: different kinds of equity ratios, sales ratios, cash flow ratios such as CF-ROI (CFR) or cash flow margin (CFM), liquidity ratios etc. Then the following steps are taken: • The discriminatory power is calculated for these ratios. • Cluster analyses reveal possible ranges for these ratios. • Correlation analyses are performed to assess whether there are significant correlations among the ratios. Such correlations are not desired as they can lead to undesired effects in the next step. • Multivariate discriminant analyses are performed (see below). There is a binary coding of all data sets of the training group (if the ratio is within an interval this interval gets coded as “1,” if the ratio is not within the interval this interval gets coded as “0”). A multivariate discriminant analyses is performed, and Balance Sheets 205,000 sets Good

Bad (Default)

202,335 sets

2,665 sets

Training

Testing

Training

Testing

121,401 sets

80,934 sets

1,599 sets

1,066 sets

Fig. 4.8 Allocation to training and testing group

58

4 Risk Modeling and Capital: Credit Risk (Loans)

Table 4.7 Grading of the figure cash flow margin

Lower limit 0 0.04 0.09 0.15 0.22

Table 4.8 Grading of the figure equity ratio

Lower limit 0 0.07 0.14 0.21 0.27 0.33 0.38

Upper limit 0 0.04 0.09 0.15 0.22

Score 0 0.11 0.29 0.50 0.76 0.89

Upper limit 0 0.07 0.14 0.21 0.27 0.33 0.38

Score 0 0.14 0.17 0.28 0.42 0.53 0.66 0.9

the result is a preliminary scorecard. The big advantage of the binary coding is the transparency and readability of the scoring. Experts can compare the results with their experience. Manual corrections can be made (Tables 4.7 and 4.8). If there is good discriminatory power for the training as well as for the test group, then as a next step the calibration of the PDs is done according to a PIT or a TTC kind of approach (also see Sect. 4.6.2.2). In this step for each overall score a probability of default is determined.

4.7

LGD Models (LGD Tools)

LGD models/tools determine the percentage of the exposure that is finally lost (after recoveries). Main ingredient for determining the LGD is the value of the security or the securities the bank holds for providing the loan. For different kind of loans, different kinds of securities are being provided. For consumer loans or loans to SMEs the securities can be cars, trucks or construction machines. Often mortgages serve as security, but also be stocks or commodities are an option. The higher the value of the security, the lower the LGD and thus the potential loss the bank faces in the case of a default. Banks using the A-IRB approach need to determine LGD values, whereas banks within the F-IRB approach do not have to do so. Since Basel III the A-IRB approach cannot be used for the following any longer: • Exposures to general corporates belonging to a group with total consolidated annual revenues greater than 500 million euros and

4.7 LGD Models (LGD Tools)

59

• Exposures in the bank asset class and other securities firms and financial institutions (including insurance companies and any other financial institutions in the corporate asset class) Since Basel III for exposures to large corporates and to financial institutions the A-IRB approach is not allowed any longer. The LGD is an intuitive ratio. If the customer defaults, with an outstanding debt of 200,000 (EAD) and the bank is able to sell the security for a net price of 160,000 (including costs related to the repurchase), then 40,000, or 20%, of the EAD are lost. The detailed formula is discussed in Sects. 4.7.1 and 4.7.2. As mentioned previously many financial institutions have put much more effort into implementing PD tools than into implementing LGD tools. As of 2020 there is still a number of financial institutions that use the Foundation-IRB approach (F-IRB) of the internal rating-based (IRB) approaches of the Basel Accords [rather than the advanced one (A-IRB)].5 The banks that use the F-IRB method do not have to estimate the LGD on their own. Some banks face the problem that the LGD estimate only represents a kind of portfolio average rather than a bespoken value for a given customer/loan. This leads to issues with pricing and thus to problems within portfolio management. Overall a granular LGD model/tool offers much bigger advantages than drawbacks. Advantages are: • Granular pricing capabilities • Reduction of cost of capital Drawbacks are: • Effort (databases and model implementation) • Model approval process with the regulator Implementing a granular internal LGD model (A-IRB) bears advantages. On the one hand, it is beneficial for risk adjusted pricing. On the other hand, a more favorable regulatory capital results. Repurchase Value Estimators (RVEs) have proven to be the best kind of tools for LGD estimates. RVEs are shown in Sects. 4.7.1 and 4.7.2.

5

See for example ECB guide to internal models—October 2019.

60

4.7.1

4 Risk Modeling and Capital: Credit Risk (Loans)

LGD Tool for Vehicles/Machinery

Many banks provide consumer loans, where, for example, cars or other goods are being financed. In Germany, France, and Italy, particularly, most car companies have subsidiaries (banks) that provide consumer loans for customers. Other banks specialize in financing trucks, buses, coaches, planes, or construction machines and so on. In this business and in the mortgage business RVEs have proven to be the best kind of tools for LGD estimates. These estimators are granular: estimates can be done in a granular way, like for each car (e.g., for a Tesla Model S or a Fiat Cinquecento) and for each point in time [considering the age of the car (more general: age of the security)]. For example, for both a Tesla Model S and a Fiat Cinquecento the repurchase value goes down over the years. Nevertheless, the depreciation is slower for the Tesla Model S than for the Cinquecento. Repurchase Value Estimators are modular (if there are no internal statistics about the repurchase price of one or the other model, for example, external information can be used, such as data from Aircraft Bluebook for planes, Clarksons for ships, or Schwacke for cars). The RVEs provide transparent results, which the experts in the bank can compare with their own expertise. The core of the following formula is the repurchase value ratio (RVR)—therefore the name Repurchase Value Estimator. The repurchase value ratio provides the percentage of the value of the vehicle/machinery at a given time (compared to its purchase price). LGDDCP ðm, t Þ ¼ 

0

max 0; LGD 

Pn

i¼1 RVRðmi , t i Þ

 DTðmi Þ  Pi þ EAD

Pn

i¼1 CRðmi , t i Þ

 Pi



EAD

LGDDCP Loss Given Default in the case of a Debt Collection Process LGD0 Loss Given Default without considering the security (in this case the machinery) EAD Exposure at Default RVR Repurchase Value Ratio (¼ Repurchase Value/Purchase Price) CR Cost Ratio (¼ Costs/Purchase Price) m Vehicle/Machinery (brand, model) t Age of the Vehicle/Machinery P Purchase Price of the Vehicle/Machinery (brand, model) DT Downturn Factor For vehicles and machinery the repurchase value ratio can be modeled very well with the help of exponential decays, as shown in Fig. 4.9. In this example the value

4.7 LGD Models (LGD Tools)

61

Repurchase Value / Purchase Price

Repurchase Value Ratio for Vehicles/Machinery 1

0.8

0.6

0.74^Years Realizations

0.4

0.2

0 0

10

20

30

40

50

60

Age of Vehicle/Machinery in Months

Fig. 4.9 Modeling of the repurchase value ratio with the help of an exponential decay

of the vehicle/machinery reduces about 50% within 2 years. The parameter (the exponent) is determined with the help of a regression. The cost ratio on the other hand shows the costs related to the repurchase—in relation to the purchase price. Costs are incurred when there are repairs prior to repurchase, when certificates have to be renewed (as is the case with planes) or when legal proceedings have to be done. Depending on the time necessary for the sale of specific machinery the repurchase value must be discounted. Up to this point the loss discussed is the one if a “real” default and thus a debt collection process begins. This is the LGD that is determined as soon as a default occurs. Nevertheless, many of the customers recover without creating a loss for the bank—there is often a high probability of a recovery. Most customers continue to repay their loans after receiving a past due letter by the bank. Sometimes people just forget to pay. For the bank there are cases that have to be considered defaults (according to Basel) but do not lead to a loss. The above discussed LGD has to be modified accordingly, considering all the recovered customers. LGDðt Þ ¼ PR  LGDR þ ð1  PR Þ  LGDDCP ðt Þ PR Probability of Recovery LGDR Loss Given Default in case of a Recovery LGDDCP Loss Given Default in the case of a Debt Collection Process

62

4 Risk Modeling and Capital: Credit Risk (Loans)

EAD and Price in US$

90’000 50%

80’000 70’000

40%

60’000 30%

50’000 40’000

20%

30’000 20’000

10%

Resulting LGD in Per Cent

60%

100’000

EAD Price LGD

10’000 0%

0 1

2

3

4

5

6

Years Fig. 4.10 LGD lens for machinery such as trucks

The LGDR is 0 per definition, so the following results: LGDðt Þ ¼ ð1  PR Þ  LGDDCP ðt Þ: Figure 4.10 shows a typical “LGD lens” (the time dependent LGD values) for a fleet of trucks. For the capital calculations the following has to be considered: in the case of an actual default the LGD jumps from the lower value LGD(t) to the higher value LGDDCP(t). Often there is also new information in the case of a default (in the case of fraud machinery might be missing; in the case of a mortgage loan an on-site inspection might lead to the conclusion that the family homes in this area lost value; in the case of income producing real estates (IPRE) the building might be damaged). If there is new information, it will be considered in the LGD.

4.7.2

LGD Tool for Mortgages

For mortgages Repurchase Value Estimators (RVE) should also be used. The previously discussed advantages are present for mortgages, too.

4.7 LGD Models (LGD Tools)

63

LGDDCP ¼ 8 9 n P > > > RVRðai ,aesi ,si ,oi , f i ,soi ,spi ,psmi ,t Þ  DTðai ,aesi ,si ,oi , f i ,soi ,spi ,psmi ,tÞ  Pi > > > > > > > > > < 0;LGD0  i¼1 = EAD max n P > > > > > > CRðai ,aesi ,si ,oi , f i ,soi ,spi ,psmi ,t Þ  Pi > > > > > > : þ i¼1 ; EAD

LGDDCP Loss Given Default in the case of a Debt Collection Process LGD0 Loss Given Default without considering the security (in this case the mortgage) EAD Exposure at Default RVR Repurchase Value Ratio (¼ Repurchase Value/Purchase Price) CR Cost Ratio (¼ Costs/Purchase Price) a Accessibility of Industrial Agglomerations aes Agglomerations—Economic Strength s Surroundings (Landscape, View, Leisure) o Type of the Object/Security (House or Apartment) f Facilities so Size of the Object (square meter) sp Size of the Property (if applicable) psm Price of Square Meter (of the Property) t Age of the House or Apartment P Purchase Price of the House or Apartment DT Downturn Factor For mortgages the core of the formula is the repurchase value ratio (RVR). It indicates the percentage of the repurchase value (in terms of the purchase price). Depending on the object, which needs to be sold, the selling can take a (longer) while: discounting of the recoveries and costs has to be done. The points about recovery stated in Sect. 4.7.1 are also made here. LGDðt Þ ¼ PR  LGDR þ ð1  PR Þ  LGDDCP ðt Þ PR Probability of Recovery LGDR Loss Given Default in case of a Recovery LGDDCP Loss Given Default in the case of a Debt Collection Process The LGDR is 0 per definition, so the following results: LGDðt Þ ¼ ð1  PR Þ  LGDDCP ðt Þ: Figure 4.11 shows the development of prices for construction ground in Germany in the last three decades.

64

4 Risk Modeling and Capital: Credit Risk (Loans) 200 180 160 140 120

EUR/square 100 meter 80 60 40 20 0 1990

1995

2000

2005

2010

2015

2020

Fig. 4.11 Development of construction ground prices in Germany (Source: Statistisches Bundesamt, www.destatis.de) 250

200

150

1'000 £ 100

50

0 1990

1995

2000

2005

2010

2015

2020

Fig. 4.12 Average price of property in the United Kingdom (Source: Land Registry UK, https:// landregistry.data.gov.uk/app/ukhpi)

It is interesting to compare Figs. 4.11 and 4.12. The figures show that there are similar patterns in Germany (around 2020) as there were in the United Kingdom before 2007—before the 2007 decline. In Switzerland the development of house prices cooled down recently (2020 perspective)—on a high price level.

4.8 Backtesting Within Credit Risk

4.8 4.8.1

65

Backtesting Within Credit Risk Backtesting Versus Validation

Within the context of this book backtesting is defined as comparison of realizations with their corresponding estimations. Backtesting is a frequent (for example, annual or semiannual) task. The terms backtesting and validation are often not clearly distinguished. In the context of this book validation stands for the in-depth assessment of models by an independent unit (validation unit). Validation is performed when these models are new and also in later years (each 3–5 years).

4.8.2

Backtesting

Backtesting—the comparison of realizations with their corresponding estimations— comes with a set of rules. These rules define whether the realization is “close enough” to the estimate. When the realization is “close enough” to the estimate, everything is considered fine; there is no need for action. In case the realization is far off the estimate (“far off” being defined within the rules), there is need for action. The rules suggest in which situations a recalibration of the model is due and in which situations the whole model itself should be questioned. For the determination of the capital there are regulatory multipliers. The more stringent the backtesting framework and the fewer the backtesting exceptions, the lower the multiplier is set. The quality of the backtesting framework and the backtesting results have significant influence on the regulatory multipliers for the capital. There is backtesting for weather forecasts as well as for estimates of probabilities of default or for VaR and ES values within Market Risk. On longer time horizons even backtesting for OpRisk is possible (see Chap. 8). As an example, weather forecasts are discussed first to illustrate the mechanisms of backtesting. There are some interesting analogies regarding complex EPE backtesting (see Chap. 5) vis-à-vis the mechanisms of backtesting of weather forecasts. In order to determine which institution provides better weather forecasts, the institutions are benchmarked with the help of backtesting their forecasts in the last year. The forecasts of the last 365 days are categorized according to the following four components:

66

• • • •

4 Risk Modeling and Capital: Credit Risk (Loans)

First the temperature Second the cloudiness Third precipitation Fourth the wind speed

For each component certain characteristics are defined. Temperature is clustered from 3 degrees Centigrade to 0 degrees Centigrade, from 0 to 3, from 3 to 6, from 6 to 9, etc. Cloudiness comes in categories like “completely clear sky” and “completely overcast,” “sky is totally obscured.” Precipitation is clustered as dry, little rain or snow, heavy rain or heavy snow. The wind speed is classified according to Beaufort scale clusters. Deviations are defined as follows: if there was little rain instead of a dry day it is a deviation of 1; if there was heavy rain instead of a dry day it is a deviation of 2; and if there is heavy rain instead of little rain it is a deviation of 1, etc. There is 1-day backtesting, in which the reality is compared with the estimate of the prior day; there is 2-day backtesting, in which reality is compared with the estimate of two days previously; and there is 3-day backtesting, in which reality is compared with the estimate of 3 days before. For each of the three backtesting categories all the deviations (of 365 days) are added. As it is more difficult to determine the weather for longer horizons than for shorter, there is a weighting of the three categories (more weight for the 1-day backtesting). Then the three backtesting categories are finally summed up and compared for the two institutions. Also in EPE backtesting (discussed in detail in Chap. 5) there is a weighting of the different time horizons as a similar reasoning (it is more difficult to determine the fair values for longer horizons than for shorter) holds true there.

4.8.3

Backtesting Framework PD

In most backtesting reports the discriminatory power can be found, even though the stability (comparable values of the realization and the estimation) is more important in this context. Nevertheless, the discriminatory power is an important and intuitive measure. In Fig. 4.13 the discriminatory power is shown for a newly developed rating tool. At this point in time there was no “filtering”—the customers who later might be rejected (when the new tool is live) are present in the data, too. As customers with bad ratings might be rejected in the live use of the tool, within backtesting (in later years) such customers are no longer present in the data. In this case the discriminatory power as shown in Fig. 4.14 goes down (compared to before)—this is natural, one just has to be aware of it. The more important element of PD backtesting are the following rules: • Backtesting rule 1: At least 80% of the rating grades shall pass the binomial test (discussed in the following). If rule 1 is fulfilled, the annual calibration is done

4.8 Backtesting Within Credit Risk Fig. 4.13 Discriminatory power—including denied cases

67

Power Curve 100%

75%

50%

25%

0% 0%

25%

50%

70.01%

Fig. 4.14 Discriminatory power—excluding denied cases

75%

100%

Optimal

Power Curve 100%

75%

50%

25%

0% 0%

25% 64.80%

50%

75% Optimal

100%

68

4 Risk Modeling and Capital: Credit Risk (Loans)

straightforwardly (see Sect. 4.6.2.2). If rule 1 is not fulfilled, action depends on rule 2. • Backtesting rule 2 (general economic situation): If the deviations (realized default rates versus estimated default rates) are mostly in one direction (in more than 80% of the rating grades), recalibration but not the in-depth validation must be done, if not, an in-depth validation of the model must be performed first. Rule 2 is meant for situations in which the general economic situation is significantly better or worse than in the past year(s), so that default rates in general (over all grades) are lower or higher. In this case the annual recalibration might be sufficient as the deviations are rather due to the general economic situation than due to a model weakness. Binomial testing is not the most sophisticated way of backtesting, as correlations between the customers are not considered, but it is illustrative and fulfills our purpose here. With the help of binomial testing lower and upper limits can be defined for each rating grade. The realization is deemed to be close enough to the estimation if it is within these boundaries. Under the assumption that the estimated probability of default is correct for a given rating grade, the realized default rates of the future years should follow a binomial distribution (with the assumption of no correlation). If there is a big deviation, the assumption of the estimated probability of default being correct is rejected. The assumption (that the realized default rate corresponds to the PD) is rejected at a certain confidence level if the realized default rate is higher than a certain threshold of dα. The upper threshold dα, which is violated with a probability of α only, is calculated as 

 XN  N  Ni i α : dα ¼ min d : PD ð1  PDÞ i¼d i The values of Table 4.9 are the result. As the limits are violated in 5 of 21 rating grades, less than 80% of the rating grades pass the binomial test; therefore, Backtesting rule 1 is violated. As also Backtesting rule 2 is violated, an in-depth validation of the model must be performed first.

4.8.4

Backtesting Framework LGD

The estimations of the Repurchase Value Estimators (RVE) are tested against the realizations. Thus, on the one hand the Repurchase Value Ratios (RVR) and on the other hand the Cost Ratios (CR) are backtested. Like within the backtesting of weather forecasts a classification is done. If the deviation of the realized (observed) RVR is lower than 3 percentage points, it is okay; if the deviation is between 3 and

4.8 Backtesting Within Credit Risk

69

Table 4.9 Backtesting example Rating grade A+ A A B+ B B C+ C C D+ D D E+ E E F+ F F G+ G G

PD 0.02% 0.03% 0.04% 0.06% 0.10% 0.14% 0.19% 0.30% 0.41% 0.70% 1.00% 1.30% 1.60% 2.00% 2.40% 3.60% 5.00% 6.40% 8.00% 10.00% 12.00%

Lower limit (assuming 1000 cases per grade)

1 3 5 8 11 20 31 43 57 75 93

Upper limit (assuming 1000 cases per grade) 2 2 3 3 4 5 6 8 10 15 19 23 27 32 37 52 69 85 103 125 147

Realization 1 1 2 2 3 4 5 5 8 14 17 24 28 7 10 18 32 44 63 80 100

8 percentage points, one deviation point is given; if the deviation is between 8 and 13 percentage points, two deviation points are given and so on. As the costs related to the debt collection process are much lower than the repurchase values, the deviation buckets for the cost ratios are smaller. If the deviation of the realized (observed) CR is lower than 2 percentage points, it is okay; if it the deviation is between 2 and 4 percentage points, one deviation point is given; if the deviation is between 4 and 6 percentage points, two deviation points are given and so on: • Backtesting rule 1: If the average deviation of all cases in the portfolio is less than 3.5 deviation points, the LGD tool is deemed to estimate well—acceptance, no further action, otherwise Backtesting rule 2 is applied. • Backtesting rule 2: If more of 70% of the deviations of the estimations of the RVRs or CRs tend into one direction (more than 70 being higher or lower than the realizations), there is the need for modification, otherwise at least the scrutiny level remains high.

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4 Risk Modeling and Capital: Credit Risk (Loans)

Table 4.10 LGD backtesting: backtesting of the repurchase value ratios and the cost ratios Trucks Truck 1 Truck 2 Truck 3 Truck 4 Truck 5 Truck 6 Truck 7 Truck 8 Truck 9

RVR estimated 70% 55% 50% 40% 60% 65% 65% 45% 80%

RVR realized 77% 70% 35% 30% 65% 80% 50% 44% 81%

Deviation Points 1 3 3 2 1 3 3 0 0

CR estimated 7% 6% 8% 8% 8% 6% 7% 7% 6%

CR realized 5.3% 8.1% 11% 8.5% 5.9% 3% 9.5% 7.1% 5%

Deviation points 0 1 1 0 1 1 1 0 0

In Table 4.10 an example is provided. In this example the average is 2.3. According to the first backtesting rule there is an acceptance. There is acceptance also according to the second backtesting rule.

Chapter 5

Risk Modeling and Capital: Counterparty Credit Risk (“EPE” and “CVA”)

5.1

Cash Flows, Exposure, Pricing, and Capital

Investments in derivatives bear Market Risk (e.g., option price movements due to the movements of the underlying stock) and Credit Risk (e.g., creditworthiness of the issuer (seller) of an option or the counterparty of a swap). Credit Risk in this context is usually referred to as Counterparty Credit Risk (CCR), counterparties are usually other banks. For pricing purposes different models and algorithms are used (see below). The cash flows, exposures, and the likelihood of the payments (creditworthiness of counterparties) need to be considered. Accounting (like IFRS 13) is often closely related to valuation/pricing. Capital wise the situation is the following: from a regulatory capital point of view the capital charges for derivatives consist of: • The Market Risk-related capital charges (see Chap. 7) and since Basel III also the CCR-related capital charges • Expected positive exposure (EPE) • “Regulatory” credit valuation adjustment (CVA) capital charge In Chap. 7 exposure modeling for interest rate derivatives is discussed. A Monte Carlo Simulation (with an integrated Longstaff–Schwartz Regression), which allows for flexible coding of trades, is shown there. This modeling serves many purposes like pricing, CVA/DVA adjustments in accounting, derivation of capital (like expected shortfall measures in Market Risk), and the derivation of the discussed EPE capital.

© Springer Nature Switzerland AG 2020 J. Wernz, Bank Management and Control, Management for Professionals, https://doi.org/10.1007/978-3-030-42866-2_5

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5 Risk Modeling and Capital: Counterparty Credit Risk (“EPE” and “CVA”)

72

5.1.1

“EPE” Capital Modeling/Capital Charge

The exposure (sum of the discounted cash flows) can develop in such a way that the counterparty owes money. This exposure is at risk—the counterparty could default. The Counterparty Credit Risk-related capital is calculated with the help of the measure exposure at default (EAD). The EAD is based on: • Potential future exposure (PFE) (standardized approach) or • “Effective EPE” (advanced approach) In both cases equity capital according to K
EAD is required (for K see the supervisory formulas provided in Appendix A).

5.1.1.1

Standardized Approach

If the bank is not able to model the potential future exposures in an advanced way, the Standardized Approach (SA-CCR) for measuring exposure at default (EAD) for Counterparty Credit Risk (CCR) has to be used. EAD ¼ 1:4
ðRC þ PFEÞ: RC is the replacement cost and PFE the potential future exposure. The potential future exposure is calculated by considering an adjusted nominal, a delta (sensitivity), a maturity factor, and a scaling factor.

5.1.1.2

Advanced EPE Modeling

The EAD in this case is calculated as the “Effective EPE” multiplied with the alpha factor. EAD ¼ α
Effective EPE: Thus, there is a direct influence of the alpha on capital. The default value of alpha is set to 1.4 (Switzerland: 1.2). Nevertheless, national regulators increase this factor if a bank is less able to precisely model the development of the exposure. Precise modeling of the future development of the exposure is complex and difficult, but it is incentivized with a lower alpha. The quality and accurateness of the exposure modeling has a great impact on the capital charge for Counterparty Credit Risk. Advanced approaches are incentivized with lower alpha values.

5.1 Cash Flows, Exposure, Pricing, and Capital

73

Cash Flows 25 20

Currency Units

15 10 5 0 -5

0

1

2

3

4

5

6

7

-10 -15 -20 -25

Months Cashflow

Fig. 5.1 Cash flows for a trade

The Effective EPE is calculated as “an average” of the first year (or the remaining time to maturity). Effective EPE ¼

X min ð1year,maturityÞ k¼1

Effective EEtk  Δt k :

And the Effective Expected Exposure is defined as Effective EEtk ¼ max ðEffective EEtk1 , EEtk Þ: Figures 5.1 and 5.2 provide a graphical explanation. For the cash flow of Fig. 5.1 the exposure values of Fig. 5.2 result. The measure Expected Exposure reflects the development of the outstanding exposure (considering the risk factors like interest rates). The measure “Effective” Expected Exposure is conservative as it does a locking (also see Fig. 5.2, the example value of 45 is “locked in”). Finally, the measure Effective EPE does an averaging of the Effective EE. For the calculation of the capital (capital ¼ K
EAD) the PD of the counterparty is considered within the corresponding supervisory formula for K (also see Appendix A; note that the correlation R for the counterparties “big banks” increased by 25% with Basel III). Starting from the two legs of the Expected Exposure (cash flows to be paid and cash flows to be received) also the Credit Valuation Adjustments for the balance sheet are derived (see Fig. 5.3)—according to IFRS or U.S. GAAP. Collateral that is potentially called within margin calls should be considered in the simulation.

5 Risk Modeling and Capital: Counterparty Credit Risk (“EPE” and “CVA”)

74

Currency Units

Exposure 50 45 40 35 30 25 20 15 10 5 0

0

1

2

3

4

5

6

7

Months Eff. EE

EE

Eff. EPE

Fig. 5.2 Effective EPE for a trade

One bigger development in Basel III is the demand for the consideration of stressed risk factors in calculating EPE. The measure EPE is to be calculated: • With the help of the actual risk factors (interest rates, FX rates, spreads) and • With the help of a stressed risk factors (shifted yield curves, evolved FX rates, and spreads) The larger of the resulting values has to be considered for further steps in the calculation. Basel III demands the consideration of stressed risk factors in the calculation of EPE.

5.1.2

CVA Capital Charge

Two approaches are available for calculating the “regulatory” CVA capital charge: • The basic approach (BA-CVA) and • The standardized approach (SA-CVA) The basic approach comes in: • A reduced and • A full version.

5.1 Cash Flows, Exposure, Pricing, and Capital Fig. 5.3 CVA and EPE

75

Model, Simulation Expected Exposure CVA/DVA

Effective EPE Alpha

EAD PD, LGD RWA

Capital

The standardized approach for CVA (SA-CVA): • Is an adaptation of the standardized approach for Market Risk under the revised Market Risk standard and • Needs regulatory approval For the standardized approach banks need to come up with sensitivities s (like the delta sensitivity, which provides the changed value of an option if the underlying price changes and the vega sensitivity, which provides the changed value of an option if the underlying volatility changes). These sensitivities need to be multiplied with defined risk weights. The products of the sensitivities and the risk weights are summed up (given correlations need to be applied). In the end a multiplier of 1.25 is applied. The multiplier can be increased (by local regulators) if the models/formulas (that provide the inputs) are deemed inadequate (in some regards).

5 Risk Modeling and Capital: Counterparty Credit Risk (“EPE” and “CVA”)

76

The quality and accurateness of the derivation of the sensitivities (for all the trades) have an impact on capital (via the multiplier m).

5.2

Wrong Way Risk

“Specific Wrong-Way Risk (WWR) arises when the exposure to a particular counterpart is positively correlated with the probability of default of the counterparty due to the nature of the transactions with the counterparty.” Specific wrong way risk arises for example due to a merger. The seller of a CDS that is protecting the buyer in the case of the default of a third party merges with the third party. On the one hand, the exposure increases as the default becomes more probable; on the other hand, in the case of the default, the seller might no longer be able to pay. In Paragraph 100 the following example is provided: “For example, a company writing put options on its own stock creates wrong way exposures for the buyer that is specific to the counterparty.” “General Wrong-Way Risk arises when the probability of default of counterparties is positively correlated with general Market Risk factors.” One example for general wrong way risk for Swiss banks is due to the FX rates CHF/EUR and CHF/US$. The more US or EU money is deposited with Swiss banks the greater the value of the CHF. On the other hand, export from Switzerland might decrease and defaults might increase. The default rate (PD) is therefore positively correlated with the FX rate. Another illustrative example for general wrong way risk was the situation in Hungary in early 2000 and in 2010. Austrian banks, particularly, expanding their business to the east, provided a great deal of mortgage loans in Hungary. The loans were provided as CHF loans. The interest rates were low in Switzerland for a long time. Thus, a positive correlation—between the Market Risk factor FX rate HUF/CHF and the Hungarian default rates—was created. Other examples are interest rates that are positively correlated with the default rates for mortgage loans or the correlation of country risk and the default rates of banks holding many sovereign bonds (e.g., the banks of Cyprus, whose default rates were positively correlated to the country risk of Greece—the issue became striking in early 2013). Paragraph 100 states: “Paragraph 57 of Annex 4 in Basel II will be revised as follows: Banks must identify exposures that give rise to a greater degree of general wrong-way risk. Stress testing and scenario analyses must be designed to identify risk factors that are positively correlated with counterparty creditworthiness. Such testing needs to address the possibility of severe shocks occurring when relationships between risk factors have changed. Banks should monitor general wrong way risk by product, by region, by industry, or by other categories that are germane to the

5.2 Wrong Way Risk

77

business. Reports should be provided to senior management and the appropriate committee of the Board on a regular basis that communicate wrong way risks and the steps that are being taken to manage that risk.” Within Basel III more emphasis is put on Wrong Way Risk. Specific wrong way risk can be assessed with the help of a structured and frequently updated database. At any instant of a new specific wrong way risk, for example, as two banks merge, the corresponding trades get flagged and an update of the risk assessment is done. General wrong way risk is more difficult to identify. In the end the bank’s economists have to monitor the market situation on a continuous basis; they have to assess the balance sheets of banks and corporations to analyze if there is general wrong way risk.

Chapter 6

Risk Modeling and Capital: Credit Risk (Securitizations)

With Basel III an important improvement on good risk management (information requirements) was introduced (see below).

6.1

Basel III Approaches: Securitization-Related Capital

Typical securitizations are: • Commercial Mortgage-Backed Securities (CMBS) • Residential Mortgage-Backed Securities (RMBS) • Asset-Backed Securities (ABS) There are three approaches to come up with the related capital: • Securitization Internal Ratings-Based Approach (SEC-IRBA) • Securitization External Ratings-Based Approach (SEC-ERBA) • Securitization Standardized Approach (SEC-SA) The underlying model of the SEC-IRBA is the “Simplified Supervisory Formula Approach (SSFA).” The formula is a modification of the older SFA. Good risk management requires complete information: one of the main ingredients of the new formula, the K_IRB parameter, must be calculated with the help of all the underlying exposures (see Chap. 4 for the calculation of K ). The other main point, the seniority of the considered tranche, is obviously considered in the SSFA, too (Table 6.1). The risk weights of the tranches within the SEC-ERBA depend on: • Seniority • Tranche maturity

© Springer Nature Switzerland AG 2020 J. Wernz, Bank Management and Control, Management for Professionals, https://doi.org/10.1007/978-3-030-42866-2_6

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6 Risk Modeling and Capital: Credit Risk (Securitizations)

Table 6.1 Basel III approaches for securitization-related capital Approach Securitization Internal Ratings-Based Approach Securitization External Ratings-Based Approach Securitization Standardized Approach

Main point Considers underlying exposures Risk weights for external ratings Simpler, but prudent

The Simplified Supervisory Formula Approach (for the Securitization Internal Ratings-Based Approach) was introduced with Basel III. Information about the underlying exposures must be considered.

6.2

History: Financial Crisis of 2007

Most securitization deals like CDOs or CDOs squared are constructed in a complex way. The modeling is challenging. In the years of the CDO hype (before the financial crisis of 2007) deals became ever more complex. Many smaller and medium-sized banks simply could not assess the risks associated with these deals. This lack of ability to assess the deals became a problem for many European and Asian banks that bought tranches of CDOs, issued by US banks, excessively. These banks neither had the tools nor the information to assess the associated risks. They largely relied on the judgment of the rating agencies. As discussed in Sect. 3.10.2 even the rating agencies did not have all the information needed to assess the risks. They judged the deals with the help of questionable assumptions. In Europe people largely relied on the optimistic judgment the rating agencies provided for the securitization deals. Though risk management standards for providing mortgage loans in the United States were significantly lower than for example the central European countries—affordability was not duly assessed etc.—Europeans and Asians relied on the quality of the securitizations being rated with best results. In the United States the widespread opinion dominated that house prices would continue to go up. Around 2007, many European banks faced problems as they owned lots of tranches of securitization deals.

Chapter 7

Risk Modeling and Capital: Market Risk

7.1

Pricing

Pricing is often done with the help of advanced Monte Carlo Simulations (see below). There are some alternative (traditional) methods and tools. A few examples are provided here: • The price and fair value of simple trades like interest rate swaps can be calculated by simply discounting the cash flows (according to the yield curve1). • The fair values of options can be assessed with the help of a Black–Scholes model. Basic inputs for the model are the price and the volatility of the underlying and the maturity of the option. Speaking of volatility, one mostly refers to “implied volatility.” The implied volatility is extracted from the market. • More complex interest rate-based deals are assessed with the help of advanced Monte Carlo Simulations (e.g., derivatives of the “Libor Market Model”).

7.2

Capital: Internal Models Approach

The Market Risk capital requirements saw quite some developments in the recent years: • With Basel 2.5 the Market Risk capital was beefed up (new elements, see Sect. 7.5). • With Basel III another change takes place (see below)—implementation date being January 2022.

1

New rates, like the Swiss Average Rate Overnight (SARON), replace the LIBOR.

© Springer Nature Switzerland AG 2020 J. Wernz, Bank Management and Control, Management for Professionals, https://doi.org/10.1007/978-3-030-42866-2_7

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7 Risk Modeling and Capital: Market Risk

Table 7.1 Liquidity horizon buckets for expected shortfall calculations within the IMA

Liquidity horizons, j 1 2 3 4 5

LH_j (days) 10 20 40 60 120

The following measures need to be considered, replacing the old measures (Basel 2.5 measures, see Sect. 7.5): • ES(97.5%), considering a set of liquidity horizons and considering portfolio stress, replaces VaR(99%) and Stressed VaR(99%), which both had a liquidity horizon of 10 days. • Default Risk Charge (DRC), replaces IRC. • Standardized Capital Charge for Unapproved Trading Desks. With Basel III the measure Expected Shortfall (97.5%)—considering a set of liquidity horizons—has to be applied in the Internal Models Approach (IMA). The Expected Shortfall has to be calculated in the following way: ffi vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u  ! 2 u X LH  LH j j1 ES ¼ t ðEST ðPÞÞ2 þ EST ðP, jÞ  : T j2 These are the inputs and requirements: • ES is the regulatory liquidity-adjusted ES. • T is the length of the base horizon: for example 10 days. • EST(P) is the ES at horizon T of a portfolio with positions P ¼ ( pi) with respect to shocks to all risk factors that the positions P are exposed to. • EST(P, j) is the ES at horizon T of a portfolio with positions P ¼ ( pi) with respect to shocks for each position pi in the subset of risk factors Q( pi, j), with all other risk factors held constant. • The ES at horizon T, EST(P) must be calculated for changes in the risk factors, and EST(P, j) must be calculated for changes in the relevant subset Q( pi, j) of risk factors, over the time interval T without scaling from a shorter horizon. • With the help of Tables 7.1 and 7.2 it needs to be determined for which liquidity horizons the different trades need to be considered, or in the words of Basel III: Q ( pi, j)j is the subset of risk factors for which liquidity horizons—as specified in [Basel III: Minimum capital requirements for market risk, paragraph 33.12], for the desk where pi is booked—are at least as long as LHj (according to Tables 7.1 and 7.2). For example, Q( pi, 5) is the set of risk factors with a 60-day horizon and a 120-day liquidity horizon. Q( pi, j) is a subset of Q( pi, j  1).

7.4 Capital: Standardized Approach

83

Table 7.2 Examples for liquidity horizons for risk factors (Basel III) Liquidity horizon n by risk factor Interest rate: specified currencies—EUR, USD, GBP, AUD, JPY, SEK, CAD and domestic currency of a bank Interest rate: unspecified currencies Interest rate: volatility Credit spread: sovereign (high yield, or HY) Credit spread: volatility

n 10

20 60 40 120

• The time series of changes in risk factors over the base time interval T may be determined by overlapping observations. • LHj is the liquidity horizon j, with lengths according to the table. For example: EUR vs. USD is considered in the Expected Shortfall calculation for 10 days only, whereas credit spread volatility needs to be considered in the calculation for all five buckets (120 days liquidity horizon). After calculating the above ES, the next capital calculation steps are: 1. 2. 3. 4.

Scaling with a stressed outcome Sum of unconstrained and constrained expected shortfall measures Addition of charge for non-modellable risk factors Application of the maximum of the following two: (a) most recent observation and (b) weighted average of the previous 60 days scaled by a multiplier (1.5 or more, depending on the assessment of backtesting) 5. Addition of Default Risk Charge and Standardized Capital Charge for Unapproved Trading Desks

7.3

P&L Attribution Testing: Internal Models Approach

If the desk experiences four or more breaches within the prior 12 months, then it must be capitalized according to the SA. P&L Attribution Testing gets very relevant under Basel III.

7.4

Capital: Standardized Approach

The Standardized Approach (SA) is a sensitivities-based method. Risk weights and sensitivities plus correlations are the main ingredients. Most important are the products of:

84

7 Risk Modeling and Capital: Market Risk

• Risk weights (RW) • Sensitivities (s)

7.5

History: Basel 2.5

Since the implementation of Basel 2.5 (in Switzerland in 2011 and in other countries in 2012), banks were required to hold a multiple of the capital charge for Market Risk that was required before. Since then a sum of the following elements had to be considered to determine the capital charge for Market Risk: • • • •

VaR(99%)—time horizon 10 days Stressed VaR IRC CRM

The resulting sum had to be multiplied with a factor of at least 3 (depending on the regulator’s assessment of the backtesting framework, the backtesting results, and the risks not covered within VaR). The approach was rather conservative. A stringent reasoning for the mentioned summation in the regulation was missing. The measure IRC was meant to cover the default and the migration risk of interest positions in the trading book. The measure was calculated for a 1-year time horizon at a confidence level of 99.9%. As an exception within securitization the capital charge for correlation-trading portfolios could be calculated with the help of the Comprehensive Risk Measure (CRM). The motivation for this exception was to avoid an overly large increase of the capital charge for trading positions that are meant as hedges for concentration and default risks. In Table 7.3 a part of a Pillar 3 report for the year 2020, showing the components of the capital charges, is provided. Already with Basel 2.5 there were massive changes for the capital charge for Market Risk.

Table 7.3 Market risk under Basel 2.5—example Market Risk VaR Stressed VaR IRC Comprehensive Risk Measure (CRM)

Basel III RWA in billions 12 16 15 7

7.6 Exposure Modeling (Pricing and Capital): Interest Rate Derivatives

85

There were risks and risk factors “not covered in VaR,” as the modeling of these risk factors for several products and trades were too complex (for example, few banks were not able to price complex interest rate trades as they did not implement the LIBOR market model; another example was a right for termination associated with M&A or IPO-like deals that caused a pricing problem for the investment bank accompanying these deals). As long as the corresponding positions were not material, many regulators accepted exceptions and simplifications for these deals. Nevertheless, these exceptions were restricted by most regulators on a step-by-step basis.

7.6

Exposure Modeling (Pricing and Capital): Interest Rate Derivatives

In the following an advanced exposure modeling example (for Interest Rate Derivatives) is discussed. This modeling is used for different purposes (“in parallel”): • Pricing (fair value): Average over the (millions of) outcomes of the MCS • CVA/DVA: Apply probabilities of default to the exposures • Market Risk capital—VaR: pick the one simulation result (out of the millions of simulations) that represents the desired VaR [e.g., VaR(99%)] • Market Risk capital—Expected shortfall: pick simulation results above the quantile (out of the millions of simulations) and average these results [e.g., ES (97.5%)] • Counterparty Credit Risk capital (“EPE”)—calculate the required (positive) exposure values and thus determine the EAD, multiply the K value (based on PD and LGD of counterparty and trade) • Limit setting (limits for counterparties) The same model is used for all the above, nevertheless it might be that for different purposes different inputs are used (e.g., historical volatility instead of implied volatility).

7.6.1

Monte Carlo Simulation

A Monte Carlo Simulation provides millions of datasets, each dataset representing the yield curve development over the upcoming years (Fig. 7.1). Another way of saying this: each dataset is representing the different forward rates for the future, e.g.: • • • • • •

1-year forward rate (once year 1 is reached) 2-year forward rate (once year 1 is reached) ... 1-year forward rate (once year 2 is reached) 2-year forward rate (once year 2 is reached) ...

86

7 Risk Modeling and Capital: Market Risk

Interest Rates 2

interest in %

1.95 1.9 1.85 1.8 1.75 1.7 1.65

0

2

4

6

8

10

12

months Fig. 7.1 Interest rates USD (example as of January 2020)

Each trade is evaluated according to all these potential developments (discounted cash flows are being calculated and summed up for each trade—according to each dataset).

7.6.2

Market Data: Caps

The available market data (yield curves, caps) are being read in. These data are the starting point (t0). The value of the caps can be decomposed into a series of caplets. The caplets provide the implied volatilities for the forward rates at the respective points in time.

7.6.3

Fitting of Volatility Curves to the Data

Volatility curves are being fitted to the data (see Fig. 7.2). The volatilities for a given point in time determine the probabilities for certain rate developments (the probability that certain rate developments are randomly picked within the MCS). For fitting of the volatility structure (often referred to as “vola smile”) the formula of Riccardo Rebonato can be used: v ¼ 100  ½ða þ b  t Þ  exp ðc  t Þ þ d, v being the volatility, t being the forward horizon (time). The parameters a, b, c, and d are used for the fitting.

7.6 Exposure Modeling (Pricing and Capital): Interest Rate Derivatives

87

Forward Rate Volatilities 12

Volatility in %

10 8 6 4 2 0

0

5

10

15

20

Years Fig. 7.2 Volatility curve

7.6.4

Correlations: Setting

The evolving of the different forward rates is correlated. The “closer” these rates are (in terms of their points in time), the more they are correlated (e.g., the 1-year forward rate now and in 1 year have a higher correlation than the 1-year forward rate now and the one in 5 years). A good approach is the following formula of Riccardo Rebonato:    correlationij ¼ LongCorr þ ð1  LongCorrÞ  exp beta  t i  t j  LongCorr is the long-term correlation (ad infinitum), 0.6 could be a good starting point. Beta determines how fast correlations go from 1 to the value of LongCorr, 0.1 could be a good starting point.

7.6.5

Longstaff–Schwartz Regression

For certain features of trades, the value at a given point in time depends on the future value. In this case a Monte Carlo Simulation within the Monte Carlo Simulation could be the solution (but increases the computational time very much). Another solution is a regression as discussed by Piterbarg and Longstaff & Schwartz. The regression (e.g., t2 values vs. t1 values) picks one path of each tree (for each tree from a t1 perspective) (Fig. 7.3).

88

7 Risk Modeling and Capital: Market Risk

Forward Rates 3

interest in %

2.5 2 1.5 1 0.5 0

t_0

t_1

t_2

time Fig. 7.3 Paths used for a regression (red paths)

7.7

Backtesting

Backtesting in Market Risk is straightforward. One compares all the daily gains and losses with the estimated ones (ES and VaR values). For example, for a VaR quantile of 99% the exceptions (larger losses than estimated) shall occur only three times within 300 days. If there are too many exceptions, regulators increase the discussed multiplier (Basel III: minimum of 1.5), which directly influences the capital. The quality of the backtesting framework and the soundness of the backtesting results have a significant influence on the multiplier and thus on the capital.

Chapter 8

Risk Modeling and Capital: Operational Risk

Operational Risk (OpRisk) saw quite some developments in the recent years: • With Basel II Operational Risk got more weight (a capital charge for Operational Risk was introduced). • With Basel III a change of paradigm in the calculation of the Operational Risk capital charge (new Standardized Measurement Approach, SMA) was provided. Bigger Operational Risk-related losses increase the capital charge (for quite some years). With the SMA for OpRisk (Basel III) there is a stronger incentive for effective governance and controls. With Basel II many banks implemented the Advanced Measurement Approach (AMA). As the AMA modeling remains relevant for Pillar II, it is also discussed below.

8.1

Standardized Measurement Approach

The Operational Risk Capital (ORC) is defined as the product of the Business Indicator Component (BIC) and the Internal Loss Multiplier (ILM), ORC ¼ BIC  ILM.

© Springer Nature Switzerland AG 2020 J. Wernz, Bank Management and Control, Management for Professionals, https://doi.org/10.1007/978-3-030-42866-2_8

89

90

8.1.1

8 Risk Modeling and Capital: Operational Risk

Business Indicator Component of the SMA

The Business Indicator (BI) is the sum of three components: • The interest, leases, and dividend component (ILDC) • The services component (SC) • The financial component (FC) All components include a 3-year average. To derive the BIC from the BI, the BI is multiplied by a factor of around 15% (depending on the dollar amount of the BI).

8.1.2

Loss Component (ILM) of the SMA

The Standardized Measurement Approach is a change of paradigm. A lot of emphasize is put on the internal losses, the ILM being  h i  LC 0:8 ILM ¼ ln e  1 þ : BIC The Loss Component (LC) is equal to 15 times the average annual Operational Risk losses (10 years being considered). Losses stay in the calculations of the capital charge for 10 years (10-year history). Discussions between banks and regulators focus strongly on the amount of the losses. With the SMA banks are strongly motivated to avoid bigger losses, or to put it differently: the benefit of investments in effective controls is bigger than in the past.

8.1.3

Loss Event Taxonomy (Categories) for SMA (and Other Approaches)

Tables 8.1, 8.2 and 8.3 provide a taxonomy with different categories (sometimes referred to as scenarios). This kind of taxonomy is typical for banks (and insurance companies). The relevance of categories/scenarios varies from bank to bank and insurance to insurance, e.g.: • For banks and insurance companies with business in the United States the category/scenario about discrimination is more relevant than for banks that do not do business in the United States. • For a Swiss bank, the category/scenario on data theft is much more relevant. • A bank without a trading desk discards the trading-specific scenarios.

8.1 Standardized Measurement Approach

91

Table 8.1 OpRisk categories/scenarios I No. 1

Category Antitrust laws and regulatory issues

2

Contractual risks

3

Client suitability

4

HR—Remuneration and discrimination, workplace safety

5

Merger and acquisition, due diligence

6

Complex products

7

Rogue and insider trading

8

Database and key documents, loss of information

9

Input failure, fat fingers

10

Privacy and company data violations by employees

Category contains – Violation of antitrust laws – Erroneous tax assumption – Defective bonus structure – Failed mandatory reporting – Risks within the setup of policies – Risks in the design of the contracts; e.g., resulting from missing or unclear “disclaimers” – Deficient or imprecise wording within the contracts – Risks within underwriting – Miss-selling, inappropriate information – Insufficient product understanding by the customer – Customer-specific suitability (recommendations not in line with the customer's risk profile or instructions) – Product suitability – Fee structures – Breach of foreign employment laws – Discrimination – Violation of health and safety obligations – General liability or reparation and compensation payments to employees – Insufficient and incomplete data in the due diligence process – No full understanding of firm to be acquired – Impact of the merger on company stability – Deficiencies in valuation techniques, underpricing could arise because of a lack of information (complexity of the product) – Poor understanding of complex structures – Selling pressure leads to positively biased estimates – Risks in the design of the SPVs – Insider trading – Unauthorized trading (“Kerviel,” “Adoboli”) – Hidden losses of traders – Incorrect reporting – Deficiencies in the data management and recovery/ retrieval – Accessibility and availability of data – Uncontrolled software change – Wrongly allocated data access – Failures in key business support processes, including payments, positions, inventory, record keeping, accounting – Human mistakes (“fat fingers”) or wrong import of data – IT security and data protection, employees misuse of privacy data or sensible information – Malicious activity or accidental disclosure through failed controls – Logical user and privileged access (continued)

92

8 Risk Modeling and Capital: Operational Risk

Table 8.1 (continued) No. 11

Category Privacy and company data violations by externals (cyber risk)

12

Model risk

13

Project failure

14

Hardware, software, and external data sources

Category contains – Misuse of privacy data or sensitive information accessed by unauthorized persons (Hacking, Trojans) – Data theft or damage – Inadequacy or failure in the design of the methodology, wrong assumptions – Deficiencies in model review – Inadequate knowledge and experience – Material project delays and project overruns that lead to additional cost – Insufficient project governance – Failed implementation of the firm’s strategy – Internal IT projects – Physical asset protection and hardware maintenance – Access disruption to external data sources – Software licensing

Table 8.2 OpRisk categories/scenarios II 15

Theft and fraud by employees

16

Theft and fraud by externals

17

Key employees, capacity, performance management

18

Erroneous output

19

Outsourcing, service providers

– Theft, (identity) theft – Complicity – Forgery – Misrepresentations – Criminals pursue illegal activities intended to defraud, misappropriate property – Fraudulent claims – Loss of key person or teams – Staff leaves due to business pressure and stress environment – Mistakes in resources planning – Lack of loyalty and poor motivation – Erroneous accounting, reporting – Output errors – Poor mutual understanding of the contract – Little or no support from client leaders receiving services – Poor knowledge transfer – Culture clash between the client and service provider

The categories/scenarios of Table 8.2 have lower significance than the ones of Table 8.1. For longer time horizons also the categories/scenarios of Table 8.3 are relevant.

8.2 AMA Model (Pillar II): Modeling and Simulation

93

Table 8.3 OpRisk categories/scenarios III 20

Natural disasters, pandemic

21

Terror, war

8.2

– Fire and flooding – Extreme weather conditions (hurricanes, earthquakes) – Infrastructure outages (power, water, transport, telecommunications) – Pandemic influenza – Wars, revolutions – Terrorist attacks

AMA Model (Pillar II): Modeling and Simulation

The AMA models use a Monte Carlo simulation: • Within this simulation (see Fig. 8.1) there are random draws from a severity distribution. • The number of these random draws is generated by randomly drawing from a frequency distribution. • As there are dependencies between risk categories, the simulated losses of different categories and locations (divisions, units) are summed up according to the Copula/strength of correlations that is used. The whole procedure is done millions of times (simulations) and in the end the x% highest numbers are discarded (as a quantile of 100x% is considered). The distributions that are used in the simulations (as described above) are: • Either defined by expert judgement (the input parameters are being provided by subject matter experts, SMEs) or • Fitted to data (if data are available for the respective category).

Freqencies Sc.1: Poisson 1

Sc. 2: Poisson 2

Severities Sc. 1: Lognormal 1

Monte Carlo Simulation

Sc. 2: Lognormal 2 uses Copulas/Correlations ...

...

Fig. 8.1 Monte Carlo simulation

94

8 Risk Modeling and Capital: Operational Risk

If expert judgement is applied, the SMEs provide risk assessments and come up with values (like “we assume that this risk strikes roughly each 20 years with a severity/an impact of roughly 50 mn USD”). The experts’ assessments can be inspired by external data (like the data provided in Table 8.4). Many banks and insurance companies for example are members of ORX (sharing of anonymized loss data). The data fits or the experts’ assessments are being translated into distributions. The distributions are used for the above discussed simulation steps. Experts’ assessments on the dependencies between risks are being translated into Copulas (defining shape and correlation strength): • Lognormal distributions or Pareto distributions are commonly used for the severity. • Poisson distributions are typically used for the frequency. • Inverse Clayton Copulas (or others) can be used to consider/model the dependency between the risks/risk categories (see Fig. 8.2). The dependencies between risks are typically assessed by the subject matter experts, correlation matrixes are being provided by them. The dependency (rank correlation) can be assessed with the help of categories like “no, little, medium, high or full dependency.” The assessments are backed up by “storylines” like: “if there is a model risk (risk 1), it is likely that it triggers a regulatory risk (risk 2).” In a next step, the qualitative assessments on the correlations are being translated into figures like 0, 0.25, 0.5, 0.75, and 1. A “high” rank correlation of 0.8 corresponds to a theta of 8 for a Clayton Copula (see Fig. 8.2). When it comes to big correlation matrixes (dependencies between risks), there are some things to be considered: before applying the matrixes, they need to be positive semi-definite, PSD. For the application within the Monte Carlo simulation a Cholesky decomposition is helpful. It is necessary to adjust the correlation matrix, which the subject matter experts provided, into a positive semi-definite matrix. At the same time, this step is a helpful tool: comparing the resulting positive semi-definite matrix with the original matrix reveals “logical contradictions” (which often cannot be avoided in coming up with bigger matrixes). The effects of correlation are illustrated in Fig. 8.3. On the left side there is no correlation (correlation ¼ 0). The second drawing out of the severity distribution is independent of the first drawing and so on. In the pictures in the middle there is an influence of the first drawing on the second and so on. The value of the second drawing is “closer” to the value of the first drawing. Mathematically this is a convolution.

8.2 AMA Model (Pillar II): Modeling and Simulation

95

Table 8.4 Examples of losses within the different categories/scenarios 1

1

2

2

2

Description Several insurers in the industry sector had to pay penalties summing up to EUR 130 million. According to the “Bundeskartellamt,” the German Federal Office in charge of questions related to trust, the insurers had a trust in the area of “industrielle Sachversicherung” since 1999. The following insurers were affected: Allianz Versicherungs-Aktiengesellschaft, AXA Versicherung AG, Gerling-Konzern Allgemeine Versicherungs-Aktiengesellschaft, HDI Haftpflichtverband der Deutschen Industrie, Versicherungsverein auf Gegenseitigkeit, Aachener und Münchener Versicherung, Gothaer Allgemeine Versicherung AG, Mannheimer Versicherung Aktiengesellschaft, R + V Allgemeine Versicherung AG, Victoria Versicherung AG, Württembergische Versicherung AG. In Spain six insurance and reinsurance companies had to pay penalties of all in all EUR 121 million for violating the antitrust law. Swiss Re had to pay EUR 22.6 million. The other affected companies were Asefa, Scor, Munich Re, Caser und Mapfre. The bank in 2008 agreed to buy back about US $1.5 billion in ARS and agreed to pay about US$23 million as penalty. Investors had previously claimed they could not withdraw funds in brokerage accounts. Due to the complexity of a deal and the imprecise reflection of the complex aspects within the contracts Chase lost about US$135 million. Silverstein Case—In January 2001, Silverstein, via Silverstein Properties, made a US$3.2 billion bid for the lease to the World Trade Center. Silverstein's bid for the lease to the World Trade Center was accepted on July 24, 2001. The lease agreement applied to 1, 2, 4, and 5 World Trade Center, and about 425,000 square feet (39,500 m2) of retail space. The terms of the lease gave Silverstein, as leaseholder, the right and the obligation to rebuild the structures if destroyed. Upon leasing the World Trade Center towers, along with 4 and 5 WTC, Silverstein insured the buildings. The insurance policies on these four buildings were underwritten by 24 insurance companies for a combined total of US$3.55

Firm Allianz/Axa. . .

Year 2005

Million 130

EUR

Swiss Re, Munich Re. . .

2009

121

EUR

Goldman Sachs

2008

1550

US$

Chase

1982

135

US$

Munich Re/Swiss RE/Allianz

2006

1000

US$

(continued)

96

8 Risk Modeling and Capital: Operational Risk

Table 8.4 (continued) Description

2

2

2

3

billion per occurrence in property damage coverage. All of the buildings at the World Trade Center, including buildings 1, 2, 3, 4, 5, 6, and 7 were destroyed or damaged beyond repair on September 11, 2001. After a protracted dispute with insurers over the amount of coverage available for rebuilding World Trade Center buildings 1, 2, 4, and 5, a series of court decisions determined that a maximum of US$4.55 billion was payable and settlements were reached with the insurers in 2007. Of the US$4.55 billion about 1 billion was “wording” related (“one event” vs. “two events”). Silverstein Case (“ex gratia element”)—An arbitration panel examining a World Trade Center (WTC) indemnification dispute between Germany-based insurer Allianz and French reinsurer Scor has ruled that Allianz did not exceed its rights and obligations. In May 2007 Scor claimed that the US$2 billion settlement between seven insurers, including Allianz, and WTC lease owner Larry Silverstein did not “respect the terms and conditions of the Certificate of Reinsurance between Scor and Allianz.” Scor claimed that the settlement contained an ex gratia element and exceeded contractual agreements. In the end additional costs for Scor were about US$58.4 million. Discriminating practices of an insurance company—Insurance salespeople charged AfroAmerican customers higher than average rates between 2003 and 2006. The insurance company was sentenced to pay at least US$6.1 million. The insurance company claimed that it did not control its business partners (the salespeople). ASR, the Dutch insurance arm of Fortis, paid a EUR 780 million compensation package to customers after clients began legal action when the Dutch market regulator AFM stated in 2006 that some Dutch insurance products were not adequate. Many German cities lost money investing in certain derivatives offered by banks. The cities recently claimed that they did not fully understand the involved risks and that the banks (in this case Deutsche Bank) did not inform

Firm

Year

Million

Scor(/Allianz)

2007

58

US$

AIG

2010

6

US$

Fortis

2008

780

EUR

Deutsche Bank—Guess

2011

500

EUR

(continued)

8.2 AMA Model (Pillar II): Modeling and Simulation

97

Table 8.4 (continued) Description

3

3

3

4

4

4

4

4

4

5

them correctly about the risks involved). There was a “BGH-Urteil” that stated the cities are correct in their claim. The amounts Deutsche Bank paid are not public. Other banks like WestLB are also affected— for example the city of Remscheid lost EUR 19 million. The Hungarian government that was elected in 2010 decided that Hungarian customers with mortgage loans from banks can repay these loans for 180 Forint per CHF. This legislative action resulted in big losses for the effected banks. Citigroup paid back US$968 million to Fannie Mae. Fannie Mae had bought many bad loans from Citigroup in the years before the mortgage bubble of 2007. In 2008, a woman working for the bank stated she had been sexually harassed by her boss since 2003. In 2009 she was dismissed. In 2010 the court decided that she would get about half a million dollars of compensation and the bank would have to pay a penalty of about US$10 million. An Asian bank worker won GBP 2.8 million in compensation for racial discrimination after losing his job. Morgan Stanley was accused of discriminating against women (in terms of salaries). In 2004 Morgan Stanley paid US$54 million. Again in 2007 Morgan Stanley was accused of discriminating against women (in terms of salaries). In 2007 Morgan Stanley paid US$46 million. Wal-Mart was accused of discriminating against women (in terms of acceptance of applications). Wal-Mart paid US$12 million. In this long-running case an employee of PWC claimed she was sexually harassed, discriminated against, victimized and bullied. In the end she got US$11 million for loss of earning, loss of clients, counseling, and damage to her reputation. BayernLB took over Hypo Alpe Adria with incomplete information, which resulted in a large loss of potentially several billion EUR for BayernLB.

Firm

Year

Million

WestLB— Guess

2011

200

EUR

Several Banks (esp. in Austria)

2011

2000

EUR

Citigroup

2013

968

US$

UBS

2008

10

US$

Abbey

2006

3

GBP

Morgan Stanley

2004

54

US$

Morgan Stanley

2007

46

US$

Wal-Mart

2010

12

US$

PWC

2004

11

US$

BayernLB/ Hypo Alpe Adria

2006

1000

EUR

(continued)

98

8 Risk Modeling and Capital: Operational Risk

Table 8.4 (continued) 6

6

7

7

7 7

7

7

Description In 2008, Goldman Sachs agreed to buy back about US$1.5 billion in ARS and agreed to pay about US$23 million as penalty. Investors had claimed they could not withdraw funds in brokerage accounts. Enrico Bondi of Parmalat filed a EUR 248 million claim against Credit Suisse First Boston International. The suit—somehow related to the complexity of the product Parmalat bought—was settled in 2008 for about EUR 170 million. An employed trader stole US$43 million from the bank and disguised the theft as a hedge. He laundered the money with the help of an offshore banking consultant. Michael Bright, the founder and CEO of Independent Insurance, together with colleagues committed internal fraud. The U.K. regulator FSA claimed GBP 357 million. Michael Bright was sentenced to prison for 7 years. The trader Jerome Kerviel traded much more than his limit and lost almost EUR 5 billion. The trader Kweku Adoboli faked hedges and traded much more than his limit allowed him. In the end UBS lost about CHF 2.3 billion. Nick Leeson from 1992 on made unauthorized speculative trades that at first made large profits for his bank (10% of the total income of the bank in 1992). The situation changed and Leeson suffered big losses that he booked to an “error account.” By the end of 1992, the account's losses exceeded GBP 2 million, which ballooned to GBP 208 million by the end of 1994. After the Kobe earthquake in 1995 the losses exploded and Leeson fled, leaving behind losses of about GBP 825 million. In 1983, Toshihide Iguchi lost US$70,000 in trading and concealed the loss to protect his reputation and job. He continued trading to recoup the loss; however, the loss snowballed. In 1988, he was joined by two other traders who also concealed their losses. Iguchi continued to conceal the losses from internal auditors and others. In September 1995, fearing the damage his losses would cause, Iguchi wrote a confession letter to the president of the bank.

Firm Goldman Sachs

Year 2008

Million 1550

US$

Credit Suisse

2008

170

EUR

43

US$

Merrill Lynch

Independent Insurance

2007

357

GBP

Société Générale UBS

2008

4820

EUR

2011

2300

CHF

Barings Bank

1995

825

GBP

Daiwa Bank

1995

1000

US$

(continued)

8.2 AMA Model (Pillar II): Modeling and Simulation

99

Table 8.4 (continued) 8

9

9

9

10

10

11

11 11

11 12

Description Due to a merger of two banks in 2008 about 1.2 million customer data had to be migrated to the new parent bank’s server. A chain of problems with the IT resulted and many data were not accessible for weeks. Direct project failure costs were estimated later at about EUR 3.2 million. Costs due to the loss of customers were estimated at about EUR 10 million. A Salomon Smith Barney trader placed an order to sell French Government bond contracts, not realizing that his F 12-key on his keyboard had an instant sell feature. He accidentally repeated the order 145 times leading to a loss of US$5 million. In 2001 a Lehman Brothers dealer in London placed a wrong trade leading to loss of US$10 million. He believed that there was an arbitrage opportunity between FTSE100 futures contracts and underlying equity stock. KfW generated a payment to Lehman of EUR 300 million on the day Lehman went bankrupt. The payment could not be stopped and recalled. Data were stolen from a bank in Liechtenstein by an employee. The data was sold to tax officials in Germany. A customer whose data was stolen went to court in Liechtenstein and received a compensation of EUR 7.3 million from the bank. A data theft of about 1500 customer data sets could potentially lead customers to file for claims for compensation of about CHF 1 billion. FSA ordered Nationwide Building Society to pay about GBP 1 million in fines because FSA considered IT security at the company lax (an employee’s laptop with confidential company data was stolen and later accessed). There was ongoing external hacking and theft of information. There was a Denial of Service (DoS) Attack on the servers of Cablecom. The services were down for 1 hour. There was a Denial of Service (DoS) Attack on the servers of the firm. A mistake in modeling and valuation of certain derivative positions held by the Tokyo Mitsubishi Financial Group led to a year-end loss of US$83 million. Tokyo Mitsubishi announced that this occurred at its New Yorkbased derivatives unit. The internal pricing model overvalued swaps and options on U.S. interest rates.

Firm Danske Bank

Year 2008

Million 13

EUR

Salomon Smith Barney

1998

5

US$

Lehman Brothers

2001

10

US$

KfW

2008

300

EUR

LGT

2010

7

EUR

Swiss Bank— Guess

2010

1200

CHF

Nationwide

2006

1

GBP

TJX

150

US$

Cablecom

up to 2010 2009

1

US$

Amazon

2008

2

US$

Tokyo Mitsubishi

1997

83

US$

(continued)

100

8 Risk Modeling and Capital: Operational Risk

Table 8.4 (continued) 14

17

18 18 18

19 19

20

20

21

21

21

Description In 1997, a compensation of US$10 million was paid to investors. A loss was generated because the bank’s system was overloaded, and the transactions were performed too late. The Manager José Ignacio López left General Motors and went to Volkswagen. He took important company information with him. In 1996, Volkswagen had to pay US$100 million and had to additionally buy material from General Motors (1 billion). Allianz had to pay a EUR 100 million supplementary tax payment in 2010. AIG had to pay a US$46.5 million supplementary tax payment in 2010. There was a clash between the bank and the local Taxation Office (concerning the accounting of equity transactions in the last 7 years). The bank announced in 2003 that it had settled the conflict for AUD 262 million. During the outsourcing of several processes an external provider lost Zurich’s data. The external provider to whom several processes of HSBC were outsourced lost HSBC’s data. Due to a fire in October 2001 a bank building in Winter Haven was destroyed, incurring a loss of about US$1.5 million for the bank. Due to an electrical fire (electrical power strip) in August 2007, the local headquarter of the bank in Wichita was destroyed, incurring a loss of about US$1 million for the bank. One bank reported losses of about US$55 million related to the terrorist attack on the World Trade Center. Four employees who had their office in World Trade Center were missing. Additionally, the closure of trading for several days created losses. Marsh & McLennan had offices in the World Trade Center and lost many employees. Three people were killed in an IRA attack in 1992. The attack took place in London where a huge bomb exploded near 30 St Mary Axe. Damage resulted in losses of almost GBP 800 million.

Firm Merrill Lynch

Year 1997

Million 10

US$

Opel/VW

1999

100

US$

Allianz

2010

100

EUR

AIG

2010

46

US$

Australia and NZ Banking Group

2003

262

AUD

Zurich

2010

2

GBP

HSBC

2009

3

GBP

Bank of America

2001

1.5

US$

Bank of America

2007

1

US$

Wells Fargo & Company

2001

55

US$

Marsh & McLennan— Guess Few firms

2001

2000

US$

1992

800

GBP

8.3 Internal Data/External Data

101

Fig. 8.2 Inverse Clayton Copula (plotted with R)

Inverse Clayton Copula - Theta=8 1.00

risk 2

0.75

0.50

0.25

0.00 0.00

0.25

0.50

0.75

1.00

risk 1

8.3

Internal Data/External Data

Typically, the experts (of the different divisions/units) assess frequencies and severities. Ideally there are at least some categories/scenarios for which internal data are available (these are mostly the high-frequency low-impact (HFLI) categories/scenarios). For other categories/scenarios (mostly the low-frequency high-impact (LFHI) scenarios) there are no internal data. The external data can provide valuable hints, inspiration, and/or challenge. Table 8.4 provides useful data. The table was created by media monitoring—this means all the information provided therein is public. Worldwide data can help assess frequencies and severities for LFHI scenarios. Filtering according to the individual bank’s or insurance company’s business model and scaling according to the individual size of course should be done where necessary. The numbering of Table 8.4 corresponds to the categories/scenarios defined in Tables 8.1 to 8.3. The amounts are provided in millions of the countries’ currency in the right column.

102

8 Risk Modeling and Capital: Operational Risk Correlation = 0

Actual Correlation

Correlation = 1

LD 1

LD 2

Fig. 8.3 Dependency of the cumulated losses within the loss distributions (LD), transmitted by the correlations

8.4

Controls

Effective controls help to minimize risks and to avoid issues. In a wider sense all mitigations should be seen as controls. Everything that reduces the probability (frequency) or the severity (impact) of a loss is mitigating a risk and thus is a “control.” For example, an insurance for cyber risks is an important mitigation of risks; it reduces the loss in case of a cyberattack. Everything that reduces the probability (frequency) or the severity (impact) of a loss is mitigating a risk and thus is a control. Control Frameworks are usually hosted within the Operational Risk department of the firm. Sometimes the broader area is referred to as Enterprise Risk Management (ERM). The framework makes sure that there are adequate controls for all material risks and that these controls are effective (Table 8.5). With Basel III effective controls got even more important, as each (bigger) loss increases the Operational Risk capital charge (significantly) within the SMA calculations. In that sense each loss now is a double hit: • The loss itself (direct impact on the profit) and • Increased capital and thus increased cost of capital (hits on the profit—for many years to come—as the loss stays in the “history” for SMA calculations)

8.5 Cost/Benefit Considerations for Controls

103

Table 8.5 Examples of important controls Control Four-eyes principle for important communication Model validation performed by independent validation unit Automated pattern controls Controls for port scans (firewall) Cyber risk insurance

Frequency Ongoing Each 2–4 years Ongoing Ongoing Policy renewal annually

Goal/objective Making sure communication is according to principles Making sure that capital models are implemented as intended and as documented Preventing credit card fraud Preventing/detecting intrusion Reducing loss in case of a cyberattack

In a sense the control “insurance” (like cyber risk insurance) for many risks addresses both of these potential hits. The claims on the insurance reduce the loss itself and make the capital increase less significantly. Insurance for potential (Operational Risk) losses can be quite attractive under Basel III (cost/benefit considerations). Often controls (and their business owners, the people in charge) are documented (more or less comprehensively) in a database; execution of the controls (whenever they are due) is signed-off in the database as well. Reminders (control execution) are being sent.

8.5

Cost/Benefit Considerations for Controls

Controls usually cost money. There are costs associated to the controls. It is a powerful tool for Operational Risk management to provide cost/benefit calculations. Whenever these cost/benefit analyses are provided, decisions can be made on the bases of these analyses. For example: a cyber risk insurance might cost the bank 100 mn USD annually. On the other hand it might reduce the losses (direct hit and cost of capital) by 200 mn USD annually (under the assumption that there is a big data issue (due to a cyberattack) each 10 years with a certain (direct) impact of for example 1.4 bn USD). Cost/benefit calculations (for controls) are a powerful tool for the Operational Risk management of the bank.

104

8.6

8 Risk Modeling and Capital: Operational Risk

Backtesting

For the SMA (Basel III) no backtesting is needed. The SMA is not a model; it is rather a formula that needs to be executed: no (model result) backtesting can be done. For the AMA (still in use for banks’ Pillar II models and similarly within insurance companies’ Solvency II models) backtesting is a relevant topic though. Backtesting within OpRisk is more difficult than in other risk categories, because the high-impact events are seldom (once in many years only). One still can do backtesting— considering lower quantiles for backtesting. Then the backtesting framework consists of rules such as: the last years’ losses should not be higher than the 50% quantile of the OpRisk VaR within more than 65% of the observed years. In the example there are 4 out of 11 (36%) exceedances of the VaR (50%). The capital level as determined by the model is assumed to be adequate (according to the backtesting rules) (Table 8.6).

Table 8.6 Operational risk capital (model) backtesting example

Year 2010 2011 2012 2013 2014 2015 2016 2017 2018 2019 2020

Predicted loss Model VaR(50%) in USD mn 450 450 480 480 480 500 500 460 460 440 440

Realized loss in USD mn 300 510 330 550 500 250 280 520 450 400 380

Chapter 9

Risk Modeling: Asset Liability Management

Often the yield curve is such that long-term interest rates are higher than short-term interest rates. Before the financial crises, there were some nice gains as a result of this difference in interest rates. Nevertheless, when the financial crisis hit in 2007, the yield curve twisted, and the asset mismatch led to big losses. Some banks like Dexia (Belgium) or Depfa (Ireland, later part of HRE, Germany) had refinancing schemes that were quite risky, because there was a big asset mismatch. Loans were provided long term whereas refinancing was done short term. Two ratios were invented with Basel III to address liquidity risks (such as the above mentioned): • First, the measure liquidity coverage ratio (LCR) was introduced. It was meant to demonstrate the ability to pay back liabilities within a time horizon of 30 days. • Second, the measure Net Stable Funding Ratio (NSFR) was introduced. It was meant to demonstrate that there is no bigger asset mismatch. Basel III invents two ratios (LCR and NSFR) to address liquidity risks.

9.1

Liquidity Coverage Ratio

The LCR measure is defined as follows: Liquidity coverage ratio ðLCRÞ ¼ ðStock of high‐quality liquid assets ðstressed conditionsÞ=total net cash outflows over the next 30 calendar daysÞ  100%

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106

9

Risk Modeling: Asset Liability Management

The LCR condition is designed in such a way that banks can demonstrate the ability to pay back liabilities within a time horizon of 30 days. In “Basel III: The Liquidity Coverage Ratio and liquidity risk monitoring tools,” details are being provided.

9.2

Net Stable Funding Ratio

The NSFR measure is defined as follows: Net stable funding ratio ðNSFRÞ ¼ ðAvailable amount of stable funding =required amount of stable fundingÞ > 100% The NSFR condition is designed in such a way that banks can demonstrate there is no bigger asset mismatch. In “Basel III: the net stable funding ratio,” details are being provided. The ASF categories and the associated maximum ASF factor to be applied in calculating an institution’s total amount of available stable funding are as shown in Table 9.1. Table 9.1 ASF categories ASF factor 100%

95% 90% 50%

0%

Components of ASF category • Total regulatory capital (excluding Tier 2 instruments with residual maturity of less than 1 year) • Other capital instruments and liabilities with effective residual maturity of 1 year or more • Stable non-maturity (demand) deposits and term deposits with residual maturity of less than 1 year provided by retail and small business customers • Less stable non-maturity deposits and term deposits with residual maturity of less than 1 year provided by retail and small business customers • Funding with residual maturity of less than 1 year provided by nonfinancial corporate customers • Operational deposits • Funding with residual maturity of less than 1 year from sovereigns, PSEs, and multilateral and national development banks • Other funding with residual maturity between 6 months and less than 1 year not included in the above categories, including funding provided by central banks and financial institutions • All other liabilities and equity not included in the above categories, including liabilities without a stated maturity (with a specific treatment for deferred tax liabilities and minority interests) • NSFR derivative liabilities net of NSFR derivative assets if NSFR derivative liabilities are greater than NSFR derivative assets • “Trade date” payables arising from purchases of financial instruments, foreign currencies and commodities

9.2 Net Stable Funding Ratio

107

Table 9.2 RSF categories RSF factor 0%

5% 10%

15%

50%

65%

85%

100%

Components of RSF category • Coins and banknotes • All central bank reserves • All claims on central banks with residual maturities of less than 6 months • “Trade date” receivables arising from sales of financial instruments, foreign currencies and commodities • Unencumbered Level 1 assets, excluding coins, banknotes and central bank reserves • Unencumbered loans to financial institutions with residual maturities of less than 6 months, where the loan is secured against Level 1 assets as defined in LCR Paragraph 50, and where the bank has the ability to freely rehypothecate the received collateral for the life of the loan • All other unencumbered loans to financial institutions with residual maturities of less than 6 months not included in the above categories • Unencumbered Level 2A assets • Unencumbered Level 2B assets • HQLA encumbered for a period of 6 months or more and less than 1 year • Loans to financial institutions and central banks with residual maturities between 6 months and less than 1 year • Deposits held at other financial institutions for operational purposes • All other assets not included in the above categories with residual maturity of less than 1 year, including loans to nonfinancial corporate clients, loans to retail and small business customers, and loans to sovereigns and PSEs • Unencumbered residential mortgages with a residual maturity of 1 year or more and with a risk weight of less than or equal to 35% under the Standardized Approach • Other unencumbered loans not included in the above categories, excluding loans to financial institutions, with a residual maturity of 1 year or more and with a risk weight of less than or equal to 35% under the standardized approach • Cash, securities or other assets posted as initial margin for derivative contracts and cash or other assets provided to contribute to the default fund of a CCP • Other unencumbered performing loans with risk weights greater than 35% under the standardized approach and residual maturities of 1 year or more, excluding loans to financial institutions • Unencumbered securities that are not in default and do not qualify as HQLA with a remaining maturity of 1 year or more and exchange-traded equities • Physical traded commodities, including gold • All assets that are encumbered for a period of 1 year or more • NSFR derivative assets net of NSFR derivative liabilities if NSFR derivative assets are greater than NSFR derivative liabilities • 20% of derivative liabilities as calculated according to Paragraph 19 • All other assets not included in the above categories, including nonperforming loans, loans to financial institutions with a residual maturity of 1 year or more, nonexchange-traded equities, fixed assets, items deducted from regulatory capital, retained interest, insurance assets, subsidiary interests, and defaulted securities

The RSF categories and the associated RSF factor to be applied in calculating an institution’s total required amount of stable funding are as shown in Table 9.2.

Appendix A: A-IRB Formulas for the Derivation of Capital

In the following, the formulas for the derivation of Credit Risk capital (and riskweighted assets) are provided. The parameters that go into these formulas are discussed in detail in Chap. 4. Generally, a capital charge of K
EAD is required. RWA ¼ 12:5
K
EAD: Within the provided formulas N(x) means the cumulative distribution function of a random variable according to a standardized normal distribution, G(z) means the inverse cumulative distribution function of a random variable according to a standardized normal distribution.

A.1 Residential Mortgage Exposure According to Paragraph 119 of Basel III (and Paragraph 328 of the Basel II Framework), K is calculated in the following way:  K¼

pffiffiffi    R  Gð0:999Þ GðPDÞ pffiffiffiffiffiffiffiffiffiffiffiffi LGD  N pffiffiffiffiffiffiffiffiffiffiffiffi þ  PD  LGD : 1R 1R

The correlation R is set to R ¼ 0.15. There is one important thing to note here: the LGD floor for residential mortgages is fixed at 5% (Paragraph 121 of Basel III).

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Appendix A: A-IRB Formulas for the Derivation of Capital

A.2 Qualifying Revolving Retail Exposures According to Paragraph 119 of Basel III (and Paragraph 329 of the Basel II Framework), K is calculated in the following way:  K¼



GðPDÞ LGD  N pffiffiffiffiffiffiffiffiffiffiffiffi þ 1R

pffiffiffi   R  Gð0:999Þ pffiffiffiffiffiffiffiffiffiffiffiffi  PD  LGD : 1R

The correlation R is set to R ¼ 0.04.

A.3 Other Retail According to Paragraph 120 of Basel III (and Paragraph 330 of the Basel II Framework), K is calculated in the following way:  K¼



GðPDÞ LGD  N pffiffiffiffiffiffiffiffiffiffiffiffi þ 1R

pffiffiffi   R  Gð0:999Þ pffiffiffiffiffiffiffiffiffiffiffiffi  PD  LGD : 1R

The correlation R is defined in the following way: R ¼ 0:03 

1  exp ð35  PDÞ 1  exp ð35  PDÞ þ 0:16  0:16  1  exp ð35Þ 1  exp ð35Þ

 0:03 þ 0:13  exp ð35  PDÞ:

A.4 Corporates and Bank Exposures According to Paragraph 53 of Basel III (and Paragraph 272 of the Basel II Framework), K is calculated in the following way: pffiffiffi     R  Gð0:999Þ GðPDÞ 1 þ ðM  2:5Þ  b pffiffiffiffiffiffiffiffiffiffiffiffi K ¼ LGD  N pffiffiffiffiffiffiffiffiffiffiffiffi þ  PD  LGD  : 1  1:5  b 1R 1R The inputs R and b are defined in the following way:

Appendix A: A-IRB Formulas for the Derivation of Capital

R ¼ 0:12 

111

1  exp ð50  PDÞ 1  exp ð50  PDÞ þ 0:24  0:24  1  exp ð50Þ 1  exp ð50Þ

 0:12 þ 0:12  exp ð50  PDÞ, b ¼ ð0:11852  0:05478  ln ðPDÞÞ2 :

A.5 Big Banks and Financial Institutions With Basel III a multiplier of 1.25 is applied to the correlation parameter of all exposures to financial institutions meeting the following criteria: • Regulated financial institutions whose total assets are greater than or equal to US $100 billion. The most recent audited financial statement of the parent company and consolidated subsidiaries must be used in order to determine asset size. For the purpose of this paragraph, a regulated financial institution is defined as a parent and its subsidiaries where any substantial legal entity in the consolidated group is supervised by a regulator that imposes prudential requirements consistent with international norms. These include, but are not limited to, prudentially regulated insurance companies, broker/dealers, banks, thrifts and futures commission merchants. • Unregulated financial institutions, regardless of size. Unregulated financial institutions are, for the purposes of this paragraph, legal entities whose main business includes: the management of financial assets, lending, factoring, leasing, provision of credit enhancements, securitization, investments, financial custody, central counterparty services, proprietary trading, and other financial services activities identified by supervisors. In the aforementioned cases the correlation is higher (in Basel III): R ¼ 0:15 

1  exp ð50  PDÞ 1  exp ð50  PDÞ þ 0:3  0:3  1  exp ð50Þ 1  exp ð50Þ

 0:15 þ 0:15  exp ð50  PDÞ:

A.6 Corporate: SME According to Paragraph 54 of Basel III (and Paragraph 273 of the Basel II Framework), K is calculated with the help of a modified correlation parameter R.

112

Appendix A: A-IRB Formulas for the Derivation of Capital

pffiffiffi     R  Gð0:999Þ GðPDÞ 1 þ ðM  2:5Þ  b pffiffiffiffiffiffiffiffiffiffiffiffi : K ¼ LGD  N pffiffiffiffiffiffiffiffiffiffiffiffi þ  PD  LGD  1  1:5  b 1R 1R The inputs R and b are defined in the following way: R ¼ 0:12 

1  exp ð50  PDÞ 1  exp ð50  PDÞ þ 0:24  0:24   0:04 1  exp ð50Þ 1  exp ð50Þ

 ð1  ðS  5Þ=45Þ  0:12 þ 0:12  exp ð50  PDÞ  0:04  ð1  ðS  5Þ=45Þ, b ¼ ð0:11852  0:05478  ln ðPDÞÞ2 : The sales component S for SME is allowed to range between EUR 5 and 50 million.

Appendix B: Credit Portfolio Modeling

A credit portfolio model (CPM) considers: • The individual risk of the customers, but also • The dependencies (between economy, sector, region, and customers). The risk/capital is calculated as Value at Risk or Expected Shortfall value (see there). Credit portfolio models are usually designed as multifactor models. The explanatory parameter Xi (“Asset-Return”) of a customer i is composed of a macroeconomic, systemic part and an individual, an idiosyncratic part. The pffiffiffiffi weighting ρs reflects the weight of the systemic risk zs within the regional or industrial sector s relative to the idiosyncratic firm or customer specific risk εi. Xi ¼

pffiffiffiffiffiffiffiffiffiffiffiffiffiffi pffiffiffiffiffi ρsi  zsi þ 1  ρsi  εi :

In a credit portfolio model, different customers from different regions and/or sectors are differently coupled to the economy and thus to the other customers. The Basel Accord formulas for Credit Risk (for the determination of capital and risk-weighted assets) represent a one factor model (as opposed to a detailed CPM). Xi ¼

pffiffiffiffiffiffiffiffiffiffiffi pffiffiffi ρ  z þ 1  ρ  εi :

In the Basel Accord formulas, all customers of an asset class are dependent on (coupled to) the economy in the same way (same strength). Compared to the Basel formulas for Credit Risk, a credit portfolio model is more granular. Also, the discussed formulas of the Basel Accords are approximations of large portfolios. On the other hand, for credit portfolio modeling, the assumption of a large portfolio does not necessarily have to be done. A good approach is to:

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Appendix B: Credit Portfolio Modeling

low R

low R

low R

higher R low R

moderate R

Economy

low R

low r

high R moderate R low r

very low R low R

high r

Switzerland high r

FX, IR… higher R

Fig. B.1 Recent correlations in Switzerland (R corresponds to rho)

• Determine correlations R between industrial sectors/regions and the country’s economy • Determine correlations r between the regional customers and the regional industrial sectors The correlation strength “shapes” the chosen Copula (Copulas determine the “details” of the dependencies). Examples for Copulas can be found in the chapter on Market Risk and in the chapter on Operational Risk. R and r correspond to rho. Figure B.1 shows the situation for Switzerland (as of 2020). Some corporations are shown—representing their regional industrial sector. In Zurich the big players are banks and insurance companies. In other areas big players are the manufacturers of machines or watches. Within other regions tourism plays a dominant role. Time series show the dependencies (correlations) of the different regional industrial sectors to the economy of the country. For example, manufacturers of watches increased their business significantly (there is a growing demand in Asia). This industrial sector proved to be less correlated to the country’s economy within the last several years. Also, insurances and reinsurances show a low correlation. Tourism on the other hand is strongly correlated to the country’s economy (because of the FX rates). Also, the correlation of local bank customers (for example, having a mortgage loan) to the local industrial sectors varies. In regions like the Engadin where the dominant industrial sector is tourism the correlation is much stronger than, for example, around the Lake Geneva, where many different firms are located.

Appendix C: Country Risk/Issuer Risk

Default risk is composed of an individual, idiosyncratic part and a systemic part. The systemic part is due to the general economic situation in the region or country (if the economy slows down, there is more unemployment and there are more defaults of corporations and private customers than there are in a booming economy). Thus, in modeling the probability of default there are the individual and the systemic parts. The systemic part is exchanged via the coupling to the economy, represented by the correlation parameter rho or R (see Appendix B). These correlations are also reflected within the formulas for deriving the risk-weighted assets. The correlations R are “hard coded” within these Basel formulas. The correlation R within these formulas is higher for the asset class corporates than for the asset class retail. In the internal multifactor model the country risk should also be considered. Banks in different countries might be correlated with their country’s economy in the same way (same R), but as the credit rating of these countries is different, the risk for these banks is different. Credit ratings of the countries are needed. Bigger banks employ economists and experts to assess the credit ratings of countries. In addition, credit ratings provided by the agencies are available if the banks do not perform their own assessment. In assessing creditworthiness, primarily the countries’ affordability is assessed. Fundamental data like the economic structure and export/import etc. are considered. In addition, the countries’ political and institutional framework, legal security, stability and so on are assessed. According to the Basel Accords sovereign bonds and loans to sovereigns require only little or no capital charge.

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Appendix D: Settlement Risk

The settlement risk, also known as “Herstatt risk,” is the risk of losing receivables during the settlement period. The Herstatt Bank of Cologne/Germany went bankrupt in 1974. A few banks had already made their payments in Deutsche Mark “DM” to Herstatt and lost the equivalent in US dollars (as Herstatt was unable to make the payment). To reduce settlement risk, in Basel III incentives were created for banks to settle their transactions via a qualifying central counterparty (QCCP). With Basel III there are incentives to settle transactions via central counterparties.

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Appendix E: Historical Data

Figures E.1, E.2, E.3, and E.4 show two historical scenarios (in parallel). First, the Great Depression in the United States—beginning in 1928—is shown. Second, in parallel, the developments of the 1973 Oil Crisis in the United States are shown, beginning in 1970.

GDP of the U.S. 140% 120% 100% 80% 60%

Great Depression Oil Crisis

40% 20% 0%

Fig. E.1 U.S. GDP during the Great Depression and the 1973 oil crisis

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Appendix E: Historical Data

Stock Prices USA 140% 120% 100% 80% Great Depression

60%

Oil Crisis

40% 20% 0%

Fig. E.2 Stock market movement in the United States during the Great Depression and the 1973 oil crisis

Unemployment USA 30% 25% 20% 15% Great Depression

10%

Oil Crisis

5% 0%

Fig. E.3 Unemployment rates in the United States during the Great Depression and the 1973 oil crisis

Appendix E: Historical Data

121

IR of U.S. Sovereign Bonds 10 yr. 10% 9% 8% 7% 6% 5% 4% 3%

Great Depression Oil Crisis

2% 1% 0%

Fig. E.4 Interests rates of US sovereign bonds during the Great Depression and the 1973 oil crisis

Appendix F: Specialized Lending/Project Finance

For specialized lending and project finance regarding capital the principles as discussed in Chap. 4 hold true. Either one goes for • the standardized approach and usually applies a risk weight of 100% (a risk weight of 100% means that 8% of the loan needs to be equity-financed) or • the advanced internal rating-based approaches (IRBA)—with corporate risk weights (see Appendix A). The former means much less effort, the latter usually allows for a more adequate reflection of the risks and thus often leads to a more favorable Return on Equity. Banks, funds and rating agencies, which do advanced modeling for specialized lending/project finance, model the cash flows and adverse events with the help of a Monte Carlo Simulation (see Chaps. 7 and 8). Ratings, probability of default (PD) values and loss given default (LGD) values result. For the different projects the modeling principles for the cash flows are usually the same, only the “risk factors” differ: • for wind energy (power plants) the main risk factor is the wind, • for infrastructural projects the main risk factor is the “traffic density” (tolls, street charges etc.). Depending on the location (country) the fees (for electricity price, tolls) might be guaranteed/fixed, or they might fluctuate. If they fluctuate, this needs to be considered in the cash flow modeling. Examples of adverse events are unforeseen maintenance costs or legal and contractual risks: • • • •

transmission failures (costs not covered by maintenance agreements), flawed and unfavorable setups of land lease agreements (e.g. for power plants), new environmental laws and unfavorable or missing maintenance agreements.

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Appendix F: Specialized Lending/Project Finance

The simulation of the cash flows factors in all the above. In the following the example of a power plant (wind energy) is discussed. • Wind: Potential fluctuations and changes (potentially also due to changes of the microclimate in that region) need to be modeled (the standard deviation can be used in the Monte Carlo Simulation). Expertise, wind forecasts and historical values (for the respective region) are being considered. • Fees: Fluctuating market values are being modeled [if there is no fixed price (e.g. power purchase agreement (PPA)] or for the time when the PPA is not there any longer (like after 10 or 12 years). As of 2020 for example in Spain there are usually no PPAs done/considered. • Adverse Events (Operational Risks that effect the cash flows): unforeseen maintenance costs and legal and contractual risks. If there are maintenance agreements, recoveries for these events are being considered/modeled as well. For the resulting ratings (based on the calculated probabilities in the MCS) adjustments are done for example • depending on the proven track record of the project management and • if the entity [often a special purpose entity (SPE)] is part of a bigger corporation or is a public sector entity (PSE). Examples for (changing) environmental laws: in Germany many species are (getting) protected: wind turbines need to be switched-off when bats are active or when black storks breed close to a power plant. For wind energy as of 2020 default rates of about 10% are being observed, nevertheless the recovery rates are high, the LGD values accordingly are quite low. As of 2020, depending on the setup and the location (country) the following leverage might be a good balance for both parties (both parties: limited partners or shareholders on the one hand and debt capital providers like banks on the other hand): • equity capital (limited partners (“Kommanditisten”) or shareholders): 40% • debt capital (banks): 60%.

Abbreviations

ABCP ABS AF A-IRBA ALM AMA ARM ARS ASF AUD AVC BaFin BCBS BIPRU BoE CBO CCAR CCF CCP CCR CDO CD CDS CET1 CHF CLO CMBS CPM

Asset-Backed Commercial Paper Asset-Backed Securities Adjustment Factor of the Capital (skipped under Basel III) Advanced Internal Ratings-Based Approach (Credit Risk) Asset Liability Management Advanced Measurement Approach (“old” approach within Basel II, nowadays mainly used in Pillar II models) Adjustable-Rate Mortgage Auction Rate Securities Available Stable Funding Australian Dollar Asset Value Correlation “Bundesanstalt für Finanzdienstleistungsaufsicht”—German Regulator Basel Committee on Banking Supervision Implementation of Basel in the United Kingdom Bank of England Collateralized Bond Obligations Comprehensive Capital Analysis and Review (United States regulatory framework) Credit Conversion Factor Central Counterparty, sometimes also QCCP Counterparty Credit Risk Collateral Debt Obligation Canadian Dollar Credit Default Swap Common Equity Tier 1 Confederation Helvetica Francs (Swiss Francs) Collateralized Loan Obligation Commercial Mortgage-Backed Security Credit Portfolio Management

© Springer Nature Switzerland AG 2020 J. Wernz, Bank Management and Control, Management for Professionals, https://doi.org/10.1007/978-3-030-42866-2

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CPM CRE CRM CRM CT CVA DCP DoS DTA DTL DVA DvP EAD EE EEPE EFH EL EPE ES EUR EWB Fannie Mae FCA Fed F-IRBA FINMA FPC Freddie Mac FSA FSB GBP (£) Ginnie Mae GSE G-SIB GuV HFLI HKD HVCRE HQLA ICAAP ICS

Abbreviations

Credit Portfolio Model Commercial Real Estate Credit Risk Mitigation Comprehensive Risk Measure Central Tendency Credit Valuation Adjustment Debt Collection Process Denial of Service Deferred Tax Asset Deferred Tax Liability Debit Valuation Adjustment Delivery-versus Payment Exposure at Default Expected Exposure Effective Expected Positive Exposure “Einfamilienhaus”—Family Home Expected Loss Expected Positive Exposure Expected Shortfall Euro “Einzelwertberichtigung”—Allowance Federal National Mortgage Association (Government-Sponsored Enterprise in the United States) Financial Conduct Authority (UK) Federal Reserve System (USA) Foundation Internal Ratings-Based Approach (Credit Risk) “Finanzmarktaufsicht”—Swiss Regulator Financial Policy Committee Federal Home Loan Mortgage Corporation (Government-Sponsored Enterprise in the United States) Financial Services Authority (now: PRA) Financial Stability Board Great British Pound National Mortgage Association in the United States Government-Sponsored Enterprise (for example, Fannie Mae and Freddie Mac) Global Systemically Important Bank “Gewinn- und Verlustrechnung”—P&L High Frequency, Low Impact Hong Kong Dollar High-Volatility Commercial Real Estate High Quality Liquid Assets Internal Capital Adequacy Assessment Process Internal Control System

Abbreviations

IKB ILS IMA IMM IPO IPRE IRBA IRC ISDA ISIN KMU LCR LFHI LGD M MaRisk M&A MBS MCS MFH MtM NOK NSFR OBS PD PF PFE PIT P&L PRA PSE PvP PSD PWB QCCP QRRE R RF RoE RMB RMBS

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IKB Bank in Dusseldorf Israeli Shekel Internal Models Approach (Market Risk) Internal Model Method (Counterparty Credit Risk) Initial Public Offering Income-Producing Real Estate Internal Ratings-Based Approach (Credit Risk) Incremental Risk Charge International Swaps and Derivatives Association International Securities Identification Number “Kleine und Mittlere Unternehmen”—SME Liquidity Coverage Ratio Low Frequency, High Impact Loss Given Default Maturity (Parameter) “Mindestanforderungen an das Risikomanagement”—one part of the German implementation of Basel II Merger and Acquisition Mortgage-Backed Securities Monte Carlo Simulation (Algorithm) “Mehrfamilienhaus”—Apartment Building Mark-to-Market Norwegian Krone Net Stable Funding Ratio Off-Balance Sheet Probability of Default Project Finance Potential Future Exposure Point in Time Profit and Loss Statement Prudential Regulation Authority (Part of the Bank of England)— successor of the FSA Public Sector Entity Payment-versus-Payment Positive Semi-Definite “Pauschalwertberichtigung”—General Allowance for Doubtful Accounts Receivable Qualifying Central Counterparty Qualifying Revolving Retail Exposures Correlation Parameter R Risk Factor Return on Equity Chinese Ren Min Bi Residential Mortgage-Backed Security

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RRP Rs RUF RVE RVR SARON SBA SBB SF SFr SFT SL S&L SMA SME SME SNB SolvV SPV SR SSFA ST TRL TTC UL US$ VaR VFE WWR ZVV

Abbreviations

Resolution and Recovery Planning Rupees Revolving Underwriting Facility Repurchase Value Estimator Repurchase Value Ratio Swiss Average Rate Overnight Scenario Based Assessment “Schweizerische Bundesbahnen”—Swiss Railway Service Supervisory Formula Swiss Francs Securities Financing Transaction Specialized Lending Savings and Loan, also called “Thrift” Standardized Measurement Approach (Operational Risk approach under Basel III, effective 2022) Small and Medium Enterprises Subject Matter Expert Schweizerische Nationalbank, Swiss National Bank “Solvabilitätsverordnung,” one part of the German implementation of Basel II (like BIPRU in the United Kingdom) Special Purpose Vehicle Saudi Riyals Simplified Supervisory Formula Approach Stress Testing Turkish Lira Through The Cycle Unexpected Loss United States Dollar Value-at-Risk “Vorfälligkeitsentschädigung,” a fee a customer has to pay, when he amortizes his loan upfront Wrong Way Risk “Zürcher Verkehrsverbund,” the local transportation firm of Zurich, Switzerland

Bibliography

Laws and Regulations (Switzerland, UK, European Union): • CH: Verordnung über die Eigenmittel und Risikoverteilung für Banken und Effektenhändler (Eigenmittelverordnung, ERV), April 2019 • UK: Prudential sourcebook for Banks, Building Societies and Investment Firms, December 2019 • EU: Capital Requirements Regulation 2013, regulation No 575/2013 on prudential requirements for credit institutions and investment firms, June 2013 Basel III (Publications by the Basel Committee on Banking Supervision, Bank for International Settlements): • • • • • •

Minimum capital requirements for market risk, February 2019 Finalising post-crisis reforms, December 2017 Revisions to the securitisation framework, July 2016 The Net Stable Funding Ratio, October 2014 The Liquidity Coverage Ratio and liquidity risk monitoring tools, January 2013 A global regulatory framework for more resilient banks and banking systems, revised version, June 2011 • International Convergence of Capital Measurement and Capital Standards, A Revised Framework Comprehensive Version, June 2006 • An Explanatory Note on the Basel II IRB Risk Weight Functions, July 2005 Examples of Specifications by the Swiss Financial Market Supervisory Authority FINMA: • Rundschreiben 2019/1 Risikoverteilung – Banken, December 2017 • Rundschreiben 2017/7 Kreditrisiken – Banken, December 2016 • Rundschreiben 2008/20 Marktrisiken Banken, September 2013 Technical Books: • Modelling, Pricing, and Hedging Counterparty Credit Exposure, Giovanni Cesari et al., 2010 © Springer Nature Switzerland AG 2020 J. Wernz, Bank Management and Control, Management for Professionals, https://doi.org/10.1007/978-3-030-42866-2

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• • • •

Bibliography

Maritime Economics, Martin Stopford, 2009 Options, Futures, and other Derivatives, John C. Hull, 2008 Option Pricing Formulas, Espen Gaarder Haug, 2007 Volatility and Correlation, Riccardo Rebonato, 2005

Some History: • The Big Short, Michael Lewis, 2010 • Lords of Finance, Liaquat Ahamed, 2009 Papers: • The Federal Reserve’s Balance Sheet and Earnings, Federal Reserve Board, Washington, D.C., Seth B. Carpenter et al., 2013 • Bank of England: Consultation Paper, CP4/13, Credit Risk: Internal Ratings Based Approaches, March 2013 • IMF: A new look at the role of sovereign credit default swaps, 2013 • Asset correlation, realized default correlation, and portfolio credit risk, Moody’s KMV, 2008 • Asset correlations and credit portfolio risk—an empirical analysis, Klaus Düllmann, Martin Scheicher, Christian Schmieder, 2007 • Granularity adjustment for Basel II, Michael B. Gordy, Eva Lütkebohmert, 2007 • Working paper, Institute of Economic Studies in Prague, Jakubik, 2006 • Auswirkungen unterschiedlicher Assetkorrelationen in Mehr-SektorenKreditportfoliomodellen, Alfred Hamerle, Michael Knapp, Nicole Wildenauer, 2005 • A comparative analysis, Journal of Banking & Finance, Dietsch and Petey, 2004 • Benchmark asset correlations, Risk, Hamerle, 2003 • Loan portfolio value, Risk, Oldrich Alfons Vasicek, 2002 • Copulas and credit models, Frey et al., 2001 • A comparative anatomy of credit risk models, Journal of Banking & Finance, Gordy, 2000 • Asset correlations, Moody’s Investor Service, Cespedes, 2000 Pages: • • • • • • • •

Schweizerische Nationalbank, Swiss National Bank (SNB), snb.ch/en Eidgenössische Finanzmarktaufsicht FINMA, finma.ch Bundesamt für Statistik, BfS, bfs.admin.ch/bfs/en/home.html Clarksons, clarksons.com Deutsche Bundesbank, bundesbank.de Statistisches Bundesamt, destatis.de UK House Price Index, landregistry.data.gov.uk/app/ukhpi Department of the Environment, Community and Local Government, environ.ie

Others: • ORX, managingrisktogether.orx.org

Glossary

Basel Accords Terms like “Basel,” the “Basel Rules,” and the “Basel Accord” are used synonymously in this book. The basic idea since Basel II is that banks quantify their risks more precisely and then determine the required capital. According to Basel II and Basel III the required capital should correspond to the risk. The idea is that the equity in most cases (usually there are “999 of 1000” cases) should be sufficient to protect the bank from an insolvency in the event of a crisis. With Basel III (and already with Basel II) risks that were not taken into account before became relevant. Operational Risk (OpRisk) for example has been classified as critical under Basel II and must be taken into account since the implementation of Basel II. Basel II and Basel III consist of three pillars (see Pillar 1, 2, and 3). CDO Collateralized Debt Obligations are a type of structured asset-backed security (ABS) with multiple “tranches.” Each tranche offers a varying degree of risk and return so as to meet investors’ demands. CDOs are split into different risk classes, or tranches, whereby “senior” tranches bear less risk and offer less return than “junior” tranches. Interest and principal payments are provided in the order of seniority. Junior tranches offer higher coupon payments—to compensate for additional default risk. CDS A Credit Default Swap is a financial swap agreement whereby the seller of the CDS (“insurance provider”) will compensate the buyer (“the insuree”) in the event of a loan default or other credit event. The buyer of the CDS makes a series of payments (the CDS “fee” or “spread”) to the seller and, in exchange, receives a payoff if the loan defaults. Creditworthiness The ability of a customer to pay back his debts. The assigned measure is the Probability of Default (PD). CRM The Comprehensive Risk Measure is used for the calculation of the capital charge for correlation-trading portfolios. Default A default or credit event occurs when a person or organization defaults on a significant transaction. Within the Basel Accords definitions of a default are provided. If one of these definitions is fulfilled, a bank has to treat the customer © Springer Nature Switzerland AG 2020 J. Wernz, Bank Management and Control, Management for Professionals, https://doi.org/10.1007/978-3-030-42866-2

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as a defaulter. The marketplace recognizes default events as related to one’s creditworthiness; credit events can trigger specific protections provided by credit derivatives (e.g., credit default swap). The events triggering a credit derivative are defined in a bilateral swap confirmation, which is a transactional document that typically refers to an International Swaps and Derivatives Association (ISDA) master agreement previously executed between the two swap counterparties. Expected Shortfall The Expected Shortfall (ES) in financial mathematics and financial risk management is a widely used measure for the risk of loss on a specific portfolio of financial assets. For example: ES(99%) ¼ 13 mn USD means that in the 1% “worst cases” [1% worst days in trading (Market Risk), 1% worst years for OpRisk etc.] an average (expected) loss of 13 mn results. The Expected Shortfall is also referred to as conditional value at risk (CVaR), average value at risk (AVaR), or expected tail loss (ETL). IRC The measure Incremental Risk Charge is meant to cover the default and the migration risk of interest positions within the trading book. The measure is calculated for a 1-year time horizon at a confidence level of 99.9%. LGD Loss Given Default is an important parameter for pricing (loans) and for the calculation of the Credit Risk related regulatory capital under Basel III. The LGD is the percentage of a defaulted exposure that is finally lost (after recoveries). Main ingredient for determining the LGD is the value of the security (or the securities) that the bank holds for providing the loan. Monte Carlo Simulation Monte Carlo Simulations are a broad class of computational algorithms that rely on repeated random sampling to obtain numerical results; i.e., by running simulations many times over in order to calculate those same probabilities heuristically just like actually playing and recording results in a real casino situation: hence the name. Monte Carlo Simulations are often used in finance (pricing and exposure calculations in Market Risk, exposure calculations in Operational Risk etc.). PD The Probability of Default is a financial term describing the likelihood of a default over a particular time horizon. It provides an estimate of the likelihood that a customer of a financial institution will be unable to meet the debt obligations. The PD is a key parameter for pricing (loans) and for the calculation of Credit Risk related regulatory capital under Basel III. Pillar 1, 2, and 3 Basel III consists of three Pillars. Pillar 1 The first pillar of the Basel Accord defines how much capital the major risks require. The major risks according to Basel are Credit Risk, Market Risk, and Operational Risk. Pillar 2 The second pillar of the Basel Accord stresses the need for adequate internal assessment of the overall risks a bank faces. In addition to the risks covered within the first pillar, other risks like pension risk or goodwill risk must be covered in the second pillar. Pillar 3 The third pillar of the Basel Accord recommends a holistic reporting of the risk and capital structure of the bank.

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Quantiles Quantiles are points taken at regular intervals from the cumulative distribution function (CDF) of a random variable. A Quantile of 99%—reflecting a probability level of 99%—covers 99% of the possible outcomes of a statistical “experiment.” The formulas for the derivation of capital within Basel III are mostly implemented at a quantile of 99.9%, reflecting the Basel philosophy that banks should not go bankrupt in 999 out of 1000 years. Risk-Weighted Asset The Risk-Weighted Assets are the bank’s exposure, weighted according to risk. This asset calculation is used in determining the capital requirement under Basel III. Securitization Securitization is the financial practice of pooling various types of contractual debt such as residential mortgages, commercial mortgages, auto loans or credit card debt obligations into collateralized mortgage obligation (CMOs) and collateralized debt obligation (CDOs) and pass the tranches of these to various investors. Securities backed by mortgage receivables are called mortgage-backed securities (MBS), while those backed by other types of receivables are asset-backed securities (ABS). Solvency II The Solvency II Directive is an EU Directive that codifies and harmonizes the EU insurance regulation. Solvency II defines the amount of capital that insurance companies (in the EU) must hold to reduce the risk of insolvency. Swiss Solvency Test The Swiss Solvency Test is the Swiss equivalent to Solvency II. VaR The Value at Risk (VaR) in financial mathematics and financial risk management is a widely used measure for the risk of loss on a specific portfolio of financial assets. The quantile is the probability that the loss on the portfolio does not exceed a given dollar amount. For example: VaR(99%) ¼ 10 mn USD means that the loss of 10 mn USD is not exceeded in 99% of the cases.