Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xi
Chapter 1: Value at Risk, Capital Management, and Capital
Allocation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1 An Introduction to Value at Risk . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.2 Capital Management and Capital Allocation: The Structure of
the Book . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
Chapter 2: What Is “Capital” Management? . . . . . . . . . . . . . . . . . . . . . 7
2.1 Regulatory Capital and the Evolution of Basel II . . . . . . . . . . . . . . . . . . . . . 8
2.1.1 The 1988 Basel I Accord and the 1996 Amendment . . . . . . . . . . . . . 8
2.1.2 The Concept of Regulatory Capital . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.2 Overview of the Basel II Capital Accord . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.2.1 Pillar 1: Minimum Capital Requirements — The Main Changes
Introduced by Basel II . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
Box 2-1: Impact of the Basel II Accord on the Level of
Minimum Regulatory Capital Requirements . . . . . . . . . . 12
2.2.2 Pillar 2: Supervisory Review Process . . . . . . . . . . . . . . . . . . . . . . . . 14
. . . . . . . . . . . . 17
2.3.1 Book Value of Capital and the Impact of IAS/IFRS . . . . . . . . . . . . . 17
2.3.2 Market Capitalization and the Double Perspective of Bank
Managers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.3.3 The Impact of Alternative Notions of Capital on Capital
Management and Allocation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

vi CONTENTS
2.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
2.5 Further Reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
Chapter 3: Market Risk . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
3.1 The Variance–Covariance Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
3.1.1 A Simplifi ed Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
3.1.2 The Choice of the Relevant Random Variables . . . . . . . . . . . . . . . . . 29
3.1.3 Mapping Exposures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
3.1.8 Implied Volatilities and Correlations . . . . . . . . . . . . . . . . . . . . . . . . . 44
Box 3-4: Deriving Implied Volatility from Option Prices . . . . . . . 45
3.2 Simulation Approaches: Historical Simulation and Monte Carlo
Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
3.2.1 Historical Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
3.2.2 Hybrid Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
3.2.3 Monte Carlo Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

3.6 Back-Testing Market Risk Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
3.6.1 Which Series Should Be Considered? Actual versus Theoretical
Portfolio Returns . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
3.6.2 Back-Testing VaR Forecasts: Unconditional Accuracy and
Independence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
3.7 Internal VaR Models and Market Risk Capital Requirements . . . . . . . . . . . 62
3.8 Stress Testing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
3.9 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
3.10 Further Reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
Chapter 4: Credit Risk . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
4.1 Defi ning Credit Risk: Expected and Unexpected Losses . . . . . . . . . . . . . . . 67
4.2 Agency Ratings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
4.2.1 External Rating Assignment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
4.2.2 Transition Matrixes and Cumulative and Marginal Default


.................................................


5.4.2 Integrating Internal Severity Data with External Data and
Scenario Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127
5.4.3 Estimating Operational Loss Frequency . . . . . . . . . . . . . . . . . . . . . . 128
5.4.4 Estimating Correlation or Dependence among Operational

Regulation, and Credit Department, Federal Reserve Bank of Boston) . . . 131
5.6 The Role of Measures of Business Risk and Earnings at Risk . . . . . . . . . . 134
5.7 Measuring Business Risk in Practice: Defi ning a Measure of Earnings
at Risk . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137
5.8 From Earnings at Risk to Capital at Risk . . . . . . . . . . . . . . . . . . . . . . . . . . . 139
5.9 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142
5.10 Further Reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143
Chapter 6: Risk Capital Aggregation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145
6.1 The Need for Harmonization: Time Horizon, Confi dence Level, and the
Notion of Capital . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146
6.2 Risk Aggregation Techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148
6.2.1 Choosing the Components to Be Aggregated: Business Units
versus Risk Types . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149

Chapter 7: Value at Risk and Risk Control for Market and
Credit Risk . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169
7.1 Defi ning VaR-Based Limits for Market Risk: Identifying Risk-Taking
Centers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171
Box 7-1: Clarifying VaR Measurement Limitations: Deutsche
Bank’s Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172
7.2 Managing VaR Limits for Market Risk: The Links between Daily VaR
and Annual Potential Losses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173

..........................

Chapter 9: Risk-Adjusted Performance Targets, Capital
Allocation, and the Budgeting Process . . . . . . . . . . . . . . . . . . . . . . . . . . . . 217
9.1 From the Bank’s Cost of Equity Capital to Performance Targets
for the Bank . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 218
9.1.1 Estimating the Cost of Equity Capital . . . . . . . . . . . . . . . . . . . . . . . . 218
9.1.2 Defi ning the Target Rate of Return . . . . . . . . . . . . . . . . . . . . . . . . . . 219
9.2 Should Business Units’ Target Returns Be Different? . . . . . . . . . . . . . . . . . 222
9.2.1 Potential Effects of a Single Hurdle Rate . . . . . . . . . . . . . . . . . . . . . 223
9.2.2 Estimating Betas for Different Businesses . . . . . . . . . . . . . . . . . . . . 224
9.2.3 Applying Different Costs of Capital: Identifying the Driver . . . . . . 226

9.4.2 Setting of Value-Creation and Capital Allocation Targets within
Planning and Control Processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 231
9.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 233
9.6 Further Reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 234
Final Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 237
Selected Free Risk Management–Related Websites . . . . . . . . . . . . . . . . . . . 239
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 245
Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 255
Probabilities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71