CONTENTS
Preface = xxi
Part One. MOTIVATION = 1
Chapter 1. The Need for Risk Management = 3
1.1 Financial Risks = 3
1.1.1 Change : The Only Constant = 4
1.1.2 But Where Is Risk Coming From? = 7
1.1.3 The Toolbox of Risk Management = 10
1.2 Derivatives and Risk Management = 11
1.2.1 What Are Derivatives? = 11
1.2.2 Types of Derivatives = 12
1.2.3 Derivatives Markets : How Big? = 12
1.3 Types of Financial Risks = 15
1.3.1 Market Risk = 15
1.3.2 Credit Risk = 16
1.3.3 Liquidity Risk = 17
1.3.4 Operational Risk = 18
1.3.5 Legal Risk = 20
1.3.6 Integrated Risk Measurement = 21
1.4 In Brief, What Is VAR? = 21
1.4.1 Definition of VAR = 22
1.4.2 Illustration of VAR = 22
1.5 VAR and the Evolution of Risk Management = 25
Chapter 2. Lessons from Financial Disasters = 31
2.1 Lessons from Recent Losses = 32
2.1.1 Losses Attributed to Derivatives = 33
2.1.2 Perspective on Financial Losses = 34
2.2 Case Studies in Risk = 36
2.2.1 Barings's Fall : A Lesson in Risk = 36
2.2.2 Metallgesellschaft = 38
2.2.3 Orange County = 40
2.2.4 Daiwa's Lost Billion = 41
2.2.5 Lessons from Case Studies = 42
2.3 Private-Sector Responses = 43
2.3.1 G-30 Report = 43
2.3.2 Derivatives Policy Group = 43
2.3.3 J.P. Morgan's RiskMetrics = 44
2.3.4 Global Association of Risk Professionals(GARP) = 45
2.4 The View of Regulators = 45
2.4.1 General Accounting Office(GAO) = 46
2.4.2 Financial Accounting Standards Board(FASB) = 46
2.4.3 Securities and Exchange Commission(SEC) = 47
2.5 Conclusions = 49
Chapter 3. Regulatory Capital Standards with VAR = 51
3.1 Why Regulation? = 52
3.2 The 1988 Basel Accord = 55
3.2.1 The Cooke Ratio = 55
3.2.2 Activity Restrictions = 57
3.2.3 Criticisms of the 1988 Approach = 57
3.3 The 1996 Amendment on Market Risks = 60
3.3.1 The Standardized Method = 61
3.3.2 The Internal Models Approach = 63
3.3.3 The Precommitment Model = 65
3.3.4 Comparison of Approaches = 66
3.3.5 Example = 68
3.4 The 1999 Credit Risk Revisions = 68
3.4.1 The Revisions = 70
3.4.2 Overall Assessment = 70
3.5 Regulation of Nonbanks = 72
3.5.1 Securities Firms = 72
3.5.2 Insurance Companies = 74
3.5.3 Pension Funds = 75
3.6 Conclusions = 75
Part Two. BUILDING BLOCKS = 79
Chapter 4. Measuring Financial Risk = 81
4.1 Market Risks = 82
4.2 Probability Distribution Functions = 86
4.2.1 A Gambler's Experiment = 86
4.2.2 Properties of Expectations = 89
4.2.3 The Normal Distribution = 91
4.2.4 Other Distributions = 93
4.3 Risk = 95
4.3.1 Risk as Dispersion = 95
4.3.2 Quantiles = 95
4.4 Asset Returns = 98
4.4.1 Measuring Returns = 98
4.4.2 Sample Estimates = 101
4.5 Time Aggregation = 102
4.5.1 Aggregation with I.I.D. Returns = 102
4.5.2 Aggregation with Correlated Returns = 104
4.5.3 The Effect of the Mean at Various Horizons = 105
Chapter 5. Computing Value at Risk = 107
5.1 Computing VAR = 108
5.1.1 Steps in Constructing VAR = 108
5.1.2 VAR for General Distributions = 109
5.1.3 VAR for Parametric Distributions = 110
5.1.4 Comparison of Approaches = 113
5.1.5 VAR as a Risk Measure = 114
5.2 Choice of Quantitative Factors = 116
5.2.1 VAR as a Benchmark Measure = 116
5.2.2 VAR as a Potential Loss Measure = 117
5.2.3 VAR as Equity Capital = 117
5.2.4 Criteria for Backtesting = 119
5.2.5 Application : The Basel 1Parameters = 119
5.2.6 Conversion of VAR Parameters = 121
5.3 Assessing VAR Precision = 122
5.3.1 The Problem of Measurement Errors = 122
5.3.2 Estimation Errors in Means and Variances = 123
5.3.3 Estimation Error in Sample Quantiles = 125
5.3.4 Comparison of Methods = 126
5.4 Conclusions = 128
Chapter 6. Backtesting VAR Models = 129
6.1 Setup for Backtesting = 130
6.1.1 An Example = 130
6.1.2 Which Return? = 131
6.2 Model Backtesting with Exceptions = 132
6.2.1 Model Verification Based on Failure Rates = 132
6.2.2 The Basel Rules = 136
6.2.3 Conditional Coverage Models = 140
6.3 Model Verification : Other Approaches = 142
6.3.1 Distribution Forecast Models = 142
6.3.2 Parametric Models = 143
6.3.3 Comparison of Methods = 144
6.4 Conclusions = 145
Chapter 7. Portfolio Risk : Analytical Methods = 147
7.1 Portfolio VAR = 148
7.2 VAR Tools = 153
7.2.1 Marginal VAR = 154
7.2.2 Incremental VAR = 155
7.2.3 Component VAR = 159
7.2.4 Summary = 161
7.3 Examples = 162
7.3.1 A Global Portfolio Equity Report = 163
7.3.2 Barings : An Example in Risks = 165
7.4 Simplifying the Covariance Matrix = 167
7.4.1 Why Simplifications? = 167
7.4.2 Zero VAR Measures = 168
7.4.3 Diagonal Model = 169
7.4.4 Factor Models = 171
7.4.5 Comparison of Methods = 175
7.5 Conclusions = 177
Appendix 7A : Matrix Multiplication = 178
Appendix 7B(Advanced) : Principal-Component Analysis = 179
Chapter 8. Forecasting Risks and Correlations = 183
8.1 Time-varying Risk or Outliers? = 184
8.2 Modeling Time-Varying Risk = 186
8.2.1 Moving Averages = 186
8.2.2 GARCH Estimation = 187
8.2.3 Long-Horizon Forecasts with GARCH = 189
8.2.4 The RiskMetrics Approach = 193
8.3 Modeling Correlation = 196
8.3.1 Moving Averages = 196
8.3.2 Exponential Averages = 197
8.3.3 Crashes and Correlations = 198
8.4 Using Options Data = 199
8.4.1 Implied Volatilities = 200
8.4.2 ISD as Risk Forecasts = 200
8.5 Conclusions = 202
Part Three. VALUE-AT-RISK SYSTEMS = 203
Chapter 9. VAR Methods = 205
9.1 Local versus Full Valuation = 206
9.1.1 Delta-Normal Valuation = 206
9.1.2 Full Valuation = 209
9.1.3 Delta-Gamma Approximations(the "Greeks") = 211
9.1.4 Comparison of Methods = 214
9.1.5 An Example : Leeson's Straddle = 215
9.2 Delta-Normal Method = 219
9.2.1 Implementation = 219
9.2.2 Advantages = 220
9.2.3 Problems = 220
9.3 Historical Simulation Method = 221
9.3.1 Implementation = 221
9.3.2 Advantages = 222
9.3.3 Problems = 223
9.4 Monte Carlo Simulation Method = 224
9.4.1 Implementation = 224
9.4.2 Advantages = 225
9.4.3 Problems = 226
9.5 Empirical Comparisons = 227
9.6 Summary = 229
Chapter 10. Stress Testing = 231
10.1 Why Stress Testing? = 232
10.2 Implementing Scenario Analysis = 235
10.3 Generating Unidimensional Scenarios = 235
10.3.1 Stylized Scenarios = 235
10.3.2 An Example : The SPAN System = 237
10.4 Multidimensional Scenario Analysis = 239
10.4.1 Unidimensional versus Multidimensional = 239
10.4.2 Prospective Scenarios = 239
10.4.3 Factor Push Method = 240
10.4.4 Conditional Scenario Method = 240
10.4.5 Historical Scenarios = 242
10.4.6 Systematic Scenarios = 245
10.5 Stress-Testing Model Parameters = 245
10.6 Managing Stress Tests = 247
10.6.1 Scenario Analysis and Risk Models = 247
10.6.2 Management Response = 247
10.7 Conclusions = 248
Appendix : Extreme Value Theory = 249
Chapter 11. Implementing Delta-Normal VAR = 255
11.1 Overview = 256
11.2 Application to Currencies = 257
11.3 Choosing "Primitive" Securities = 259
11.3.1 Lessons from Exchanges = 262
11.3.2 Specific Risk = 263
11.4 Fixed-Income Portfolios = 264
11.4.1 Mapping Approaches = 264
11.4.2 Risk Factors = 264
11.4.3 Comparison of Mapping Approaches = 266
11.4.4 Assigning Weights to Vertices = 269
11.4.5 Benchmarking a Portfolio = 271
11.5 Linear Derivatives = 274
11.5.1 Forward Contracts = 274
11.5.2 Commodity Forwards = 278
11.5.3 Forward Rate Agreements = 279
11.5.4 Interest Rate Swaps = 282
11.6 Derivatives : Options = 285
11.7 Equity Portfolios = 287
Chapter 12. Simulation Methods = 291
12.1 Simulations with One Random Variable = 292
12.1.1 Simulating a Price Path = 292
12.1.2 Creating Random Numbers = 295
12.1.3 The Bootstrap = 296
12.1.4 Computing VAR = 298
12.1.5 Risk Management and Pricing Methods = 298
12.2 Speed versus Accuracy = 299
12.2.1 Accuracy = 300
12.2.2 Acceleration Methods = 301
12.3 Simulations with Multiple Variables = 302
12.3.1 From Independent to Correlated Variables = 302
12.3.2 The Cholesky Factorization = 303
12.3.3 Number of Independent Factors = 304
12.4 Deterministic Simulation = 306
12.5 Scenario Simulation = 307
12.6 Choosing the Model = 309
12.7 Conclusions = 311
Chapter 13. Credit Risk = 313
13.1 The Nature of Credit Risk = 314
13.1.1 Sources of Risk = 314
13.1.2 Credit Risk as a Short Option = 316
13.1.3 Time and Portfolio Effects = 316
13.2 Default Risk = 318
13.2.1 Default Rates = 318
13.2.2 Recovery Rates = 321
13.2.3 Estimating Default Risk = 321
13.3 Credit Exposure = 323
13.3.1 Bonds versus Derivatives = 323
13.3.2 Expected and Worst Exposure = 325
13.4 Netting Arrangements = 327
13.5 Measuring and Managing Credit Risk = 329
13.5.1 Expected and Unexpected Credit Loss = 329
13.5.2 Pricing Credit Risk = 330
13.5.3 Portfolio Credit Risk = 332
13.5.4 Managing Credit Risk = 333
13.5.5 Horizon and Confidence Level = 334
13.6 The Basel Risk Charges for Derivatives = 334
13.7 Portfolio Credit Risk Models = 336
13.8 Conclusions = 337
Chapter 14. Liquidity Risk = 339
14.1 Defining Liquidity Risk = 340
14.1.1 Asset Liquidity Risk = 340
14.1.2 Funding Liquidity Risk = 342
14.2 Dealing with Asset Liquidity Risk = 343
14.2.1 Bid-Ask Spread Cost = 344
14.2.2 Trading Strategies = 346
14.2.3 Practical Issues = 349
14.3 Gauging Funding Liquidity Risk = 351
14.4 Lessons from LTCM = 352
14.4.1 LTCM's Leverage = 353
14.4.2 LTCM's "Bulletproofing" = 353
14.4.3 LTCM's Downfall = 354
14.4.4 LTCM's Liquidity = 355
14.5 Conclusions = 357
Part Four. APPLICATIONS OF RISK-MANAGEMENT SYSTEMS = 359
Chapter 15. Using VAR to Measure and Control Risk = 361
15.1 Who Can Use VAR? = 363
15.1.1 The Trend to Global Risk Management = 363
15.1.2 Proprietary Trading Desks = 365
15.1.3 Nonfinancial Corporations = 366
15.2 VAR as an Information-Reporting Tool = 370
15.2.1 Why Risk-Management Disclosures? = 371
15.2.2 Trends in Disclosure = 373
15.2.3 Disclosure Examples = 375
15.3 VAR as a Risk-Control Tool = 376
15.3.1 Adjusting Firm-Wide VAR = 377
15.3.2 Adjusting Unit-Level VAR = 379
15.4 Conclusions = 381
Chapter 16. Using VAR for Active Risk Management = 383
16.1 Risk Capital = 384
16.1.1 VAR as Risk Capital = 384
16.1.2 Choosing the Confidence Level = 385
16.2 Risk-Adjusted Performance Measurement = 387
16.3 Earnings-Based RAPM Methods = 389
16.4 VAR-Based RAPM Methods = 391
16.5 Firm-Wide Performance Measurement = 394
16.6 VAR as a Strategic Tool = 398
16.6.1 Shareholder Value Analysis = 398
16.6.2 Choosing the Discount Rate = 400
16.6.3 Implementing SVA = 401
16.7 Conclusions = 402
Appendix : A Closer Look at Economic Capital = 403
Chapter 17. VAR in Investment Management = 407
17.1 Is VAR Applicable to Investment Management? = 408
17.2 What Are the Risks? = 410
17.2.1 Absolute and Relative Risks = 411
17.2.2 Policy Mix and Active Management Risk = 411
17.2.3 Funding Risk = 413
17.2.4 Sponsor Risk = 414
17.3 Using VAR to Monitor and Control Risks = 415
17.3.1 Using VAR to Check Compliance = 416
17.3.2 Using VAR to Design Guidelines = 417
17.3.3 Using VAR to Monitor Risk = 418
17.3.4 The Role of the Global Custodian = 419
17.3.5 The Role of the Money Manager = 420
17.4 Using VAR to Manage Risks = 420
17.4.1 Strategic Asset Allocation = 420
17.4.2 VAR as a Guide to Investment Decisions = 422
17.4.3 VAR for Risk-Adjusted Returns = 424
17.4.4 Risk Budgeting = 425
17.5 The Risk Standards = 426
17.6 Conclusions = 428
Chapter 18. The Technology of Risk = 431
18.1 Systems = 432
18.2 The Need for Integration = 434
18.3 The Risk-Management Industry = 438
18.4 How to Structure VAR Reports = 442
18.5 An Application = 443
18.6 Conclusions = 445
Chapter 19. Operational Risk Management = 447
19.1 The Importance of Operational Risk = 448
19.2 Defining Operational Risk = 449
19.3Approaches to Operational Risk = 451
19.4 Measuring Operational Risk = 452
19.4.1 Top-Down versus Bottom-Up Approaches = 453
19.4.2 Loss Distributions = 453
19.4.3 The Data Challenge = 457
19.5 Managing Operational Risk = 459
19.5.1 Expected versus Unexpected Losses = 460
19.5.2 Controlling Operational Risk = 460
19.5.3 Funding Operational Risk = 461
19.6 Conclusions = 462
Appendix : Constructing Loss Distributions = 463
Chapter 20. Integrated Risk Management = 467
20.1 The Galaxy of Risks = 468
20.2 Event Risks = 469
20.2.1 Legal Risk = 469
20.2.2 Reputational Risk = 470
20.2.3 Disaster Risk = 470
20.2.4 Regulatory and Political Risk = 470
20.3 Integrated Risk Management = 472
20.3.1 Measuring Firm-Wide Risk = 472
20.3.2 Controlling Firm-Wide Risk = 473
20.3.3 Managing Firm-Wide Risk : The Final Frontier = 474
20.4 Why Risk Management? = 475
20.4.1 Why Bother? = 475
20.4.2 Why Hedge? = 477
20.5 Conclusions = 478
Part Five. THE RISK-MANAGEMENT PROFESSION = 481
Chapter 21. Risk Management : Guidelines and Pitfalls = 483
21.1 Milestone Documents in Risk Management = 484
21.1.1 "Best Practices" Recommendations from G-30 = 484
21.1.2 The Bank of England Report on Barings = 486
21.1.3 The CRMPG Report on LTCM = 486
21.2 Limitations of VAR = 488
21.2.1 Risk of Exceedences = 488
21.2.2 Changing Positions Risks = 488
21.2.3 Event and Stability Risks = 489
21.2.4 Transition Risk = 491
21.2.5 Data-Inadequacy Risks = 492
21.2.6 Model Risks = 492
21.3 Side Effects of VAR = 498
21.3.1 The "Man in the White Coat" Syndrome = 498
21.3.2 Traders Gaming the System = 499
21.3.3 Dynamic Hedging = 502
21.4 Risk-Management Lessons from LTCM = 503
21.4.1 LTCM's Risk Controls = 503
21.4.2 Portfolio Optimization = 504
21.4.3 LTCM's Short Option Position = 507
21.5 Conclusions = 508
Chapter 22. Conclusions = 511
22.1 The Evolution of Risk Management = 512
22.2 The Role of the Risk Manager = 513
22.2.1 Controlling Trading = 513
22.2.2 Organizational Guidelines = 514
22.2.3 Risk Managers = 516
REFERENCES = 521
INDEX = 531
