Risk Management and Financial Institutions

Business Snapshots xvii Preface xix CHAPTER 1 Introduction 1 1.1 Risk vs. Return for Investors 2 1.2 The Efficient Frontier 5 1.3 The Capital Asset Pricing Model 8 1.4 Arbitrage Pricing Theory 13 1.5 Risk vs. Return for Companies 13 1.6 Risk Management by Financial Institutions 16 1.7 Credit Ratings 18 Summary 18 Further Reading 19 Practice Questions and Problems 19 Further Questions 20 CHAPTER 2 Banks 21 2.1 Commercial Banking 22 2.2 The Capital Requirements of a Small Commercial Bank 24 2.3 Deposit Insurance 26 2.4 Investment Banking 27 2.5 Securities Trading 32 2.6 Potential Conflicts of Interest in Banking 33 2.7 Today's Large Banks 34 2.8 The Risks Facing Banks 37 Summary 38 Further Reading 38 Practice Questions and Problems 38 Further Questions 39 CHAPTER 3 Insurance Companies and Pension Plans 41 3.1 Life Insurance 41 3.2 Annuity Contracts 45 3.3 Mortality Tables 46 3.4 Longevity and Mortality Risk 50 3.5 Property-Casualty Insurance 51 3.6 Health Insurance 53 3.7 Moral Hazard and Adverse Selection 55 3.8 Reinsurance 56 3.9 Capital Requirements 56 3.10 The Risks Facing Insurance Companies 58 3.11 Regulation 58 3.12 Pension Plans 59 Summary 62 Further Reading 64 Practice Questions and Problems 64 Further Questions 65 CHAPTER 4 Mutual Funds and Hedge Funds 67 4.1 Mutual Funds 67 4.2 Hedge Funds 74 4.3 Hedge Fund Strategies 79 4.4 Hedge Fund Performance 83 Summary 84 Further Reading 85 Practice Questions and Problems 85 Further Questions 86 CHAPTER 5 Trading in Financial Markets 89 5.1 The Markets 89 5.2 Long and Short Positions in Assets 90 5.3 Derivatives Markets 92 5.4 Plain Vanilla Derivatives 93 5.5 Clearing Houses 103 5.6 Margin 104 5.7 Non-Traditional Derivatives 107 5.8 Exotic Options and Structured Products 111 5.9 Risk Management Challenges 114 Summary 115 Further Reading 115 Practice Questions and Problems 116 Further Questions 118 CHAPTER 6 The Credit Crisis of 2007 121 6.1 The U.S. Housing Market 121 6.2 Securitization 124 6.3 The Crisis 131 6.4 What Went Wrong? 131 6.5 Lessons from the Crisis 133 Summary 134 Further Reading 135 Practice Questions and Problems 136 Further Questions 136 CHAPTER 7 How Traders Manage Their Risks 137 7.1 Delta 137 7.2 Gamma 144 7.3 Vega 146 7.4 Theta 148 7.5 Rho 149 7.6 Calculating Greek Letters 150 7.7 Taylor Series Expansions 151 7.8 The Realities of Hedging 152 7.9 Hedging Exotic Options 153 7.10 Scenario Analysis 154 Summary 156 Further Reading 156 Practice Questions and Problems 156 Further Questions 157 CHAPTER 8 Interest Rate Risk 159 8.1 The Management of Net Interest Income 159 8.2 LIBOR and Swap Rates 162 8.3 Duration 164 8.4 Convexity 168 8.5 Generalization 169 8.6 Nonparallel Yield Curve Shifts 172 8.7 Interest Rate Deltas in Practice 174 8.8 Principal Components Analysis 176 8.9 Gamma and Vega 179 Summary 179 Further Reading 180 Practice Questions and Problems 181 Further Questions 181 CHAPTER 9 Value at Risk 183 9.1 Definition of VaR 183 9.2 Examples of the Calculation of VaR 185 9.3 VaR vs. Expected Shortfall 186 9.4 VaR and Capital 188 9.5 Coherent Risk Measures 190 9.6 Choice of Parameters for VaR 191 9.7 Marginal VaR, Incremental VaR, and Component VaR 195 9.8 Euler's Theorem 196 9.9 Aggregating VaRs 197 9.10 Back-Testing 197 Summary 200 Further Reading 201 Practice Questions and Problems 201 Further Questions 202 CHAPTER 10 Volatility 205 10.1 Definition of Volatility 205 10.2 Implied Volatilities 208 10.3 Are Daily Percentage Changes in Financial Variables Normal? 209 10.4 The Power Law 211 10.5 Monitoring Daily Volatility 213 10.6 The Exponentially Weighted Moving Average Model 216 10.7 The GARCH(1,1) Model 218 10.8 Choosing Between the Models 220 10.9 Maximum Likelihood Methods 220 10.10 Using GARCH(1,1) to Forecast Future Volatility 225 Summary 229 Further Reading 229 Practice Questions and Problems 230 Further Questions 231 CHAPTER 11 Correlations and Copulas 233 11.1 Definition of Correlation 233 11.2 Monitoring Correlation 235 11.3 Multivariate Normal Distributions 238 11.4 Copulas 240 11.5 Application to Loan Portfolios: Vasicek's Model 246 Summary 252 Further Reading 253 Practice Questions and Problems 253 Further Questions 254 CHAPTER 12 Basel I, Basel II, and Solvency II 257 12.1 The Reasons for Regulating Banks 257 12.2 Bank Regulation Pre-1988 258 12.3 The 1988 BIS Accord 259 12.4 The G-30 Policy Recommendations 262 12.5 Netting 263 12.6 The 1996 Amendment 265 12.7 Basel II 268 12.8 Credit Risk Capital Under Basel II 269 12.9 Operational Risk Capital Under Basel II 277 12.10 Pillar 2: Supervisory Review 278 12.11 Pillar 3: Market Discipline 278 12.12 Solvency II 279 Summary 280 Further Reading 281 Practice Questions and Problems 281 Further Questions 283 CHAPTER 13 Basel 2.5, Basel III, and Dodd-Frank 285 13.1 Basel 2.5 285 13.2 Basel III 289 13.3 Contingent Convertible Bonds 295 13.4 Dodd-Frank Act 296 13.5 Legislation in Other Countries 298 Summary 299 Further Reading 300 Practice Questions and Problems 300 Further Questions 301 CHAPTER 14 Market Risk VaR: The Historical Simulation Approach 303 14.1 The Methodology 303 14.2 Accuracy 308 14.3 Extensions 309 14.4 Computational Issues 313 14.5 Extreme Value Theory 314 14.6 Applications of EVT 317 Summary 319 Further Reading 320 Practice Questions and Problems 320 Further Questions 321 CHAPTER 15 Market Risk VaR: The Model-Building Approach 323 15.1 The Basic Methodology 323 15.2 Generalization 326 15.3 Correlation and Covariance Matrices 327 15.4 Handling Interest Rates 330 15.5 Applications of the Linear Model 334 15.6 Linear Model and Options 335 15.7 Quadratic Model 338 15.8 Monte Carlo Simulation 340 15.9 Non-Normal Assumptions 341 15.10 Model-Building vs. Historical Simulation 342 Summary 343 Further Reading 343 Practice Questions and Problems 343 Further Questions 345 CHAPTER 16 Credit Risk: Estimating Default Probabilities 347 16.1 Credit Ratings 347 16.2 Historical Default Probabilities 349 16.3 Recovery Rates 351 16.4 Credit Default Swaps 352 16.5 Credit Spreads 357 16.6 Estimating Default Probabilities from Credit Spreads 360 16.7 Comparison of Default Probability Estimates 362 16.8 Using Equity Prices to Estimate Default Probabilities 367 Summary 370 Further Reading 371 Practice Questions and Problems 371 Further Questions 373 CHAPTER 17 Counterparty Credit Risk in Derivatives 375 17.1 Credit Exposure on Derivatives 375 17.2 Bilateral Clearing 376 17.3 Central Clearing 380 17.4 CVA 382 17.5 The Impact of a New Transaction 385 17.6 CVA Risk 387 17.7 Wrong Way Risk 388 17.8 DVA 389 17.9 Some Simple Examples 389 Summary 394 Further Reading 395 Practice Questions and Problems 395 Further Questions 396 CHAPTER 18 Credit Value at Risk 399 18.1 Ratings Transition Matrices 400 18.2 Vasicek's Model 402 18.3 Credit Risk Plus 403 18.4 CreditMetrics 405 18.5 Credit VaR in the Trading Book 406 Summary 410 Further Reading 410 Practice Questions and Problems 411 Further Questions 411 CHAPTER 19 Scenario Analysis and Stress Testing 413 19.1 Generating the Scenarios 413 19.2 Regulation 419 19.3 What to Do with the Results 423 Summary 426 Further Reading 426 Practice Questions and Problems 427 Further Questions 428 CHAPTER 20 Operational Risk 429 20.1 What is Operational Risk? 430 20.2 Determination of Regulatory Capital 431 20.3 Categorization of Operational Risks 433 20.4 Loss Severity and Loss Frequency 434 20.5 Implementation of AMA 435 20.6 Proactive Approaches 439 20.7 Allocation of Operational Risk Capital 440 20.8 Use of Power Law 441 20.9 Insurance 442 20.10 Sarbanes-Oxley 443 Summary 444 Further Reading 445 Practice Questions and Problems 445 Further Questions 446 CHAPTER 21 Liquidity Risk 447 21.1 Liquidity Trading Risk 447 21.2 Liquidity Funding Risk 454 21.3 Liquidity Black Holes 462 Summary 468 Further Reading 469 Practice Questions and Problems 470 Further Questions 470 CHAPTER 22 Model Risk 473 22.1 Marking to Market 473 22.2 Models for Linear Products 475 22.3 Physics vs. Finance 476 22.4 How Models are Used for Pricing Standard Products 478 22.5 Hedging 484 22.6 Models for Nonstandard Products 485 22.7 Dangers in Model Building 486 22.8 Detecting Model Problems 487 Summary 488 Further Reading 488 Practice Questions and Problems 489 Further Questions 489 CHAPTER 23 Economic Capital and RAROC 491 23.1 Definition of Economic Capital 491 23.2 Components of Economic Capital 493 23.3 Shapes of the Loss Distributions 495 23.4 Relative Importance of Risks 497 23.5 Aggregating Economic Capital 498 23.6 Allocation of Economic Capital 501 23.7 Deutsche Bank's Economic Capital 503 23.8 RAROC 503 Summary 505 Further Reading 506 Practice Questions and Problems 506 Further Questions 507 CHAPTER 24 Risk Management Mistakes to Avoid 509 24.1 Risk Limits 509 24.2 Managing the Trading Room 512 24.3 Liquidity Risk 514 24.4 Lessons for Nonfinancial Corporations 517 24.5 A Final Point 518 Further Reading 519 Appendix A Compounding Frequencies for Interest Rates 521 Appendix B Zero Rates, Forward Rates, and Zero-Coupon Yield Curves 525 Appendix C Valuing Forward and Futures Contracts 529 Appendix D Valuing Swaps 531 Appendix E Valuing European Options 533 Appendix F Valuing American Options 535 Appendix G Taylor Series Expansions 539 Appendix H Eigenvectors and Eigenvalues 543 Appendix I Principal Components Analysis 547 Appendix J Manipulation of Credit Transition Matrices 549 Appendix K Valuation of Credit Default Swaps 551 Appendix L Synthetic CDOs and Their Valuation 555 Answers to Questions and Problems 559 Glossary 595 DerivaGem Software 615 Table for N(x) when x Table for N(x) when x >= 0 623 Index 625