Risk Management and Financial Institutions

TABLE OF CONTENTS
Business Snapshots xxiii

Preface xxv

Chapter 1 Introduction 1

1.1 Risk vs. Return for Investors 2

1.2 The Efficient Frontier 6

1.3 The Capital Asset Pricing Model 8

1.4 Arbitrage Pricing Theory 14

1.5 Risk vs. Return for Companies 14

1.6 Risk Management by Financial Institutions 18

1.7 Credit Ratings 19

Summary 20

Further Reading 20

Practice Questions and Problems (Answers at End of Book) 21

Further Questions 22

Part 1: Financial Institutions and Their Trading 23

Chapter 2 Banks 25

2.1 Commercial Banking 26

2.2 The Capital Requirements of a Small Commercial Bank 28

2.3 Deposit Insurance 30

2.4 Investment Banking 31

2.5 Securities Trading 36

2.6 Potential Conflicts of Interest in Banking 38

2.7 Today’s Large Banks 39

2.8 The Risks Facing Banks 42

Summary 43

Further Reading 43

Practice Questions and Problems (Answers at End of Book) 44

Further Questions 44

Chapter 3 Insurance Companies and Pension Plans 47

3.1 Life Insurance 48

3.2 Annuity Contracts 51

3.3 Mortality Tables 52

3.4 Longevity and Mortality Risk 56

3.5 Property-Casualty Insurance 57

3.6 Health Insurance 60

3.7 Moral Hazard and Adverse Selection 61

3.8 Reinsurance 62

3.9 Capital Requirements 63

3.10 The Risks Facing Insurance Companies 64

3.11 Regulation 64

3.12 Pension Plans 66

Summary 70

Further Reading 71

Practice Questions and Problems (Answers at End of Book) 71

Further Questions 72

Chapter 4 Mutual Funds, ETFs, and Hedge Funds 75

4.1 Mutual Funds 75

4.2 Exchange-Traded Funds 79

4.3 Active vs. Passive Management 80

4.4 Regulation 82

4.5 Hedge Funds 83

4.6 Hedge Fund Strategies 88

4.7 Hedge Fund Performance 93

Summary 94

Further Reading 95

Practice Questions and Problems (Answers at End of Book) 95

Further Questions 96

Chapter 5 Trading in Financial Markets 97

5.1 The Markets 97

5.2 Clearing Houses 98

5.3 Long and Short Positions in Assets 99

5.4 Derivatives Markets 101

5.5 Plain Vanilla Derivatives 102

5.6 Non-Traditional Derivatives 114

5.7 Exotic Options and Structured Products 117

5.8 Risk Management Challenges 118

Summary 120

Further Reading 122

Practice Questions and Problems (Answers at End of Book) 122

Further Questions 125

Chapter 6 The Credit Crisis of 2007–2008 127

6.1 The U.S. Housing Market 128

6.2 Securitization 131

6.3 The Losses 137

6.4 What Went Wrong? 138

6.5 Lessons from the Crisis 140

Summary 141

Further Reading 142

Practice Questions and Problems (Answers at End of Book) 142

Further Questions 143

Chapter 7 Valuation and Scenario Analysis: The Risk-Neutral and Real Worlds 145

7.1 Volatility and Asset Prices 146

7.2 Risk-Neutral Valuation 147

7.3 Scenario Analysis 152

7.4 When Both Worlds Have to Be Used 153

7.5 The Calculations in Practice 154

7.6 Estimating Real-World Processes 155

Summary 156

Further Reading 157

Practice Questions and Problems (Answers at End of Book) 157

Further Questions 158

Part 2: Market Risk 159

Chapter 8 How Traders Manage Their Risks 161

8.1 Delta 161

8.2 Gamma 169

8.3 Vega 171

8.4 Theta 173

8.5 Rho 174

8.6 Calculating Greek Letters 174

8.7 Taylor Series Expansions 175

8.8 The Realities of Hedging 177

8.9 Hedging Exotic Options 178

8.10 Scenario Analysis 180

Summary 181

Further Reading 181

Practice Questions and Problems (Answers at End of Book) 181

Further Questions 182

Chapter 9 Interest Rate Risk 185

9.1 The Management of Net Interest Income 186

9.2 Types of Rates 188

9.3 Duration 193

9.4 Convexity 196

9.5 Generalization 198

9.6 Nonparallel Yield Curve Shifts 200

9.7 Principal Components Analysis 204

9.8 Gamma and Vega 207

Summary 208

Further Reading 209

Practice Questions and Problems (Answers at End of Book) 209

Further Questions 210

Chapter 10 Volatility 213

10.1 Definition of Volatility 213

10.2 Implied Volatilities 215

10.3 Are Daily Percentage Changes in Financial

Variables Normal? 217

10.4 The Power Law 220

10.5 Monitoring Daily Volatility 222

10.6 The Exponentially Weighted Moving Average Model 225

10.7 The GARCH(1,1) Model 227

10.8 Choosing Between the Models 229

10.9 Maximum Likelihood Methods 229

10.10 Using GARCH(1,1) to Forecast Future Volatility 235

Summary 239

Further Reading 239

Practice Questions and Problems (Answers at End of Book) 240

Further Questions 241

Chapter 11 Correlations and Copulas 243

11.1 Definition of Correlation 243

11.2 Monitoring Correlation 245

11.3 Correlation and Covariance Matrices 248

11.4 Multivariate Normal Distributions 250

11.5 Copulas 252

11.6 Application to Loan Portfolios: Vasicek’s Model 258

Summary 264

Further Reading 264

Practice Questions and Problems (Answers at End of Book) 265

Further Questions 266

Chapter 12 Value at Risk and Expected Shortfall 269

12.1 Definition of VaR 271

12.2 Examples of the Calculation of VaR 272

12.3 A Drawback of VaR 273

12.4 Expected Shortfall 274

12.5 Coherent Risk Measures 274

12.6 Choice of Parameters for VaR and ES 278

12.7 Marginal, Incremental, and Component Measures 283

12.8 Euler’s Theorem 284

12.9 Aggregating VaRs and ESs 285

12.10 Back-Testing 285

Summary 289

Further Reading 289

Practice Questions and Problems (Answers at End of Book) 290

Further Questions 291

Chapter 13 Historical Simulation and Extreme Value Theory 293

13.1 The Methodology 293

13.2 Accuracy of VaR 299

13.3 Extensions 301

13.4 Computational Issues 306

13.5 Extreme Value Theory 307

13.6 Applications of EVT 310

Summary 313

Further Reading 313

Practice Questions and Problems (Answers at End of Book) 314

Further Questions 314

Chapter 14 Model-Building Approach 317

14.1 The Basic Methodology 318

14.2 Generalization 321

14.3 The Four-Index Example Revisited 323

14.4 Handling Term Structures 326

14.5 Extensions of the Basic Procedure 331

14.6 Risk Weights and Weighted Sensitivities 332

14.7 Handling Non-Linearity 333

14.8 Model-Building vs.Historical Simulation 339

Summary 340

Further Reading 340

Practice Questions and Problems (Answers at End of Book) 341

Further Questions 342

Part 3: Regulation 345

Chapter 15 Basel I, Basel II, and Solvency II 347

15.1 The Reasons for Regulating Banks 347

15.2 Bank Regulation Pre-1988 348

15.3 The 1988 BIS Accord 350

15.4 The G-30 Policy Recommendations 353

15.5 Netting 354

15.6 The 1996 Amendment 356

15.7 Basel II 359

15.8 Credit Risk Capital Under Basel II 360

15.9 Operational Risk Capital Under Basel II 369

15.10 Pillar 2: Supervisory Review 370

15.11 Pillar 3: Market Discipline 370

15.12 Solvency II 371

Summary 372

Further Reading 373

Practice Questions and Problems (Answers at End of Book) 373

Further Questions 375

Chapter 16 Basel II.5, Basel III, and Other Post-Crisis Changes 377

16.1 Basel II.5 378

16.2 Basel III 381

16.3 Contingent Convertible Bonds 390

16.4 Use of Standardized Approaches and SA-CCR 390

16.5 Dodd–Frank Act 392

16.6 Legislation in Other Countries 394

Summary 396

Further Reading 397

Practice Questions and Problems (Answers at End of Book) 397

Further Questions 398

Chapter 17 Regulation of the OTC Derivatives Market 399

17.1 Clearing in OTC Markets 400

17.2 Post-Crisis Regulatory Changes 404

17.3 Impact of the Changes 408

17.4 CCPs and Bankruptcy 412

Summary 412

Further Reading 413

Practice Questions and Problems (Answers at End of Book) 413

Further Questions 414

Chapter 18 Fundamental Review of the Trading Book 415

18.1 Background 416

18.2 Standardized Approach 417

18.3 Internal Models Approach 421

18.4 Trading Book vs. Banking Book 425

Summary 426

Further Reading 426

Practice Questions and Problems (Answers at End of Book) 426

Further Question 427

Part 4: Credit Risk 429

Chapter 19 Estimating Default Probabilities 431

19.1 Credit Ratings 431

19.2 Historical Default Probabilities 434

19.3 Recovery Rates 436

19.4 Credit Default Swaps 437

19.5 Credit Spreads 442

19.6 Estimating Default Probabilities from Credit Spreads 444

19.7 Comparison of Default Probability Estimates 447

19.8 Using Equity Prices to Estimate Default Probabilities 452

Summary 454

Further Reading 455

Practice Questions and Problems (Answers at End of Book) 455

Further Questions 457

Chapter 20 CVA and DVA 459

20.1 Credit Exposure on Derivatives 460

20.2 CVA 461

20.3 The Impact of a New Transaction 465

20.4 CVA Risk 467

20.5 Wrong-Way Risk 468

20.6 DVA 469

20.7 Some Simple Examples 470

Summary 474

Further Reading 475

Practice Questions and Problems (Answers at End of Book) 475

Further Questions 476

Chapter 21 Credit Value at Risk 479

21.1 Ratings Transition Matrices 480

21.2 Vasicek’s Model 482

21.3 Credit Risk Plus 483

21.4 Creditmetrics 486

21.5 Credit Spread Risk 488

Summary 492

Further Reading 492

Practice Questions and Problems (Answers at End of Book) 492

Further Questions 493

Part 5: Other Topics 495

Chapter 22 Scenario Analysis and Stress Testing 497

22.1 Generating the Scenarios 497

22.2 Regulation 504

22.3 What to Do with the Results 507

Summary 511

Further Reading 511

Practice Questions and Problems (Answers at End of Book) 512

Further Questions 513

Chapter 23 Operational Risk 515

23.1 Defining Operational Risk 517

23.2 Categorization of Operational Risks 518

23.3 Regulatory Capital Under Basel II 519

23.4 The Standardized Measurement Approach 525

23.5 Preventing Operational Risk Losses 527

23.6 Allocation of Operational Risk Capital 530

23.7 Use of Power Law 530

23.8 Insurance 531

23.9 Sarbanes–Oxley 533

Summary 533

Further Reading 534

Practice Questions and Problems (Answers at End of Book) 535

Further Questions 536

Chapter 24 Liquidity Risk 537

24.1 Liquidity Trading Risk 538

24.2 Liquidity Funding Risk 545

24.3 Liquidity Black Holes 554

Summary 561

Further Reading 562

Practice Questions and Problems (Answers at End of Book) 562

Further Questions 563

Chapter 25 Model Risk Management 565

25.1 Regulatory Requirements 566

25.2 Models in Physics and Finance 572

25.3 Simple Models: Expensive Mistakes 572

25.4 Models for Pricing Actively Traded Products 575

25.5 Models for Less Actively Traded Products 578

25.6 Accounting 580

25.7 What Makes a Successful Pricing Model? 580

25.8 Model Building Missteps 581

Summary 582

Further Reading 583

Practice Questions and Problems (Answers at End of Book) 583

Further Questions 584

Chapter 26 Economic Capital and RAROC 585

26.1 Definition of Economic Capital 586

26.2 Components of Economic Capital 588

26.3 Shapes of the Loss Distributions 590

26.4 Relative Importance of Risks 591

26.5 Aggregating Economic Capital 592

26.6 Allocation of Economic Capital 596

26.7 Deutsche Bank’s Economic Capital 597

26.8 RAROC 598

Summary 600

Further Reading 600

Practice Questions and Problems (Answers at End of Book) 600

Further Questions 601

Chapter 27 Enterprise Risk Management 603

27.1 Risk Appetite 604

27.2 Risk Culture 610

27.3 Identifying Major Risks 614

27.4 Strategic Risk Management 616

Summary 617

Further Reading 618

Practice Questions and Problems (Answers at End of Book) 618

Further Questions 619

Chapter 28 Financial Innovation 621

28.1 Technological Advances 622

28.2 Payment Systems 625

28.3 Lending 629

28.4 Wealth Management 632

28.5 Insurance 633

28.6 Regulation and Compliance 635

28.7 How Should Financial Institutions Respond? 638

Summary 640

Further Reading 641

Practice Questions and Problems (Answers at End of Book) 641

Further Questions 642

Chapter 29 Risk Management Mistakes to Avoid 643

29.1 Risk Limits 643

29.2 Managing the Trading Room 647

29.3 Liquidity Risk 649

29.4 Lessons for Nonfinancial Corporations 652

29.5 A Final Point 653

Further Reading 654

Part 6: Appendices 655

Appendix A Compounding Frequencies for Interest Rates 657

Appendix B Zero Rates, Forward Rates, and Zero-Coupon Yield Curves 661

Appendix C Valuing Forward and Futures Contracts 667

Appendix D Valuing Swaps 669

Appendix E Valuing European Options 673

Appendix F Valuing American Options 677

Appendix G Taylor Series Expansions 681

Appendix H Eigenvectors and Eigenvalues 685

Appendix I Principal Components Analysis 689

Appendix J Manipulation of Credit Transition Matrices 691

Appendix K Valuation of Credit Default Swaps 693

Appendix L Synthetic CDOs and Their Valuation 697

Answers to Questions and Problems 701

Glossary 745

RMFI Software 773

Table for N(x) When x ≥ 0 777

Table for N(x) When x ≤ 0 779

Index 781