Risk management and Financial institutions 4th

Risk Management
and Financial
Institutions


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Risk Management
and Financial
Institutions
Fourth Edition

JOHN C. HULL


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Copyright © 2015 by John C. Hull. All rights reserved.
Published by John Wiley & Sons, Inc., Hoboken, New Jersey.
The Third Edition was published by John Wiley & Sons, Inc. in 2012. The first and second editions of
this book was published by Prentice Hall in 2006 and 2009.

Published simultaneously in Canada.
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Library of Congress Cataloging-in-Publication Data:
Hull, John, 1946–
Risk management and financial institutions / John C. Hull. — Fourth Edition.
pages cm. — (Wiley finance series)
Includes index.
ISBN 978-1-118-95594-9 (paper); ISBN 978-1-118-95596-3 (ePDF);

ISBN 978-1-118-95595-6 (ePUB)
1. Risk management. 2. Financial institutions—Management. I. Title.
HD61.H83 2015
332.1068'1—dc23
2014037477
Printed in the United States of America
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9

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6

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4

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2

1


To Michelle, Peter, and David

Contents in Brief
Business Snapshots
Preface
Chapter 1: Introduction

xxi
xxiii
1

PART ONE : FINANCIAL INSTITUTIONS AND THEIR TRADING
Chapter 2: Banks
Chapter 3: Insurance Companies and Pension Plans
Chapter 4: Mutual Funds and Hedge Funds
Chapter 5: Trading in Financial Markets
Chapter 6: The Credit Crisis of 2007
Chapter 7: Valuation and Scenario Analysis: The Risk-Neutral and Real Worlds

25
45
71
93
121
137

PART TWO : MARKET RISK
Chapter 8: How Traders Manage Their Risks
Chapter 9: Interest Rate Risk
Chapter 10: Volatility
Chapter 11: Correlations and Copulas

Chapter 12: Value at Risk and Expected Shortfall
Chapter 13: Historical Simulation and Extreme Value Theory
Chapter 14: Model-Building Approach

153
175
201
231
255
277
299

PART THREE : REGULATION
Chapter 15: Basel I, Basel II, and Solvency II
Chapter 16: Basel II.5, Basel III, and Other Post-Crisis Changes
Chapter 17: Fundamental Review of the Trading Book

325
353
373

PART FOUR : CREDIT RISK
Chapter 18: Managing Credit Risk: Margin, OTC Markets, and CCPs
Chapter 19: Estimating Default Probabilities
Chapter 20: CVA and DVA
Chapter 21: Credit Value at Risk

383
401
429

447

PART FIVE : OTHER TOPICS
Chapter 22: Scenario Analysis and Stress Testing
Chapter 23: Operational Risk
Chapter 24: Liquidity Risk
Chapter 25: Model Risk
Chapter 26: Economic Capital and RAROC
Chapter 27: Enterprise Risk Management
Chapter 28: Risk Management Mistakes to Avoid

463
481
501
527
547
565
579

PART SIX : APPENDICES
Appendices
Answers to Questions and Problems
Glossary
DerivaGem Software
Tables for N(x)
Index

591
629
669

689
695
699

vii



Contents

Business Snapshots
Preface

xxiii

CHAPTER 1
Introduction
1.1
1.2
1.3
1.4
1.5
1.6
1.7

xxi

Risk vs. Return for Investors
The Efficient Frontier
The Capital Asset Pricing Model

Arbitrage Pricing Theory
Risk vs. Return for Companies
Risk Management by Financial Institutions
Credit Ratings
Summary
Further Reading
Practice Questions and Problems (Answers at End of Book)
Further Questions

1

2
5
8
13
13
17
18
19
19
19
20

PART ONE

FINANCIAL INSTITUTIONS AND THEIR TRADING
CHAPTER 2
Banks
2.1
2.2

2.3
2.4
2.5
2.6
2.7
2.8

Commercial Banking
The Capital Requirements of a Small Commercial Bank
Deposit Insurance
Investment Banking
Securities Trading
Potential Conflicts of Interest in Banking
Today’s Large Banks
The Risks Facing Banks
Summary
Further Reading
Practice Questions and Problems (Answers at End of Book)
Further Questions

25

26
28
30
31
36
37
38
41

42
43
43
44

ix


x

CONTENTS

CHAPTER 3
Insurance Companies and Pension Plans
3.1
3.2
3.3
3.4
3.5
3.6
3.7
3.8
3.9
3.10
3.11
3.12

Life Insurance
Annuity Contracts
Mortality Tables

Longevity and Mortality Risk
Property-Casualty Insurance
Health Insurance
Moral Hazard and Adverse Selection
Reinsurance
Capital Requirements
The Risks Facing Insurance Companies
Regulation
Pension Plans
Summary
Further Reading
Practice Questions and Problems (Answers at End of Book)
Further Questions

CHAPTER 4
Mutual Funds and Hedge Funds
4.1
4.2
4.3
4.4

Mutual Funds
Hedge Funds
Hedge Fund Strategies
Hedge Fund Performance
Summary
Further Reading
Practice Questions and Problems (Answers at End of Book)
Further Questions

CHAPTER 5
Trading in Financial Markets
5.1
5.2
5.3
5.4
5.5
5.6
5.7
5.8
5.9

The Markets
Clearing Houses
OTC Market Changes
Long and Short Positions in Assets
Derivatives Markets
Plain Vanilla Derivatives
Non-Traditional Derivatives
Exotic Options and Structured Products
Risk Management Challenges
Summary
Further Reading
Practice Questions and Problems (Answers at End of Book)
Further Questions

45

45
49

50
53
54
56
58
59
60
61
61
63
66
67
68
69

71

71
79
84
88
89
90
90
91

93

93
94

95
96
97
98
108
112
114
116
116
117
119


xi

Contents

CHAPTER 6
The Credit Crisis of 2007
6.1
6.2
6.3
6.4
6.5

The U.S. Housing Market
Securitization
The Crisis
What Went Wrong?
Lessons from the Crisis

Summary
Further Reading
Practice Questions and Problems (Answers at End of Book)
Further Questions

CHAPTER 7
Valuation and Scenario Analysis: The Risk-Neutral and Real Worlds
7.1
7.2
7.3
7.4
7.5
7.6

Volatility and Asset Prices
Risk-Neutral Valuation
Scenario Analysis
When Both Worlds Have to be Used
The Calculations in Practice
Estimating Real-World Processes
Summary
Further Reading
Practice Questions and Problems (Answers at End of Book)
Further Questions

121

121
124
130

131
133
134
135
135
136

137

138
139
144
144
145
146
147
148
148
148

PART TWO

MARKET RISK
CHAPTER 8
How Traders Manage Their Risks

8.1
Delta
8.2
Gamma

8.3
Vega
8.4
Theta
8.5
Rho
8.6
Calculating Greek Letters
8.7
Taylor Series Expansions
8.8
The Realities of Hedging
8.9
Hedging Exotic Options
8.10 Scenario Analysis
Summary
Further Reading
Practice Questions and Problems (Answers at End of Book)
Further Questions

153

153
160
162
164
165
166
167
168

169
170
172
172
172
173


xii

CONTENTS

CHAPTER 9
Interest Rate Risk
9.1
9.2
9.3
9.4
9.5
9.6
9.7
9.8
9.9

CHAPTER 10
Volatility
10.1
10.2
10.3
10.4

10.5
10.6
10.7
10.8
10.9
10.10

175
178
182
185
187
189
191
193
196
197
197
198
199

Definition of Volatility
Implied Volatilities
Are Daily Percentage Changes in Financial Variables Normal?
The Power Law
Monitoring Daily Volatility
The Exponentially Weighted Moving Average Model
The GARCH(1,1) Model
Choosing Between the Models
Maximum Likelihood Methods

Using GARCH(1,1) to Forecast Future Volatility
Summary
Further Reading
Practice Questions and Problems (Answers at End of Book)
Further Questions

201
204
205
207
209
212
214
216
216
222
225
226
227
228

CHAPTER 11
Correlations and Copulas
11.1
11.2
11.3
11.4
11.5

175

The Management of Net Interest Income
Types of Rates
Duration
Convexity
Generalization
Nonparallel Yield Curve Shifts
Interest Rate Deltas in Practice
Principal Components Analysis
Gamma and Vega
Summary
Further Reading
Practice Questions and Problems (Answers at End of Book)
Further Questions

Definition of Correlation
Monitoring Correlation
Multivariate Normal Distributions
Copulas
Application to Loan Portfolios: Vasicek’s Model
Summary
Further Reading
Practice Questions and Problems (Answers at End of Book)
Further Questions

201

231

231

233
236
238
244
250
250
250
252


xiii

Contents

CHAPTER 12
Value at Risk and Expected Shortfall
12.1
12.2
12.3
12.4
12.5
12.6
12.7
12.8
12.9
12.10

Definition of VaR
Examples of the Calculation of VaR
A Drawback of VaR

Expected Shortfall
Coherent Risk Measures
Choice of Parameters for VaR and ES
Marginal, Incremental, and Component Measures
Euler’s Theorem
Aggregating VaRs and ESs
Back-Testing
Summary
Further Reading
Practice Questions and Problems (Answers at End of Book)
Further Questions

CHAPTER 13
Historical Simulation and Extreme Value Theory
13.1
13.2
13.3
13.4
13.5
13.6

The Methodology
Accuracy of VaR
Extensions
Computational Issues
Extreme Value Theory
Applications of EVT
Summary
Further Reading
Practice Questions and Problems (Answers at End of Book)

Further Questions

CHAPTER 14
Model-Building Approach
14.1
14.2
14.3
14.4
14.5
14.6
14.7
14.8
14.9
14.10

The Basic Methodology
Generalization
Correlation and Covariance Matrices
Handling Interest Rates
Applications of the Linear Model
Linear Model and Options
Quadratic Model
Monte Carlo Simulation
Non-Normal Assumptions
Model-Building vs. Historical Simulation
Summary
Further Reading
Practice Questions and Problems (Answers at End of Book)
Further Questions

255

255
257
258
259
260
263
268
269
270
270
273
274
274
275

277

277
282
284
289
289
292
295
295
296
297

299

299
302
303
307
310
311
314
316
317
318
319
319
319
321


xiv

CONTENTS

PART THREE

REGULATION
CHAPTER 15
Basel I, Basel II, and Solvency II

15.1
The Reasons for Regulating Banks

15.2
Bank Regulation Pre-1988
15.3
The 1988 BIS Accord
15.4
The G-30 Policy Recommendations
15.5
Netting
15.6
1996 Amendment
15.7
Basel II
15.8
Credit Risk Capital Under Basel II
15.9
Operational Risk Capital Under Basel II
15.10 Pillar 2: Supervisory Review
15.11 Pillar 3: Market Discipline
15.12 Solvency II
Summary
Further Reading
Practice Questions and Problems (Answers at End of Book)
Further Questions

CHAPTER 16
Basel II.5, Basel III, and Other Post-Crisis Changes
16.1
16.2
16.3
16.4

16.5

Basel II.5
Basel III
Contingent Convertible Bonds
Dodd–Frank Act
Legislation in other Countries
Summary
Further Reading
Practice Questions and Problems (Answers at End of Book)
Further Questions

CHAPTER 17
Fundamental Review of the Trading Book
17.1
17.2
17.3

New Market Risk Measures
Trading Book vs. Banking Book
Credit Trades
Summary
Further Reading
Practice Questions and Problems (Answers at End of Book)
Further Questions

325

325
326

327
330
331
333
336
337
346
346
347
347
349
349
350
351

353

353
357
365
366
368
370
371
371
372

373

373

377
378
379
379
379
380


xv

Contents

PART FOUR

CREDIT RISK
CHAPTER 18
Managing Credit Risk: Margin, OTC Markets, and CCPs
18.1
18.2
18.3
18.4

Margin and Exchanges
OTC Markets
Consequences of New OTC Regulations
The Risk of a CCP Failure
Summary
Further Reading
Practice Questions and Problems (Answers at End of Book)
Further Questions

CHAPTER 19
Estimating Default Probabilities
19.1
19.2
19.3
19.4
19.5
19.6
19.7
19.8

Credit Ratings
Historical Default Probabilities
Recovery Rates
Credit Default Swaps
Credit Spreads
Estimating Default Probabilities from Credit Spreads
Comparison of Default Probability Estimates
Using Equity Prices to Estimate Default Probabilities
Summary
Further Reading
Practice Questions and Problems (Answers at End of Book)
Further Questions

CHAPTER 20
CVA and DVA
20.1
20.2
20.3

20.4
20.5
20.6
20.7

Credit Exposure on Derivatives
CVA
The Impact of a New Transaction
CVA Risk
Wrong-Way Risk
DVA
Some Simple Examples
Summary
Further Reading
Practice Questions and Problems (Answers at End of Book)
Further Questions

383

383
388
392
396
396
397
397
398

399

399
401
403
404
409
412
414
419
422
422
423
424

427

427
429
432
434
435
436
437
441
442
442
443


xvi

CONTENTS

CHAPTER 21
Credit Value at Risk
21.1
21.2
21.3
21.4
21.5

Ratings Transition Matrices
Vasicek’s Model
Credit Risk Plus
Creditmetrics
Credit-Sensitive Instruments in the Trading Book
Summary
Further Reading
Practice Questions and Problems (Answers at End of Book)
Further Questions

445

446
448
449
451
454
457
458
458

459

PART FIVE

OTHER TOPICS
CHAPTER 22
Scenario Analysis and Stress Testing
22.1
22.2
22.3

Generating the Scenarios
Regulation
What to Do with the Results
Summary
Further Reading
Practice Questions and Problems (Answers at End of Book)
Further Questions

CHAPTER 23
Operational Risk

23.1
Defining Operational Risk
23.2
Determination of Regulatory Capital
23.3
Categorization of Operational Risks
23.4
Loss Severity and Loss Frequency

23.5
Implementation of AMA
23.6
Proactive Approaches
23.7
Allocation of Operational Risk Capital
23.8
Use of Power Law
23.9
Insurance
23.10 Sarbanes-Oxley
Summary
Further Reading
Practice Questions and Problems (Answers at End of Book)
Further Questions

CHAPTER 24
Liquidity Risk
24.1
24.2

Liquidity Trading Risk
Liquidity Funding Risk

463

463
469
473
476

476
477
478

479

481
481
483
484
485
489
492
492
493
494
495
496
496
497

499

499
507


xvii

Contents

24.3

Liquidity Black Holes
Summary
Further Reading
Practice Questions and Problems (Answers at End of Book)
Further Questions

CHAPTER 25
Model Risk
25.1
25.2
25.3
25.4
25.5
25.6
25.7
25.8

Marking to Market
Models for Linear Products
Physics vs. Finance
How Models are Used for Pricing Standard Products
Hedging
Models for Nonstandard Products
Dangers in Model Building
Detecting Model Problems
Summary
Further Reading

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

CHAPTER 26
Economic Capital and RAROC
26.1
26.2
26.3
26.4
26.5
26.6
26.7
26.8

Definition of Economic Capital
Components of Economic Capital
Shapes of the Loss Distributions
Relative Importance of Risks
Aggregating Economic Capital
Allocation of Economic Capital
Deutsche Bank’s Economic Capital
RAROC
Summary
Further Reading
Practice Questions and Problems (Answers at End of Book)
Further Questions

CHAPTER 27
Enterprise Risk Management
27.1

27.2
27.3
27.4

Risk Appetite
Risk Culture
Identifying Major Risks
Strategic Risk Management
Summary
Further Reading
Practice Questions and Problems (Answers at End of Book)
Further Questions

515
522
522
523
524

525

525
527
529
530
536
537
540
541
542

542
543
543

545

545
547
549
551
552
555
557
557
559
559
559
560

563

564
568
572
574
575
576
576
576

xviii

CONTENTS

CHAPTER 28
Risk Management Mistakes to Avoid
28.1
28.2
28.3
28.4
28.5

Risk Limits
Managing the Trading Room
Liquidity Risk
Lessons for Nonfinancial Corporations
A Final Point
Further Reading

577

577
580
582
585
586
587

PART SIX

APPENDICES
Appendix A
Compounding Frequencies for Interest Rates

591

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

595

Appendix C
Valuing Forward and Futures Contracts

599

Appendix D
Valuing Swaps

601

Appendix E
Valuing European Options

603

Appendix F
Valuing American Options

605

Appendix G
Taylor Series Expansions

609

Appendix H
Eigenvectors and Eigenvalues

613

Appendix I
Principal Components Analysis

617

Appendix J
Manipulation of Credit Transition Matrices

619

Appendix K
Valuation of Credit Default Swaps

621


Contents

xix

Appendix L
Synthetic CDOs and Their Valuation

625

Answers to Questions and Problems

629

Glossary

669

DerivaGem Software

689

Table for N(x) when x ≤ 0

Table for N(x) when x ≥ 0
Index

695
697
699

Business Snapshots

1.1
2.1
2.2
2.3
3.1
3.2
4.1
5.1
5.2
5.3
5.4
5.5
6.1
6.2
8.1
8.2
8.3
10.1
10.2
12.1
15.1
16.1
18.1
19.1
19.2
19.3
22.1
22.2

23.1
23.2
24.1
24.2
24.3
24.4
25.1
25.2
25.3

The Hidden Costs of Bankruptcy
Google’s IPO
PeopleSoft’s Poison Pill
How to Keep Loans Performing
Equitable Life
A Perfect Storm
Mutual Fund Returns Can Be Misleading
The Unanticipated Delivery of a Futures Contract
A Software Error?
Microsoft’s Hedging
Procter and Gamble’s Bizarre Deal
SocGen’s Big Loss in 2008
All BBBs Are Not the Same
A Trading Opportunity?
Hedging by Gold Mining Companies
Dynamic Hedging in Practice
Is Delta Hedging Easier or More Difficult for Exotics?
What Causes Volatility?
Making Money from Foreign Currency Options
Historical Perspectives on VaR

Systemic Risk
Credit Suisse’s CoCo Bond Issues
Rehypothecation
The CDS Market
Is the CDS Market a Fair Game?
Contagion
Long-Term Capital Management’s Big Loss
Traffic Light Options
The Hammersmith and Fulham Story
Rogue Trader Insurance
Northern Rock
Ashanti Goldfields
Metallgesellschaft
The Crash of 1987
Kidder Peabody’s Embarrassing Mistake
Exploiting the Weaknesses of a Competitor’s Model
Crashophobia

15
35
36
40
52
65
78
102
103
113
114
115

130
134
156
169
170
203
206
256
326
366
395
405
407
418
467
473
490
494
508
511
512
518
528
529
533

xxi


xxii

25.4
26.1
27.1
27.2
28.1

BUSINESS SNAPSHOTS

The London Whale
The EGT Fund
The Santander Rail Deal
Abacus
Big Losses

539
551
570
571
578


Preface

R

isk management practices and the regulation of financial institutions have continued to evolve in the past three years. Risk Management and Financial Institutions
has been expanded and updated to reflect this. Like my other popular text Options,
Futures, and Other Derivatives, the book is designed to be useful to practicing managers as well as college students. Those studying for GARP and PRMIA qualifications
will find the book particularly helpful.
The book is appropriate for university courses in either risk management or

financial institutions. It is not necessary for students to take a course on options and
futures markets prior to taking a course based on this book. But if they have taken
such a course, some of the material in the first nine chapters does not need to be
covered.
The level of mathematical sophistication and the way material is presented have
been managed carefully so that the book is accessible to as wide an audience as possible. For example, when covering copulas in Chapter 11, I present the intuition followed by a detailed numerical example; when covering maximum likelihood methods
in Chapter 10 and extreme value theory in Chapter 13, I provide numerical examples
and enough details for readers to develop their own Excel spreadsheets. I have also
provided my own Excel spreadsheets for many applications on my website:
www-2.rotman.utoronto.ca/∼hull
This is a book about risk management, so there is very little material on the
valuation of derivatives. (This is the main focus of my other two books, Options,
Futures, and Other Derivatives and Fundamentals of Futures and Options Markets.)
The appendices at the end of the book include material that summarizes some of
the valuation key results that are important in risk management, and the DerivaGem
software can be downloaded from my website.

NEW MATERIAL
The fourth edition has been fully updated and contains much new material. In
particular:
1. There is a new chapter comparing scenario analysis to valuation (Chapter 7).
The chapter introduces the reader to the statistical processes often assumed for

xxiii