Finacial risk manager handbook

Financial Risk Manager

Handbook
Second Edition


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Financial Risk Manager

Handbook
Second Edition
Philippe Jorion

GARP

Wiley
John Wiley & Sons, Inc.


Copyright 䊚 2003 by Philippe Jorion, except for FRM sample questions, which are

copyright 1997–2001 by GARP. The FRM designation is a GARP trademark. All rights
reserved.
Published by John Wiley & Sons, Inc., Hoboken, New Jersey
Published simultaneously in Canada
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Printed in the United States of America.

10 9 8 7 6 5 4 3 2 1


About the Author
Philippe Jorion is Professor of Finance at the Graduate School of Management at the
University of California at Irvine. He has also taught at Columbia University, Northwestern University, the University of Chicago, and the University of British Columbia.
He holds an M.B.A. and a Ph.D. from the University of Chicago and a degree in engineering from the University of Brussels.
Dr. Jorion has authored more than seventy publications directed to academics
and practitioners on the topics of risk management and international finance. Dr.
Jorion has written a number of books, including Big Bets Gone Bad: Derivatives and
Bankruptcy in Orange County, the first account of the largest municipal failure in U.S.
history, and Value at Risk: The New Benchmark for Managing Financial Risk, which is
aimed at finance practitioners and has become an “industry standard.”
Philippe Jorion is a frequent speaker at academic and professional conferences.
He is on the editorial board of a number of finance journals and is editor in chief of
the Journal of Risk.

About GARP
The Global Association of Risk Professionals (GARP), established in 1996, is a notfor-profit independent association of risk management practitioners and researchers.
Its members represent banks, investment management firms, governmental bodies,
academic institutions, corporations, and other financial organizations from all over
the world.
GARP’s mission, as adopted by its Board of Trustees in a statement issued in February 2003, is to be the leading professional association for risk managers, managed by
and for its members dedicated to the advancement of the risk profession through
education, training and the promotion of best practices globally.
In just seven years the Association’s membership has grown to over 27,000 individuals from around the world. In the just six years since its inception in 1997, the
FRM program has become the world’s most prestigious financial risk management
certification program. Professional risk managers having earned the FRM credential
are globally recognized as having achieved a minimum level of professional competency along with a demonstrated ability to dynamically measure and manage financial
risk in a real-world setting in accord with global standards. Further information about

GARP, the FRM Exam, and FRM readings are available at www.garp.com.

v



Contents
Preface

xix

Introduction

xxi

Part I: Quantitative Analysis
Ch. 1

Ch. 2

1

Bond Fundamentals
1.1 Discounting, Present, and Future Value . .
1.2 Price-Yield Relationship . . . . . . . . . .
1.2.1 Valuation . . . . . . . . . . . . . .
1.2.2 Taylor Expansion . . . . . . . . . .
1.2.3 Bond Price Derivatives . . . . . . .
1.2.4 Interpreting Duration and Convexity
1.2.5 Portfolio Duration and Convexity . .

1.3 Answers to Chapter Examples . . . . . . .

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3
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6
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7
9
16
23
26

Fundamentals of Probability
2.1 Characterizing Random Variables . . . . . . . . . . . . . . .
2.1.1 Univariate Distribution Functions . . . . . . . . . . .
2.1.2 Moments . . . . . . . . . . . . . . . . . . . . . . . .
2.2 Multivariate Distribution Functions . . . . . . . . . . . . . .
2.3 Functions of Random Variables . . . . . . . . . . . . . . . .
2.3.1 Linear Transformation of Random Variables . . . . . .
2.3.2 Sum of Random Variables . . . . . . . . . . . . . . .
2.3.3 Portfolios of Random Variables . . . . . . . . . . . . .

2.3.4 Product of Random Variables . . . . . . . . . . . . . .
2.3.5 Distributions of Transformations of Random Variables
2.4 Important Distribution Functions . . . . . . . . . . . . . . .
2.4.1 Uniform Distribution . . . . . . . . . . . . . . . . . .
2.4.2 Normal Distribution . . . . . . . . . . . . . . . . . . .
2.4.3 Lognormal Distribution . . . . . . . . . . . . . . . . .
2.4.4 Student’s t Distribution . . . . . . . . . . . . . . . . .
2.4.5 Binomial Distribution . . . . . . . . . . . . . . . . . .
2.5 Answers to Chapter Examples . . . . . . . . . . . . . . . . .

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viii
Ch. 3

Ch. 4

CONTENTS
Fundamentals of Statistics

3.1 Real Data . . . . . . . . . . . .
3.1.1 Measuring Returns . . .
3.1.2 Time Aggregation . . . .
3.1.3 Portfolio Aggregation . .
3.2 Parameter Estimation . . . . . .
3.3 Regression Analysis . . . . . .
3.3.1 Bivariate Regression . .
3.3.2 Autoregression . . . . .
3.3.3 Multivariate Regression .
3.3.4 Example . . . . . . . . .
3.3.5 Pitfalls with Regressions
3.4 Answers to Chapter Examples .

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Monte Carlo Methods
4.1 Simulations with One Random Variable
4.1.1 Simulating Markov Processes . .
4.1.2 The Geometric Brownian Motion
4.1.3 Simulating Yields . . . . . . . .
4.1.4 Binomial Trees . . . . . . . . .
4.2 Implementing Simulations . . . . . . .
4.2.1 Simulation for VAR . . . . . . .
4.2.2 Simulation for Derivatives . . .
4.2.3 Accuracy . . . . . . . . . . . .
4.3 Multiple Sources of Risk . . . . . . . .
4.3.1 The Cholesky Factorization . . .
4.4 Answers to Chapter Examples . . . . .

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83
83
84
84
88
89
93
93
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96
97
99

Part II: Capital Markets

103

Ch. 5

105
105
107
107
110
112

113
117
117
119
119
120

Introduction to Derivatives
5.1 Overview of Derivatives Markets . . . . . . . . . . . . . .
5.2 Forward Contracts . . . . . . . . . . . . . . . . . . . . .
5.2.1 Definition . . . . . . . . . . . . . . . . . . . . . .
5.2.2 Valuing Forward Contracts . . . . . . . . . . . . .
5.2.3 Valuing an Off-Market Forward Contract . . . . . .
5.2.4 Valuing Forward Contracts with Income Payments .
5.3 Futures Contracts . . . . . . . . . . . . . . . . . . . . . .
5.3.1 Definitions of Futures . . . . . . . . . . . . . . . .
5.3.2 Valuing Futures Contracts . . . . . . . . . . . . .
5.4 Swap Contracts . . . . . . . . . . . . . . . . . . . . . . .
5.5 Answers to Chapter Examples . . . . . . . . . . . . . . .

Financial Risk Manager Handbook, Second Edition

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CONTENTS
Ch. 6

Ch. 7

Ch. 8

ix

Options
6.1 Option Payoffs . . . . . . . . . . . . .
6.1.1 Basic Options . . . . . . . . . .
6.1.2 Put-Call Parity . . . . . . . . . .

6.1.3 Combination of Options . . . .
6.2 Valuing Options . . . . . . . . . . . .
6.2.1 Option Premiums . . . . . . . .
6.2.2 Early Exercise of Options . . . .
6.2.3 Black-Scholes Valuation . . . . .
6.2.4 Market vs. Model Prices . . . . .
6.3 Other Option Contracts . . . . . . . . .
6.4 Valuing Options by Numerical Methods
6.5 Answers to Chapter Examples . . . . .

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123
123
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126
128
132
132
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136
142
143
146
149

Fixed-Income Securities
7.1 Overview of Debt Markets . . . . . . .
7.2 Fixed-Income Securities . . . . . . . . .
7.2.1 Instrument Types . . . . . . . .
7.2.2 Methods of Quotation . . . . . .
7.3 Analysis of Fixed-Income Securities . .
7.3.1 The NPV Approach . . . . . . .
7.3.2 Duration . . . . . . . . . . . . .
7.4 Spot and Forward Rates . . . . . . . .
7.5 Mortgage-Backed Securities . . . . . . .
7.5.1 Description . . . . . . . . . . .
7.5.2 Prepayment Risk . . . . . . . .
7.5.3 Financial Engineering and CMOs
7.6 Answers to Chapter Examples . . . . .

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153
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170
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177
183

Fixed-Income Derivatives
8.1 Forward Contracts . . . . . . . .
8.2 Futures . . . . . . . . . . . . . .
8.2.1 Eurodollar Futures . . . .
8.2.2 T-bond Futures . . . . . .
8.3 Swaps . . . . . . . . . . . . . . .
8.3.1 Definitions . . . . . . . .
8.3.2 Quotations . . . . . . . .
8.3.3 Pricing . . . . . . . . . . .
8.4 Options . . . . . . . . . . . . . .
8.4.1 Caps and Floors . . . . . .
8.4.2 Swaptions . . . . . . . . .

8.4.3 Exchange-Traded Options .
8.5 Answers to Chapter Examples . .

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187
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201
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207

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Financial Risk Manager Handbook, Second Edition


x
Ch. 9

Ch. 10

CONTENTS
Equity Markets
9.1 Equities . . . . . . . . . . . . .
9.1.1 Overview . . . . . . . .

9.1.2 Valuation . . . . . . . .
9.1.3 Equity Indices . . . . . .
9.2 Convertible Bonds and Warrants
9.2.1 Definitions . . . . . . .
9.2.2 Valuation . . . . . . . .
9.3 Equity Derivatives . . . . . . .
9.3.1 Stock Index Futures . . .
9.3.2 Single Stock Futures . .
9.3.3 Equity Options . . . . .
9.3.4 Equity Swaps . . . . . .
9.4 Answers to Chapter Examples .

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Currencies and Commodities Markets
10.1 Currency Markets . . . . . . . . . . . . .
10.2 Currency Swaps . . . . . . . . . . . . . .
10.2.1 Definitions . . . . . . . . . . . .
10.2.2 Pricing . . . . . . . . . . . . . . .
10.3 Commodities . . . . . . . . . . . . . . .
10.3.1 Products . . . . . . . . . . . . . .
10.3.2 Pricing of Futures . . . . . . . . .

10.3.3 Futures and Expected Spot Prices .
10.4 Answers to Chapter Examples . . . . . .

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225
225
227
227
228
231
231
232
235
238

Part III: Market Risk Management

241

Ch. 11

243
243
246
246
249
249
252
252
253
255
256

257
257
257

Introduction to Market Risk Measurement
11.1 Introduction to Financial Market Risks .
11.2 VAR as Downside Risk . . . . . . . . .
11.2.1 VAR: Definition . . . . . . . . .
11.2.2 VAR: Caveats . . . . . . . . . .
11.2.3 Alternative Measures of Risk . .
11.3 VAR: Parameters . . . . . . . . . . . .
11.3.1 Confidence Level . . . . . . . .
11.3.2 Horizon . . . . . . . . . . . . .
11.3.3 Application: The Basel Rules . .
11.4 Elements of VAR Systems . . . . . . .
11.4.1 Portfolio Positions . . . . . . .
11.4.2 Risk Factors . . . . . . . . . . .
11.4.3 VAR Methods . . . . . . . . . .

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CONTENTS

xi

11.5 Stress-Testing . . . . . . . . . . . . . . . . . . . . . . . . . . 258
11.6 Cash Flow at Risk . . . . . . . . . . . . . . . . . . . . . . . . 260
11.7 Answers to Chapter Examples . . . . . . . . . . . . . . . . . 261
Ch. 12

Ch. 13

Identification of Risk Factors
12.1 Market Risks . . . . . . . . . . . . .
12.1.1 Absolute and Relative Risk . .
12.1.2 Directional and Nondirectional
12.1.3 Market vs. Credit Risk . . . . .
12.1.4 Risk Interaction . . . . . . . .
12.2 Sources of Loss: A Decomposition . .
12.2.1 Exposure and Uncertainty . .
12.2.2 Specific Risk . . . . . . . . . .

12.3 Discontinuity and Event Risk . . . . .
12.3.1 Continuous Processes . . . . .
12.3.2 Jump Process . . . . . . . . .
12.3.3 Event Risk . . . . . . . . . . .
12.4 Liquidity Risk . . . . . . . . . . . . .
12.5 Answers to Chapter Examples . . . .
Sources of Risk
13.1 Currency Risk . . . . . . . . . . . . .
13.1.1 Currency Volatility . . . . . .
13.1.2 Correlations . . . . . . . . . .
13.1.3 Devaluation Risk . . . . . . .
13.1.4 Cross-Rate Volatility . . . . .
13.2 Fixed-Income Risk . . . . . . . . . .
13.2.1 Factors Affecting Yields . . . .
13.2.2 Bond Price and Yield Volatility
13.2.3 Correlations . . . . . . . . . .
13.2.4 Global Interest Rate Risk . . .
13.2.5 Real Yield Risk . . . . . . . .
13.2.6 Credit Spread Risk . . . . . .
13.2.7 Prepayment Risk . . . . . . .
13.3 Equity Risk . . . . . . . . . . . . . .
13.3.1 Stock Market Volatility . . . .
13.3.2 Forwards and Futures . . . . .
13.4 Commodity Risk . . . . . . . . . . .
13.4.1 Commodity Volatility Risk . .
13.4.2 Forwards and Futures . . . . .
13.4.3 Delivery and Liquidity Risk . .

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xii

CONTENTS
13.5 Risk Simplification . . . . . . . . .
13.5.1 Diagonal Model . . . . . . .
13.5.2 Factor Models . . . . . . . .
13.5.3 Fixed-Income Portfolio Risk .
13.6 Answers to Chapter Examples . . .

Ch. 14

Ch. 15

Ch. 16

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Hedging Linear Risk
14.1 Introduction to Futures Hedging . . .
14.1.1 Unitary Hedging . . . . . . . .
14.1.2 Basis Risk . . . . . . . . . . .
14.2 Optimal Hedging . . . . . . . . . . .
14.2.1 The Optimal Hedge Ratio . . .
14.2.2 The Hedge Ratio as Regression
14.2.3 Example . . . . . . . . . . . .
14.2.4 Liquidity Issues . . . . . . . .
14.3 Applications of Optimal Hedging . .
14.3.1 Duration Hedging . . . . . . .
14.3.2 Beta Hedging . . . . . . . . .
14.4 Answers to Chapter Examples . . . .

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302
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305
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Coefficient
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326

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351

Nonlinear Risk: Options
15.1 Evaluating Options . . . . . . . . . . . . . .
15.1.1 Definitions . . . . . . . . . . . . . .
15.1.2 Taylor Expansion . . . . . . . . . . .
15.1.3 Option Pricing . . . . . . . . . . . . .

15.2 Option “Greeks” . . . . . . . . . . . . . . .
15.2.1 Option Sensitivities: Delta and Gamma
15.2.2 Option Sensitivities: Vega . . . . . . .
15.2.3 Option Sensitivities: Rho . . . . . . .
15.2.4 Option Sensitivities: Theta . . . . . .
15.2.5 Option Pricing and the “Greeks” . . .
15.2.6 Option Sensitivities: Summary . . . .
15.3 Dynamic Hedging . . . . . . . . . . . . . . .
15.3.1 Delta and Dynamic Hedging . . . . .
15.3.2 Implications . . . . . . . . . . . . . .
15.3.3 Distribution of Option Payoffs . . . .
15.4 Answers to Chapter Examples . . . . . . . .

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Modeling Risk Factors
355
16.1 The Normal Distribution . . . . . . . . . . . . . . . . . . . . 355
16.1.1 Why the Normal? . . . . . . . . . . . . . . . . . . . . 355

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CONTENTS

xiii

16.1.2 Computing Returns . .
16.1.3 Time Aggregation . . .
16.2 Fat Tails . . . . . . . . . . . .
16.3 Time-Variation in Risk . . . .
16.3.1 GARCH . . . . . . . .
16.3.2 EWMA . . . . . . . . .
16.3.3 Option Data . . . . . .
16.3.4 Implied Distributions .
16.4 Answers to Chapter Examples
Ch. 17

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17.1 VAR: Local vs. Full Valuation . . . . . .
17.1.1 Local Valuation . . . . . . . . .
17.1.2 Full Valuation . . . . . . . . . .
17.1.3 Delta-Gamma Method . . . . . .
17.2 VAR Methods: Overview . . . . . . . .
17.2.1 Mapping . . . . . . . . . . . . .
17.2.2 Delta-Normal Method . . . . . .
17.2.3 Historical Simulation Method . .
17.2.4 Monte Carlo Simulation Method
17.2.5 Comparison of Methods . . . .
17.3 Example . . . . . . . . . . . . . . . . .
17.3.1 Mark-to-Market . . . . . . . . .
17.3.2 Risk Factors . . . . . . . . . . .
17.3.3 VAR: Historical Simulation . . .
17.3.4 VAR: Delta-Normal Method . . .
17.4 Risk Budgeting . . . . . . . . . . . . .
17.5 Answers to Chapter Examples . . . . .

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372
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384
386
388
389

Part IV: Credit Risk Management
Ch. 18

Introduction to Credit Risk
18.1 Settlement Risk . . . . . . . . . . . . . .
18.1.1 Presettlement vs. Settlement Risk
18.1.2 Handling Settlement Risk . . . . .
18.2 Overview of Credit Risk . . . . . . . . .
18.2.1 Drivers of Credit Risk . . . . . . .
18.2.2 Measurement of Credit Risk . . .
18.2.3 Credit Risk vs. Market Risk . . . .

18.3 Measuring Credit Risk . . . . . . . . . .
18.3.1 Credit Losses . . . . . . . . . . .
18.3.2 Joint Events . . . . . . . . . . . .

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393
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396
396
397
398
399
399
399


xiv

CONTENTS
18.3.3 An Example . . . . . . . . . . . . . . . . . . . . . . . 401
18.4 Credit Risk Diversification . . . . . . . . . . . . . . . . . . . 404
18.5 Answers to Chapter Examples . . . . . . . . . . . . . . . . . 409

Ch. 19

Ch. 20

Ch. 21

Measuring Actuarial Default Risk
19.1 Credit Event . . . . . . . . . . . . . . . . . . .
19.2 Default Rates . . . . . . . . . . . . . . . . . .
19.2.1 Credit Ratings . . . . . . . . . . . . . .
19.2.2 Historical Default Rates . . . . . . . . .
19.2.3 Cumulative and Marginal Default Rates
19.2.4 Transition Probabilities . . . . . . . . .
19.2.5 Predicting Default Probabilities . . . . .
19.3 Recovery Rates . . . . . . . . . . . . . . . . .
19.3.1 The Bankruptcy Process . . . . . . . .
19.3.2 Estimates of Recovery Rates . . . . . .
19.4 Application to Portfolio Rating . . . . . . . . .
19.5 Assessing Corporate and Sovereign Rating . .
19.5.1 Corporate Default . . . . . . . . . . . .
19.5.2 Sovereign Default . . . . . . . . . . . .
19.6 Answers to Chapter Examples . . . . . . . . .
Measuring Default Risk from Market Prices
20.1 Corporate Bond Prices . . . . . . . . . .
20.1.1 Spreads and Default Risk . . . . .
20.1.2 Risk Premium . . . . . . . . . . .
20.1.3 The Cross-Section of Yield Spreads
20.1.4 The Time-Series of Yield Spreads .
20.2 Equity Prices . . . . . . . . . . . . . . .
20.2.1 The Merton Model . . . . . . . . .
20.2.2 Pricing Equity and Debt . . . . . .
20.2.3 Applying the Merton Model . . . .

20.2.4 Example . . . . . . . . . . . . . .
20.3 Answers to Chapter Examples . . . . . .

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411
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441
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455
457

Credit Exposure

21.1 Credit Exposure by Instrument . . . . . . . . .
21.2 Distribution of Credit Exposure . . . . . . . .
21.2.1 Expected and Worst Exposure . . . . .
21.2.2 Time Profile . . . . . . . . . . . . . . .
21.2.3 Exposure Profile for Interest-Rate Swaps
21.2.4 Exposure Profile for Currency Swaps . .

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460
462
463
463
464
473

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Financial Risk Manager Handbook, Second Edition


CONTENTS

xv

21.2.5 Exposure Profile for Different Coupons
21.3 Exposure Modifiers . . . . . . . . . . . . . . .
21.3.1 Marking to Market . . . . . . . . . . .
21.3.2 Exposure Limits . . . . . . . . . . . . .
21.3.3 Recouponing . . . . . . . . . . . . . .
21.3.4 Netting Arrangements . . . . . . . . .
21.4 Credit Risk Modifiers . . . . . . . . . . . . . .
21.4.1 Credit Triggers . . . . . . . . . . . . .
21.4.2 Time Puts . . . . . . . . . . . . . . . .
21.5 Answers to Chapter Examples . . . . . . . . .
Ch. 22

Ch. 23

Credit Derivatives
22.1 Introduction . . . . . . . . . . . . . . . .
22.2 Types of Credit Derivatives . . . . . . . . .
22.2.1 Credit Default Swaps . . . . . . . .

22.2.2 Total Return Swaps . . . . . . . . .
22.2.3 Credit Spread Forward and Options
22.2.4 Credit-Linked Notes . . . . . . . . .
22.3 Pricing and Hedging Credit Derivatives . .
22.3.1 Methods . . . . . . . . . . . . . . .
22.3.2 Example: Credit Default Swap . . .
22.4 Pros and Cons of Credit Derivatives . . . .
22.5 Answers to Chapter Examples . . . . . . .

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Managing Credit Risk
23.1 Measuring the Distribution of Credit Losses . . . .
23.2 Measuring Expected Credit Loss . . . . . . . . . .
23.2.1 Expected Loss over a Target Horizon . . . .
23.2.2 The Time Profile of Expected Loss . . . . .
23.3 Measuring Credit VAR . . . . . . . . . . . . . . .
23.4 Portfolio Credit Risk Models . . . . . . . . . . . .
23.4.1 Approaches to Portfolio Credit Risk Models
23.4.2 CreditMetrics . . . . . . . . . . . . . . . .
23.4.3 CreditRisk+ . . . . . . . . . . . . . . . . .
23.4.4 Moody’s KMV . . . . . . . . . . . . . . . .

23.4.5 Credit Portfolio View . . . . . . . . . . . .
23.4.6 Comparison . . . . . . . . . . . . . . . . .
23.5 Answers to Chapter Examples . . . . . . . . . . .

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474
479
479
481
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486
486

487
487

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491
491
492
493
496
497
498
501
502
502
505
506

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509
510
513
513
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518
518
519
522
523
524
524
527


xvi

CONTENTS

Part V: Operational and Integrated Risk Management
Ch. 24

Ch. 25

Ch. 26

Ch. 27

531

Operational Risk
24.1 The Importance of Operational Risk . .
24.1.1 Case Histories . . . . . . . . . .
24.1.2 Business Lines . . . . . . . . . .
24.2 Identifying Operational Risk . . . . . .
24.3 Assessing Operational Risk . . . . . . .
24.3.1 Comparison of Approaches . . .
24.3.2 Acturial Models . . . . . . . . .
24.4 Managing Operational Risk . . . . . . .
24.4.1 Capital Allocation and Insurance
24.4.2 Mitigating Operational Risk . . .
24.5 Conceptual Issues . . . . . . . . . . .
24.6 Answers to Chapter Examples . . . . .

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533
534
534
535
537
540
540
542
545
545
547
549
550

Risk Capital and RAROC
25.1 RAROC . . . . . . . . . . . . . . . .
25.1.1 Risk Capital . . . . . . . . . .
25.1.2 RAROC Methodology . . . . .
25.1.3 Application to Compensation .
25.2 Performance Evaluation and Pricing .
25.3 Answers to Chapter Examples . . . .

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563
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569
571

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573
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576
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581
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Best Practices Reports
26.1 The G-30 Report . . . . . . . . . . . .
26.2 The Bank of England Report on Barings
26.3 The CRMPG Report on LTCM . . . . . .
26.4 Answers to Chapter Examples . . . . .
Firmwide Risk Management
27.1 Types of Risk . . . . . . . . . . . .
27.2 Three-Pillar Framework . . . . . . .
27.2.1 Best-Practice Policies . . . .
27.2.2 Best-Practice Methodologies
27.2.3 Best-Practice Infrastructure .
27.3 Organizational Structure . . . . . .
27.4 Controlling Traders . . . . . . . . .
27.4.1 Trader Compensation . . . .
27.4.2 Trader Limits . . . . . . . .
27.5 Answers to Chapter Examples . . .

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CONTENTS

xvii

Part VI: Legal, Accounting, and Tax Risk Management

587

Ch. 28

Ch. 29

Legal Issues
28.1 Legal Risks with Derivatives . . . . . .

28.2 Netting . . . . . . . . . . . . . . . . .
28.2.1 G-30 Recommendations . . . . .
28.2.2 Netting under the Basel Accord .
28.2.3 Walk-Away Clauses . . . . . . .
28.2.4 Netting and Exchange Margins .
28.3 ISDA Master Netting Agreement . . . .
28.4 The 2002 Sarbanes-Oxley Act . . . . .
28.5 Glossary . . . . . . . . . . . . . . . .
28.5.1 General Legal Terms . . . . . .
28.5.2 Bankruptcy Terms . . . . . . .
28.5.3 Contract Terms . . . . . . . . .
28.6 Answers to Chapter Examples . . . . .

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Accounting and Tax Issues
29.1 Internal Reporting . . . . . . . . . . . . . . . .
29.1.1 Purpose of Internal Reporting . . . . . .
29.1.2 Comparison of Methods . . . . . . . . .
29.1.3 Historical Cost versus Marking-to-Market
29.2 External Reporting: FASB . . . . . . . . . . . . .
29.2.1 FAS 133 . . . . . . . . . . . . . . . . . .

29.2.2 Definition of Derivative . . . . . . . . . .
29.2.3 Embedded Derivative . . . . . . . . . . .
29.2.4 Disclosure Rules . . . . . . . . . . . . .
29.2.5 Hedge Effectiveness . . . . . . . . . . . .
29.2.6 General Evaluation of FAS 133 . . . . . .
29.2.7 Accounting Treatment of SPEs . . . . . .
29.3 External Reporting: IASB . . . . . . . . . . . . .
29.3.1 IAS 37 . . . . . . . . . . . . . . . . . . .
29.3.2 IAS 39 . . . . . . . . . . . . . . . . . . .
29.4 Tax Considerations . . . . . . . . . . . . . . . .
29.5 Answers to Chapter Examples . . . . . . . . . .

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589
590
593
593
594
595
596
596
600
601
601
602
602
603

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605
606
606
607
610
612
612
613
614
615
616
617
617
620
620
621
622
623

Part VII: Regulation and Compliance

627

Ch. 30

629
629
631
632

Regulation of Financial Institutions
30.1 Definition of Financial Institutions . . . . . . . . . . . . . . .
30.2 Systemic Risk . . . . . . . . . . . . . . . . . . . . . . . . . .
30.3 Regulation of Commercial Banks . . . . . . . . . . . . . . . .

Financial Risk Manager Handbook, Second Edition


xviii

CONTENTS
30.4 Regulation of Securities Houses . . . . . . . . . . . . . . . . 635
30.5 Tools and Objectives of Regulation . . . . . . . . . . . . . . 637
30.6 Answers to Chapter Examples . . . . . . . . . . . . . . . . . 639

Ch. 31

Ch. 32

The Basel Accord
31.1 Steps in The Basel Accord . . . . . . . . . . . . .
31.1.1 The 1988 Accord . . . . . . . . . . . . . .
31.1.2 The 1996 Amendment . . . . . . . . . . .
31.1.3 The New Basel Accord . . . . . . . . . . .
31.2 The 1988 Basel Accord . . . . . . . . . . . . . . .

31.2.1 Risk Capital . . . . . . . . . . . . . . . . .
31.2.2 On-Balance-Sheet Risk Charges . . . . . . .
31.2.3 Off-Balance-Sheet Risk Charges . . . . . . .
31.2.4 Total Risk Charge . . . . . . . . . . . . . .
31.3 Illustration . . . . . . . . . . . . . . . . . . . . .
31.4 The New Basel Accord . . . . . . . . . . . . . . .
31.4.1 Issues with the 1988 Basel Accord . . . . .
31.4.2 The New Basel Accord: Credit Risk Charges
31.4.3 Securitization and Credit Risk Mitigation . .
31.4.4 The Basel Operational Risk Charge . . . . .
31.5 Answers to Chapter Examples . . . . . . . . . . .
31.6 Further Information . . . . . . . . . . . . . . . .
The Basel Market Risk Charges
32.1 The Standardized Method . . . . .
32.2 The Internal Models Approach . . .
32.2.1 Qualitative Requirements . .
32.2.2 The Market Risk Charge . . .
32.2.3 Combination of Approaches
32.3 Stress-Testing . . . . . . . . . . . .
32.4 Backtesting . . . . . . . . . . . . .
32.4.1 Measuring Exceptions . . . .
32.4.2 Statistical Decision Rules . .
32.4.3 The Penalty Zones . . . . . .
32.5 Answers to Chapter Examples . . .

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641
641
641
642
642
645
645
647
648
652
654
656
657
658

660
661
663
665

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669
669
671
671
672
674
677
679
680
680
681
684
695

Financial Risk Manager Handbook, Second Edition


Preface
The FRM Handbook provides the core body of knowledge for financial risk managers.
Risk management has rapidly evolved over the last decade and has become an indispensable function in many institutions.
This Handbook was originally written to provide support for candidates taking the
FRM examination administered by GARP. As such, it reviews a wide variety of practical topics in a consistent and systematic fashion. It covers quantitative methods,
capital markets, as well as market, credit, operational, and integrated risk management. It also discusses the latest regulatory, legal, and accounting issues essential to
risk professionals.
Modern risk management systems cut across the entire organization. This breadth
is reflected in the subjects covered in this Handbook. This Handbook was designed to
be self-contained, but only for readers who already have some exposure to financial
markets. To reap maximum benefit from this book, readers should have taken the
equivalent of an MBA-level class on investments.
Finally, I wanted to acknowledge the help received in the writing of this second edition. In particular, I would like to thank the numerous readers who shared comments
on the previous edition. Any comment and suggestion for improvement will be welcome. This feedback will help us to maintain the high quality of the FRM designation.
Philippe Jorion
April 2003

xix