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Value at Risk
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VALUE AT RISK:The New Benchmark forManaging Financial Risk
SECOND EDITION
PHILIPPE JORION
McGraw-HillNew York San Francisco Washington, D.C. Auckland BogotáCaracas Lisbon London Madrid Mexico City MilanMontreal New Delhi San Juan SingaporeSydney Tokyo Toronto
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Library of Congress Cataloging-in-Publication DataJorion, Philippe
Value at risk : the new benchmark for managing financial risk / Philippe Jorion.—2nd ed.p. cm.
ISBN 0-07-135502-21. Financial futures. 2. Risk management. I. Title: New benchmark for managing
financial risk. II. Title.
HG6024.3.J683 2000658.15�5—dc21 00–033239
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C o n t e n t s
Preface xix
The Risk Management Revolution xix
What Is VAR? xx
Who Can Use VAR? xx
Purpose of the Book xxiii
Structure of the Book xxiv
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? 121.3 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
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1.4 In Brief, What is VAR? 21
1.4.1 Definition of VAR 22
1.4.2 Illustration of VAR 221.5 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 342.2 Case Studies in Risk 36
2.2.1 Barings’ 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 422.3 Private-Sector Responses 43
2.3.1 G30 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) 452.4 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) 472.5 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
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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 683.4 The 1999 Credit Risk Revisions 68
3.4.1 The 1999 Credit Risk Revisions 70
3.4.2 Overall Assessment 703.5 Regulation of NonBanks 72
3.5.1 Securities Firms 72
3.5.2 Insurance Companies 74
3.5.3 Pension Funds 753.6 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 934.3 Risk 95
4.3.1 Risk as Dispersion 95
4.3.2 Quantiles 954.4 Asset Returns 98
4.4.1 Measuring Returns 98
4.4.2 Sample Estimates 101
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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 1085.1.2 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 1145.2 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 Parameters 119
5.2.6 Conversion of VAR Parameters 1215.3 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 Quantities 125
5.3.4 Comparison of Methods 1265.4 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? 1316.2 Model Backtesting with Exceptions 132
6.2.1 Model Verification Based on Failure Rates 132
6.2.2 The Basel Rules 136
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6.2.3 Conditional Coverage Models 1406.3 Model Verification: Other Approaches 142
6.3.1 Distribution Forecast Models 142
6.3.2 Parametric Models 143
6.3.3 Comparison of Methods 1446.4 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 1617.3 Examples 162
7.3.1 A Global Portfolio Equity Report 163
7.3.2 Barings: An Example in Risks 1657.4 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 1757.5 Conclusions 177
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
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8.3 Modeling Correlation 196
8.3.1 Moving Averages 196
8.3.2 Exponential Averages 197
8.3.3 Crashes and Correlations 1988.4 Using Options Data 199
8.4.1 Implied Volatilities 200
8.4.2 ISD as Risk Forecasts 2008.5 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 2159.2 Delta-Normal Method 219
9.2.1 Implementation 219
9.2.2 Advantages 220
9.2.3 Problems 2209.3 Historical Simulation Method 221
9.3.1 Implementation 221
9.3.2 Advantages 222
9.3.3 Problems 2239.4 Monte Carlo Simulation Method 224
9.4.1 Implementation 224
9.4.2 Advantages 225
9.4.3 Problems 2269.5 Empirical Comparisons 227
9.6 Summary 229
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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 23710.4 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 24510.5 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 24710.7 Conclusions 248
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 26311.4 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 27111.5 Linear Derivatives 274
11.5.1 Forward Contracts 274
11.5.2 Commodity Forwards 278
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11.5.3 Forward Rate Agreements 279
11.5.4 Interest Rate Swaps 28211.6 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 29812.2 Speed versus Accuracy 299
12.2.1 Accuracy 300
12.2.2 Acceleration Methods 30112.3 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 30412.4 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 31613.2 Default Risk 318
13.2.1 Default Rates 318
13.2.2 Recovery Rates 321
13.2.3 Estimating Default Risk 321
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13.3 Credit Exposure 323
13.3.1 Bonds versus Derivatives 323
13.3.2 Expected and Worst Exposure 32513.4 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 33413.6 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 34214.2 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 34914.3 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 35514.5 Conclusions 357
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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 36615.2 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 37515.3 VAR as a Risk-Control Tool 376
15.3.1 Adjusting Firm-Wide VAR 377
15.3.2 Adjusting Unit-Level VAR 37915.4 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 38516.2 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 40116.7 Conclusions 402
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Chapter 17.
VAR in Investment Management 407
17.1 Is VAR Applicable to Investment Management? 40817.2 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 41417.3 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 42017.4 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 42517.5 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
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19.3 Approaches 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 45719.5 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 46119.6 Conclusions 462
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 47020.3 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 47420.4 Why Risk Management? 475
20.4.1 Why Bother? 475
20.4.2 Why Hedge? 47720.5 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
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21.1.2 The Bank of England Report on Barings 486
21.1.3 The CRMPG Report on LTCM 48621.2 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 49221.3 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 50221.4 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 50721.5 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 51622.3 VAR Revisited 517
REFERENCES 521
INDEX 531
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P R E F A C E
THE RISK MANAGEMENT REVOLUTION
Risk management has truly experienced a revolution in the last few years.This was started by value at risk (VAR), a new method to measure fi-nancial market risk that was developed in response to the financial dis-asters of the early 1990s. By now, the VAR methodology has spread wellbeyond derivatives and is totally changing the way institutions approachtheir financial risk.
The first edition of this book provided the first comprehensive de-scription of value at risk. It quickly established itself as an indispensablereference on VAR, and has been called the “industry standard.” Transla-tions into Chinese, Hungarian, Japanese, Korean, Polish, Portuguese, andSpanish soon followed.
The last few years, however, have seen such advances in the field ofrisk management that a new edition became necessary. Initially confinedto measuring market risk, VAR is now being used to control and managerisk actively, both credit risk and operational risk. The VAR methodologyis now leading to the holy grail of firm-wide risk management.
This book is a completely revised version of the previous edition.The revision parallels the enormous increase in the body of knowledge inrisk management. Just the number of references, for instance, has bal-looned from 80 to more than 200. For many of these, the book now pro-vides Web addresses for convenient updates.
Brand new chapters have been added on the topics of back testing,stress testing, liquidity risk, operational risk, and integrated risk manage-ment. Applications of VAR have also been further developed, with sepa-rate chapters on using VAR to measure and control risk, to manage risk,and in investment management. An entire chapter is devoted to the tech-nology of risk. The last chapters describe the rapidly-evolving functionof the financial risk manager. The text also contains new material on prin-cipal components, extreme value theory, and loss distributions.
Since the last edition, unfortunately, there have been new occur-rences of financial disasters. This book draws lessons from these crises,in particular from Long Term Capital Management (LTCM). Finally, thebook has thoroughly updated the relevant regulatory requirements andnow uses terms and definitions that have become industry standards. Allin all, the book has been expanded more than 60 percent.
The broader scope of this book is reflected in its new subtitle. It hasbeen changed from The New Benchmark for Controlling Market Risk toThe New Benchmark for Managing Financial Risk.
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WHAT IS VAR?
VAR (value at risk) traces it roots to the infamous financial disasters ofthe early 1990s that engulfed Orange County, Barings, Metallgesellschaft,Daiwa, and so many others. The common lesson of these disasters is thatbillions of dollars can be lost because of poor supervision and manage-ment of financial risks. Spurred into action, financial institutions and reg-ulators turned to value at risk, an easy-to-understand method for quanti-fying market risk.
What is VAR? VAR is a method of assessing risk that uses standardstatistical techniques routinely used in other technical fields. Formally,VAR measures the worst expected loss over a given horizon under nor-mal market conditions at a given confidence level. Based on firm scien-tific foundations, VAR provides users with a summary measure of mar-ket risk. For instance, a bank might say that the daily VAR of its tradingportfolio is $35 million at the 99 percent confidence level. In other words,there is only 1 chance in a 100, under normal market conditions, for aloss greater than $35 million to occur. This single number summarizesthe bank’s exposure to market risk as well as the probability of an ad-verse move. Equally important, it measures risk using the same units asthe bank’s bottom line—dollars. Shareholders and managers can then de-cide whether they feel comfortable with this level of risk. If the answeris no, the process that led to the computation of VAR can be used to de-cide where to trim the risk.
In contrast with traditional risk measures, VAR provides an aggre-gate view of a portfolio’s risk that accounts for leverage, correlations, andcurrent positions. As a result, it is truly a forward-looking risk measure.VAR, however, applies not only to derivatives but to all financial instru-ments. Furthermore, the methodology can also be broadened from mar-ket risk to other types of financial risks.
The VAR revolution has been brought about by a convergence offactors. These include (1) the pressure from regulators for better controlof financial risks, (2) the globalization of financial markets, which has ledto exposure to more sources of risk, and (3) technological advances, whichhave made enterprise-wide risk management a not-so-distant reality.
WHO CAN USE VAR?
Basically, VAR should be used by any institution exposed to financial risk.We can classify applications of VAR methods as follows.
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■ Passive: information reporting The earliest application of VARwas for measuring aggregate risk. VAR can be used to apprisesenior management of the risks run by trading and investmentoperations. VAR also communicates the financial risks of a cor-poration to its shareholders in nontechnical, user-friendly terms.
■ Defensive: controlling risk The next step was to use VAR toset position limits for traders and business units. The advantageof VAR is that it creates a common denominator with which tocompare risky activities in diverse markets.
■ Active: managing risk VAR is now increasingly used to allo-cate capital across traders, business units, products, and even tothe whole institution. This process starts with adjusting returnsfor risk. Risk-adjusted performance measures (RAPM) automat-ically correct incentives for traders to take on extra risk due tothe option-like feature of bonuses. Once implemented, risk-based capital charges can guide the institution toward a betterrisk/return profile. The VAR methodology can also assist portfo-lio managers in making better decisions by offering a compre-hensive view of the impact of a trade on portfolio risk. Ulti-mately, it will help to create greater shareholder value added(SVA).
As a result, VAR is being adopted en masse by institutions all overthe world. These include:
■ Financial institutions Banks with large trading portfolios havebeen at the vanguard of risk management. Institutions that dealwith numerous sources of financial risk and complicated instru-ments are now implementing centralized risk management sys-tems. Those that do not expose themselves to expensive fail-ures, such as occurred with Barings and Daiwa.
■ Regulators The prudential regulation of financial institutionsrequires the maintenance of minimum levels of capital as re-serves against financial risks. The Basel Committee on BankingSupervision, the U.S. Federal Reserve Bank, the U.S. Securitiesand Exchange Commission, and regulators in the EuropeanUnion have converged on VAR as a benchmark risk measure.
■ Nonfinancial corporations Centralized risk management isuseful to any corporation that has exposure to financial risks.
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Multinationals, for instance, have cash inflows and outflows de-nominated in many currencies, and suffer from adverse currencyswings. “Cash flow at risk analysis” can be used to tell howlikely a firm will be to face a critical shortfall of funds.
■ Asset managers Institutional investors are now turning to VARto manage their financial risks. The director of the Chryslerpension fund, for instance, stated that after the purchase of aVAR system, “We can now view our total capital at risk on aportfolio basis, by asset class and by individual manager. Ourmain goal was to . . . have the means to evaluate our portfoliorisk going forward.”
VAR also has direct implications for the recent crisis in Asia. Onewidespread interpretation is that the crisis was made worse by the “opac-ity’’ and poor risk management practices of financial institutions. If thistheory is correct, VAR systems would have helped. Professor Dornbusch(1998a) recently argued that “An effective supervisory system would, atthe least, put in place a mandatory VAR analysis not only for the indi-vidual financial institutions (as is in place in the US, for example) but infact for the entire country.” By drawing attention to potentially dangerousscenarios, a VAR analysis would induce countries to consider hedging for-eign currency liabilities, lengthening debt maturities, and taking othermeasures to reduce risk levels. Some have even proposed judging the cred-ibility of central banks by asking them to report their VAR.1
Many derivatives and banking disasters could have been avoided ifreporting systems had been more transparent. Time and again, losses areallowed to accumulate because positions are reported at book value, or atcost. When market values are available, this is inexcusable. Simply mark-ing-to-market brings attention to potential problems. VAR goes one stepfurther, asking what could happen under changes in market values.
In the end, the greatest benefit of VAR probably lies in the imposi-tion of a structured methodology for critically thinking about risk. Insti-tutions that go through the process of computing their VAR are forced toconfront their exposure to financial risks and set up an independent riskmanagement function supervising the front and back offices. Thus theprocess of getting to VAR may be as important as the number itself. In-
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1See Blejer and Schumacher (2000).
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deed, judicious use of VAR may have avoided many of the financial dis-asters experienced over the past years. There is no doubt that VAR is hereto stay.
PURPOSE OF THE BOOK
The purpose of this book is to provide a comprehensive presentation of the measurement and applications of value at risk. It is targeted to practitioners, students, and academics interested in understanding the recent revolution in financial risk management. This book can alsoserve as a text for advanced graduate seminars on risk management. Thefirst edition, for instance, has been used in business schools all over theworld.
To reap maximum benefit from this book, readers should have hadthe equivalent of an MBA-level class on investments. In particular, read-ers should have some familiarity with concepts of probability distribution,statistical analysis, and portfolio risk. Prior exposure to derivatives andthe fixed-income market is also a plus. The book provides a brief reviewof these concepts, then extends the analysis in the direction of measuringaggregate financial risks.
The variety of these topics reflects the fundamental nature of riskmanagement, which is integration. Risk managers must be thoroughly fa-miliar with a variety of financial markets, with the intricacies of the trad-ing process, and with financial and statistical modeling. Risk managementintegrates fixed-income markets, currency markets, equity markets, andcommodity markets. In each of these, financial instruments must be de-composed into fundamental building blocks, then reassembled for riskmeasurement purposes. No doubt this is why risk management has beencalled “the theory of particle finance.” All of this information then coa-lesces into one single number, a firm’s VAR.
The approach to this book reflects the trend and motivation to VAR.As VAR is based on firm scientific foundations, I have adopted a rigor-ous approach to the topic. Yet the presentation is kept short and enter-taining. Whenever possible, important concepts are illustrated with ex-amples. In particular, the recent string of financial disasters provides awealth of situations that illustrate various facets of financial risks. Thesecan serve as powerful object lessons in the need for better risk manage-ment.
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STRUCTURE OF THE BOOK
The book is broadly divided into five parts:
1. Motivation. Chapters 1 to 3 describe the evolving environmentthat has led to the widespread acceptance of VAR.
2. Building blocks. Chapters 4 to 8 provide a statistical and finan-cial foundation for the quantification of risk.
3. Value-at-risk systems. Chapters 9 to 14 compare and analyze indetail various approaches to financial risk measurement.
4. Applications of risk management systems. Chapters 15 to 20discuss applications of VAR systems, from measuring risk tomanaging market risk to enterprise-wide risk management.
5. The risk management profession. Finally, the last two chapters,21 and 22, discuss common pitfalls in risk management andprovide some thought on the rapid evolution of the risk man-agement profession.
Chapters 6, 10, 14, 16, 17, 18, 19, and 20 are completely new to thisedition. Most other chapters have been substantially improved. Chapters5 and 6, which in the last edition introduced fixed-income markets andderivatives, have been dropped, as they were relatively elementary.Going into more detail concerning the structure of the book, Chapter 1paints a broad picture of the evolution of risk management, which is in-extricably linked to the growth of the derivatives markets. The chapter de-scribes the types of financial risks facing corporations and provides a briefintroduction to VAR.
Chapter 2 draws lessons from recent financial disasters. It presentsthe stories of Barings, Metallgesellschaft, Orange County, and Daiwa. Theonly constant across these hapless cases is the absence of consistent riskmanagement policies. These losses have led to increasing regulatory ac-tivity as well as notable private-sector responses, such as J.P. Morgan’sRiskMetrics systems.2
Chapter 3 analyzes recent regulatory initiatives for using VAR. Wediscuss the Basel Agreement and the Capital Adequacy Directive imposedby the European Union, both of which use VAR to determine minimumcapital requirements for commercial banks. The regulation of other insti-
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2RiskMetrics and CreditMetrics are trademarks of J.P. Morgan. CorporateMetrics is a trademark ofthe Riskmetrics Group.
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tutions, pension funds, insurance companies, and securities firms is alsobriefly presented.
Chapter 4 explains how to characterize financial risks. We discussrisk and returns and the statistical concepts that underlie the measurementof VAR. Initially, only one source of financial risk is considered.
Chapter 5 turns to a formal definition of VAR. We show how VARcan be estimated from a normal distribution or from a completely generaldistribution. The chapter also discusses the choice of quantitative param-eters, such as the confidence level and target horizon.
Next, Chapter 6 turns to the verification of VAR models. Backtest-ing consists of systematically matching the history of VAR forecasts withtheir associated portfolio returns. This process enables the checking of theaccuracy of VAR forecasts and also provides ideas for model improve-ment.
Chapter 7 then turns to analytical methods for portfolio risk. Weshow how to build VAR using a variance-covariance matrix. To managerisk, however, we also need to understand what will reduce it. Thus thechapter provides a new analysis of VAR tools, such as marginal VAR, in-cremental VAR, and component VAR. These tools have become essentialto control and manage portfolio risk. Given that the dimensions of VARrisk structures can quickly become cumbersome, we also discuss meth-ods to simplify the covariance matrix used in VAR computations.
Chapter 8 discusses the measurement of dynamic inputs. The chap-ter covers the latest developments in the modeling of volatility and cor-relations, including moving averages and GARCH. Particular attention ispaid to the model used by RiskMetrics.
The next six chapters turn to the measurement of VAR for complexportfolios. Chapter 9 first compares the different methods available tocompute VAR. The first and easiest method is the delta-normal approach,which assumes that all instruments are linear combinations of primitivefactors and relies on delta valuation. For nonlinear instruments, however,the linear approximation is inadequate. Instead, risk should be measuredwith a full valuation method, such as historical simulation or Monte Carlosimulation. The chapter discusses the pros and cons of each method, aswell as situations where some methods are more appropriate.
Chapter 10 is an entirely new chapter devoted to stress testing, whichhas received increased attention recently and is a complement to tradi-tional probability-based VAR methods.
Chapter 11 develops applications of the delta-normal method, some-
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times called variance-covariance method. We show how to decomposeportfolios of bonds, derivatives and equities into sets of payoffs on “prim-itive” factors for the purpose of computing VAR.
Chapter 12 then turns to simulation methods. Monte Carlo methodssimulate risk factors with random numbers, from which complex portfo-lios can be priced. Because of its flexibility, Monte Carlo is by far themost powerful method to compute value at risk. It can potentially accountfor a wide range of risks, including price risk, volatility risk, credit risk,and model risk. This flexibility, however, comes at a heavy cost in termsof intellectual and systems development.
Chapter 13 tackles an increasingly important topic, the quantitativemeasurement of credit risk. Credit risk encompasses both default risk andmarket risk. The potential loss on a derivatives contract, for instance, de-pends both on the value of the contract and on the possibility of default.It is only recently that the banking industry has learned to measure creditrisk in the context of a portfolio. Once measured, credit risk can be man-aged and better diversified, like any financial risk.
One of the lessons of the LTCM disaster is the importance of li-quidity risk. This is why Chapter 14 is an entirely new chapter devotedto this topic.
The next six chapters are new, dealing with applications of VAR, atopic barely touched upon in the first edition of the book. Applicationsrange from passive to defensive to active. Chapter 15 shows how VARcan be used to quantify and to control risk, while Chapter 16 explainshow VAR can be used to manage risk actively. For the first time, institu-tions have a consistent measure of risk that can be used to compute risk-adjusted performance measures such as risk-adjusted return on capital(RAROC). This is because VAR can be viewed as a measure of “eco-nomic” risk capital necessary to support a position.
VAR applications are not limited to the banking sector, however. VARis now slowly spreading to the investment management industry, as it pro-vides a consistent method for setting risk limits and risk budgeting. Ap-plications, however, must be tailored to the specific needs of this industry.
Chapter 18 discusses the technology of risk, an oft-neglected topic.This ranges from the choice of a spreadsheet to large systems that sup-port strategic business initiatives. Global risk management systems re-quire a central repository for trades, positions, and valuation models,which allow institutions to measure and manage their risk profile mostefficiently.
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Chapter 19 then discusses operational risk, which has defied attemptsat quantification until recently. We are learning to quantify such risks us-ing tools borrowed from the insurance industry and from VAR techniques.Once quantified, operational risk can be subject to controls and capitalcharges.
The final step is to put together market, credit, and operational risk.Integration of these risks is important, as financial risks tend to slip to-ward areas where they are not measured. Thus the ideas behind the VARrevolution are quickly spreading to enterprise-wide risk management,which is described in Chapter 20.
For all their technical elegance, VAR methods do not, and are notdesigned to, measure catastrophic risks. Chapter 21 discusses pitfalls inthe interpretation of value at risk. We discuss a notable failure of a sup-posedly sophisticated risk management system, that of LTCM. This is whyrisk management is still as much an art as a science.
Finally, Chapter 22 offers some concluding thoughts. Once the do-main of a few exclusive pioneers, risk management is now wholly em-braced by the financial industry. It is also spreading fast among the cor-porate world. As a result, the financial risk manager function is nowacquiring strategic importance within the corporate structure. By pro-moting sound risk management practices, this book will hopefully con-tinue to foster a safer environment in financial markets.
Philippe JorionIrvine, California
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A C K N O W L E D G M E N T S
This book has benefited from the comments of numerous practitionersand academics. In particular, I would like to thank James Overdahl, of theOffice of the Comptroller and Currency, for his detailed review of the firstversion of this book. This original project also benefited from the help ofLester Seigel, formerly at World Bank, and of Jacob Boudoukh, at NewYork University.
The success of the first edition of this book is also largely attribut-able to its readers. In particular, the Global Association of Risk Profes-sionals (GARP) was kind enough to select this book as the main text forits fast-expanding Financial Risk Manager (FRM) examination.
The second edition of this book has also been enriched by discus-sions with Robert Ceske at NetRisk, Till Guldimann, formerly of J.P. Morgan and now at Infinity, Leo de Bever and his crew at Ontario Teach-ers’ Pension Plan, Raza Hasan at Merrill Lynch, Dan Rosen at Algorith-mics, Barry Schachter at Chase Manhattan, Deborah Williams at Meri-dien Research, and many others. Todd Wolter, now at Credit Suisse AssetManagement, provided solid research support during the project. Myapologies to anyone I inadvertently missed. Needless to say, I assume re-sponsibility for any remaining errors.
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