RiskMetrics
Ô
—Technical Document
Fourth Edition (December 1996)
Table of contents
Part I Risk Measurement Framework
Chapter 1. Introduction 3
1.1 An introduction to Value-at-Risk and RiskMetrics 6
1.2 A more advanced approach to Value-at-Risk using RiskMetrics 7
1.3 What RiskMetrics provides 16
Chapter 2. Historical perspective of VaR 19
2.1 From ALM to VaR 22
2.2 VaR in the framework of modern financial management 24
2.3 Alternative approaches to risk estimation 26
Chapter 3. Applying the risk measures 31
3.1 Market risk limits 33
3.2 Calibrating valuation and risk models 34
3.3 Performance evaluation 34
3.4 Regulatory reporting, capital requirement 36
Part II Statistics of Financial Market Returns
Chapter 4. Statistical and probability foundations 43
4.1 Definition of financial price changes and returns 45
4.2 Modeling financial prices and returns 49
4.3 Investigating the random-walk model 54
4.4 Summary of our findings 64
4.5 A review of historical observations of return distributions 64
4.6 RiskMetrics model of financial returns: A modified random walk 73
4.7 Summary 74
Chapter 5. Estimation and forecast 75
5.1 Forecasts from implied versus historical information 77
5.2 RiskMetrics forecasting methodology 78
5.3 Estimating the parameters of the RiskMetrics model 90
5.4 Summary and concluding remarks 100
Part III Risk Modeling of Financial Instruments
Chapter 6. Market risk methodology 105
6.1 Step 1—Identifying exposures and cash flows 107
6.2 Step 2—Mapping cash flows onto RiskMetrics vertices 117
6.3 Step 3—Computing Value-at-Risk 121
6.4 Examples 134
Chapter 7. Monte Carlo 149
7.1 Scenario generation 151
7.2 Portfolio valuation 155
7.3 Summary 157
7.4 Comments 159
Part IV RiskMetrics Data Sets
Chapter 8. Data and related statistical issues 163
8.1 Constructing RiskMetrics rates and prices 165
8.2 Filling in missing data 170
8.3 The properties of correlation (covariance) matrices and VaR 176
8.4 Rebasing RiskMetrics volatilities and correlations 183
8.5 Nonsynchronous data collection 184
Chapter 9. Time series sources 197
9.1 Foreign exchange 199
9.2 Money market rates 199
9.3 Government bond zero rates 200
9.4 Swap rates 202
9.5 Equity indices 203
9.6 Commodities 205
Chapter 10. RiskMetrics volatility and correlation files 207
10.1 Availability 209
10.2 File names 209
10.3 Data series naming standards 209
10.4 Format of volatility files 211
10.5 Format of correlation files 212
10.6 Data series order 214
10.7 Underlying price/rate availability 214
Part V Backtesting
Chapter 11. Performance assessment 217
11.1 Sample portfolio 219
11.2 Assessing the RiskMetrics model 220
11.3 Summary 223
Appendices
Appendix A. Tests of conditional normality 227
Appendix B. Relaxing the assumption of conditional normality 235
Appendix C. Methods for determining the optimal decay factor 243
Appendix D. Assessing the accuracy of the delta-gamma approach 247
Appendix E. Routines to simulate correlated normal random variables 253
Appendix F. BIS regulatory requirements 257
Appendix G. Using the RiskMetrics examples diskette 263
Appendix H. RiskMetrics on the Internet 267
Reference
Glossary of terms 271
Bibliography 275