THE VaR IMPLEMENTATION HANDBOOK GREG N. GREGORIOU EDITOR New York Chicago San Francisco Lisbon London Madrid Mexico City Milan New Delhi San Juan Seoul Singapore Sydney Toronto Copyright © 2009 by The McGraw-Hill Companies, Inc. All rights reserved. Except as permitted under the United States Copyright Act of 1976, no part of this publication may be reproduced or distributed in any form or by any means, or stored in a database or retrieval system, without the prior written permission of the publisher. ISBN: 978-0-07-161514-3 MHID: 0-07-161514-8 The material in this eBook also appears in the print version of this title: ISBN: 978-0-07-161513-6, MHID: 0-07-161513-X. All trademarks are trademarks of their respective owners. Rather than put a trademark symbol after every occurrence of a trademarked name, we use names in an editorial fashion only, and to the benefit of the trademark owner, with no intention of infringement of the trademark. 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C O N T E N T S EDITOR xv CONTRIBUTORS xvii PART ONE VaR MEASUREMENT Chapter 1 Calculating VaR for Hedge Funds 3 Monica Billio,Mila Getmansky,and Loriana Pelizzon Introduction 4 Hedge Funds 5 Value at Risk 6 Data 13 Results and Discussion 14 Conclusion 20 References 20 Appendix: Strategic Decisions 22 Chapter 2 Efficient VaR: Using Past Forecast Performance to Generate Improved VaR Forecasts 25 Kevin Dowd and Carlos Blanco Introduction 25 ABacktesting Framework 27 Using Backtest Results to Recalibrate the Parameters of the VaR Model 29 Some Examples 31 Conclusion 36 References 37 Appendix 38 v vi Contents Chapter 3 Applying VaR to Hedge Fund Trading Strategies: Limitations and Challenges 41 R. McFall Lamm,Jr. Introduction 41 Background 43 Analytical Approach 44 Application Considerations 46 Impact of VaR Control 47 Short versus Long History for Setting VaR Risk Limits 51 Implications 53 Conclusion 55 References 56 Chapter 4 Cash Flow at Risk: Linking Strategy and Finance 59 Ulrich Hommel Introduction 59 AProcess View of the Corporate Risk Management Function 62 Value-Based Motives of Firm-Level Risk Management 66 The Incompatibility of Simple Value at Risk with Corporate Risk Management 70 Operationalizing CFaR 72 Governance Implications 78 Conclusion 80 References 81 Chapter 5 Plausible Operational Value-at-Risk Calculations for Management Decision Making 85 Wilhelm Kross,Ulrich Hommel,and Martin Wiethuechter Introduction 85 Operational Risk under Basel II 86 Desirable Side Effects of Operational Risk Initiatives 91 Toward Strategy-Enhancing Operational Risk Initiatives 95 Employment of Real Option Techniques in Operational Risk Initiatives 99 Contents vii Conclusion 102 References 103 Chapter 6 Value-at-Risk Performance Criterion:A Performance Measure for Evaluating Value-at-Risk Models 105 Zeno Adams and Roland Füss Introduction 106 Value-at-RiskPerformance Criterion (VPC) 107 Effects of Changing Volatility and Return Distribution 109 Conclusion 115 References 119 Chapter 7 Explaining Cross-Sectional Differences in Credit Default Swap Spreads:An Alternative Approach Using Value at Risk 121 Bastian Breitenfellner and Niklas Wagner Introduction 122 Estimation Methodology 126 Data and Explanatory Variables 128 Empirical Results 131 Conclusion 135 References 135 Chapter 8 Some Advanced Approaches to VaR Calculation and Measurement 139 François-Éric Racicot and Raymond Théoret Introduction 139 Parametric VaR and the Normal Distribution 141 Using Historical Simulation to Compute VaR 142 The Delta Method for Computing VaR 145 The Monte Carlo Simulation 147 The Bootstrapping Method 149 Cornish-Fisher Expansion and VaR 155 viii Contents Value at Risk for a Distribution Other Than the Normal but Using a Normal Coefficient 156 Copulas, Fourier’s Transform, and the VaR 157 Conclusion 162 References 163 Chapter 9 Computational Aspects of Value at Risk 167 Germán Navarro and Ignacio Olmeda Introduction 168 Supercomputing Technologies 169 Graphics Processing Unit Computing 171 An Example 174 Conclusion 182 References 182 PART 2 RISK AND ASSET MANAGEMENT Chapter 10 Value-at-Risk–Based Stop-Loss Trading 187 Bernd Scherer Introduction 188 Stop-Loss Rules for Alternative Return Processes 189 Some Well-known Strategies 192 Conditional Autocorrelation: Threshold Autoregressive Models 196 Conclusion 202 References 203 Appendix: Currency Universe and Data Availability 205 Chapter 11 Modeling Portfolio Risks with Time-Dependent Default Rates in Venture Capital 207 Andreas Kemmerer,Jan Rietzschel,and Henry Schoenball Introduction 208 Contents ix Initial Model 208 Risk Modeling with Time-Dependent Default Rates 215 Empirical Evidence 220 Conclusion 226 References 226 Chapter 12 Risk Aggregation and Computation of Total Economic Capital 229 Peter Grundke Introduction 229 Additive Approach 232 Correlation-Based Square-Root Formula 232 Top-Down Approach 233 Bottom-Up Approach 240 Conclusion 241 References 247 Chapter 13 Value at Risk for High-Dimensional Portfolios: A Dynamic Grouped t-Copula Approach 253 Dean Fantazzini Introduction 254 Dynamic Grouped t-Copula Modeling: Definition and Estimation 256 Simulation Studies 259 Empirical Analysis 271 Conclusion 277 References 279 Appendix: List of Analyzed Stocks 282 Chapter 14 A Model to Measure Portfolio Risks in Venture Capital 283 Andreas Kemmerer Introduction 284 Toward a Risk Model in Venture Capital 285 ARisk Model for Venture Capital 290 x Contents Data Sample 297 Empirical Evidence 299 Conclusion 308 References 308 Chapter 15 Risk Measures and Their Applications in Asset Management 311 S. Ilker Birbil,Hans Frenk,Bahar Kaynar,and Nilay Noyan Introduction 312 Risk Measures 315 ASingle-Period Portfolio Optimization Problem 320 Elliptical World 324 Modified Michelot Algorithm 328 Computational Results 331 Conclusion 336 References 336 Chapter 16 Risk Evaluation of Sectors Traded at the ISE with VaR Analysis 339 Mehmet Orhan and Gökhan Karaahmet Introduction 339 Value-at-Risk Comparison of Sectors Traded at the Istanbul Stock Exchange (ISE) 343 Performance of VaR in Evaluating Risk 350 Conclusion 356 References 357 PART THREE MODELING Chapter 17 Aggregating and Combining Ratings 361 Rafael Weißbach,Frederik Kramer,and Claudia Lawrenz Introduction 362 Contents xi Mathematical Background 364 Aggregating Ratings 365 Impact Studies 367 Conclusion 379 References 381 Chapter 18 Risk-Managing the Uncertainty in VaR Model Parameters 385 Jason C. Hsu and Vitali Kalesnik The Subprime Crisis of 2008 386 Parameter Uncertainty 389 An Illustrative Example with Mean Uncertainty 390 An Illustrative Example with Variance Uncertainty 394 An Illustrative Example with Correlation Uncertainty 396 Conclusion 398 Acknowledgment 400 References 400 Chapter 19 Structural Credit Modeling and Its Relationship To Market Value at Risk:An Australian Sectoral Perspective 403 David E. Allen and Robert Powell Introduction 404 Structural Model 406 Methodology 407 Results 410 Conclusion 412 References 412 Chapter 20 Model Risk in VAR Calculations 415 Peter Schaller Introduction 415 Sources of Model Risk 416 xii Contents Backtesting 420 Bias versus Uncertainty 422 Pivotal Quantile Estimates 428 Applications 432 Conclusion 436 References 436 Chapter 21 Option Pricing with Constant and Time-Varying Volatility 439 Willi Semmler and Karim M. Youssef Introduction 439 The Black Scholes PDE 441 Solution Methods 444 What We Get and What We Do Not Get from Black Scholes 447 Seeking Sigma 448 Historical Volatility 449 GARCH(1,1) 450 Heston’s Volatility 452 The Heston Valuation Equation 453 Calibrating the Heston Parameters and Results 457 Conclusion 460 References 460 Chapter 22 Value at Risk under Heterogeneous Investment Horizons and Spatial Relations 463 Viviana Fernandez Introduction 464 Methodological Issues 466 Empirical Testing of Spatial Linkages 471 Conclusion 480 References 481