THE var IMPLEMENTATION HANDBOOK GREG n GREGORIOU

Advance Praise for The VaR Implementation Handbook A valuable survey of the latest developments in VaR methodology This book will be of interest to both academics and practitioners working in the arcane field of financial market risk management —Professor Moorad Choudhry, Department of Economics, London Metropolitan University The current VAR book edited by Professor Gregoriou is a serious and well-thought contribution to the finance academic literature Today Value-at-Risk is considered by many academics as an immense area of research with continued explosive growth The content of the book is designed to advance the knowledge of scholars worldwide, while guiding practitioners through the modern techniques of risk measurement —Dr Sotiris K Staikouras, Associate Professor of Banking & Finance and Director Undergraduate Programmes, Cass Business School, London This timely book contains in-depth analyses of VaR measurement and modeling, as well as useful discussions of various managerial applications I highly recommend this book for anyone wanting to deepen their understanding of VaR theory and practice —Paul Brockman, Matteson Professor of Financial Services, University of Missouri, College of Business To successfully manage even the strongest market turbulences like the subprime credit crises market participants need efficient instruments to continuously measure their risk This book perfectly helps practitioners to qualify and to quantify the specific types of risk exposure by providing the tools for modelling the uncertainties inherent in their portfolios However,Value at Risk is a value adding compendium not only in difficult times.” —Christian Hoppe, Senior Specialist Securitization and Credit Derivatives, Commerzbank AG This book provides a broad overview of different Value-at-Risk applications for the banking and insurance sector as well as for the portfolio management especially for alternative investments Professor Gregoriou has collected an excellent composition of articles which feature advanced Value-at-Risk applications and their usage in different fields of the financial industry —Oliver Schwindler, Investment Analyst Hedge Funds at Feri Institutional Advisors GmbH THE VaR IMPLEMENTATION HANDBOOK This page intentionally left blank 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 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the possibility of such damages This limitation of liability shall apply to any claim or cause whatsoever whether such claim or cause arises in contract, tort or otherwise C O N T E N T S EDITOR xv CONTRIBUTORS xvii PART ONE VaR MEASUREMENT Chapter Calculating VaR for Hedge Funds Monica Billio, Mila Getmansky, and Loriana Pelizzon Introduction Hedge Funds Value at Risk Data 13 Results and Discussion 14 Conclusion 20 References 20 Appendix: Strategic Decisions 22 Chapter Efficient VaR: Using Past Forecast Performance to Generate Improved VaR Forecasts 25 Kevin Dowd and Carlos Blanco Introduction 25 A Backtesting 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 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 Cash Flow at Risk: Linking Strategy and Finance 59 Ulrich Hommel Introduction 59 A Process 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 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 Value-at-Risk Performance Criterion: A Performance Measure for Evaluating Value-at-Risk Models 105 Zeno Adams and Roland Füss Introduction 106 Value-at-Risk Performance Criterion (VPC) 107 Effects of Changing Volatility and Return Distribution Conclusion 115 References 119 109 Chapter 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 Some Advanced Approaches to VaR Calculation and Measurement 139 Franỗois-ẫric 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 155 514 Bond flows strategy (BFLOW), 193–194 conditional expected returns of, 199 in SETAR estimated results, 198, 201 Bond yields, 124 Bootstrapping method for calculating VaR, 149–154 concept of, 149–150 of one stock, 151–153 of TSX, 151–153 VBA and, 153 Bottom-up approach, to risk aggregation, 231 costs of, 246 CreditMetrics and, 240–242 dynamic version of, 246 example of, 241–245 literature review, 240–246 Monte Carlo simulations v., 246 problems with, 245–246 simulation in, 241 top-down approach v., 247 Box-Cox transformation, of GARCH model, 156 Brazilian firms, spatial effects on, 471–474 Brown, Robert, 439 Brownian motion process, 441–442, 444 Bull NovaScale, 173 CAD See Capital Adequacy Directive Calculation, of VaR delta method for, 145–147, 341–342 historical simulation for, 142–145, 341 Call ATM, 447–448 European, 161, 444–446, 456 PDE and, 444–446 plain vanilla, 457 Canadian exchange rates, 148–149 Canadian interest rates, 142–144, 146, 148, 150 Canonical maximum likelihood (CML), 236 Capital accord, Basel, 86, 140, 168, 230, 266 Capital Adequacy Accord of 1988, 168 Capital Adequacy Directive (CAD), 386 Capital adequacy violations, 389 Capital allocation, efficient, 108 Capital asset pricing model (CAPM), 140 See also Spatial CAPM asset returns explained by, 464 heterogeneous investment and, 463–464, 472 SAR error model v., 479 standard, 472, 477 CAPM See Capital asset pricing model Carried interests, 286 Carry strategy (CARRY), 192, 194–195 conditional expected returns of, 199 in SETAR estimated results, 198, 201 Cash flow at risk (CFaR) analysis, 61–62 cone of uncertainty and, 61 coordination hypothesis and, 68–69 dynamic, 77 implementations of, 72 as minimum cash flow, 71 operationalizing, 72–77 risk factors linked to corporate performance in, 74 Index shareholder value and, 81 value-based management and, 59 VaR v., 72 Cash flow based motives, 67 Cash-flow statements, 71, 74–75 Cash-flow targets, 71 Cauchy distributions, 387 CAViaR family, 109 CDD See Conditional DD CDF See Cumulative distribution function CDS See Credit default swap Central Bank of Turkey, 350–351 Central limit theorem, PDE and, 445 Central quantiles, 271 Centralization divisions overcome by, 80 full-scale, 64 of risk management function, 63, 78, 80 CF VaR model See Cornish-Fisher VaR model CFaR See Cash flow at risk Chilean firms, spatial effects on, 471–474 Chinese Investment Corporation, 386 Chi-squared distribution, 71, 428 Cholesky factorization, 178 Citigroup, 386 Clustering, volatility, 452–453, 460 CML See Canonical maximum likelihood Coherent risk measures properties satisfied by, 319 theory of, 314 Cointegration analysis, 465 Collateral, 285 Combined estimator, external generator v., 373 Combining, of ratings, 367–375 Commodity trading advisors (CTAs), 45 Commonwealth Bank, 404 Communications sector, 298, 300, 302 Compounded VPC, 115, 117 Compute unified device architecture (CUDA), 171 Computer sector, 298, 300, 302 Conditional autocorrelation, stop-loss trading and, 196–202 Conditional coverage test, 255, 275 Conditional DD (CDD), 409–410 Conditional probability of default (CPD) CVaR and, 405 nonparametric, 409–411 parametric, 410 in structural modeling, 403, 409–410 Conditional quantile estimation asymmetric linear loss function in, 275 CDF and, 266 central quantiles in, 271 extreme quantiles in, 271 high-dimensional portfolios and, 265–271 Monte Carlo simulation and, 267–270 Conditional standard deviation, 409–410 Conditional value at risk (CVaR) CPD and, 405 definition of, 319 downside risk measured by, 316 market, 407 in Markowitz model, 311 in risk management, 311, 314 Index role of, 312 VaR and, 317, 324–326 Conditional variance, 451 Cone of uncertainty, CFaR and, 61 Confidence level, 230 Constant Conditional Correlation, 272 Constant t-copula, 255–256 Consumer price index (CPI), 351 Consumer sector, 298, 300, 302 Contiguity, 465 Control rights, 285 Convergence, speed of, 265 Convertible bond arbitrage strategy, 15, 22 Convexity, 448 Coordination centralized, 80 hypothesis, 62, 68–69 Copula(s) See also t-copula advantages of, 238 basics of, 234–235, 254 with degrees of freedom, 237–238 density function and, 234–235 estimation issues with, 235–236 Gaussian, 160, 254 normal, 237 problems with, 238–240 in simulation, 237–238 theory of, 254 top-down approach to risk aggregation and, 233–240 VaR and, 157–161 Cornish-Fisher (CF) VaR model, 4, excess returns and VaR estimates for, 16–17 expansion, 155–156 percentage of failures for, 17–19 performance of, 20 Corporate accounting, 102 Corporate governance, adequacy of risk management system ensured by, 60 Corporate headquarters, subsidiary management v., 79 Corporate hedging policies extreme events and, 70 financial and operative instruments in, 73–74 guidelines for the design of, 69 Corporate risk management cash-flow-based implementation of, 75 challenges of, 62–63 effectiveness of, 63 formal system of risk controls in, 63 incompatibility with simple VaR, 70–72 inflexible guidelines of, 68 minimum standards for, in Europe, 68 process view of, 62–63 shareholder value created by, 66–67 Corporate strategy, risk management v., 60–61 Correlation Constant Conditional, 272 Dynamic Conditional, 272 between macroeconomic factors, 299 parameters, unconditional, 260 spatial, 464 structural, 409 uncertainty, 396–398 515 Correlation-based square-root formula, 232–233 Counterparty risk, 241 Covariance, wavelet-based, 465 Cox regression, 380 CPD See Conditional probability of default CPI See Consumer price index CPU codes, 172 CRB commodity index, 47–48 Credit default swap (CDS) bond yields’ relationship with, 124 characteristics of, 122 cross-sectional differences in, 121–122, 125–126 data set and, 128–129 descriptive statistics of, 130–131 explanatory variables and, 129 mispricing of, 134–135 panel data analysis and, 126–127, 131–133 portfolio analysis and, 127–128, 134–135 pricing of, 122–123 spread values of, 125–126 stock markets and, 124 VaR and, 121–122, 125–135 volatility of, 127, 132–133 Credit model PD, 410 Credit modeling See Structural credit modeling Credit portfolio model, 240 Credit ratings aggregation of, 361, 365–367, 379–381 in Australia, 405 combining of, 367–375 CreditMetrics and, 375–376 EC implications of, 375–379 exemplary history, 370 external, 361, 363, 371–372, 381 from German bank, 371, 381 grouped t-copula and, 272 impact studies of, 367–379 by independent rating agencies, 363, 381 internal, 361, 363, 371–372, 381 as key parameter, 361 mathematical background of, 364–365 migration histories of, 363–364 Monte Carlo simulations and, 377 S&P, 363, 370–371, 381, 408 typical history of, 362 Credit risk, 140, 240, 246, 405 Credit risk market, 122 Credit spread, changes in, 244 Credit Suisse Financial Products, 291 Credit VaR Basel II and, 160 copulas for estimating, 157–161 CreditMetrics, 209, 236, 405 bottom-up approach and, 240–242 credit ratings and, 375–376 portfolio risk model and, 287 procedure of, 376 CreditPortfolioView, 209, 287–288, 404–405 CreditRisk model, 405 default risk and, 211, 301–303 model sector analysis approaches of, 289, 293 portfolio risk model and, 283–284, 288–290, 292–293, 308 516 CreditRisk model (Cont.) probability-generating function of, 289 rating model for adjusting, 292 time-dependent default rates and, 207–211, 215, 218–219, 226 Cross-autocorrelation, 239 Cross-section CDS differences in, 121–122, 125–126 linkages, 466–467 tools, from spatial econometrics, 465 CSFB/Tremont hedge fund index returns, 13–14 CTAs See Commodity trading advisors CUDA See Compute unified device architecture Cumulative default probability, 159 Cumulative distribution function (CDF), 266 Currency strategies, 192–195 Currency universe, data availability and, 205–206 CVaR See Conditional value at risk Daily returns, volatility of, 422 Data generating processes (DGPs), 256, 260, 271 Data set, CDS and, 128–129 Data tranches, 411–412 DCC model See Dynamic conditional correlation model DD See Distance to default Debt ratios, 466, 471–472, 475 Decay factor, 433 Decision making analysis of, 102 flexibility of, 99–100 models of, 312 under risk, 311 theory of, 312 Decomposition, wavelet-based, 465, 470, 475–477 Dedicated short bias strategies, 16–17, 22 Deep out-of-the-money options, 69 Default rates, 159–160 See also Time-dependent default rates, in venture capital CreditRisk modeling, 211, 301–303 distribution of, 303 estimated default frequency, 406 idiosyncratic risk and, 219 by industrial sector, 298, 302 long-term, 208, 221 models based on, 288 sector, 212–213, 302 single-sector, 295 stage and, 221 Default risk creditRisk model and, 211, 301–303 distance to, 406 probability of, 291–292, 362–363, 377–378 by sector, 212–213, 302 single-sector, 295 time-independent, 218 unbiased estimation of, 362 Degrees of freedom copulas with, 237–238 elliptical distributions and, 325 high-dimensional portfolios and, 265 ML estimator of, 258 quarterly data and, 472–473 Index Delta method equation for, 145 for VaR calculation, 145–147, 341–342 variance-covariance matrix in, 146–147 Density function copulas and, 234–235 of investment with correlation uncertainty, 398 of investment with mean uncertainty, 391–392 of investment with variance uncertainty, 395 properties of, 446 spectral, 161 Derivatives, hedge funds trading in, Derivatives Market, 344 Deutsche Bank, 386 DGPs See Data generating processes Diffusion term, 442 Directional strategies, 13–14 Discount factor, 76 Discrete wavelet transform (DWT), 470 Distance to default (DD) conditional, 409–410 definition of, 406, 408 Distressed high-yield strategies, 23 Distribution chi-squared, 428 of contract prices, 145 of default rates, 303 degrees of freedom and, 325 of excesses, 421 fat-tailed, 424–425 function, 28 Gaussian, historical return, levy, 387 lognormal, 449 of loss, 233, 314, 323–324 moments of, 155–156 other than normal, 156–157 Pareto, 426 P/L, 436 return, 109–115 severity, 425–426, 435 spherical, 324–326 stable, 324 Student’s, 148, 429 t-, 323, 333 of TSX index, 152, 154 two-parameter family of, 430 uncertainty in, 388 Diversification effects, 304, 306 portfolio diversification theory and, 139–140, 154, 320 quantification of, 465 venture capital and, 285 DJ CDS.NA.IG Index See Dow Jones CDS North America Investment Grade Index DJIA See Dow Jones Industrial Average Dow Jones CDS North America Investment Grade (DJ CDS.NA.IG) Index, 128–129 Dow Jones Euro Stoxx 50 (Stoxx), 296 Dow Jones Industrial Average (DJIA), 458–459 Dow Jones Industrial Index, 255, 272, 276, 278, 458 Index Downside risk, 46 CVaR measuring, 316 VaR measuring, 6, 316 Drift term, 442 Durbin-Watson test, 301 DWT See Discrete wavelet transform DXY index, 47–48 Dynamic cash flow at risk analysis, 77 Dynamic Conditional Correlation, 272 Dynamic conditional correlation (DCC) model, 254–255, 278 Dynamic grouped t-copula constant v., 255–256 definition of, 257–259, 277–279 modeling of, 256–259 performance of, 278 SPA test and, 275 Dynamic risk factors, 3, Dynamic strategies, implemented by hedge funds, EAR See Earnings-at-risk Early risk indicators, 62 Earnings before interest, taxes, depreciation, and amortization (EBITDA), 466, 471–472, 475 Earnings per share at risk (EPSaR), 72 Earnings-at-risk (EAR), 72 EBITDA See Earnings before interest, taxes, depreciation, and amortization EC See Economic capital ECMI See European Capital Markets Institute Economic capital (EC) See also Total economic capital confidence level and, 230 credit ratings implications of, 375–379 necessary amount of, 231 risk-specific numbers of, 232–233 EDF See Empirical distribution function; Estimated default frequency Efficient VaR as analogue of efficient markets, 36 backtesting and, 27–31 as benchmark, 25 examples of, 31–36 GARCH(1,1) VaR model and, 34–36 modeler’s false beliefs in, 38–39 moment matching in, 29, 33, 35 natural default forecasts provided by, 36–37 parameters recalibrated in, 29–31 random loss variable in, 38 Effort provision, 80 EFLOW See Equity flow strategy Elliptically distributed loss returns, 233, 314 class of, 324 definition of, 326 degrees of freedom and, 325 multivariate, 323 in risk management, 324–328 EM Latin America index See Emerging Markets Latin America index Embedded optionalities, 71 Emerging market momentum (EMOM) strategy, 14, 16–17, 22, 193–195 517 conditional expected returns of, 199 in SETAR estimated results, 198, 201 Emerging Markets (EM) Latin America index, 472, 478 EMOM strategy See Emerging market momentum strategy Empirical distribution function (EDF), 110, 408 EMV See Expected market values EMWA volatility, 434 Enterprise value (EV), 466, 471–472, 475 EPSaR See Earnings per share at risk Equilibrium-equivalent measures, 510 Equity flow strategy (EFLOW), 193–195 conditional expected returns of, 199 in SETAR estimated results, 198, 201 Equity hedge strategy See Long/short equity strategy Equity market neutral strategy, 23 returns, 124 Equity returns, standard deviation of, 408 Equivariance of MLE, 432 pivotal quantile estimates and, 431 standard deviation and, 433 Estimated default frequency (EDF), 406, 408 Estimation bias, 222 Euclidean distance, 468 Euribor Interest, 296 Euro Stoxx 50 returns, 107, 110 Euro-Dollar Exchange Rate, 296 European call Fourier’s transform and, 161 Heston model pricing of, 456 PDE and, 444–446 European Capital Markets Institute (ECMI), 343 European Central Bank, 387 European private equity industry, 221 European put, PDE and, 444 EV See Enterprise value EV/EBITDA ratio, 466, 471–472, 475 Event-driven multistrategy, 23 Ex-ante preventive control, 66, 78 Excesses, uniform distribution of, 421 Exemplary rating history, 370 Exogenous incomes, 499, 506 Expected loss, realized v., 306 Expected market values (EMV), 377 Expected shortfall, 314, 417 Expected values, comparison of, 312 Expected-utility approach, 497–500, 503–510 Ex-post asset returns uncertainty, 389–390 Exposure mapping, 73, 74–75 Exposure measurement, 65 Exposure profile, modeling of, 80 Exposure to market risk factor, 14 External finance, 69 External generator, combined estimator v., 373 External ratings, 361, 363, 371–372, 381 External risk governance, 78 Extreme quantiles, 271 Factor market risks, as nonhedgeable, 62 Factor model, 518 Fast Fourier transformation, 426 Fat tails market risk and, 424–425 model parameters and, 387–391, 394, 396–397, 399 model risk and, 434–435 pivotal quantile estimates and, 434 Federal Reserve banks, 387 Financial hedge, operative losses compensated for by, 73 Financial ratios, 472 Financial Services Agency (FSA), 386 Financial services sector, dynamics of, 92 Firm-level risk management overview of, 66–68 real-world limitations of, 68 value-based motives of, 67 Firms betas of, 476 Brazilian, 471–474 characteristics of, as risks, 464 Chilean, 471–474 Mexican, 471–474 neighboring, 466, 469 nonfinancial, 70–72 size of, 471 Fitch, 363 step risk management process, 64 Formal risk architecture, 66 Forward contract delta method for, 146–147 gains/losses of, 151 historical simulation for, 142–145 Monte Carlo simulations for, 147–151 Forward entry regression, 294 Four-eyes principle, 90 Fourier’s transform European call and, 161 fast, 426 valuation equation and, 455 VaR and, 161–162 FSA See Financial Services Agency F-test, 202 Full-scale centralization, 64 Garbage in-garbage out paradigm, 88 GARCH(1,1) VaR model, 4, 7–8 Box-Cox transformation of, 156 efficient VaR and, 34–36 excess returns and VaR estimates for, 16–17 factor specification in, 10 lags in, 450 options and, 450–451 parameters of, 434 percentage of failures for, 17–19 performance of, 20 time-dependent volatilities modeled by, 434 VPC and, 107, 110–111 Gaussian copula, 160, 254 Gaussian distribution, hedge fund return series deviating from, GBM See Geometric Brownian motion Index GDP See Gross Domestic Product Generalized autoregressive conditional heteroscedasticity model See GARCH(1,1) VaR model Geometric Brownian motion (GBM), 148 GIC See Government Investment Corporation GoF test See Goodness-of-fit test Goodness-of-fit (GoF) test, 16, 238 Governance implications, 78–80 Governance regulations, 66 Government Investment Corporation (GIC), 386 GPUs See Graphics processing units Graphics processing units (GPUs), 167 advantages of, 173, 181–182 architecture of, 171–172 classical approach to, 174–175 codes of, 172 computing by, 169–173, 182 cost of, 181 drawback of, 172 efficiency gains of, 169, 178, 180 example of, 174–181 parallelization and, 175–177 Greeks of Black-Scholes model, 447–449 of portfolios, 182 Grid computing, 169–170 Gross Domestic Product (GDP), 296 Grouped t-copula, 254–256, 272, 275, 277–279 Hazard function, 158 HD 3870 X2, 172 Heavy tails, 323, 425 Hedge funds ad epitome of active management, built-in risk-control devices of, 42 derivatives traded by, dynamic strategies implemented by, increase in number of, institutional investment in, 42–43 metamorphosis of, 41 nonlinear risk-return characteristics of strategies of, rise of, 43–44 strategies of, 44 as substitutes for traditional investment vehicles, VaR applied to, 41–55 Hedging benefits from, 69 financial activities divided from, 80 ratio for, 443 speculation mixed with, 65 Hedging objective selection of, 66 specification of, 63–64 Hedging strategy, derivation and implementation of, 65 Heston model based on time-varying volatility, 441, 452–453 Black-Scholes model v., 452, 455, 457, 460 calibration results of, 457–459 development of, 452 European call option priced with, 456 Index Fourier’s transform and, 455 jump processes in, 460 Monte Carlo engine for, 456–457 parameters of, 457–459 valuation equation of, 453–457 weighting in, 458 Heston, Steven, 452 Heterogeneous investment, VaR under CAPM and, 463–464, 472 S-CAPM and, 463, 465, 470–471 wavelet analysis and, 465, 480–481 High VaR low spread level (HL) portfolio, 134–135 High volatility regime, 15 High-dimensional portfolios, VaR for actual VaR exceedances and, 277 algorithm for, 273–274 CDF and, 266 conditional quantile estimation and, 265–271 degrees of freedom and, 265 DGPs and, 256, 260 Dow Jones Industrial Index and, 255, 272, 276, 278 empirical analysis of, 271–277 evaluation of, 274–275 future research on, 279 Kendall’s tau matrix and, 257–258 multivariate distribution specifications and, 272 null hypothesis and, 274 out-of-sample results of, 275–277 RMSE and, 260–264, 267–270 simulation studies of, 259–265, 267–270 t-copula approach to, 253 High-frequency components, of time series, 470 Historical return distribution, Historical simulation for computing VaR, 142–145, 341 contract value computed in, 144 distribution of contract prices in, 145 equation for, 142 for forward contract, 142–145 historical data variations in, 143 Monte Carlo simulation v., 341 Historical volatility, 449–450 Hit ratios, 106–107, 111–112, 115–116 HL portfolio See High VaR low spread level portfolio Holding period, 340 Homogeneity advantages of, 380 in Markov regime-switching models, 361, 365–367, 379 Idiosyncratic risk, 140, 213–214 calculation of, 216–217 default rate and, 219 in portfolio risk model, 283, 286–287, 295, 304 IFM See Inference functions for margins IGARCH(1,1) VaR model, 4, 8–9 excess returns and VaR estimates for, 16–17 percentage of failures for, 17–19 performance of, 20 IMF See International Monetary Fund Implied portfolio views, 31 Independent rating agencies, 363 519 Individual loss level, 491 Industrial sector default rates by, 298, 302 recovery rates by, 299 stopwise entry regression by, 300 Inference functions for margins (IFM), 236 Influence factors, optimality hindered by, 369–370 Initial public offerings (IPOs), 344 Insurance, 90, 163 Integrated market model, 240 Intensity of default, 158 Intensity-based credit portfolio model, 240 Interest rate swaps, 241 Internal funds, 69 Internal ratings, 361, 363, 371–372, 381 Internal risk governance, 78 International Market, 344 International Monetary Fund (IMF), 350–351 International Securities Services Association (ISSA), 343 In-the-money (ITM), 447–448 Intraday stop out, 197 Investment beliefs, 398–399 Investment expenditure flow, long-term competitiveness and, 68 Investment grade, 370, 372, 376 IPOs See Initial public offerings Iron laws, for process design and project management, 101 ISE See Istanbul Stock Exchange ISSA See International Securities Services Association Issuer default, model of, 124 Istanbul Stock Exchange (ISE) IPOs of, 344 losses on, 342 normality tests and, 345–346 null hypothesis and, 345–346 overview of, 343–344 returns behaviors of, 353 sectors traded at, 339, 344–350 VaRs of, 344–350 IT mega-projects, 94 ITM See In-the-money Ito’s lemma, 443, 449 iTraxx spreads, 124 Japan Securities Dealers Association (JSDA), 343 Jarque-Bera statistic, 151 J.P Morgan, 340, 375, 386 global losses estimated by, 386–387 VaR originating at, 464 JSDA See Japan Securities Dealers Association Jump processes, 460 Kendall’s tau matrix, 257–258 KIC See Korean Investment Corporation KMV Credit Monitor, 405–406 KMV model, 406, 408, 410 Kolmogorov-Smirnov test, 344 Korean Investment Corporation (KIC), 386 Latin America index See Emerging Markets Latin America index 520 Least cost dealing, 100 Lehman aggregate bond index, 47–48 Levy distributions, 387 LH portfolio See Low VaR high spread level portfolio Likelihood function, 432 Linearity assumption, 313 Liquid assets, 70 Liquidity-based financial distress motive, 69 Location-scale transformation, 430 Logistic forward entry regression, 213 Lognormal assumptions, 391, 449 Long convexity, 448 Long history, short history v., 51–53 Long/short equity strategy, 23–24 Long-Term Capital Management (LTCM), 43, 386–387 Long-term competitiveness, investment expenditure flow and, 68 Long-term default rates, 208, 221 Long-term traders, 470 Long-term volatility, 434 Look-back period, length of, 424 Loss in annual loss maxima, 425 attitudes toward, 485–487, 489–492, 501–503, 506–511 definitions of, 239 elliptical distributions of, 233, 314, 323–324 financial hedge and operative, 73 on ISE, 342 mean excess, 314, 317 mLA, 497, 506 realized v expected, 306 single, approximation of, 435–436 from subprime crisis, 386–387 Loss-aversion coefficient, 490–491 Low VaR high spread level (LH) portfolio, 134–135 Lower-tier management, 80 Low-frequency components, of time series, 470 Low-volatility regimes, 195 LSTAR model, 202–203 LTCM See Long-Term Capital Management MACD model See Moving average convergence/divergence model Machines, for simulations, requirements of, 167 Macroeconomic factors choice of, 295 correlation between, 299 predictability of, 212 stage and, 218, 294 time-dependent default rate and, 212, 218 Mainframes, 169–170 Majority rule process, 391–392, 394 Managed futures funds, 45 Margin calls, 389 Marginal risk, 225, 306, 308 Market capitalization, 466, 471, 473–475 Market CVaR, 407 Market risk, 140 credit risk and, 240, 246 exposure to, factor, 14 factor, 62 Index fat-tailed distribution and, 424–425 financial instruments’ value and, 243–244 operational risk and, 416 product, 62 time-dependent volatility and, 422–424 uncertainty and, 416 Market VaR, 407 Market-implied probability of defaults, 361 Market-to-book value, 472, 475 Marking to market, 70 Markov chains, 14 Markov regime-switching models, hedge fund tail risk exposure captured by, 20 RSBM, 11 SRSM, 10–11 time-continuous homogenous, 361, 365–367, 379 Markowitz, Harry, 139–140, 154, 321, 386 Markowitz model, 139–140, 154 analytical solution to, 321 approach of, 313 CVaR in, 311 optimization from, 328, 336 problems with, 316 semivariance used in, 321 VaR in, 311 variance used in, 311, 316, 321 MATLAB, 161–162 iterations statistics of, 332 Michelot algorithm v., 331–332 quadprog of, 331–332 risk management and, 315, 331 Maximum liklihood estimation (MLE), 7, 236, 369 equivariant, 432 operational risk and, 435 parameters estimated by, 451 Mean excess loss, 314, 317 See also Conditional value at risk Mean return estimate, 392 Mean reversion (MR) model advantages of, 47 analytical approach to, 45–46 application considerations of, 46–47 MACD model v., 48 return predictions of, 55 subprime securities and, 54 VaR control influencing, 47–51 volatility clustering and, 452–453 Mean uncertainty, 390–394 Mean-risk models See also Markowitz model implementation of, 321–323 types of, 311, 316 Mega-projects, 94–95 Merger arbitrage See Risk arbitrage strategy Merrill Lynch, 386 Merton model, 287, 407–409, 410, 439 Merton, Robert, 440 Merton-KMV approach, to structural credit modeling, 406, 410 Method-of-moments estimation, 258 Metric distance, 468 Mexican firms, spatial effects on, 471–474 Mezzanine funds, 297 Michelot algorithm computation time of, 332 Index iterations statistics of, 332 MATLAB v., 331–332 matrix inversions and, 330 modified, 328–330 original, 328 performance of, 331–336 steps of, 329 Micro shocks, 474 Migration histories of credit ratings, 363–364 intensity, 371, 373 matrices, 364–365 probabilities, 242, 368 Milstein discretization, 456 Mispricing, 419 ML estimator, 258 mLA See Myopic loss aversion Mode return estimate, 392 Model parameters, VaR challenges of, 389 correlation uncertainty example of, 396–398 distribution influenced by, 385 ex-post asset returns uncertainty and, 389–390 fat tails and, 387–391, 394, 396–397, 399 GARCH, 434 mean uncertainty example of, 390–394 subprime crisis and, 386–388 uncertainty in, 385, 389–390 variance uncertainty example of, 394–396 Model risk, in VaR calculations applications of, 432–436 backtesting and, 420–421 bias v uncertainty in, 422–427 definition of, 415–416 fat tails and, 434–435 operational risk and, 425–427, 435–436 pivotal quantile estimates and, 428–432, 434–435 pricing models in, 418–419 profit-and-loss distribution and, 436 sources of, 416–420 statistical modeling in, 419–420 time-dependent volatility and, 432–434 types of, 417 uncertainty in, 415–416 venture capital and, 211–214 Moment matching, 29, 33, 35 Monotone transformation, 430 Monte Carlo simulations adaptability of, 71, 313 bottom-up approach v., 246 conditional quantile estimation and, 267–270 credit ratings and, 377 disadvantages of, 168–169 flexibility of, 168 for forward contract, 147–151 GBM in, 148 GPU approach and, 167 for Heston model, 456–457 high-dimensional portfolios, VaR and, 259–265, 267–270 historical simulation v., 341 for nonlinear returns, 341 pricing models and, 418–419 S-CAPM and, 477–480 521 TEC and, 237, 241 of VaR, 105, 147–151, 341, 477–480 VBA program and, 148–151 of VPC, 105 Moody’s, 363, 408 Morgan Stanley, 386, 472 Moving average convergence/ divergence (MACD) model advantages of, 47 analytical approach to, 44–46 application considerations of, 46–47 downside risk managed in, 46 MR model v., 48 return predictions of, 55 risk limits and, 51–53 subprime securities and, 54 VaR control influencing, 47–51 VaR time horizon influencing, 53 weight changes for, 51 Moving volatility cap, 48 MR model See Mean reversion model MRD See Multiresolution decomposition MSCI world equity index, 47–48 Multicollinearity, 299 Multinational companies, treasury departments of, 79–80 Multiresolution decomposition (MRD), 471 Multisector model, 210, 293, 303–304 Multivariate elliptical distributions, 323 Multivariate t-distribution, 323, 333 Multiyear time horizons, 72 Myopia, 488 Myopic loss aversion (mLA), 497, 506 Naive strategy (NAIVE), 192–195 conditional expected returns of, 199 in SETAR estimated results, 198, 201 Narrow framing, 488 National Market, 344 Neighboring firms, 466, 469 Net loss boundary, 340 Net-exposure, 211–212 Next days return, 189 9800 GX2, 172 1974 Merton model, 287 No-arbitrage condition, 444 Nondirectional strategies, 13–14 Nonfinancial firms, VaR and, 70–72 Nonlinear optionlike payoffs See Asset-based style factors Nonlinear returns, 341 Nonparametric CPD, 409–411 Nonprofessional investors definition of, 488 exogenous incomes of, 499, 506 expected-utility approach and, 497–500, 503–510 individual perceptions of, 489–492 loss attitudes of, 485–487, 489–492, 501–503, 506–511 in one-dimensional utility framework, 487–495 risky v risk-free assets and, 487–495 in two-dimensional utility framework, 495–500, 510 522 Nontransaction exposures, 80 Normal coefficient, VaR using, 156–157 Normal distribution, parametric VaR and, 141 Normality assumption, 313 Null hypothesis, 11–12, 19–20 high-dimensional portfolios and, 274 ISE and, 345–346 Objective function, selection of, 66 Off-balance sheet activities, 312 Oil Price, 296 One-dimensional utility framework, 487 One-sector model, 210, 293, 303–304 Operational risk, 96, 140, 245 analysis of, 426 conservative estimate of, 425–427 market risk and, 416 MLE and, 435 model risk and, 425–427, 435–436 Operational VaR calculations under Basel II, 86–91 desirable side effects of, 91–95 integrated management of, 85 real option techniques employed in, 99–102 risk factor categories and business lines in, 88–89 risk management frameworks and, 96–97 shareholder value creation and, 96 strategy-enhancing initiatives of, 95–99 Operative cash flows, nature of, 74 Opportunity costs, for volatility, 66, 113 Optimization models elementary example and, 333–334 limits of, 312 single-period portfolio problem of, 320–324 stochastic, 316 VaR in, 319–320 Options See also Black-Scholes model; Heston model calibrated prices of, 458–459 call, 161, 444, 447–448, 456 delta, 443, 447–448 DJIA, 458–459 gamma, 447–448 GARCH and, 450–451 ITM, 447–448 OTM, 69, 447–448 payoff, 163 pricing techniques, 77 put, 444 sigma, 448–449 theories of, 163 vega, 447–448 volatility influencing, 125, 448–450 Orbits, properties of, 432 Organizational matrix, 78 Ornstein-Uhlenbeck process, 243 Orthogonal mapping, 324 OTM See Out-of-the-money Out-of-sample results, of VaR for high-dimensional portfolios, 275–277 Out-of-the-money (OTM), 69, 447–448 Overperformance, 316 Index Palisade’s Decision Tool Suite, 72, 76 Panel data analysis, 126–127, 131–133 Parallelization by assets, 176–177, 180–181 GPUs and, 175–177 Parameter estimation equivariance and, 431 of Heston model, 457–459 procedure, 238–239 for profit-and-loss distribution, 436 Parameters See Model parameters, VaR Parametric CPD, 410 Parametric models, 7, 25, 341 Parametric VaR, 141, 340–341 Pareto distribution, 426, 435 Partial differential equation (PDE), 440 Call and, 444–446 central limit theorem and, 445 derivation of, 440–444 imaginary portfolio and, 441–442 solution methods for, 444–447 Payoff options, 163 PD See Probability of default PDE See Partial differential equation P/E See Price-to-earnings ratio Pearson’s coefficient, 157, 468 Pecking order argument, 69 Percentage return See Return(s) Performance review, 65–66 Performance volatility, opportunity costs associated with, 66–67 Per-period cash flows, 77 Personal computing, 170 PF test See Proportion of failure test pgf See Probability-generating function PIT See Probability Integral Transformation Pivotal functions role of, 429 standard deviation and, 433 transformation providing, 435 Pivotal quantile estimates abstract formulation of problem and, 428 algorithm for, 435 equivariance and, 431 fat tails and, 434 general definition of, 429–430 guiding case in, 428–429 orbits in, 432 structural models of, 430–432 systematic construction of, 430 uniqueness and, 430 P/L distribution See Profit-and-loss distribution Plain vanilla call, 457 Poisson approximation, 289 Portfolio(s) See also High-dimensional portfolios, VaR for; Time-dependent default rates, in venture capital analysis of, 127–128, 134–135 bivariate, 276, 279 CDS and, 127–128, 134–135 choosing between, 321 diversification theory, 139–140, 154, 320 greeks of, 182 HL, 134–135 Index imaginary, PDE and, 441–442 insurance cost of, 163 optimal, Markowitz model and, 328, 336 returns, standard deviation of, 386 risk, 215–220, 283 single-period optimization problem, 320–324 single-risk-type models of, 246 views, 31 Portfolio risk model, in venture capital analysis of risk models in, 287–288 CreditMetrics and, 287 CreditRisk model and, 283–284, 288–290, 292–293, 308 data sample in, 297–299 empirical evidence for, 299–308 expected loss v realized in, 306 idiosyncratic risk in, 283, 286–287, 295, 304 input parameters of, 290–292 multivariate regressions in, 294 predictability of, 301 risk in, 283 risk-adjusted portfolio from, 307 sector analysis in, 292–296, 299–301 systematic risk in, 283, 295, 304 VaR for, 305 VBAs and, 290 PortfolioManager, 209, 287 PPI See Producer Price Index Price-to-earnings ratio (P/E), 72 Pricing models, 418–419 Probabilistic events, 440 Probability density function of investment with correlation uncertainty, 398 of investment with mean uncertainty, 392 of investment with variance uncertainty, 395 Probability Integral Transformation (PIT), 28 Probability of default (PD), 362–363, 379 See also Conditional probability of default in Australia, 403 credit model, 410 market-implied, 361 sectoral, structural credit modeling and, 403, 408 undiversified, 410–411 Probability-generating function (pgf), 289 Producer Price Index (PPI), 296 Product innovation, 91–92 Product market risks, as nonhedgeable, 62 Production sector, 298, 300, 302 Profit-and-loss (P/L) distribution, 436 Profit-loss function, estimation of, 313 Project-related real options, 77 Proportion of failure (PF) test, 12, 19–20 Proportionality factor, 369–370 Prudent valuation, 419 Quadprog, 331–332 Quadratic programming, algorithm for, 314 Quantiles, 317 See also Conditional quantile estimation central, 271 extreme, 271 523 pivotal estimates of, 428–432, 434–435 risk underestimated by, 427 time-dependent volatility multiplied with, 433 Quantitative management, 187–188 Random outcomes comparison of, 312, 315 reality of, 440 risk of, 212, 315, 332 Rate of return See Return(s) Rating-grade changes, 288 Ratings See Credit ratings Real estate prices, decline in, 400 Real option techniques as decision-making flexibility, 99–100 in operational VaR calculations, 99–102 Realized loss, expected v., 306 Recovery rate, 211, 292, 299, 376 Recovery-of-treasury assumption, 245 Reference entity, 122 Regime switching actual regimes in, 15 Markov approach to, model of, Regime-switching beta models (RSBM), 11 advantages of, 16, 19 excess returns and VaR estimates for, 16–17 percentage of failures for, 17–19 performance of, 20 risk factors in, 14 Regression-based tornado diagram, 76 Regulatory capital, 381 Regulatory compliance, as threshold, 95 Relative RMSE (RRMSE), 260–264, 267–270 Reporting, interactions among, 95–96 Return(s) See also Elliptically distributed loss returns absolute, behaviors of, in ISE, 353 CF VaR model and excess, 16–17 conditional expected, 199 CSFB/Tremont hedge fund index, 13–14 daily, volatility of, 422 distribution, 7, 109–115, 388 of EMOM strategy, 199 equity market, 124 Euro Stoxx 50, 107, 110 ex-post, of asset(s), 389–390 mean estimate, 392 mode estimate, 392 next days, 189 nonlinear returns, Monte Carlo simulations for, 341 predictions of MACD model, 55 processes, stop-loss rules for, 189–192 risk values for, 335 in single-period portfolio optimization problem, 320 SRSM and excess, 16–17 standard deviation of, 386, 408 TEXL, 346–348, 356 univariate, with t-distribution, 323 weighting of, 433 WOPP, 346–348 524 Return on equity (ROE), 72, 91–93 Risk(s) See also Default risk; Idiosyncratic risk; market risk; Model risk, in VaR calculations; Time-dependent default rates, in venture capital; Value at risk architecture, formal, 66 Basel II on modeling of, 404 classes of, 293 counterparty, 241 credit, 140, 240, 246, 405 decision making under, 311 downside, 6, 46, 316 EC and, 232–233 firm characteristics as, 464 governance, 78 lack of information in, 415 marginal, 225, 306, 308 measures, 315–320 as multidimensional concept, 162 operational, 140, 245, 425–427, 435–436 payoff options measuring, 163 portfolio, 215–220, 283 quantification of, 313 quantiles underestimating, 427 of random outcomes, 212, 315, 332 sectoral, 404 systematic, 140, 213, 215–216, 301 tail, 20, 202, 387–391, 394, 396–397, 399 theories of, 139–140, 162, 314 transfer, 439 uncertainty as, 427 of venture capital, 285–287, 301–308 in VPC, 105 Risk aggregation accurate, 229–230 additive approach to, 232 bottom-up approach to, 231, 240–247 correlation-based square-root formula for, 232–233 role of, 247 top-down approach to, 231, 233–240, 247 Risk arbitrage strategy, 5, 23 Risk aversion, excessive, 101 Risk controls, formal system of, 63 Risk factors corporate performance and, 74 dynamic, 3, in operational VaR calculations, 88–89 projected distribution for financial, 75 in RSBM, 14 strategic, 91 Risk limits, setting of, 51–53 Risk management See also Corporate risk management; Firm-level risk management automated, 187 axiomatic approach to, 319 for bank trading, 63 centralization of, 63, 78, 80 corporate strategy v., 60–61 CVaR in, 311, 314 design and implementation of, 63–64 as dynamic problem, 65 elliptically distributed loss returns in, 324–328 exemplary process of, 98 Index with expected shortfall, 314, 417 firm-wide system of, 59–60, 80–81 step process of, 64 formal system of, 63–64 formalized operational, 99 frameworks for, 96–97 function, organization of, 64–65 guidelines for, 101 importance of, 20 internal control measures in, 312 MATLAB and, 315, 331 mindset change of, 103 modified Michelot algorithm and, 328–336 profit-loss function estimated in, 313 random shocks and, 385 RiskMetrics as universal tool for, 386 role of, 63 supply chain, 99 traditional, 43 VaR in, 311, 314 vertical incentive structure and, 79 Risk managers, traders v., 54 Risk neutral probabilities, 159 Risk precaution, accurate, 105 Risk premium, time-varying equity, 389 Risk profile, transparency of, 63 Risk protection, 108 Risk simulation output, 76 Risk-free assets, risky v., 487–495 Risk-free interest rates, 243 RiskMetrics See also IGARCH(1,1) VaR model; Variance-covariance method software, 340 as universal risk management tool, 386 Risk-neutralization pricing, 30 Risky assets, risk-free v., 487–495 RMSE See Root mean square error ROE See Return on equity Rolling forecasting scheme, 273 Rolling windows, seven-year, 411–412 Root mean square error (RMSE), 260–264, 267–270 RRMSE See Relative RMSE RSBM See Regime-switching beta models Russian-Asian financial crisis, 386 Sampling threshold, 426 SAR error model See Spatial autoregressive error model Scale-shift transformation, 434 S-CAPM See Spatial CAPM Scenario modeling, 76 Scholes, Myron, 440–441 See also Black-Scholes model SEC See Securities and Exchange Commission Second pillar, Basel II and, 86–87 Sector(s) bio-technology, 298, 300, 302 communications, 298, 300, 302 computer, 298, 300, 302 consumer, 298, 300, 302 default rates, 212–213, 302 industrial, 298–299, 302 recovery rates, 299 Index risk, 404 traded at ISE, 339, 344–350 Sector analysis in CreditRisk model, 289, 293 in portfolio risk model, 292–296, 299–301 time-dependent default rates and, 218–220 Securities and Exchange Commission (SEC), 343 Selective hedging, 69 Self-assessment, 90 Self-inflicting threshold autoregressive model (SETAR), 196–202 AKAIKE criterion and, 202 conditional expected returns of, 199 estimation of, 201 estimation results from, 198, 201 for long NZD/short YEN position, 200 LSTAR model and, 202–203 Semivariance, variance v., 321 Sensitivity analysis, 480 Separation of power doctrine, 54–55 SETAR See Self-inflicting threshold autoregressive model Severity distributions, 425–426, 435 Shapiro-Wilk test, 344 Shareholder value behavioral motives as driver of, 63 CFaR analysis and, 81 corporate risk management creating, 66–67 operational VaR calculations and, 96 Shareholder value creation, operational risk management and, 96 Sharpe, William F., 140 Short history, long history v., 51–53 Short-period portfolio See Single-period portfolio optimization problem Short-term traders, 470 SIMD See Single instruction multiple data Simple regime-switching models (SRSM), 10–11 excess returns and VaR estimates for, 16–17 percentage of failures for, 17–19 performance of, 20 Single instruction multiple data (SIMD), 171 Single loss approximation, 435–436 Single-period portfolio optimization problem, 320–324 decision variables in, 320–321 mean-risk model implemented in, 321–323 return in, 320 Single-risk-type portfolio models, 246 Single-sector default rates, 295 Single-sector model, 210, 214, 293, 303–304 Six-sigma event, 399 Sklar’s Theorem, 234 Smile structure, volatility, 449, 460 Soft factors, 98, 103 S&P See Standard & Poor’s SPA test See Superior predictive ability test Spatial autoregressive (SAR) error model, 466, 468, 473–474, 481 Spatial CAPM (S-CAPM), 463 contiguity and, 465 cross-sectional linkages and, 466–467 empirical testing of linkages and, 471–480 estimation of spatial effects and, 471–474 525 heterogeneous investment and, 463, 465, 470–471 methodological issues of, 466–471 metric distance and, 468 Monte Carlo simulation and, 477–480 spatial correlation in, 464 spatial VaR and, 468–469, 474–477 Spatial lag model, 466–469, 473–474, 477, 480–481 Spatial VaR calculation of, 474–476, 478–480 estimates of, 475, 478 S-CAPM and, 468–469, 474–476 wavelet-based, 478 Spatial weights matrix, 465 Spearman’s coefficient, 157, 468 Spectral density function, 161 Speculation, hedging mixed with, 65 Spherical distribution, 324–326 Spot yield, 244–245 Spread, 122 SPSS See Statistical Package for the Social Sciences SRSM See Simple regime-switching models Stable distributions, 324 Stage default rates and, 221 macroenvironment and, 218, 294 Standard & Poor’s (S&P) categories of, 408 500 index, 45, 501 ratings by, 363, 370–371, 381, 408 Standard deviation conditional, 409–410 of equity returns, 408 equivariant estimator of, 433 of intensities, 373 pivotal function and, 433 portfolio diversification and, 139–140 of portfolio returns, 386 Standard uniformity tests, 28 Standardized exposure, 290 State contingent bets, Statistical modeling, 419–420 Statistical Package for the Social Sciences (SPSS), 344 Stochastic market volatility, 389 Stochastic optimization models, 316 Stock Market, Bonds and Bills Market, 344 Stock markets, 124 Stocks bootstrapping of, 151–153 volatility of, 450 Stop-loss trading, VaR-based bond flows strategy of, 193–194, 198–199, 201 carry strategy of, 192, 194–195, 198–199, 201 conditional autocorrelation and, 196–202 currency universe, data availability and, 205–206 emerging market momentum strategy of, 193–195, 198–199, 201 equity flow strategy of, 193–195, 198–199, 201 as hidden momentum strategy, 192 naive strategy of, 192–195, 198–199, 201 526 Stop-loss trading, VaR-based (Cont.) opportunity costs and, 189, 191, 195 as random market timing strategy, 187–188 rules of, for alternative return processes, 189–192 threshold autoregressive models and, 196–202 value of, 187 Stopwise entry regression, by industrial sector, 300 Stoxx See Dow Jones Euro Stoxx 50 Strategic interdependence, 69 Strategic risk factors, 91 Structural credit modeling Basel II and, 362, 403 CPD in, 403, 409–410 credit models methodology in, 407–409 distance to default in, 406, 408 estimated default frequency in, 406, 408 market VaR methodology in, 407 Merton-KMV approach to, 406, 410 results of, 410–411 sectoral PD and, 403, 408 structural correlation in, 409 support for, 412 techniques of, 412 Structural models, of pivotal quantile estimates, 430–432 Student’s distribution, 148, 429 Student’s t-copula, 254, 278 Subinvestment grade, 370, 372, 376 Subprime crisis of 2008 Bear Stearns collapse during, 386–387, 390 global crisis triggered by, 386 impact of, 16, 386–387, 399 MACD model and, 54 MR model and, 54 VaR model parameters, uncertainty and, 386–388 Subsidiary management, corporate headquarters v., 79 Supercomputing See also Graphics processing units definition of, 170 execution models of, 172 grid computing, 169–170 by mainframes, 169–170 technologies of, 169–171 world’s most powerful, 173 Superior predictive ability (SPA) test, 255, 274–276 Supply chain risk management, 99 Survivorship bias, 13 Systematic risk, 140, 213, 215–216 in portfolio risk model, 283, 295, 304 weight of, 301 Tail(s) dependence, 266 fat, 387–391, 394, 396–397, 399, 424–425, 434–435 heavy, 323, 425 market risk and, 424–425 risk, 20, 202, 387–391, 394, 396–397, 399 in risk modeling, 387–391, 394, 396–397, 399 Tail VaR See Conditional value at risk Taleb, Nassim, 387 TAR models See Threshold autoregressive models Index Taylor series expansion, 155 T-bill See U.S Treasury bill t-copula constant v dynamic, 255–256 grouped, 254–259, 275, 277–279, 278 high-dimensional portfolios and, 253 Student’s, 254, 278 TEC See Total economic capital Temasek, 386 TEXL returns, 346–348, 356 Textiles, 356 θ percent VaR, 105 Thompson, G J., 404 Thorpe, Edward, 440 3D graphics, 171 Threshold autoregressive (TAR) models, 190, 196–202 Time lags, 296 Time series decomposition of, 465, 470, 475–477, 480–481 high- and low-frequency components of, 470 length of, 417 Time until first failure (TUFF) test, 12, 19–20 Time-dependent default rates, in venture capital advantages of, 217 calculation of, 216–218 CreditRisk model and, 207–211, 215, 218–219, 226 database and, 220–221 diversification effects and, 285 empirical evidence in, 214–215, 220–226 expected v realized losses and, 222–223 initial model for, 208–215 macroeconomic factors and, 212, 218 multisector model and, 210 New Model v Original Model and, 222–226 one-sector model and, 210 portfolio risks modeled with, 215–220 sector analysis and, 218–220 single-sector model and, 210, 214 specifications in, 211–214 Time-dependent volatility GARCH processes modeling, 434 market risk and, 422–424 model risk and, 432–434 quantile multiplied with, 433 Time-independent default rate, 218 Time-varying equity risk premium, 389 Time-varying volatility, 441, 452–453 Top-down approach, to risk aggregation, 231 accuracy of, 239–240 advantages of, 238 assumptions of, 239 bottom-up approach v., 247 copula approach and, 233–240 estimation issues with, 235–236 GoF test and, 238 IFM and, 236 literature review, 233–240 parameter estimation procedure for, 238–239 problems with, 238–240 simulation and, 237–238 Total economic capital (TEC) See also Risk aggregation Index correct aggregation for, 229–230 Monte Carlo simulations and, 237, 241 problems calculating, 233 Tourism, 350 Trade-off coefficient, 322 Traders, risk managers v., 54 Transparency, 93 Treasury bill See U.S Treasury bill Treasury departments, of multinational companies, 79–80 Trend followers, 45, 55 TSX index bootstrapping of, 151–153 distribution of, 152, 154 TUFF test See Time until first failure test Turkey See also Istanbul Stock Exchange Central Bank of, 350–351 crisis in, 351 economic conditions of, 343, 350–356 as emerging market, 342 textiles of, 356 Turnover margin, 93 Two-dimensional utility framework, 495–500, 510 Two-fund separation theorem, 494 Two-parameter family of distributions, 430 UHF-GARCH future research on, 141 one-step ahead forecast, 157 Ullmer, Michael, 404 Ultra-high frequency data, 156–157 Uncertainty as additional risk source, 427 in asset return distribution parameters, 388 backtesting influenced by, 416, 425 bias v., 422–427 complexity increasing, 425 cone of, 61 correlation, 396–398 in distribution, 388 ex-post asset returns, 389–390 market risk and, 416 mean, 390–394 in model parameters, VaR, 385, 389–390 in sophisticated models, 420 subprime crisis and, 386–388 in in VaR calculations in model risk, 415–416 variance, 394–396 volatility and, 424 Unconditional correlation parameters, 260 Unconditional coverage test, 255, 275 Unconditional variance, 451 Underperformance, 316 Undiversified PD, 410–411 United Kingdom, banks failing in, 404 Univariate t-distribution, 323 U.S Treasury bill, 472, 501 Valuation, 419 Value at risk (VaR), See also Cash flow at risk; Conditional value at risk; Cornish-Fisher VaR model; Efficient VaR; GARCH(1,1) VaR model; Heterogeneous investment, VaR under; High-dimensional portfolios, 527 VaR for; IGARCH(1,1) VaR model; Model parameters, VaR; Model risk, in VaR calculations; Operational VaR calculations; Spatial VaR; Stop-loss trading, VaR-based; VaR performance criterion actual, exceedances, 277 advantages of, 168, 416, 418 assumptions of, 419–420 banks using, 41–42, 102 bootstrapping method for calculating, 149–154 CDS and, 121–122, 125–135 CFaR v., 72 choice of, 416–418 Copulas and, 157–161 Corporate risk management incompatibility with, 70–72 credit, 157–161 during crises, 356–357 CVaR and, 317, 324–326 delta method for computing, 145–147, 341–342 downside risk measured by, 6, 316 drawbacks of, 182, 319–320, 340, 356–357, 416–417 dynamic risk factor exposures in, empirical analysis of, 13–20 estimates for RSBM and SRSM, 16–17 estimation methods of, 6–7 evaluation methods and, 11–12 Fourier’s transform and, 161–162 for hedge funds, 41–55 historical simulation for computing, 142–145, 341 history of, 43–44, 140, 464 HL and LH portfolios of, 134–135 impact of, 47–51, 53, 312 of ISE, 344–350 liquid assets required by, 70 market, 407 Markov regime-switching models, 6, 10–11 in Markowitz model, 311 modeling steps of, 25–26 models compared, 4, 342 Monte Carlo simulations of, 105, 147–151, 341, 477–480 nonfinancial firms and, 70–72 using normal coefficient, 156–157 in optimization models, 319–320 parametric, 141, 340–341 performance of, 350–356 for portfolio risk model, in venture capital, 305 regime switching of hedge fund returns and, risk limits set for, 51–53 in risk management, 311, 314 role of, 339–340 sample size for calculations of, 70–71 theoretical definition of, θ percent, 105 tight v loose systems of, 42, 44, 55 time horizon of, 53 variance-covariance method and, 71 wealth allocation and, 492–495 Value levers, 100 Value of Retail Sales, 296 528 Value-based management, CFaR and, 59 Value-based motives, 67 VaR See Value at risk VaR performance criterion (VPC) aim of, 118–119 benchmarks and, 118 changing volatility influencing, 109–118 compounded, 115, 117 for different settings of volatility and persistence, 117 equation for, 108–109 GARCH(1,1) VaR model and, 107, 110–111 hit ratios and, 106–107, 111–112, 115 Monte Carlo simulations of, 105 return distribution influencing, 109–115 risk characteristics in, 105 θ percent VaR and, 105 variability in proportions of, 118 Variance conditional, 451 Markowitz model using, 311, 316, 321 semivariance v., 321 uncertainty, 394–396 unconditional, 451 Variance-covariance method delta normal version of, 70 matrix in, 146–147, 313, 327 popularity of, 323 VaR and, 71 Vasicek model, 243 VBAs See Visual Basics for Applications Vector error correction models, 75 Venture capital See also Portfolio risk model, in venture capital; Time-dependent default rates, in venture capital carried interests of, 286 collateral and, 285 diversification and, 285 dynamics of, 284 exposure for, 291 financial statements and, 212 idiosyncratic risk and, 214 risk profile of, 285–287, 301–308 specifications to model risks in, 211–214 stages and, 221 volume of, 207 Venture Economics, 220, 297 Vertical incentive structure, 79 Visual Basics for Applications (VBAs) bootstrapping and, 153 in Monte Carlo simulations, 148–151 portfolio risk model and, 290 Volatility Black-Scholes model and, 448–450 Index cap, 48, 52 of CDS, 127, 132–133 changing, effects of, 109–118 clustering, 452–453, 460 of daily returns, 422 downside of, 340 EMWA, 434 estimate of, uncertainty influencing, 424 flexibility for, 114 forecastability of, 273 high, 15 historical, 449–450 hit values for, 112, 116 implied, 458 long-term, 434 long-term average for, 423 low, 195 opportunity costs for, 66, 113 option value influenced by, 125, 448–450 performance, 66–67 sigma, 448–449 smile structure of, 449, 460 stochastic market, 389 of stocks, 450 time-dependent, 422–424, 432–434 time-varying, 441, 452–453 VPC for different settings of, 117 Von Neumann architecture, 169 VPC See VaR performance criterion Wavelet analysis DWT utilized by, 470 heterogeneous investment and, 465, 480–481 scales of, 471 spatial VaR estimates based on, 478 time series decomposed with, 465, 470, 475–476, 480–481 Wealth allocation determination of, 485 estimated, in expected-utility equilibrium, 509 individual utility sources and, 495 optimal, 486–488, 492–495, 502 VaR and, 492–495 variables of, 511 Weights matrix, 468, 473–475, 477 WFE See World Federation of Exchanges Wiener process, 441, 453 WOPP returns, 346–348 World Bank, 350 World Federation of Exchanges (WFE), 343 Zero coupon bond, 245 ... Institutional Advisors GmbH THE VaR IMPLEMENTATION HANDBOOK This page intentionally left blank THE VaR IMPLEMENTATION HANDBOOK GREG N GREGORIOU EDITOR New York Chicago San Francisco Lisbon London Madrid... Journal of Financial and Quantitative Analysis, Journal of Banking and Finance, European Journal of Finance, Journal of Economics and Business, and Journal of Empirical Finance and has presented... conferences including the American Finance Association, Western Finance Association, and Institutional Investor meetings She is a referee for several journals including the Journal of Finance,