HANDBOOK OF Market Risk CHRISTIAN SZYLAR WILEY
Contents FOREWORD ACKNOWLEDGMENTS ABOUT THE AUTHOR INTRODUCTION XV XVII XIX XXI 1 INTRODUCTION TO FINANCIAL MARKETS t 1.1 The Money Market 4 1.2 The Capital Market 5 1.2.1 The Bond Market 6 1.2.1.1 The Present Value Concept 7 1.2.1.2 Types of Bonds 10 1.2.2 The Stock Market 16 1.3 The Futures and Options Market 19 1.4 The Foreign Exchange Market 22 1.5 The Commodity Market 22 Further Reading 26 2 THE EFFICIENT MARKETS THEORY 27 2.1 Assumptions behind a Perfectly Competitive Market 28 2.2 The Efficient Market Hypothesis 30 2.2.1 Strong EMH 31 2.2.2 Semi-Strong EMH 32 2.2.3 Weak-Form EMH 32 2.3 Critics of Efficient Markets Theory 33 2.4 Development of Behavioral Finance 35 2.5 Beating the Market: Fundamental versus Technical 35 2.5.1 Fundamental Methods 36 2.5.1.1 Price Earnings Ratio 37 2.5.1.2 Price to Book 37 vii
viii Contents 2.5.1.3 Price to Cash Flow 38 2.5.1.4 Return on Equity 38 2.5.1.5 Price to Earnings to Growth Ratio 38 2.5.2 Technical Analysis 39 2.5.2.1 Average True Range 39 2.5.2.2 Rate of Change 39 2.5.2.3 Relative Strength Index 40 2.5.2.4 Money Flow Index 41 2.5.2.5 Moving Averages 41 Further Reading 42 RETURN AND VOLATILITY ESTIMATES 44 3.1 Standard Deviation 47 3.2 Standard Deviation with a Moving Observation Window 48 3.3 Exponentially Weighted Moving Average (EWMA) 50 3.4 Double (Holt) Exponential Smoothing Model (DES) 53 3.5 Principal Component Analysis (PCA) Models 53 3.6 The VIX 54 3.7 Geometric Brownian Motion Process 55 3.8 GARCH 56 3.9 Estimator Using the Highest and Lowest 56 3.9.1 Parkinson Estimator 56 3.9.2 Rogers Satchell Estimator 57 3.9.3 Garman-Klass Estimator 57 Further Reading 58 4 DIVERSIFICATION, PORTFOLIOS OF RISKY ASSETS, AND THE EFFICIENT FRONTIER 59 4.1 Variance and Covariance 61 4.2 Two-Asset Portfolio: Expected Return and Risk 61 4.3 Correlation Coefficient 63 4.3.1 Correlation Coefficient and Its Impact on Portfolio Risk 63 4.3.1.1 Zero Correlation Case 65 4.3.1.2 Perfect Negative Correlation Case 65 4.3.1.3 Perfect Positive Correlation Case 65 4.3.2 The Number of Assets in a Portfolio and Its Impact on Portfolio Risk 66 4.3.3 The Effect of Diversification on Risk 68 4.4 The Efficient Frontier 69 4.5 Correlation Regime Shifts and Correlation Estimates 80 4.5.1 Increased Correlation 80 4.5.2 Severity of Correlation Changes 84 4.6 Correlation Estimates 88 4.6.1 Copulas 90 4.6.2 Moving Average 91
Contents ix 4.6.3 Correlation Estimators in Matrix Notation 92 4.6.4 Bollerslev's Constant Conditional Correlation Model 93 4.6.5 Engle's Dynamic Conditional Correlation Model 94 4.6.6 Estimating the Parameters of the DCC Model 95 4.6.7 Implementing the DCC Model 97 Further Reading 100 THE CAPITAL ASSET PRICING MODEL AND THE ARBITRAGE PRICING THEORY lot 5.1 Implications of the CAPM Assumptions 102 5.1.1 The Same Linear Efficient Frontier for All Investors 102 5.1.2 Everyone Holds the Market Portfolio 102 5.2 The Separation Theorem 105 5.3 Relationships Defined by the CAPM 107 5.3.1 The Capital Market Line 107 5.3.2 The Security Market Line 109 5.4 Interpretation of Beta 110 5.5 Determining the Level of Diversification of a Portfolio 112 5.6 Investment Implications of the CAPM 112 5.7 Introduction to the Arbitrage Pricing Theory (APT) 115 Further Reading 119 MARKET RISK AND FUNDAMENTAL MULTIFACTORS MODEL 120 6.1 Why a Multifactors Model? 122 6.2 The Returns Model 124 6.2.1 The Least-Squares Regression Solution 124 6.2.1.1 Assumptions of the Least-Squares Solution 125 6.2.1.2 Solving the Problem of Heteroskedasticity 125 6.2.1.3 Outliers 128 6.2.1.4 Robust Regression 129 6.2.2 Statistical Approaches 131 6.2.2.1 Principal Components 131 6.2.2.2 Asymptotic Principal Components 132 6.2.2.3 Maximum-Likelihood Estimation 133 6.2.3 Hybrid Solutions 134 6.3 Estimation Universe 134 6.4 Model Factors 135 6.4.1 Market Factor or Intercept 135 6.4.2 Industry Factors 135 6.4.2.1 Thin Industries 136 6.4.2.2 Treatment of Thin Industries 137
X Contents 6.4.3 Style Factors 138 6.4.3.1 Standardization of Style Factors 138 6.4.4 Country Factors 140 6.4.5 Currency Factors 140 6.4.6 The Problem of Multicollinearity 142 6.5 The Risk Model 143 6.5.1 Factor Covariance Matrix 143 6.5.2 Autocorrelation in the Factor Returns 145 Further Reading 147 MARKET RISK: A HISTORICAL PERSPECTIVE FROM MARKET EVENTS AND DIVERSE MATHEMATICS TO THE VALUE-AT-RlSK 148 7.1 A Brief History of Market Events 149 7.2 Toward the Development of the Value-at-Risk 158 7.2.1 Diverse Mathematics 159 7.2.1.1 Safety-First Principli 7.2.1.2 Condorcet 7.2.1.3 Tetens 7.2.1.4 Actuarial Works 7.2.1.5 Laplace 7.2.1.6 Lacro ix 7.2.1.7 Political Economy 7.2.1.8 1930s England 7.2.1.9 Financial Theory 159 160 160 161 162 163 164 166 166 167 7.2.1.10 The VaR Concept 7.3 Definition of the Value-at-Risk 169 7.4 VaR Calculation Models 171 7.4.1 Variance Covariance 171 7.4.1.1 The Standard Normal Distribution or Z Distribution 173 7.4.1.2 Skew and Kurtosis 174 7.4.1.3 Standard Deviation and Correlation 175 7.4.1.4 VaR Calculation Using Variance-Covariance 178 7.4.2 Historical Simulation 180 7.4.3 Monte Carlo Simulation 185 7.4.4 Incremental VaR 1 gg 7.4.5 Marginal VaR 188 7.4.6 Component VaR 189 7.4.7 Expected Shortfall 189 7.4.8 VaR Models Summary 190
Contents xi 7.4.9 Mapping of Complex Instruments 191 7.4.10 Cornish Fisher VaR 192 7.4.11 Extreme Value Theory (EVT) 193 Further Reading 193 8 FINANCIAL DERIVATIVE INSTRUMENTS 195 8.1 Introducing Financial Derivatives Instruments 195 8.1.1 Swap 195 8.1.1.1 Total Return Swap (TRS) 196 8.1.1.2 Credit-Default Swap (CDS) 197 8.1.1.3 First to Default (FTD) 199 8.1.1.4 Collateralized Debt Obligation (CDO) 200 8.1.1.5 Credit Linked Note (CLN) 201 8.1.1.6 Currency Swap 201 8.1.1.7 Swaption 202 8.1.1.8 Variance Swap 203 8.1.1.9 Contract for Difference (CFD) 203 8.1.2 The Forward Contract 204 8.1.3 The Futures Contract 205 8.1.3.1 Currency Future 205 8.1.3.2 Interest Rate Future 205 8.1.3.3 Bond Future 206 8.1.4 Options 206 8.1.4.1 Currency Option 207 8.1.4.2 Equity Option 207 8.1.4.3 Interest Rate Option 207 8.1.5 Warrant 208 8.2 Market Risk and Global Exposure 208 8.2.1 Global Exposure 209 8.2.2 Sophisticated versus Nonsophisticated UCITS 210 8.2.3 The Commitment Approach with Examples on Some Financial Derivatives 211 8.2.4 Calculation of Global Exposure Using VaR 216 8.3 Options 218 8.3.1 Different Strategies Using Options 218 8.3.2 Black Scholes Formula 218 8.3.3 The Greeks 221 8.3.3.1 Delta 221 8.3.3.2 Delta Hedging 222 8.3.3.3 Gamma 224 8.3.3.4 Vega 225 8.3.3.5 Theta 226 8.3.4 Option Value and Risk under Monte Carlo Simulation 227
xii Contents 8.3.5 Evaluating Options and Taylor Expansion 228 8.3.6 The Binomial and Trinomial Option Pricing Models 228 Further Reading 233 9 FIXED INCOME AND INTEREST RATE RISK 235 9.1 Bond Valuation 236 9.2 The Yield Curve 236 9.3 Risk of Holding a Bond 240 9.3.1 Duration 240 9.3.2 Modified Duration 240 9.3.3 Convexity 241 9.3.4 Factor Models for Fixed Income 241 9.3.5 Hedge Ratio 242 9.3.6 Duration Hedging 246 Further Reading 246 10 LIQUIDITY RISK 247 10.1 Traditional Methods and Techniques to Measure Liquidity Risk 249 10.1.1 Average Traded Volume 249 10.1.2 Bid Ask Spread 250 10.1.3 Liquidity and VaR 251 10.2 Liquidity at Risk 253 10.2.1 Incorporation of Endogenous Liquidity Risk into the VaR Model 254 10.2.2 Incorporation of Exogenous Liquidity Risk into the VaR Model 259 10.2.3 Exogenous and Endogenous Liquidity Risk in VaR Model 261 10.3 Other Liquidity Risk Metrics 263 10.4 Methods to Measure Liquidity Risk on the Liability Side 264 Further Reading 267 11 ALTERNATIVES INVESTMENT: TARGETING ALPHA, IDIOSYNCRATIC RISK 269 11.1 Passive Investing 269 11.2 Active Management 271 11.3 Main Alternative Strategies 272 11.4 Specific Hedge Fund Metrics 273 11.4.1 Market Factor versus Multifactor Regression 274 11.4.2 The Sharpe Ratio 275
Contents xiii 11.4.3 The Information Ratio 275 11.4.4 i?-square (Ä 2 ) 276 11.4.5 Downside Risk 276 Farther Reading 288 12 STRESS TESTING AND BACK TESTING 289 12.1 Definition and Introduction to Stress Testing 290 12.2 Stress Test Approaches 294 12.2.1 Piecewise Approach 294 12.2.2 Integrated Approach 296 12.2.3 Designing and Calibrating a Stress Test 298 12.3 Historical Stress Testing 300 12.3.1 Some Examples of Historical Stress Test Scenarios 301 12.3.2 Other Stress Test Scenarios 302 12.3.2.1 Interest Rate Scenarios 302 12.3.2.2 Relative FX Scenarios 302 12.3.2.3 Dynamic FX Scenarios 302 12.3.2.4 Progression Scenarios 302 12.4 Reverse Stress Test 303 12.5 Stress Testing Correlation and Volatility 303 12.6 Multivariate Stress Testing 304 12.7 What Is Back Testing? 306 12.7.1 VaR Is Not Always an Accurate Measure 308 12.8 Back Testing: A Rigorous Approach Is Required 310 12.8.1 Test of Frequency of Tail Losses or Kupiec's Test 311 12.8.2 Conditional Coverage of Frequency and Independence of Tail Losses 312 12.8.3 Clean and Dirty Back Testing 313 Further Reading 314 13 BANKS AND BASEL II/III 315 13.1 A Brief History of Banking Regulations 316 13.2 The 1988 Basel Accord 317 13.2.1 Definition of Capital 318 13.2.2 Credit Risk Charge 319 13.2.3 Off-Balance Sheet Items 320 13.2.4 Drawbacks from the Basel Accord 323 13.2.5 1996 Amendment 324 13.3 Basel II 325 13.3.1 The Credit Risk Charge 326 13.3.1.1 The Standardized Approach 326 13.3.1.2 The Internal Ratings-Based (IRB) Approach 328
xiv Contents 13.3.2 Operational Risk Charge 329 13.3.2.1 The Basic Indicator Approach 329 13.3.2.2 The Standardized Approach 330 13.3.2.3 The Advanced Measurement Approach 330 13.3.3 The Market Risk Charge 331 13.3.3.1 The Standardized Method 332 13.3.3.2 The Internal Models Approach 352 13.4 Example of the Calculation of the Capital Ratio 364 13.5 Basel III and the New Definition of Capital; The Introduction of Liquidity Ratios 365 Further Reading 371 14 CONCLUSION 373 INDEX 378