Handbook of Market Risk

CHRISTIAN SZYLAR, PHD, is Global Head of Risk at Marshall Wace, LLP. Dr. Szylar has over eighteen years of working experience with international financial organizations and has advised numerous financial institutions on how best to implement efficient risk management in banking as well as in both UCITS and hedge fund markets. Dr. Szylar has taught multiple master's-level courses on market risk and speaks regularly at international conferences.

Foreword xv

Acknowledgments xvii

About the Author xix

Introduction xxi

1 Introduction to Financial Markets 1

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

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

3 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

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

5 The Capital Asset Pricing Model and the Arbitrage Pricing Theory 101

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

6 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

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

7 Market Risk: A Historical Perspective from Market Events and Diverse Mathematics to the Value-at-Risk 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 Principle 159

7.2.1.2 Condorcet 160

7.2.1.3 Tetens 160

7.2.1.4 Actuarial Works 161

7.2.1.5 Laplace 162

7.2.1.6 Lacroix 163

7.2.1.7 Political Economy 164

7.2.1.8 1930s England 166

7.2.1.9 Financial Theory 166

7.2.1.10 The VaR Concept 167

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 188

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

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

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

11.4.3 The Information Ratio 275

11.4.4 R-Square (R2) 276

11.4.5 Downside Risk 276

Further 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

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