Investment Theory and Risk Management

Preface xv Acknowledgments xix CHAPTER 1 Discount Rates and Returns 1 Estimating Returns 1 Geometric and Arithmetic Averages 4 Caveats to Return Extrapolation 5 Discounting Present Values of Cash Flow Streams 7 Internal Rate of Return and Yield to Maturity 11 Real and Nominal Returns 14 Summary 14 CHAPTER 2 Fixed Income Securities 17 Coupon-Bearing Bonds 19 Infinite Cash Flow Streams (Perpetuities) 21 General Pricing Formulas for Finite Cash Flow Streams 22 Interest Rate Risk 24 Analysis of Duration 29 Interest Rate Risk Dynamics 31 Immunization and Duration 32 Applications--Liability Discounting and Cash Matching 36 Pension Logic 39 Risky Coupons 42 Inflation Risk and TIPS 43 A Bond Portfolio Strategy (Optional) 45 Summary 48 Appendix 2.1: Solving Infinite and Finite Power Series 49 Reference 50 CHAPTER 3 Term Structure 51 Discounting Using Spot Rates 51 Forward Rates 53 NPV Revisited 56 Short Rates 57 The Bootstrap Method 58 Duration Redux 62 Summary 66 CHAPTER 4 Equity 67 The Determination of Stock Prices 68 Discount Rates Redux 70 Price and Dividend Multiples 73 Extrapolating Multiples to Forecast Returns 74 Pitfalls of Trend Analysis 75 The Gordon Growth Model 78 Sources of Return 82 Summary 85 References 86 CHAPTER 5 Portfolio Construction 87 Stochastic Returns and Risk 87 Diversification 92 The Efficient Frontier 93 Markowitz Portfolio Selection Criteria 97 Capital Market Line and the CAPM 101 Performance Evaluation 106 Summary 108 Appendix 5.1: Statistical Review 108 Appendix 5.2: Risk-Adjusted Performance 112 Reference 113 CHAPTER 6 Optimal Portfolios 115 Portfolio 1: Minimum Variance Portfolio (Fully Invested) 115 Portfolio 2: Minimum Variance Portfolios with Targeted Return 118 Portfolio 3: Minimum Variance Portfolios with No Short Sales 119 Portfolio 4: Minimum Variance Portfolios with Capped Allocations 122 Portfolio 5: Maximum Risk-Adjusted Return 123 Performance Attribution 125 The Efficient Frontier (Again) 127 Summary 129 Appendix 6.1: Matrix Operations 129 CHAPTER 7 Data and Applications 135 Analyzing Returns on a 10-Asset Portfolio 135 Performance Attribution 137 Changing the Investment Horizon Returns Frequency 139 Benchmarking to the Market Portfolio 141 The Cost of Constraints 144 A Bond Strategy 145 Summary 147 CHAPTER 8 Anomalies 149 Deviations from the CAPM 150 Behavioral Finance 155 Summary 161 References 162 CHAPTER 9 Factor Models 165 Arbitrage Pricing Theory (APT) 166 Factor Selection 170 Model Estimation 172 Principal Components 177 Applications and Examples 181 Summary 186 References 186 CHAPTER 10 Active Portfolio Management 187 Active Portfolio Construction and Attribution Analysis 190 Performance Attribution 192 Summary 194 Appendix 10.1: Active Space 195 CHAPTER 11 Risk 197 The Failure of VaR 198 Taxonomy of Risk 200 Visualizing Risk 202 Estimating Volatilities 208 Maximum Likelihood Estimation (Optional) 213 Credit Risk 215 Adjusting for Leverage 217 Adjusting for Illiquidity 221 Other Risks 221 Summary 222 References 222 CHAPTER 12 Monte Carlo Methods 225 Example 12.1: Generating Random Numbers--Estimating P 226 Example 12.2: Confirming the Central Limit Theorem 227 Example 12.3: Credit Default Risk 228 Non-Normal Distributions 232 The Gaussian Copula 234 Summary 239 References 239 CHAPTER 13 Systemic Risk 241 Extreme Value Theory 242 Estimating the Hazards of Downside Risks 246 A Systemic Risk Indicator 252 Summary 255 References 256 CHAPTER 14 Incorporating Subjective Views 257 Methodological Concepts 258 An Example Using Black-Litterman 263 Active Space 266 Risk Attribution 267 Summary 268 References 269 CHAPTER 15 Futures, Forwards, and Swaps 271 Institutional Detail and Futures Mechanics 271 The Relationship between Spot Prices and Forward (Futures) Prices 274 Hedging Basis Risk 276 Hedging Portfolio Risk 278 Futures Pricing 280 Swaps 287 Summary 291 References 292 CHAPTER 16 Introduction to Options 293 Option Payoffs and Put-Call Parity 294 Pricing European Call Options 297 Pricing European Put Options 301 Option Strategies 302 Real Options 308 Summary 314 References 314 CHAPTER 17 Models of Stock Price Dynamics 315 Stock Price Dynamics 315 Ito Processes 318 Lognormal Stock Prices 321 Deriving the Parameters of the Binomial Lattice 325 Black-Scholes-Merton Model 327 The Greek Letters 330 Monte Carlo Methods 335 Summary 338 Appendix 17.1: Derivation of Ito's Lemma 339 CHAPTER 18 Hedging Portfolio Risk 341 Simple Hedging Strategies 341 S&P 500 Index Puts 343 Selling Volatility 345 VIX Calls 346 Liability-Driven Investment 350 Summary 353 References 354 CHAPTER 19 Private Equity 355 The Private Equity Model 357 Return and Risk Methodology 360 Summary 366 Appendix 19.1: CAPM 366 References 369 CHAPTER 20 Structured Credit 371 Securitization 372 Credit Enhancement 374 Basics of Pricing Interest Rate Derivatives 379 Interest Rate Dynamics 381 CMO Valuation 383 The Crash of the Housing Bubble 385 Summary 387 Reference 388 CHAPTER 21 Optimal Rebalancing 389 Trigger Strategies and No-Trade Regions 390 An Optimal Control Problem 392 Implications 395 Optimal Rebalancing in a Static Optimization Model 396 The Comparative Statics of Transaction Costs 398 Reference 400 CHAPTER 22 Data Problems 401 Covariance Estimation 402 An Example 405 Empirical Results 407 Overlapping Observations 413 Conclusions 416 Appendix 22.1: Covariance Matrix Estimation 417 References 420 About the Author 423 Index 425