Investment Theory and Risk Management
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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
