List of Figures xiii List of Tables xv Preface xix 1 Introduction 3 1.1 Organization of the Book 4 1.2 Useful Background 6 1.2.1 Mathematics Background 6 1.2.2 Probability and Statistics Background 6 1.2.3 Finance Theory Background 7 1.3 Notation 8 1.4 Prices, Returns, and Compounding 9 1.4.1 Definitions and Conventions 9 1.4.2 The Marginal, Conditional, and Joint Distribution of Returns 13 1.5 Market Efficiency 20 1.5.1 Efficient Markets and the Law of Iterated Expectations 22 1.5.2 Is Market Efficiency Testable? 24 2 The Predictability of Asset Returns 27 2.1 The Random Walk Hypotheses 28 2.1.1 The Random Walk 1: IID Increments 31 2.1.2 The Random Walk 2: Independent Increments 32 2.1.3 The Random Walk 3: Uncorrelated Increments 33 2.2 Tests of Random Walk 1: IID Increments 33 2.2.1 Traditional Statistical Tests 33 2.2.2 Sequences and Reversals, and Runs 34 2.3 Tests of Random Walk 2: Independent Increments 41 2.3.1 Filter Rules 42 2.3.2 Technical Analysis 43 2.4 Tests of Random Walk 3: Uncorrelated Increments 44 2.4.1 Autocorrelation Coefficients 44 2.4.2 Portmanteau Statistics 47 2.4.3 Variance Ratios 48 2.5 Long-Horizon Returns 55 2.5.1 Problems with Long-Horizon Inferences 57 2.6 Tests For Long-Range Dependence 59 2.6.1 Examples of Long-Range Dependence 59 2.6.2 The Hurst-Mandelbrot Rescaled Range Statistic 62 2.7 Unit Root Tests 64 2.8 Recent Empirical Evidence 65 2.8.1 Autocorrelations 66 2.8.2 Variance Ratios 68 2.8.3 Cross-Autocorrelations and Lead-Lag Relations 74 2.8.4 Tests Using Long-Horizon Returns 78 2.9 Conclusion 80 3 Market Microstructure 83 3.1 Nonsynchronous Trading 84 3.1.1 A Model of Nonsynchronous Trading 85 3.1.2 Extensions and Generalizations 98 3.2 The Bid-Ask Spread 99 3.2.1 Bid-Ask Bounce 101 3.2.2 Components of the Bid-Ask Spread 103 3.3 Modeling Transactions Data 107 3.3.1 Motivation 108 3.3.2 Rounding and Barrier Models 114 3.3.3 The Ordered Probit Model 122 3.4 Recent Empirical Findings 128 3.4.1 Nonsynchronous Trading 128 3.4.2 Estimating the Effective Bid-Ask Spread 134 3.4.3 Transactions Data 136 3.5 Conclusion 144 5 The Capital Asset Pricing Model 181 5.1 Review of the CAPM 181 5.2 Results from Efficient-Set Mathematics 184 5.3 Statistical Framework for Estimation and Testing 188 5.3.1 Sharpe-Lintner Version 189 5.3.2 Black Version 196 5.4 Size of Tests 203 5.5 Power of Tests 204 5.6 Nonnormal and Non-IID Returns 208 5.7 Implementation of Tests 211 5.7.1 Summary of Empirical Evidence 211 5.7.2 Illustrative Implementation 212 5.7.3 Unobservability of the Market Portfolio 213 5.8 Cross-Sectional Regressions 215 5.9 Conclusion 217 6 Multifactor Pricing Models 219 6.1 Theoretical Background 219 6.2 Estimation and Testing 222 6.2.1 Portfolios as Factors with a Riskfree Asset 223 6.2.2 Portfolios as Factors without a Riskfree Asset 224 6.2.3 Macroeconomic Variables as Factors 226 6.2.4 Factor Portfolios Spanning the Mean-Varianceprotect Frontier 228 6.3 Estimation of Risk Premia and Expected Returns 231 6.4 Selection of Factors 233 6.4.1 Statistical Approaches 233 6.4.2 Number of Factors 238 6.4.3 Theoretical Approaches 239 6.5 Empirical Results 240 6.6 Interpreting Deviations from Exact Factor Pricing 242 6.6.1 Exact Factor Pricing Models, Mean-Variance Analysis, and the Optimal Orthogonal Portfolio 243 6.6.2 Squared Sharpe Ratios 245 6.6.3 Implications for Separating Alternative Theories 246 6.7 Conclusion 251 7 Present-Value Relations 253 7.1 The Relation between Prices, Dividends, and Returns 254 7.1.1 The Linear Present-Value Relation with Constant Expected Returns 255 7.1.2 Rational Bubbles 258 7.1.3 An Approximate Present-Value Relation with Time-Varying Expected Returns 260 7.1.4 Prices and Returns in a Simple Example 264 7.2 Present-Value Relations and US Stock Price Behavior 267 7.2.1 Long-Horizon Regressions 267 7.2.2 Volatility Tests 275 7.2.3 Vector Autoregressive Methods 279 7.3 Conclusion 286 8 Intertemporal Equilibrium Models 291 8.1 The Stochastic Discount Factor 293 8.1.1 Volatility Bounds 296 8.2 Consumption-Based Asset Pricing with Power Utility 304 8.2.1 Power Utility in a Lognormal Model 306 8.2.2 Power Utility and Generalized Method ofprotect Moments 314 8.3 Market Frictions 314 8.3.1 Market Frictions and Hansen-Jagannathanprotect Bounds 315 8.3.2 Market Frictions and Aggregate Consumptionprotect Data 316 8.4 More General Utility Functions 326 8.4.1 Habit Formation 326 8.4.2 Psychological Models of Preferences 332 8.5 Conclusion 334 9 Derivative Pricing Models 339 9.1 Brownian Motion 341 9.1.1 Constructing Brownian Motion 341 9.1.2 Stochastic Differential Equations 346 9.2 A Brief Review of Derivative Pricing Methods 349 9.2.1 The Black-Scholes and Merton Approach 350 9.2.2 The Martingale Approach 354 9.3 Implementing Parametric Option Pricing Models 355 9.3.1 Parameter Estimation of Asset Price Dynamics 356 9.3.2 Estimating $sigma $ in the Black-Scholes Model 361 9.3.3 Quantifying the Precision of Option Price Estimators 367 9.3.4 The Effects of Asset Return Predictability 369 9.3.5 Implied Volatility Estimators 377 9.3.6 Stochastic Volatility Models 379 9.4 Pricing Path-Dependent Derivatives Via Monte Carlo Simulation 382 9.4.1 Discrete Versus Continuous Time 383 9.4.2 How Many Simulations to Perform 384 9.4.3 Comparisons with a Closed-Form Solution 384 9.4.4 Computational Efficiency 386 9.4.5 Extensions and Limitations 390 9.5 Conclusion 391 10 Fixed-Income Securities 395 10.1 Basic Concepts 396 10.1.1 Discount Bonds 397 10.1.2 Coupon Bonds 401 10.1.3 Estimating the Zero-Coupon Term Structure 409 10.2 Interpreting the Term Structure of Interest Rates 413 10.2.1 The Expectations Hypothesis 413 10.2.2 Yield Spreads and Interest Rate Forecasts 418 10.3 Conclusion 423 11 Term-Structure Models 427 11.1 Affine-Yield Models 428 11.1.1 A Homoskedastic Single-Factor Model 429 11.1.2 A Square-Root Single-Factor Model 435 11.1.3 A Two-Factor Model 438 11.1.4 Beyond Affine-Yield Models 441 11.2 Fitting Term-Structure Models to the Data 442 11.2.1 Real Bonds, Nominal Bonds, and Inflation 442 11.2.2 Empirical Evidence on Affine-Yield Models 445 11.3 Pricing Fixed-Income Derivative Securities 455 11.3.1 Fitting the Current Term Structure Exactly 456 11.3.2 Forwards and Futures 458 11.3.3 Option Pricing in a Term-Structure Model 461 11.4 Conclusion 464 12 Nonlinearities in Financial Data 467 12.1 Nonlinear Structure in Univariate Time Series 468 12.1.1 Some Parametric Models 470 12.1.2 Univariate Tests for Nonlinear Structure 475 12.2 Models of Changing Volatility 479 12.2.1 Univariate Models 481 12.2.2 Multivariate Models 490 12.2.3 Links between First and Second Moments 494 12.3 Nonparametric Estimation 498 12.3.1 Kernel Regression 500 12.3.2 Optimal Bandwidth Selection 502 12.3.3 Average Derivative Estimators 504 12.3.4 Application: Estimating State-Price Densities 507 12.4 Artificial Neural Networks 512 12.4.1 Multilayer Perceptrons 512 12.4.2 Radial Basis Functions 516 12.4.3 Projection Pursuit Regression 518 12.4.4 Limitations of Learning Networks 518 12.4.5 Application: Learning the Black-Scholes Formula 519 12.5 Overfitting and Data-Snooping 523 12.6 Conclusion 524 Appendix 527 A.1 Linear Instrumental Variables 527 A.2 Generalized Method of Moments 532 A.3 Serially Correlated and Heteroskedastic Errors 534 A.4 GMM and Maximum Likelihood 536 References 541 Author Index 587 Subject Index 597