Table of Contents

List of Figures xiii
List of Tables xv
Preface xix



1Introduction 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



2The 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



3Market 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



4Event-Study Analysis 149
4.1 Outline of an Event Study 150
4.2 An Example of an Event Study 152
4.3 Models for Measuring Normal Performance 153
4.3.1 Constant-Mean-Return Model 154
4.3.2 Market Model 155
4.3.3 Other Statistical Models 155
4.3.4 Economic Models 156
4.4 Measuring and Analyzing Abnormal Returns 157
4.4.1 Estimation of the Market Model 158
4.4.2 Statistical Properties of Abnormal Returns 159
4.4.3 Aggregation of Abnormal Returns 160
4.4.4 Sensitivity to Normal Return Model 162
4.4.5 CARs for the Earnings-Announcement Example 163
4.4.6 Inferences with Clustering 166
4.5 Modifying the Null Hypothesis 167
4.6 Analysis of Power 168
4.7 Nonparametric Tests 172
4.8 Cross-Sectional Models 173
4.9 Further Issues 175
4.9.1 Role of the Sampling Interval 175
4.9.2 Inferences with Event-Date Uncertainty 176
4.9.3 Possible Biases 177
4.10 Conclusion 178



5The 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



6Multifactor 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-Variance\protect\\ 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



7Present-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



8Intertemporal 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 of\protect\\ Moments 314
8.3 Market Frictions 314
8.3.1 Market Frictions and Hansen-Jagannathan\protect\\ Bounds 315
8.3.2 Market Frictions and Aggregate Consumption\protect\\ 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



9Derivative 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



10Fixed-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



11Term-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



12Nonlinearities 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