Non-Random Walk Down Wall Street

Andrew W. Lo is the Harris & Harris Group Professor of Finance at the Sloan School of Management, Massachusetts Institute of Technology. A. Craig MacKinlay is Joseph P.Wargrove Professor of Finance at the Wharton School, University of Pennsylvania. With John Y. Campbell, they are the authors of The Econometrics of Financial Markets (Princeton), which received the Paul A. Samuelson Award in 1997.

"What Andrew W. Lo and A. Craig MacKinlay impressively do ... [is look] for hard statistical evidence of predictable patterns in stock prices... Here they marshal the most sophisticated techniques of financial theory to show that the market is not completely random after all."--Jim Holt, Wall Street Journal "With all its equations, this book is going to turn out to be a classic text in the theory of finance. But it is also one for practitioners."--Diane Coyle, The Independent (London) "Where are today's exploitable anomalies? Lo and MacKinlay argue that fast computers, chewing on newly available, tick-by-tick feeds of market-transaction data, can detect regularities in stock prices that would have been invisible as recently as five years ago. One example: 'clientele bias,' in which certain stocks are popular with investors who have certain trading styles. A case in point that doesn't take a supercomputer to detect, is day traders' current enthusiasm for Internet stocks. Lo says that day traders tend to overreact to news--whether that news is positive or negative--so it should be possible to profit by taking the opposite side of their trades."--Peter Coy, Business Week

• List of Figures List of Tables Preface 1 Introduction 1.1 The Random Walk and Efficient Markets 1.2 The Current State of Efficient Markets 1.3 Practical Implications Part I 2 Stock Market Prices Do Not Follow Random Walks: Evidence from a Simple Specification Test 2.1 The Specification Test 2.1.1 Homoskedastic Increments 2.1.2 Heteroskedastic Increments 2.2 The Random Walk Hypothesis for Weekly Returns 2.2.1 Results for Market Indexes 2.2.2 Results for Size-Based Portfolios 2.2.3 Results for Individual Securities 2.3 Spurious Autocorrelation Induced by Nontrading 2.4 The Mean-Reverting Alternative to the Random Walk 2.5 Conclusion Appendix A2: Proof of Theorems 3 The Size and Power of the Variance Ratio Test in Finite Samples: A Monte Carlo Investigation 3.1 Introduction 3.2 The Variance Ratio Test 3.2.1 The IID Gaussian Null Hypothesis 3.2.2 The Heteroskedastic Null Hypothesis 3.2.3 Variance Ratios and Autocorrelations 3.3 Properties of the Test Statistic under the Null Hypotheses 3.3.1 The Gaussian IID Null Hypothesis 3.3.2 A Heteroskedastic Null Hypothesis 3.4 Power 3.4.1 The Variance Ratio Test for Large q 3.4.2 Power against a Stationary AR(1) Alternative 3.4.3 Two Unit Root Alternatives to the Random Walk 3.5 Conclusion 4 An Econometric Analysis of Nonsynchronous Trading 4.1 Introduction 4.2 A Model of Nonsynchronous Trading 4.2.1 Implications for Individual Returns 4.2.2 Implications for Portfolio Returns 4.3 Time Aggregation 4.4 An Empirical Analysis of Nontrading 4.4.1 Daily Nontrading Probabilities Implicit in Autocorrelations 4.4.2 Nontrading and Index Autocorrelations 4.5 Extensions and Generalizations Appendix A4: Proof of Propositions 5 When Are Contrarian Profits Due to Stock Market Overreaction? 5.1 Introduction 5.2 A Summary of Recent Findings 5.3 Analysis of Contrarian Profitability 5.3.1 The Independently and Identically Distributed Benchmark 5.3.2 Stock Market Overreaction and Fads 5.3.3 Trading on White Noise and Lead-Lag Relations 5.3.4 Lead-Lag Effects and Nonsynchronous Trading 5.3.5 A Positively Dependent Common Factor and the Bid-Ask Spread 5.4 An Empirical Appraisal of Overreaction 5.5 Long Horizons Versus Short Horizons 5.6 Conclusion Appendix A5 6 Long-Term Memory in Stock Market Prices 6.1 Introduction 6.2 Long-Range Versus Short-Range Dependence 6.2.1 The Null Hypothesis 6.2.2 Long-Range Dependent Alternatives 6.3 The Rescaled Range Statistic 6.3.1 The Modified R/S Statistic 6.3.2 The Asymptotic Distribution of Qn 6.3.3 The Relation Between Qn and [tilde]Qn 6.3.4 The Behavior of Qn Under Long Memory Alternatives 6.4 R/S Analysis for Stock Market Returns 6.4.1 The Evidence for Weekly and Monthly Returns 6.5 Size and Power 6.5.1 The Size of the R/S Test 6.5.2 Power Against Fractionally-Differenced Alternatives 6.6 Conclusion Appendix A6: Proof of Theorems Part II 7 Multifactor Models Do Not Explain Deviations from the CAPM 7.1 Introduction 7.2 Linear Pricing Models, Mean-Variance Analysis, and the Optimal Orthogonal Portfolio 7.3 Squared Sharpe Measures 7.4 Implications for Risk-Based Versus Nonrisk-Based Alternatives 7.4.1 Zero Intercept F-Test 7.4.2 Testing Approach 7.4.3 Estimation Approach 7.5 Asymptotic Arbitrage in Finite Economies 7.6 Conclusion 8 Data-Snooping Biases in Tests of Financial Asset Pricing Models 8.1 Quantifying Data-Snooping Biases With Induced Order Statistics 8.1.1 Asymptotic Properties of Induced Order Statistics 8.1.2 Biases of Tests Based on Individual Securities 8.1.3 Biases of Tests Based on Portfolios of Securities 8.1.4 Interpreting Data-Snooping Bias as Power 8.2 Monte Carlo Results 8.2.1 Simulation Results for [theta]p 8.2.2 Effects of Induced Ordering on F-Tests 8.2.3 F-Tests With Cross-Sectional Dependence 8.3 Two Empirical Examples 8.3.1 Sorting By Beta 8.3.2 Sorting By Size 8.4 How the Data Get Snooped 8.5 Conclusion 9 Maximizing Predictability in the Stock and Bond Markets 9.1 Introduction 9.2 Motivation 9.2.1 Predicting Factors vs. Predicting Returns 9.2.2 Numerical Illustration 9.2.3 Empirical Illustration 9.3 Maximizing Predictability 9.3.1 Maximally Predictable Portfolio 9.3.2 Example: One-Factor Model 9.4 An Empirical Implementation 9.4.1 The Conditional Factors 9.4.2 Estimating the Conditional-Factor Model 9.4.3 Maximizing Predictability 9.4.4 The Maximally Predictable Portfolios 9.5 Statistical Inference for the Maximal R2 9.5.1 Monte Carlo Analysis 9.6 Three Out-of-Sample Measures of Predictability 9.6.1 Naive vs. Conditional Forecasts 9.6.2 Merton's Measure of Market Timing 9.6.3 The Profitability of Predictability 9.7 Conclusion Part III 10 An Ordered Probit Analysis of Transaction Stock Prices 10.1 Introduction 10.2 The Ordered Probit Model 10.2.1 Other Models of Discreteness 10.2.2 The Likelihood Function 10.3 The Data 10.3.1 Sample Statistics 10.4 The Empirical Specification 10.5 The Maximum Likelihood Estimates 10.5.1 Diagnostics 10.5.2 Endogeneity of [Delta]tk and IBSk 10.6 Applications 10.6.1 Order-Flow Dependence 10.6.2 Measuring Price Impact Per Unit Volume of Trade 10.6.3 Does Discreteness Matter? 10.7 A Larger Sample 10.8 Conclusion 11 Index-Futures Arbitrage and the Behavior of Stock Index Futures Prices 11.1 Arbitrage Strategies and the Behavior of Stock Index Futures Prices 11.1.1 Forward Contracts on Stock Indexes (No Transaction Costs) 11.1.2 The Impact of Transaction Costs 11.2 Empirical Evidence 11.2.1 Data 11.2.2 Behavior of Futures and Index Series 11.2.3 The Behavior of the Mispricing Series 11.2.4 Path Dependence of Mispricing 11.3 Conclusion 12 Order Imbalances and Stock Price Movements on October 19 and 20, 1987 12.1 Some Preliminaries 12.1.1 The Source of the Data 12.1.2 The Published Standard and Poor's Index 12.2 The Constructed Indexes 12.3 Buying and Selling Pressure 12.3.1 A Measure of Order Imbalance 12.3.2 Time-Series Results 12.3.3 Cross-Sectional Results 12.3.4 Return Reversals 12.4 Conclusion Appendix A12 A12.1 Index Levels A12.2 Fifteen-Minute Index Returns References Index