Preface xvii 1 Introduction 1 1.1 Why Read This Book? . . . . . . . . . . . . . . . . . . . . 2 1.1.1 Value to Proponents of Traditional Asset Pricing . . 2 1.1.2 Value to Proponents of Behavioral Asset Pricing . . 5 1.2 Organization: How the Ideas in This Book Tie Together . . 6 1.2.1 Heuristics and Representativeness: Experimental Evidence . . . . . . . . . . . . . . . . . . . . . . . . 7 1.2.2 Heuristics and Representativeness: Investor Expectations . . . . . . . . . . . . . . . . . . . . . . 7 1.2.3 Developing Behavioral Asset Pricing Models . . . . . 7 1.2.4 Heterogeneity in Risk Tolerance and Time Discounting . . . . . . . . . . . . . . . . . . . 8 1.2.5 Sentiment and Behavioral SDF . . . . . . . . . . . . 9 1.2.6 Applications of Behavioral SDF . . . . . . . . . . . 9 1.2.7 Prospect Theory . . . . . . . . . . . . . . . . . . . . 11 1.2.8 Closure . . . . . . . . . . . . . . . . . . . . . . . . . 12 1.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 vi Contents I Heuristics and Representativeness: Experimental Evidence 13 2 Representativeness and Bayes Rule: Psychological Perspective 15 2.1 Explaining Representativeness . . . . . . . . . . . . . . . . 16 2.2 Implications for Bayes Rule . . . . . . . . . . . . . . . . . . 16 2.3 Experiment . . . . . . . . . . . . . . . . . . . . . . . . . . 16 2.3.1 Three Groups . . . . . . . . . . . . . . . . . . . . . 17 2.3.2 Bayesian Hypothesis . . . . . . . . . . . . . . . . . . 18 2.3.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . 18 2.4 Representativeness and Prediction . . . . . . . . . . . . . . 19 2.4.1 Two Extreme Cases . . . . . . . . . . . . . . . . . . 20 2.4.2 Representativeness and Regression to the Mean . . . 21 2.4.3 Results for the Prediction Study . . . . . . . . . . . 21 2.4.4 Strength of Relationship Between Signal and Prediction . . . . . . . . . . . . . . . . . . . . . . . 21 2.4.5 How Regressive? . . . . . . . . . . . . . . . . . . . . 22 2.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 3 Representativeness and Bayes Rule: Economics Perspective 25 3.1 The Grether Experiment . . . . . . . . . . . . . . . . . . . 25 3.1.1 Design . . . . . . . . . . . . . . . . . . . . . . . . . 25 3.1.2 Experimental Task: Bayesian Approach . . . . . . . 26 3.2 Representativeness . . . . . . . . . . . . . . . . . . . . . . 28 3.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 3.3.1 Underweighting Base Rate Information . . . . . . . 31 3.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 4 A Simple Asset Pricing Model Featuring Representativeness 33 4.1 First Stage, Modified Experimental Structure . . . . . . . . 34 4.2 Expected Utility Model . . . . . . . . . . . . . . . . . . . . 34 4.2.1 Bayesian Solution . . . . . . . . . . . . . . . . . . . 36 4.3 Equilibrium Prices . . . . . . . . . . . . . . . . . . . . . . . 37 4.4 Representativeness . . . . . . . . . . . . . . . . . . . . . . 38 4.5 Second Stage: Signal-Based Market Structure . . . . . . . . 39 4.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 5 Heterogeneous Judgments in Experiments 43 5.1 Grether Experiment . . . . . . . . . . . . . . . . . . . . . . 43 5.2 Heterogeneity in Predictions of GPA . . . . . . . . . . . . . 44 Contents vii 5.3 The De Bondt Experiment . . . . . . . . . . . . . . . . . . 46 5.3.1 Forecasts of the S&P Index: Original Study . . . . . 46 5.3.2 Replication of De Bondt Study . . . . . . . . . . . . 52 5.3.3 Overconfidence . . . . . . . . . . . . . . . . . . . . . 54 5.4 Why Some Bet on Trends and Others Commit Gambler’s Fallacy . . . . . . . . . . . . . . . . . . . . . . . 55 5.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 II Heuristics and Representativeness: Investor Expectations 59 6 Representativeness and Heterogeneous Beliefs Among Individual Investors, Financial Executives, and Academics 61 6.1 Individual Investors . . . . . . . . . . . . . . . . . . . . . . 61 6.1.1 Bullish Sentiment and Heterogeneity . . . . . . . . . 62 6.1.2 The UBS–Gallup Survey . . . . . . . . . . . . . . . 63 6.1.3 Heterogeneous Beliefs . . . . . . . . . . . . . . . . . 63 6.1.4 Trend Following . . . . . . . . . . . . . . . . . . . . 64 6.1.5 The Impact of Demographic Variables . . . . . . . . 66 6.1.6 Own Experience: Availability Bias . . . . . . . . . . 67 6.1.7 Do Individual Investors Bet on Trends? Perceptions and Reactions to Mispricing . . . . . . . 68 6.2 The Expectations of Academic Economists . . . . . . . . . 69 6.2.1 Heterogeneous Beliefs . . . . . . . . . . . . . . . . . 70 6.2.2 Welch’s 1999 and 2001 Surveys . . . . . . . . . . . . 72 6.3 Financial Executives . . . . . . . . . . . . . . . . . . . . . 73 6.3.1 Volatility and Overconfidence . . . . . . . . . . . . . 74 6.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74 7 Representativeness and Heterogeneity in the Judgments of Professional Investors 75 7.1 Contrasting Predictions: How Valid? . . . . . . . . . . . . . 75 7.2 Update to Livingston Survey . . . . . . . . . . . . . . . . . 76 7.2.1 Heterogeneity . . . . . . . . . . . . . . . . . . . . . 77 7.3 Individual Forecasting Records . . . . . . . . . . . . . . . . 80 7.3.1 Frank Cappiello . . . . . . . . . . . . . . . . . . . . 82 7.3.2 Ralph Acampora . . . . . . . . . . . . . . . . . . . 86 7.4 Gambler’s Fallacy . . . . . . . . . . . . . . . . . . . . . . . 88 7.4.1 Forecast Accuracy . . . . . . . . . . . . . . . . . . . 89 7.4.2 Excessive Pessimism . . . . . . . . . . . . . . . . . . 90 7.4.3 Predictions of Volatility . . . . . . . . . . . . . . . . 91 viii Contents 7.5 Why Heterogeneity Is Time Varying . . . . . . . . . . . . . 93 7.5.1 Heterogeneity and Newsletter Writers . . . . . . . . 94 7.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94 III Developing Behavioral Asset Pricing Models 97 8 A Simple Asset Pricing Model with Heterogeneous Beliefs 99 8.1 A Simple Model with Two Investors . . . . . . . . . . . . . 99 8.1.1 Probabilities . . . . . . . . . . . . . . . . . . . . . . 100 8.1.2 Utility Functions . . . . . . . . . . . . . . . . . . . . 100 8.1.3 State Prices . . . . . . . . . . . . . . . . . . . . . . 100 8.1.4 Budget Constraint . . . . . . . . . . . . . . . . . . . 101 8.1.5 Expected Utility Maximization . . . . . . . . . . . . 101 8.2 Equilibrium Prices . . . . . . . . . . . . . . . . . . . . . . . 102 8.2.1 Formal Argument . . . . . . . . . . . . . . . . . . . 103 8.2.2 Representative Investor . . . . . . . . . . . . . . . . 104 8.3 Fixed Optimism and Pessimism . . . . . . . . . . . . . . . 104 8.3.1 Impact of Heterogeneity . . . . . . . . . . . . . . . . 107 8.4 Incorporating Representativeness . . . . . . . . . . . . . . . 107 8.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109 9 Heterogeneous Beliefs and Inefficient Markets 111 9.1 Defining Market Efficiency . . . . . . . . . . . . . . . . . . 111 9.1.1 Riskless Arbitrage . . . . . . . . . . . . . . . . . . . 113 9.1.2 Risky Arbitrage . . . . . . . . . . . . . . . . . . . . 113 9.1.3 Fundamental Value . . . . . . . . . . . . . . . . . . 114 9.1.4 When Π Is Nonexistent . . . . . . . . . . . . . . . . 114 9.2 Market Efficiency and Logarithmic Utility . . . . . . . . . . 115 9.2.1 Example of Market Inefficiency . . . . . . . . . . . . 115 9.3 Equilibrium Prices as Aggregators . . . . . . . . . . . . . . 116 9.4 Market Efficiency: Necessary and Sufficient Condition . . . 117 9.5 Interpreting the Efficiency Condition . . . . . . . . . . . . . 119 9.5.1 When the Market Is Naturally Efficient . . . . . . . 119 9.5.2 Knife-Edge Efficiency . . . . . . . . . . . . . . . . . 120 9.5.3 When the Market Is Naturally Inefficient . . . . . . 120 9.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122 10 A Simple Market Model of Prices and Trading Volume 123 10.1 The Model . . . . . . . . . . . . . . . . . . . . . . . . . . . 123 10.1.1 Expected Utility Maximization . . . . . . . . . . . . 123 Contents ix 10.2 Analysis of Returns . . . . . . . . . . . . . . . . . . . . . . 126 10.2.1 Market Portfolio . . . . . . . . . . . . . . . . . . . . 126 10.2.2 Risk-Free Security . . . . . . . . . . . . . . . . . . . 127 10.3 Analysis of Trading Volume . . . . . . . . . . . . . . . . . . 127 10.3.1 Theory . . . . . . . . . . . . . . . . . . . . . . . . . 129 10.4 Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131 10.4.1 Stochastic Processes . . . . . . . . . . . . . . . . . . 131 10.4.2 Available Securities . . . . . . . . . . . . . . . . . . 133 10.4.3 Initial Portfolios . . . . . . . . . . . . . . . . . . . . 134 10.4.4 Equilibrium Portfolio Strategies . . . . . . . . . . . 134 10.4.5 Markov Structure, Continuation, and Asymmetric Volatility . . . . . . . . . . . . . . . . . 137 10.5 Arbitrage . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139 10.5.1 State Prices . . . . . . . . . . . . . . . . . . . . . . 139 10.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140 11 Efficiency and Entropy: Long-Run Dynamics 141 11.1 Introductory Example . . . . . . . . . . . . . . . . . . . . . 142 11.1.1 The Market . . . . . . . . . . . . . . . . . . . . . . 143 11.1.2 Budget Share Equations . . . . . . . . . . . . . . . 144 11.1.3 Portfolio Relationships . . . . . . . . . . . . . . . . 144 11.1.4 Wealth Share Equations . . . . . . . . . . . . . . . . 145 11.2 Entropy . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147 11.3 Numerical Illustration . . . . . . . . . . . . . . . . . . . . . 148 11.4 Markov Beliefs . . . . . . . . . . . . . . . . . . . . . . . . . 149 11.5 Heterogeneous Time Preference, Entropy, and Efficiency . . 150 11.5.1 Modeling Heterogeneous Rates of Time Preference . . . . . . . . . . . . . . . . . . . . . . . 151 11.5.2 Market Portfolio . . . . . . . . . . . . . . . . . . . . 152 11.5.3 Digression: Hyperbolic Discounting . . . . . . . . . . 153 11.5.4 Long-Run Dynamics When Time Preference Is Heterogeneous . . . . . . . . . . . . . . . . . . . . 154 11.6 Entropy and Market Efficiency . . . . . . . . . . . . . . . . 154 11.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157 IV Heterogeneity in Risk Tolerance and Time Discounting 159 12 CRRA and CARA Utility Functions 161 12.1 Arrow–Pratt Measure . . . . . . . . . . . . . . . . . . . . . 161 12.2 Proportional Risk . . . . . . . . . . . . . . . . . . . . . . . 162 12.3 Constant Relative Risk Aversion . . . . . . . . . . . . . . . 162 12.3.1 Graphical Illustration . . . . . . . . . . . . . . . . . 163 12.3.2 Risk Premia . . . . . . . . . . . . . . . . . . . . . . 163 x Contents 12.4 Logarithmic Utility . . . . . . . . . . . . . . . . . . . . . . 164 12.4.1 Risk Premium in a Discrete Gamble . . . . . . . . . 164 12.5 CRRA Demand Function . . . . . . . . . . . . . . . . . . . 165 12.6 Representative Investor . . . . . . . . . . . . . . . . . . . . 166 12.7 Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167 12.7.1 Aggregation and Exponentiation . . . . . . . . . . . 169 12.8 CARA Utility . . . . . . . . . . . . . . . . . . . . . . . . . 170 12.8.1 CARA Demand Function . . . . . . . . . . . . . . . 171 12.8.2 Aggregate Demand and Equilibrium . . . . . . . . . 172 12.9 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . 174 13 Heterogeneous Risk Tolerance and Time Preference 175 13.1 Survey Evidence . . . . . . . . . . . . . . . . . . . . . . . . 175 13.1.1 Questions to Elicit Relative Risk Aversion . . . . . . 175 13.1.2 Two Waves . . . . . . . . . . . . . . . . . . . . . . . 177 13.1.3 Status Quo Bias . . . . . . . . . . . . . . . . . . . . 178 13.1.4 Risky Choice . . . . . . . . . . . . . . . . . . . . . . 179 13.2 Extended Survey . . . . . . . . . . . . . . . . . . . . . . . 179 13.3 Time Preference . . . . . . . . . . . . . . . . . . . . . . . . 182 13.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183 14 Representative Investors in a Heterogeneous CRRA Model 185 14.1 Relationship to Representative Investor Literature . . . . . 186 14.1.1 Additional Literature . . . . . . . . . . . . . . . . . 188 14.2 Modeling Preliminaries . . . . . . . . . . . . . . . . . . . . 189 14.3 Efficient Prices . . . . . . . . . . . . . . . . . . . . . . . . . 190 14.4 Representative Investor Characterization Theorem . . . . . 191
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