A Behavioral Approach to Asset Pricing

A Behavioral Approach to Asset Pricing Second Edition Hersh Shefrin Mario L. Belotti Professor of Finance Leavey School of Business Santa Clara University AMSTERDAM BOSTON HEIDELBERG LONDON NEW YORK OXFORD PARIS SAN DIEGO SAN FRANCISCO SINGAPORE SYDNEY TOKYO Academic Press is an imprint of Elsevier

Preface to Second Edition Preface to First Edition About the Author xix xxiii xxix 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 Behavioral Preferences 11 1.2.8 Future Directions and Closing Comments 13 1.3 Summary 13

Heuristics and Representativeness: Experimental Evidence 15 Representativeness and Bayes Rule: Psychological Perspective 17 2.1 Explaining Representativeness 18 2.2 Implications for Bayes Rule 18 2.3 Experiment 18 2.3.1 Three Groups 19 2.3.2 Bayesian Hypothesis 20 2.3.3 Results 20 2.4 Representativeness and Prediction 20 2.4.1 Two Extreme Cases 22 2.4.2 Representativeness and Regression to the Mean.. 23 2.4.3 Results for the Prediction Study 23 2.4.4 Strength of Relationship Between Signal and Prediction 23 2.4.5 How Regressive? 24 2.5 Summary 25 Representativeness and Bayes Rule: Economics Perspective 27 3.1 The Grether Experiment 27 3.1.1 Design 27 3.1.2 Experimental Task: Bayesian Approach 28 3.2 Representativeness 30 3.3 Results 30 3.3.1 Underweight ing Base Rate Information 33 3.4 Summary 34 A Simple Asset Pricing Model Featuring Representativeness 35 4.1 First Stage, Modified Experimental Structure 36 4.2 Expected Utility Model 36 4.2.1 Bayesian Solution 38 4.3 Equilibrium Prices 39 4.4 Representativeness 40 4.5 Second Stage: Signal-Based Market Structure 42 4.6 Sentiment, State Prices, and the Pricing Kernel 44 4.7 Summary 46 Heterogeneous Judgments in Experiments 47 5.1 Grether Experiment 47 5.2 Heterogeneity in Predictions of GPA 48

vii 5.3 The De Bondt Experiment 50 5.3.1 Forecasts of the S&P Index: Original Study... 50 5.3.2 Replication of De Bondt Study 56 5.3.3 Overconfidence 58 5.4 Why Some Commit "Hot Hand" Fallacy and Others Commit Gambler'sFallacy 59 5.5 Summary 61 II Heuristics and Representativeness: Investor Expectations 63 6 Representativeness and Heterogeneous Beliefs Among Individual Investors, Financial Executives, and Academics 65 6.1 Individual Investors 65 6.1.1 Bullish Sentiment and Heterogeneity 66 6.1.2 The UBS/Gallup Survey 67 6.1.3 Heterogeneous Beliefs 67 6.1.4 Hot Hand Fallacy 68 6.1.5 The Impact of Demographic Variables 70 6.1.6 Own Experience: Availability Bias 71 6.1.7 Do Individual Investors Bet on Trends? Perceptions and Reactions to Mispricing 72 6.2 The Expectations of Academic Economists 73 6.2.1 Heterogeneous Beliefs 74 6.2.2 Welch's 1999 and 2001 Surveys 76 6.3 Financial Executives.. / 77 6.3.1 Volatility and Overconfidence 78 6.4 Summary T" 78 7 Representativeness and Heterogeneity in the Judgments of Professional Investors 79 7.1 Contrasting Predictions: How Valid? 79 7.2 Update to Livingston Survey 80 7.2.1 Heterogeneity 81 7.3 Individual Forecasting Records 84 7.3.1 Frank Cappiello 86 7.3.2 Ralph Acampora 91 7.4 Gambler's Fallacy 93 7.4.1 Forecast Accuracy 93 7.4.2 Excessive Pessimism 94 7.4.3 Predictions of Volatility 94

7.5 Why Heterogeneity Is Time Varying 97 7.5.1 Heterogeneity and Newsletter Writers 98 7.6 Summary 99 III Developing Behavioral Asset Pricing Models 101 8 A Simple Asset Pricing Model with Heterogeneous Beliefs 103 8.1 A Simple Model with Two Investors 103 8.1.1 Probabilities 104 8.1.2 Utility Functions 104 8.1.3 State Prices 104 8.1.4 Budget Constraint 105 8.1.5 Expected Utility Maximization 105 8.2 Equilibrium Prices 106 8.2.1 Formal Argument 107 8.2.2 Representative Investor 108 8.3 Fixed Optimism and Pessimism 108 8.3.1 Impact of Heterogeneity Ill 8.4 Incorporating Representativeness Ill 8.5 Summary 113 9 Heterogeneous Beliefs and Inefficient Markets 115 9.1 Defining Market Efficiency 115 9.1.1 Riskless Arbitrage 117 9.1.2 Risky Arbitrage 117 9.1.3 Fundamental Value 118 9.1.4 When n Is Nonexistent 118 9.2 Market Efficiency and Logarithmic Utility 119 9.2.1 Example of Market Inefficiency 119 9.2.2 Sentiment and the Log-Pricing Kernel 120 9.3 Equilibrium Prices as Aggregators 122 9.4 Market Efficiency: Necessary and Sufficient Condition... 123 9.5 Interpreting the Efficiency Condition 125 9.5.1 When the Market Is Naturally Efficient 125 9.5.2 Knife-Edge Efficiency 126 9.5.3 When the Market Is Naturally Inefficient 128 9.6 Summary 129 10 A Simple Market Model of Prices and Trading Volume 131 10.1 The Model 131 10.1.1 Expected Utility Maximization 131

ix 10.2 Analysis of Returns 134 10.2.1 Market Portfolio 134 10.2.2 Risk-Free Security 135 10.3 Analysis of Trading Volume 136 10.3.1 Theory 137 10.4 Example 139 10.4.1 Stochastic Processes 140 10.4.2 Available Securities 140 10.4.3 Initial Portfolios 141 10.4.4 Equilibrium Portfolio Strategies 142 10.4.5 Markov Structure, Continuation, and Asymmetric Volatility 146 10.5 Arbitrage 147 10.5.1 State Prices 148 10.6 Summary 148 11 Efficiency and Entropy: Long-Run Dynamics 149 11.1 Introductory Example 150 11.1.1 The Market 151 11.1.2 Budget Share Equations 152 11.1.3 Portfolio Relationships 152 11.1.4 Wealth Share Equations 153 11.2 Entropy 155 11.3 Numerical Illustration 156 11.4 Markov Beliefs 157 11.5 Heterogeneous Time Preference, Entropy, and Efficiency. 158 11.5.1 Modeling Heterogeneous Rates of Time Preference ' 159 11.5.2 Market Portfolio,.' 160 11.5.3 Digression: Hyperbolic Discounting 161 11.5.4 Long-Run Dynamics When Time Preference Is Heterogeneous 162 11.6 Entropy and Market Efficiency 163 11.7 Summary 166 IV Heterogeneity in Risk Tolerance and Time Discounting 167 12 CRRA and CARA Utility Functions 169 12.1 Arrow-Pratt Measure 169 12.2 Proportional Risk 170 12.3 Constant Relative Risk Aversion 170 12.3.1 Graphical Illustration 171 12.3.2 Risk Premia 171

x Contents 12.4 Logarithmic Utility 172 12.4.1 Risk Premium in a Discrete Gamble 172 12.5 CRRA Demand Function 173 12.6 Representative Investor 174 12.7 Example 175 12.7.1 Aggregation and Exponentiation 177 12.8 CARA Utility 178 12.8.1 CARA Demand Function 180 12.8.2 Aggregate Demand and Equilibrium 180 12.9 Summary 182 13 Heterogeneous Risk Tolerance and Time Preference 183 13.1 Survey Evidence 183 13.1.1 Questions to Elicit Relative Risk Aversion 184 13.1.2 Two Waves 185 13.1.3 Status Quo Bias 186 13.1.4 Risky Choice 187 13.2 Extended Survey 188 13.3 Time Preference 190 13.4 Summary 191 14 Representative Investors in a Heterogeneous CRRA Model 193 14.1 Relationship to Representative Investor Literature 194 14.1.1 Additional Literature 196 14.2 Modeling Preliminaries 197 ; 14.3 Efficient Prices 198 14.4 Representative Investor Characterization Theorem 199 ' 14.4.1 Discussion... 203 14.4.2 Nonuniqueness 205 14.5 Comparison Example 205 14.6 Pitfall: The Representative Investor Theorem Is False... 208 14.6.1 Argument Claiming That Theorem 14.1 Is False.. 209 14.6.2 Identifying the Flaw 210 14.7 Summary 210 V Sentiment and Behavioral SDF 211 15 Sentiment 213 15.1 Intuition: Kahneman's Perspective 213 15.1.1 Relationship to Theorem 14.1 214 15.1.2 Defining Market Efficiency 216

xi 15.2 Sentiment 216 15.2.1 Formal Definition 217 15.3 Example Featuring Heterogeneous Risk Tolerance 217 15.4 Example Featuring Log-Utility 219 15.4.1 Representativeness: Errors in First Moments... 219 15.4.2 Overconfidence: Errors in Second Moments 221 15.4.3 Link to Empirical Evidence 225 15.4.4 Evidence of Clustering 226 15.5 Sentiment as a Stochastic Process 228 15.6 Summary 229 16 Behavioral SDF and the Sentiment Premium 231 16.1 The SDF 232 16.2 Sentiment and the SDF 233 16.2.1 Example 234 16.3 Pitfalls 236 16.3.1 Pitfall: The Behavioral Framework Admits a Traditional SDF 237 16.3.2 Pitfall: Heterogeneity Need Not Imply Sentiment. 237 16.3.3 Pitfall: Heterogeneity in Risk Tolerance Is Sufficient to Explain Asset Pricing 238 16.4 Sentiment and Expected Returns 240 16.4.1 Interpretation and Discussion 243 16.4.2 Example Illustrating Theorem 16.2 244 16.5 Entropy and Long-Run Efficiency 244 16.5.1 Formal Argument 245 16.6 Learning: Bayesian and Non-Bayesian 247 16.7 Summary / 248 VI Applications of Behavioral SDF 249 17 Behavioral Betas and Mean-Variance Portfolios 251 17.1 Mean-Variance Efficiency and Market Efficiency 251 17.2 Characterizing Mean-Variance Efficient Portfolios 252 17.3 The Shape of Mean-Variance Returns 254 17.4 The Market Portfolio 257 17.5 Risk Premiums and Coskewness 259 17.6 Behavioral Beta: Decomposition Result 264 17.6.1 Informal Discussion: Intuition 264 17.6.2 Formal Argument 265 17.6.3 Example 267 17.7 Summary 268

xii Contents 18 Cross-Section of Return Expectations 269 18.1 Literature Review 270 18.1.1 Winner-Loser Effect 270 18.1.2 Book-to-Market Equity and the Winner-Loser Effect 271 18.1.3 January and Momentum 272 18.1.4 General Momentum Studies 273 18.1.5 Glamour and Value 274 18.2 Factor Models and Risk 275 18.3 Differentiating Fundamental Risk and Investor Error... 276 18.3.1 Psychology of Risk and Return 277 18.3.2 Evidence About Judgments of Risk and Return.. 278 18.3.3 Psychology Underlying a Negative Relationship Between Risk and Return 279 18.4 Implications for the Broad Debate 281 18.5 Analysts' Return Expectations 284 18.6 How Consciously Aware Are Investors When Forming Judgments? 285 18.7 How Reliable Is the Evidence on Expected Returns?... 286 18.8 Alternative Theories 288 18.8.1 The Dynamics of Expectations: Supporting Data. 291 18.9 Summary 294 19 Testing for a Sentiment Premium 295 19.1 Diether Malloy Scherbina: Returns Are Negatively Related to Dispersion 296 19.2 AGJ: Dispersion Factor. 298 19.2.1 Basic Approach 298 19.2.2 Factor Structure 298 19.2.3 General Properties"bf the Data 299 19.2.4 Expected Returns 300 19.2.5 Findings 300 19.2.6 Volatility 301 19.2.7 Direction of Mispricing 301 19.2.8 Opposite Signs for Short and Long Horizons... 302 19.3 Estimating a Structural SDF-Based Model 302 19.3.1 Proxy for h z,o 303 19.3.2 Findings 303 19.4 Summary 304 20 A Behavioral Approach to the Term Structure of Interest Rates 305 20.1 The Term Structure of Interest Rates 305

xiii 20.2 Pitfall: The Bond Pricing Equation in Theorem 20.1 Is False 306 20.2.1 Identifying the Flaw in the Analysis 308 20.3 Volatility 308 20.3.1 Heterogeneous Risk Tolerance 311 20.4 Expectations Hypothesis 312 20.4.1 Example 314 20.5 Summary 315 21 Behavioral Black-Scholes 317 21.1 Call and Put Options 317 21.2 Risk-Neutral Densities and Option Pricing 318 21.2.1 Option Pricing Equation 1 318 21.2.2 Option Pricing Equations 2 and 3 320 21.3 Option Pricing Examples 321 21.3.1 Discrete Time Example 321 21.3.2 Continuous Time Example 324 21.4 Smile Patterns 327 21.4.1 Downward-Sloping Smile Patterns in the IVF Function 330 21.5 Heterogeneous Risk Tolerance 332 21.6 Pitfall: Equation (21.12) Is False 333 21.6.1 Locating the Flaw 334 21.7 Pitfall: Beliefs Do Not Matter in Black-Scholes 334 21.7.1 Locating the Flaw 335 21.8 Summary 335 22 Irrational Exuberance and Option Smiles 337 22.1 Irrational Exuberance: Brief History 338 22.1.1 Sentiment. T 340 22.2 Risk-Neutral Densities and Index Option Prices 344 22.2.1 Butterfly Position Technique 345 22.3 Continuation, Reversal, and Option Prices 347 22.4 Price Pressure: Was Arbitrage Fully Carried Out? 353 22.5 Heterogeneous Beliefs 354 22.6 General Evidence on the Mispricing of Options 354 22.7 Summary 356 23 Empirical Evidence in Support of Behavioral SDF 359 23.1 Bollen-Whaley: Price Pressure Drives Smiles 360 23.1.1 Data 361 23.1.2 Trading Patterns 361 23.1.3' Buying Pressure and Smile Effects 362

xvi Contents 27.9 Real-World Portfolios and Securities 455 27.9.1 Empirical Evidence 455 27.9.2 Examples 458 27.10 Summary 459 28 Equilibrium with Behavioral Preferences 461 28.1 The Model 462 28.2 Simple Example 463 28.2.1 Neoclassical Case 463 28.2.2 Prospect Theory Investors 464 28.3 Boundary Value Property 468 28.4 Equilibrium Pricing 469 28.4.1 Additional Insights Regarding Convexity and Existence 471 28.4.2 Weighting and Heterogeneous Beliefs 471 28.5 Portfolio Insurance 472 28.5.1 Testable Prediction 474 28.6 Risk and Return: Portfolio Insurance in a Mean-Variance Example 474 28.7 Heterogeneous Preferences and Heterogeneous Beliefs: Equilibrium with a Mix of SP/A Investors and EU-Investors 478 28.7.1 Behavioral Preferences and the Signature of Sentiment 481 28.7.2 Further Remarks on Skewness and Coskewness... 482 28.8 Summary 484 ; 29 The Disposition Effect: Trading Behavior and Pricing 487 29.1 Psychological Basis for the Disposition Effect 487 29.2 Evidence for the Disposition Effect 492 29.3 Investor Beliefs 497 29.3.1 Odean's Findings 497 29.3.2 A Size Effect 498 29.3.3 A Volume Effect 499 29.4 Momentum and the Disposition Effect 500 29.4.1 Theoretical Hypotheses 501 29.4.2 Empirical Evidence 502 29.4.3 Extensions 503 29.5 Summary 504 30 Reflections on the Equity Premium Puzzle 505 30.1 Basis for Puzzles in Traditional Framework 505 30.1.1 Brief Review 506 30.1.2 Attaching Numbers to Equations 507

xvii 30.2 Erroneous Beliefs 509 30.2.1 Livingston Data 509 30.2.2 The Market and the Economy: Upwardly Biased Covariance Estimate 512 30.3 Alternative Rationality-Based Models 513 30.3.1 Habit Formation 514 30.3.2 Habit Formation SDF 514 30.3.3 Habit Formation SDF Versus the Empirical SDF. 515 30.4 Behavioral Preferences and the Equity Premium 516 30.4.1 Myopic Loss Aversion 516 30.4.2 Transaction Utility 518 30.5 Risks, Small and Large 521 30.6 Summary 522 VIII Future Directions and Closing Comments 523 31 Continuous Time Behavioral Equilibrium Models 525 31.1 General Structure 526 31.1.1 Continuous Time Analogue 527 31.1.2 Linear Risk-Tolerance Utility Function 529 31.1.3 Dynamics Driven by a Single Brownian Motion.. 530 31.2 Analyzing the Impact of a Public Signal 533 31.2.1 Two-Investor Example When One Investor Holds Objectively Correct Beliefs 534 31.2.2 Signal Structure: General Issues 535 31.2.3 Continuous Time, Signal Structure 535 31.3 Jump Processes and Stochastic Volatility 542 31.3.1 Theoretical Framework 544 31.3.2 Empirical Procedure 545 31.4 Issues Pertaining to Future Directions 546 31.5 Summary 550 32 Conclusion 551 32.1 Recapitulating the Main Points 551 32.2 Current and Future Directions 554 32.2.1 Issues Involving Investor Benefits 554 32.2.2 Issues Involving Behavioral Preferences 555 32.2.3 Issues Involving Behavioral Beliefs and Behavioral Preferences 558 32.3 Final Comments 560 References 563 Index 587