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

14.4.1 Discussion . . . . . . . . . . . . . . . . . . . . . . . 194
14.4.2 Nonuniqueness . . . . . . . . . . . . . . . . . . . . . 195
14.5 Comparison Example . . . . . . . . . . . . . . . . . . . . . 195
14.6 Pitfall: The Representative Investor Theorem Is False . . . 198
14.6.1 Argument Claiming that Theorem 14.1 Is False . . . 198
14.6.2 Identifying the Flaw . . . . . . . . . . . . . . . . . . 199
14.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . 200
V Sentiment and Behavioral SDF 201
15 Sentiment 203
15.1 Intuition: Kahneman’s Perspective . . . . . . . . . . . . . . 203
15.1.1 Relationship to Theorem 14.1 . . . . . . . . . . . . . 204
15.1.2 Defining Market Efficiency . . . . . . . . . . . . . . 206
15.2 Sentiment . . . . . . . . . . . . . . . . . . . . . . . . . . . 206
15.2.1 Formal Definition . . . . . . . . . . . . . . . . . . . 207
Contents xi
15.3 Example Featuring Heterogeneous Risk Tolerance . . . . . . 207
15.4 Example Featuring Log-Utility . . . . . . . . . . . . . . . . 209
15.4.1 Representativeness: Errors in First Moments . . . . 209
15.4.2 Overconfidence: Errors in Second Moments . . . . . 212
15.4.3 Link to Empirical Evidence . . . . . . . . . . . . . . 215
15.4.4 Evidence of Clustering . . . . . . . . . . . . . . . . 216
15.5 Sentiment as a Stochastic Process . . . . . . . . . . . . . . 218
15.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . 219
16 Behavioral SDF and the Sentiment Premium 221
16.1 The SDF . . . . . . . . . . . . . . . . . . . . . . . . . . . . 222
16.2 Sentiment and the SDF . . . . . . . . . . . . . . . . . . . . 223
16.2.1 Example . . . . . . . . . . . . . . . . . . . . . . . . 224
16.3 Pitfalls . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 226
16.3.1 Pitfall: The Behavioral Framework Admits
a Traditional SDF . . . . . . . . . . . . . . . . . . . 226
16.3.2 Pitfall: Heterogeneity Need Not Imply Sentiment . . 227
16.3.3 Pitfall: Heterogeneity in Risk Tolerance Is Sufficient
to Explain Asset Pricing . . . . . . . . . . . . . . . 228
16.4 Sentiment and Expected Returns . . . . . . . . . . . . . . . 230
16.4.1 Interpretation and Discussion . . . . . . . . . . . . . 232
16.4.2 Example Illustrating Theorem 16.2 . . . . . . . . . . 233
16.5 Entropy and Long-Run Efficiency . . . . . . . . . . . . . . 234
16.5.1 Formal Argument . . . . . . . . . . . . . . . . . . . 235
16.6 Learning: Bayesian and Non-Bayesian . . . . . . . . . . . . 236
16.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . 237
VI Applications of Behavioral SDF 239
17 Behavioral Betas and Mean-Variance Portfolios 241
17.1 Mean-Variance Efficiency and Market Efficiency . . . . . . 241
17.2 Characterizing Mean-variance Efficient Portfolios . . . . . . 242
17.3 The Shape of Mean-Variance Returns . . . . . . . . . . . . 244
17.4 The Market Portfolio . . . . . . . . . . . . . . . . . . . . . 247
17.5 Behavioral Beta: Decomposition Result . . . . . . . . . . . 249
17.5.1 Informal Discussion: Intuition . . . . . . . . . . . . 249
17.5.2 Formal Argument . . . . . . . . . . . . . . . . . . . 250
17.5.3 Example . . . . . . . . . . . . . . . . . . . . . . . . 252
17.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . 253
18 Cross-section of Return Expectations 255
18.1 Literature Review . . . . . . . . . . . . . . . . . . . . . . . 256
18.1.1 Winner–Loser Effect . . . . . . . . . . . . . . . . . . 256
xii Contents
18.1.2 Book-to-Market Equity and the Winner–Loser
Effect . . . . . . . . . . . . . . . . . . . . . . . . . . 257
18.1.3 January and Momentum . . . . . . . . . . . . . . . 258
18.1.4 General Momentum Studies . . . . . . . . . . . . . . 259
18.1.5 Glamour and Value . . . . . . . . . . . . . . . . . . 260
18.2 Factor Models and Risk . . . . . . . . . . . . . . . . . . . . 261
18.3 Differentiating Fundamental Risk and Investor Error . . . . 262
18.3.1 Psychology of Risk and Return . . . . . . . . . . . . 263
18.3.2 Evidence About Judgments of Risk and Return . . . 264
18.3.3 Psychology Underlying a Negative Relationship
Between Risk and Return . . . . . . . . . . . . . . . 265
18.4 Implications for the Broad Debate . . . . . . . . . . . . . . 267
18.5 Analysts’ Return Expectations . . . . . . . . . . . . . . . . 268
18.6 How Consciously Aware Are Investors When Forming
Judgments? . . . . . . . . . . . . . . . . . . . . . . . . . . 269
18.7 How Reliable Is the Evidence on Expected Returns? . . . . 270
18.8 Alternative Theories . . . . . . . . . . . . . . . . . . . . . . 272
18.8.1 The Dynamics of Expectations: Supporting Data . . 275
18.9 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . 277
19 Testing for a Sentiment Premium 279
19.1 Diether–Malloy–Scherbina: Returns Are Negatively
Related to Dispersion . . . . . . . . . . . . . . . . . . . . . 280
19.2 Ghysels–Juergens: Dispersion Factor . . . . . . . . . . . . . 282
19.2.1 Basic Approach . . . . . . . . . . . . . . . . . . . . 282
19.2.2 Factor Structure . . . . . . . . . . . . . . . . . . . . 282
19.2.3 General Properties of the Data . . . . . . . . . . . . 283
19.2.4 Expected Returns . . . . . . . . . . . . . . . . . . . 284
19.2.5 Findings . . . . . . . . . . . . . . . . . . . . . . . . 284
19.2.6 Volatility . . . . . . . . . . . . . . . . . . . . . . . . 285
19.2.7 Direction of Mispricing . . . . . . . . . . . . . . . . 285
19.2.8 Opposite Signs for Short and Long Horizons . . . . . 286
19.3 Estimating a Structural SDF-Based Model . . . . . . . . . 286
19.3.1 Proxy for hZ,0 . . . . . . . . . . . . . . . . . . . . . 287
19.3.2 Findings . . . . . . . . . . . . . . . . . . . . . . . . 287
19.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . 288
20 A Behavioral Approach to the Term Structure
of Interest Rates 289
20.1 The Term Structure of Interest Rates . . . . . . . . . . . . 289
20.2 Pitfall: The Bond Pricing Equation in Theorem 20.1
Is False . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 290
20.2.1 Identifying the Flaw in the Analysis . . . . . . . . . 292
Contents xiii
20.3 Volatility . . . . . . . . . . . . . . . . . . . . . . . . . . . . 292
20.3.1 Heterogeneous Risk Tolerance . . . . . . . . . . . . 295
20.4 Expectations Hypothesis . . . . . . . . . . . . . . . . . . . 296
20.4.1 Example . . . . . . . . . . . . . . . . . . . . . . . . 298
20.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . 299
21 Behavioral Black–Scholes 301
21.1 Call and Put Options . . . . . . . . . . . . . . . . . . . . . 301
21.2 Risk-Neutral Densities and Option Pricing . . . . . . . . . 302
21.2.1 Option Pricing Equation 1 . . . . . . . . . . . . . . 302
21.2.2 Option Pricing Equations 2 and 3 . . . . . . . . . . 304
21.3 Option Pricing Examples . . . . . . . . . . . . . . . . . . . 305
21.3.1 Discrete Time Example . . . . . . . . . . . . . . . . 305
21.3.2 Continuous Time Example . . . . . . . . . . . . . . 309
21.4 Smile Patterns . . . . . . . . . . . . . . . . . . . . . . . . . 311
21.4.1 Downward Sloping Smile Patterns in the
IVF Function . . . . . . . . . . . . . . . . . . . . . 314
21.5 Heterogeneous Risk Tolerance . . . . . . . . . . . . . . . . 316
21.6 Pitfall: Equation (21.12) Is False . . . . . . . . . . . . . . . 317
21.6.1 Locating the Flaw . . . . . . . . . . . . . . . . . . . 318
21.7 Pitfall: Beliefs Do Not Matter in Black–Scholes . . . . . . . 318
21.7.1 Locating the Flaw . . . . . . . . . . . . . . . . . . . 319
21.8 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . 319
22 Irrational Exuberance and Option Smiles 321
22.1 Irrational Exuberance: Brief History . . . . . . . . . . . . . 322
22.1.1 Sentiment . . . . . . . . . . . . . . . . . . . . . . . 324
22.2 Risk-Neutral Densities and Index Option Prices . . . . . . . 326
22.2.1 Butterfly Position Technique . . . . . . . . . . . . . 328
22.3 Continuation, Reversal, and Option Prices . . . . . . . . . . 330

22.4 Price Pressure: Was Arbitrage Fully Carried Out? . . . . . 335
22.5 Heterogeneous Beliefs . . . . . . . . . . . . . . . . . . . . . 337
22.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . 337
23 Empirical Evidence in Support of Behavioral SDF 339
23.1 Bollen–Whaley: Price Pressure Drives Smiles . . . . . . . . 340
23.1.1 Data . . . . . . . . . . . . . . . . . . . . . . . . . . 340
23.1.2 Trading Patterns . . . . . . . . . . . . . . . . . . . 341
23.1.3 Buying Pressure and Smile Effects . . . . . . . . . . 342
23.1.4 Price Pressure or Learning? . . . . . . . . . . . . . . 343
23.1.5 Arbitrage Profits . . . . . . . . . . . . . . . . . . . 343
23.2 Han: Smile Effects, Sentiment, and Gambler’s Fallacy . . . 344
23.2.1 Price Pressure . . . . . . . . . . . . . . . . . . . . . 345
23.2.2 Impact of a Market Drop: Gambler’s Fallacy . . . . 345
xiv Contents
23.2.3 Impact of Sentiment . . . . . . . . . . . . . . . . . . 345
23.2.4 Time-Varying Uncertainty . . . . . . . . . . . . . . 346
23.3 David–Veronesi: Gambler’s Fallacy and
Negative Skewness . . . . . . . . . . . . . . . . . . . . . . . 346
23.4 Jackwerth: Estimating Market Risk Aversion . . . . . . . . 348
23.4.1 Behavioral Risk Neutral Density . . . . . . . . . . . 348
23.5 Rosenberg–Engle: Signature of Sentiment in the SDF . . . . 350
23.5.1 Two Approaches to Estimating the EPK . . . . . . 350
23.5.2 Estimating Market Risk Aversion . . . . . . . . . . 351
23.5.3 Empirical Results: Estimates of SDF . . . . . . . . . 351
23.5.4 Estimates of Risk Aversion . . . . . . . . . . . . . . 351
23.6 Comparing the Behavioral SDF and Empirical SDF . . . . 352
23.6.1 Empirical Evidence for Clustering: Mode in the Left
Tail Reflecting Pessimism . . . . . . . . . . . . . . . 353
23.6.2 Investors and Predictions of Continuation . . . . . . 355
23.6.3 Mode in the Left Tail and Crashophobia . . . . . . . 357
23.6.4 Time Variation in the SDF . . . . . . . . . . . . . . 358
23.7 Heterogeneous Perspectives . . . . . . . . . . . . . . . . . . 359
23.8 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . 362
VII Prospect Theory 363
24 Prospect Theory: Introduction 365
24.1 Experimental Evidence . . . . . . . . . . . . . . . . . . . . 366
24.1.1 Common Ratio Effect . . . . . . . . . . . . . . . . . 366
24.1.2 Subcertainty and Expected Utility . . . . . . . . . . 367
24.1.3 Allais Paradox and the Independence Axiom . . . . 368
24.1.4 Isolation and Common Consequence Effect . . . . . 370
24.1.5 Isolation and the Independence Axiom . . . . . . . . 371
24.1.6 Loss Aversion . . . . . . . . . . . . . . . . . . . . . 372
24.1.7 Ambiguity . . . . . . . . . . . . . . . . . . . . . . . 372
24.2 Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 374
24.2.1 The Weighting Function . . . . . . . . . . . . . . . 374
24.2.2 Value Function . . . . . . . . . . . . . . . . . . . . . 376
24.2.3 Interaction Between Value Function and
Weighting Function . . . . . . . . . . . . . . . . . . 377
24.2.4 Framing . . . . . . . . . . . . . . . . . . . . . . . . 378
24.3 Subtle Aspects Associated with Risk Aversion . . . . . . . 379
24.3.1 Caveats . . . . . . . . . . . . . . . . . . . . . . . . . 380
24.4 Generalized Utility Theories . . . . . . . . . . . . . . . . . 381
24.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . 382
Contents xv
25 Behavioral Portfolios 383
25.1 Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 384
25.1.1 Prospect Theory: Uncertainty Weights . . . . . . . . 384
25.1.2 Utility Function . . . . . . . . . . . . . . . . . . . . 384
25.1.3 Prospect Theory Functional . . . . . . . . . . . . . 385
25.2 Prospect Theory: Indifference Map . . . . . . . . . . . . . . 385
25.3 Portfolio Choice: Single Mental Account . . . . . . . . . . . 386
25.3.1 Exposure to Loss: Single Mental Account . . . . . . 387
25.3.2 Portfolio Payoff Return: Single Mental Account . . . 388
25.4 Multiple Mental Accounts: Example . . . . . . . . . . . . . 389
25.4.1 General Comments About Multiple Mental
Accounts . . . . . . . . . . . . . . . . . . . . . . . . 391
25.4.2 Prospect Theory and Mean-Variance Efficiency . . . 392
25.5 SP/A Theory . . . . . . . . . . . . . . . . . . . . . . . . . . 392
25.5.1 SP/A Efficient Frontier . . . . . . . . . . . . . . . . 394
25.5.2 Example . . . . . . . . . . . . . . . . . . . . . . . . 394
25.5.3 Formal Analysis . . . . . . . . . . . . . . . . . . . . 396
25.5.4 Additional Comments . . . . . . . . . . . . . . . . . 398
25.6 Real World Portfolios and Securities . . . . . . . . . . . . . 398
25.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . 400
26 Prospect Theory Equilibrium 401
26.1 The Model . . . . . . . . . . . . . . . . . . . . . . . . . . . 402
26.2 Simple Example . . . . . . . . . . . . . . . . . . . . . . . . 403
26.2.1 Neoclassical Case . . . . . . . . . . . . . . . . . . . 403
26.2.2 Prospect Theory Investors . . . . . . . . . . . . . . 403
26.3 On the Boundary . . . . . . . . . . . . . . . . . . . . . . . 407
26.4 Equilibrium Pricing . . . . . . . . . . . . . . . . . . . . . . 408
26.4.1 Equiprobable Loss States . . . . . . . . . . . . . . . 410
26.5 Portfolio Insurance . . . . . . . . . . . . . . . . . . . . . . 410
26.5.1 Qualification: Probability Weighting . . . . . . . . . 411
26.5.2 Testable Prediction . . . . . . . . . . . . . . . . . . 412
26.6 Risk and Return: Portfolio Insurance
in a Mean-Variance Example . . . . . . . . . . . . . . . . . 413
26.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . 417
27 Pricing and Prospect Theory: Empirical Studies 419
27.1 Combining Behavioral Preferences and Beliefs . . . . . . . . 419
27.2 Disposition Effect: The Empirical Evidence . . . . . . . . . 420
27.3 Investor Beliefs . . . . . . . . . . . . . . . . . . . . . . . . 422
27.3.1 Odean’s Findings . . . . . . . . . . . . . . . . . . . 422
27.3.2 A Size Effect . . . . . . . . . . . . . . . . . . . . . . 423
27.3.3 A Volume Effect . . . . . . . . . . . . . . . . . . . . 424
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27.4 Momentum and the Disposition Effect . . . . . . . . . . . . 426
27.4.1 Theoretical Hypotheses . . . . . . . . . . . . . . . . 426
27.4.2 Empirical Evidence . . . . . . . . . . . . . . . . . . 427
27.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . 428
28 Reflections on the Equity Premium Puzzle 429
28.1 Basis for Puzzles in Traditional Framework . . . . . . . . . 429
28.1.1 Brief Review . . . . . . . . . . . . . . . . . . . . . . 430
28.1.2 Attaching Numbers to Equations . . . . . . . . . . . 431
28.2 Erroneous Beliefs . . . . . . . . . . . . . . . . . . . . . . . 433
28.2.1 Livingston Data . . . . . . . . . . . . . . . . . . . . 433
28.2.2 The Market and the Economy: Upwardly Biased
Covariance Estimate . . . . . . . . . . . . . . . . . . 436
28.3 Alternative Rationality-Based Models . . . . . . . . . . . . 437
28.3.1 Habit Formation . . . . . . . . . . . . . . . . . . . . 437
28.3.2 Habit Formation SDF . . . . . . . . . . . . . . . . . 438
28.3.3 Habit Formation SDF Versus the Empirical SDF . . 439
28.4 Behavioral Preferences and the Equity Premium . . . . . . 440
28.4.1 Myopic Loss Aversion . . . . . . . . . . . . . . . . . 440
28.4.2 Transaction Utility . . . . . . . . . . . . . . . . . . 442
28.5 Risks, Small and Large . . . . . . . . . . . . . . . . . . . . 444
28.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . 445
VIII Closure 447
29 Conclusion 449
29.1 Recapitulating the Main Points . . . . . . . . . . . . . . . . 449
29.2 Testable Predictions . . . . . . . . . . . . . . . . . . . . . . 452
29.3 Future Directions . . . . . . . . . . . . . . . . . . . . . . . 453
References 457
Index 47

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