CHAPTER 1
Thought and Behavior Contagion
in Capital Markets
David Hirshleifer and Siew Hong Teoh
Merage School of Business
University of California–Irvine
1.1. Introduction 2
1.2. Sources of Behavioral Convergence 5
1.3. Rational Learning and Information Cascades: Basic Implications 7
1.4. What Is Communicated or Observed? 9
1.4.1. Observation of Past Actions Only 10
1.4.2. Observation of Consequences of Past Actions 15
1.4.3. Conversation, Media, and Advertising 16
1.5. Psychological Bias 17
1.6. Reputation, Contracts, and Herding 18
1.7. Security Analysis 20
1.7.1. Investigative Herding 20
1.7.2. Herd Behavior by Stock Analysts and Other Forecasters 21
1.8. Herd Behavior and Cascades in Security Trading 24
1.8.1. Evidence on Herding in Securities Trades 24
1.8.2. Financial Market Runs and Contagion 27
1.8.3. Exploiting Herding and Cascades 28
1.9. Markets, Equilibrium Prices, and Bubbles 29
1.10. Cascades and Herding in Firm Behavior 36
1.10.1. Investment and Financing Decisions 36
1.10.2. Disclosure and Reporting Decisions 38
1.11. Contagion of Financial Memes 39
1.12. Conclusion 44
References 46

CHAPTER 2
How Markets Slowly Digest Changes
in Supply and Demand
Jean-Philippe Bouchaud
Science & Finance, Capital Fund Management, Paris
J. Doyne Farmer
Santa Fe Institute and LUISS Guido Carli, Rome
Fabrizio Lillo
University of Palermo and Santa Fe Institute
2.1. Introduction 59
2.1.1. Overview 59
2.1.2. Organization 60
2.1.3. Motivation and Scope 61
2.1.4. Approach to Model Building 63
2.2. Market Structure 64
2.3. Information, Liquidity, and Efficiency 65
2.3.1. Information and Fundamental Values 66
2.3.2. Market Efficiency 67
2.3.3. Trading and Information 68
2.3.4. Different Explanations for Market Impact 69
2.3.5. Noise Trader Models and Informed vs. Uninformed Trading 70
2.3.6. A Critique of the Noise Trader Explanation of Market Impact 71
2.3.7. The Liquidity Paradox: Prices Are Not in Equilibrium 72
2.3.8. Time Scales and Market Ecology 73

2.3.9. The Volatility Puzzle 75
2.3.10. The Kyle Model 76
2.4. Large Fluctuations and Long Memory of Order Flow 77
2.4.1. Empirical Evidence for Long Memory of Order Flow 77
2.4.2. On the Origin of Long Memory of Order Flow 79
2.4.3. Theory for Long Memory in Order Flow Based on Strategic
Order Splitting 80
2.4.4. Evidence Based on Exchange Membership Codes 82
2.4.5. Evidence for Heavy Tails in Volume 83
2.5. Summary of Empirical Results for Diverse Types of Market Impact 84
2.5.1. Impact of Individual Transactions 86
2.5.2. Impact of Aggregate Transactions 86
2.5.3. Hidden Order Impact 88
2.5.4. Upstairs Market Impact 90
2.6. Theory of Market Impact 90
2.6.1. Why Is Individual Transaction Impact Concave? 91
2.6.2. A Fixed Permanent Impact Model 93
2.6.3. The MRR Model 94
2.6.4. A Transient Impact Framework 95
2.6.5. History Dependent, Permanent Impact 99
2.6.6. Empirical Results 103
2.6.7. Impact of a Large Hidden Order 106
2.6.8. Aggregated Impact 108
2.7. The Determinants of the Bid–Ask Spread 111
2.7.1. The Basic Economics of Spread and Impact 111
2.7.2. Models for the Bid–Ask Spread 114
2.7.3. Limit vs. Market Orders: The Microstructure Phase Diagram 117
2.7.4. Spread Dynamics After a Temporary Liquidity Crisis 123
2.8. Liquidity and Volatility 125
2.8.1. Liquidity and Large Price Changes 125
2.8.2. Volume vs. Liquidity Fluctuations as Proximate Causes of Volatility 127
2.8.3. Spread vs. Volatility 129
2.8.4. Market Cap Effects 132
2.9. Order Book Dynamics 133
2.9.1. Heavy Tails in Order Placement and the Shape of the Order Book 133
2.9.2. Volume at Best Prices: The Glosten-Sandas Model 135
2.9.3. Statistical Models of Order Flow and Order Books 137
2.10. Impact and Optimized Execution Strategies 142
2.11. Toward an Empirical Characterization of a Market Ecology 144
2.11.1. Identifying Hidden Orders 145
2.11.2. Specialization of Strategies 146
2.12. Conclusion 148
Appendix 2.1: Mechanical vs. Nonmechanical Impact 150
A2.1.1. Definition of Mechanical Impact for Order Books 150
A2.1.2. Empirical Results 152
Appendix 2.2: Volume Fluctuations 153
Appendix 2.3: The Bid–Ask Spread in the MRR Model 155
References 156

CHAPTER 3
Stochastic Behavioral Asset-Pricing
Models and the Stylized Facts
Thomas Lux
Department of Economics, University of Kiel
and Kiel Institute for the World Economy
3.1. Introduction 162
3.2. The Stylized Facts of Financial Data 164
3.2.1. Martingales, Lack of Predictability, and Informational Efficiency 164
3.2.2. Fat Tails of Asset Returns 167
3.2.3. Volatility Clustering and Dependency in Higher Moments 173
3.2.4. Other Stylized Facts 174
3.3. The Stylized Facts as “Scaling Laws” 175
3.4. Behavioral Asset-Pricing Models with Interacting Agents 178
3.4.1. Interaction of Chartists and Fundamentalists and Nonlinear
Dynamics of Asset Prices 179
3.4.2. Kirman’s Model of Opinion Formation and Speculation 185
3.4.3. Beyond Local Interactions: Socioeconomic Group Dynamics
in Financial Markets 191
3.4.4. Lattice Topologies of Agents’ Connections 207
3.5. Conclusion 210
References

CHAPTER 4
Complex Evolutionary Systems
in Behavioral Finance
Cars Hommes and FlorianWagener
CeNDEF, School of Economics, University of Amsterdam
4.1. Introduction 218
4.2. An Asset-Pricing Model with Heterogeneous Beliefs 221
4.2.1. The Fundamental Benchmark with Rational Agents 222
4.2.2. Heterogeneous Beliefs 223
4.2.3. Evolutionary Dynamics 224
4.2.4. Forecasting Rules 225
4.3. Simple Examples 226
4.3.1. Costly Fundamentalists vs. Trend Followers 227
4.3.2. Fundamentalists vs. Opposite Biases 229
4.3.3. Fundamentalists vs. Trend and Bias 230
4.3.4. Efficiency 230
4.3.5. Wealth Accumulation 232
4.3.6. Extensions 236
4.4. Many Trader Types 236
4.5. Empirical Validation 241
4.5.1. The Model in Price-to-Cash Flows 242
4.5.2. Estimation of a Simple Two-Type Example 246
4.5.3. Empirical Implications 251
4.6. Laboratory Experiments 253
4.6.1. Learning to Forecast Experiments 255
4.6.2. The Price-Generating Mechanism 256
4.6.3. Benchmark Expectations Rules 257
4.6.4. Aggregate Behavior 259
4.6.5. Individual Prediction Strategies 259
4.6.6. Profitability 262
4.7. Conclusion 264

Appendix 4.1: Bifurcation Theory 266
Appendix 4.2: Bifurcation Scenarios 268
References 271

CHAPTER 5
Heterogeneity, Market Mechanisms,
and Asset Price Dynamics
Carl Chiarella
University of Technology, Sydney
Roberto Dieci
University of Bologna
Xue-Zhong He
University of Technology, Sydney
5.1. Introduction 279
5.2. Heterogeneity and Market-Clearing Mechanisms 283
5.2.1. Portfolio Optimization 283
5.2.2. Utility Functions 284
5.2.3. Market-Clearing Mechanisms 285
5.2.4. Noise 287
5.2.5. Expectations Feedback 287
5.3. Price Dynamics Implied by the CARA Utility Function 288
5.3.1. Fundamental Price and the Optimal Demand 288
5.3.2. Formation of Heterogeneous Beliefs 289
5.3.3. Performance Measure and Switching 290
5.3.4. Price Behavior under the Walrasian Auctioneer Mechanism 291
5.3.5. Price Behavior under the Market-Maker Mechanism 298
5.4. Price behavior and Wealth Dynamics Implied by the CRRA Utility 302
5.4.1. Optimal Portfolio and Wealth Dynamics 302

5.4.2. Price and Wealth Behavior with a Walrasian Auctioneer 303
5.4.3. Price and Wealth Behavior with a Market Maker 306
5.5. Empirical Behavior 314
5.5.1. Stylized Facts in the S&P 500 314
5.5.2. A Market Fraction Model and Its Stylized Behavior 316
5.5.3. Econometric Characterization of the Power-Law Behavior 319
5.6. Heterogeneity in a Dynamic Multiasset Framework 321
5.6.1. Optimization of a Many Risky Asset Portfolio with
Heterogeneous Beliefs 322
5.6.2. An Example of Two Risky Assets and Two Beliefs 326
5.7. The Continuous Stochastic Dynamics of Speculative Behavior 330
5.7.1. Stochastic Models with Heterogeneous Beliefs 330
5.7.2. A Continuous Stochastic Model with Fundamentalists and Chartists 331
5.7.3. A Random Dynamical System and Stochastic Bifurcations 332
5.8. Conclusion 338
References 340

573.
CHAPTER 6
Perfect Forecasting, Behavioral
Heterogeneities, and Asset Prices
JanWenzelburger
Keele University
6.1. Introduction 346
6.2. The CAPM as a Two-Period Equilibrium Model 349
6.2.1. Portfolio Selection with One Risk-Free Asset 349
6.2.2. Two-Fund Separation 351
6.2.3. Existence and Uniqueness of Equilibrium 355
6.2.4. Equilibria with Heterogeneous Beliefs 358
6.3. Heterogeneous Beliefs and Social Interaction 359
6.3.1. Temporary Equilibria 359
6.3.2. Perfect Forecasting Rules 362
6.3.3. Systematic and Nonsystematic Risk 366
6.3.4. Selecting Mediators 369
6.3.5. Dynamic Stability with Rational Expectations 371
6.4. Multiperiod Planning Horizons 374
6.4.1. Overlapping Cohorts of Investors 375
6.4.2. Temporary Equilibria 378
6.4.3. Perfect Forecasting Rules 379
6.4.4. Portfolio Holdings 385
6.5. Nonergodic Asset Prices 387
6.5.1. Characterization of Long-Run Equilibria 389
6.5.2. Convergence to Long-Run Equilibria 390
6.5.3. Performance of Efficient Portfolios 391
6.5.4. A Boom-and-Bust Scenario 394
6.6. Conclusion 397
References 398

CHAPTER 7
Market Selection and Asset Pricing
Lawrence Blume
Cornell University, IHS, and Santa Fe Institute
David Easley
Department of Economics
Cornell University
7.1. Introduction 405
7.1.1. Evolution in Biology and Economics 405
7.1.2. A Short History of the Market Selection Hypothesis 407
7.1.3. Scope of This Chapter 409
7.2. The Economy 411
7.2.1. Traders 411
7.2.2. Beliefs 412
7.3. Equilibrium Allocations and Prices 413
7.3.1. Pareto Optimality 413
7.3.2. Competitive Equilibrium 414
7.4. Selection 416
7.4.1. Literature 416
7.4.2. A Leading Example 416
7.4.3. Selection in Complete IID Markets 419
7.4.4. The Basic Equations 420
7.4.5. Who Survives? Necessity 421
7.4.6. Selection and Market Equilibrium 421
7.4.7. More General Stochastic Processes 422
7.5. Multiple Survivors 423
7.5.1. Who Survives? Sufficiency 423
7.6. The Life and Death of Noise Traders 426
7.6.1. The Importance of Market Structure 426
7.6.2. Laws of Large Numbers

7.7. Robustness 431
7.7.1. Unbounded Economies 431
7.7.2. Incomplete Markets 432
7.7.3. Differential Information 432
7.7.4. Selection over Non-EU Traders 432
7.7.5. Selection over Rules 434
7.8. Conclusion 435
References 436

CHAPTER 8
Rational Diverse Beliefs
and Market Volatility
Mordecai Kurz
Stanford University
8.1. Introduction 440
8.2. Can Market Dynamics Be Explained by Asymmetric Private Information? 445
8.2.1. A General Model of Asset Pricing under Asymmetric Information 445
8.2.2. Dynamic Infinite Horizon Models 450
8.2.3. Is Asymmetric Information a Satisfactory Theory of Market Dynamics? 453
8.3. Diverse Beliefs with Common Information: The General Theory 454
8.3.1. A Basic Principle: Rational Diversity Implies Volatility 455
8.3.2. Stability and Rationality in a General Nonstationary Economy 457
8.3.3. Belief Rationality and the Conditional Stability Theorem 461
8.3.4. Describing Individual and Market Beliefs with Markov State Variables 464
8.3.5. Asset Pricing with Heterogeneous Beliefs: An Illustrative
Model and Implications 474
8.4. Explaining Market Dynamics with Simulation Models of Diverse Beliefs 485
8.4.1. Introduction: On Simulation Methods and the Main Results 485
8.4.2. Anatomy of Market Volatility 486
8.4.3. Volatility of Foreign Exchange Rates and the Forward Discount Bias 498
8.4.4. Macroeconomic Applications 499
8.5. Conclusion and Open Problems 501
References 502

2003.
CHAPTER 9
Evolutionary Finance
Igor V. Evstigneev
Economic Studies, University of Manchester
Thorsten Hens
Swiss Banking Institute, University of Zurich
Klaus Reiner Schenk-Hopp´e
Leeds University Business School and School
of Mathematics, University of Leeds
9.1. Introduction 509
9.1.1. Motivation and Background 509
9.1.2. Applications and Real-World Implications 511
9.1.3. Structure of Chapter 511
9.1.4. Dynamics and Evolution 512
9.1.5. Horse Races and the Kelly Rule 515
9.2. Evolutionary Models of Financial Markets 518
9.2.1. Components of the Models 519
9.2.2. Discussion of the Assumptions 521
9.2.3. Outline of the Dynamics 523
9.3. An Evolutionary Model with Short-Lived Assets 524
9.3.1. The Model 524
9.3.2. Analysis of Local Dynamics 528
9.3.3. An Example 530
9.3.4. The Generalized Kelly Rule 532
9.3.5. Global Dynamics with Adaptive Strategies 534
9.4. An Evolutionary Stock Market Model 537
9.4.1. Local Dynamics 540
9.4.2. Global Dynamics with Constant Strategies 543
9.4.3. Kelly Rule in General Equilibrium 546

9.5. Applications 547
9.5.1. Simulation Studies 548
9.5.2. Dynamics of Strategies: Genetic Programming 552
9.5.3. Empirical Tests of Evolutionary Asset Pricing 557
9.6. Continuous-Time Evolutionary Finance 560
9.7. Conclusion 563
References 564