Evolution of Market Heuristics (An Explanation of an Asset-Pricing - PowerPoint PPT Presentation

Learning Experiment Homogeneous Expectations Individual Predictions Model Other Experiments Conclusion Evolution of Market Heuristics (An Explanation of an Asset-Pricing Experiment) Mikhail Anufriev Cars Hommes CeNDEF, Faculty of Economics and Business University of Amsterdam Seminar at the Paris School of Economics 22 June 2009 Mikhail Anufriev, Cars Hommes CeNDEF, University of Amsterdam Evolution of Market Heuristics

Learning Experiment Homogeneous Expectations Individual Predictions Model Other Experiments Conclusion Question How do people behave (form expectations and learn) in the expectations feedback system? ◮ expectations are shaped given the market history ◮ expectations affect the outcome (e.g. price) Mikhail Anufriev, Cars Hommes CeNDEF, University of Amsterdam Evolution of Market Heuristics

Learning Experiment Homogeneous Expectations Individual Predictions Model Other Experiments Conclusion Possible Answers ◮ Fully rational (Rational Expectations) ◮ Belief-based and econometric learning ◮ Jordan (GEB, 1991), Bray and Savin (E, 1986), Kalai and Lehrer (E, 1993), Cheung and Friedman (GEB, 1997), ... ◮ Evans and Honkapohja (2001) ◮ Reinforcement learning ◮ Arthur (AER, 1991), Arthur (JEE, 1993), Roth and Erev (GEB, 1995), Erev and Roth (AER, 1998), Camerer and Ho (E, 1999) Mikhail Anufriev, Cars Hommes CeNDEF, University of Amsterdam Evolution of Market Heuristics

Learning Experiment Homogeneous Expectations Individual Predictions Model Other Experiments Conclusion Here we present... ◮ a descriptive model of “reinforcement” learning in a non-game-theoretic setting with limited information about environment... ◮ ...explaining the results of a recent experiment where ◮ subject predicted future price ◮ price process depended on the expectations in forecasting agents rely on simple heuristics in learning agents update their “active” heuristics on the basis of heuristics’ performances Mikhail Anufriev, Cars Hommes CeNDEF, University of Amsterdam Evolution of Market Heuristics

Learning Experiment Homogeneous Expectations Individual Predictions Model Other Experiments Conclusion Experiment Hommes, Sonnemans, Tuinstra, van de Velden (2005, RFS) participants forecast the next realization of an endogenous price process and are rewarded for a precision of their forecasts ◮ two assets in a market ◮ riskless with interest r ◮ risky with price p t and dividend y t whose mean is ¯ y ◮ price p t is derived from equilibrium between demand and supply ◮ positive relation between their forecast and demand ◮ in the beginning of time t every participant h knows the past prices (up to p t − 1 ), own past forecasts (up to p t , h ) and own earnings (up to e t − 1 , h ) Mikhail Anufriev, Cars Hommes CeNDEF, University of Amsterdam Evolution of Market Heuristics

Learning Experiment Homogeneous Expectations Individual Predictions Model Other Experiments Conclusion Experiment Hommes, Sonnemans, Tuinstra, van de Velden (2005, RFS) participants forecast the next realization of an endogenous price process and are rewarded for a precision of their forecasts ◮ two assets in a market ◮ riskless with interest r ◮ risky with price p t and dividend y t whose mean is ¯ y ◮ price p t is derived from equilibrium between demand and supply ◮ positive relation between their forecast and demand ◮ in the beginning of time t every participant h knows the past prices (up to p t − 1 ), own past forecasts (up to p t , h ) and own earnings (up to e t − 1 , h ) Mikhail Anufriev, Cars Hommes CeNDEF, University of Amsterdam Evolution of Market Heuristics

Learning Experiment Homogeneous Expectations Individual Predictions Model Other Experiments Conclusion Formal Presentation of the Experiment ◮ fundamental price of the risky asset p f = ¯ y r = 60 ◮ 6 participants in the beginning of period t submit forecasts p e t + 1 , h ◮ fraction n t of “robot” traders predict p f 200 | p t − 1 − p f | � 1 � n t = 1 − exp − ◮ realized price depends on the next-period price forecasts p e t + 1 , 1 + ··· + p e � + n t p f + ¯ � 1 t + 1 , 6 p t = ( 1 − n t ) y + ε t 1 + r 6 with noise ε t ∼ N ( 0 , 0 . 25 ) for periods t = 0 , . . . , 50 ◮ subjects are paid according to the precision of their forecast 1 − 1 49 ( p t − p e t , h ) 2 , 0 × 1 � � e t , h = max 2 euro Mikhail Anufriev, Cars Hommes CeNDEF, University of Amsterdam Evolution of Market Heuristics

Learning Experiment Homogeneous Expectations Individual Predictions Model Other Experiments Conclusion Formal Presentation of the Experiment ◮ fundamental price of the risky asset p f = ¯ y r = 60 ◮ 6 participants in the beginning of period t submit forecasts p e t + 1 , h ◮ fraction n t of “robot” traders predict p f 200 | p t − 1 − p f | � 1 � n t = 1 − exp − ◮ realized price depends on the next-period price forecasts p e t + 1 , 1 + ··· + p e � + n t p f + ¯ � 1 t + 1 , 6 p t = ( 1 − n t ) y + ε t 1 + r 6 with noise ε t ∼ N ( 0 , 0 . 25 ) for periods t = 0 , . . . , 50 ◮ subjects are paid according to the precision of their forecast 1 − 1 49 ( p t − p e t , h ) 2 , 0 × 1 � � e t , h = max 2 euro Mikhail Anufriev, Cars Hommes CeNDEF, University of Amsterdam Evolution of Market Heuristics

Learning Experiment Homogeneous Expectations Individual Predictions Model Other Experiments Conclusion Formal Presentation of the Experiment ◮ fundamental price of the risky asset p f = ¯ y r = 60 ◮ 6 participants in the beginning of period t submit forecasts p e t + 1 , h ◮ fraction n t of “robot” traders predict p f 200 | p t − 1 − p f | � 1 � n t = 1 − exp − ◮ realized price depends on the next-period price forecasts p e t + 1 , 1 + ··· + p e � + n t p f + ¯ � 1 t + 1 , 6 p t = ( 1 − n t ) y + ε t 1 + r 6 with noise ε t ∼ N ( 0 , 0 . 25 ) for periods t = 0 , . . . , 50 ◮ subjects are paid according to the precision of their forecast 1 − 1 49 ( p t − p e t , h ) 2 , 0 × 1 � � e t , h = max 2 euro Mikhail Anufriev, Cars Hommes CeNDEF, University of Amsterdam Evolution of Market Heuristics

Learning Experiment Homogeneous Expectations Individual Predictions Model Other Experiments Conclusion Formal Presentation of the Experiment ◮ fundamental price of the risky asset p f = ¯ y r = 60 ◮ 6 participants in the beginning of period t submit forecasts p e t + 1 , h ◮ fraction n t of “robot” traders predict p f 200 | p t − 1 − p f | � 1 � n t = 1 − exp − ◮ realized price depends on the next-period price forecasts p e t + 1 , 1 + ··· + p e � + n t p f + ¯ � 1 t + 1 , 6 p t = ( 1 − n t ) y + ε t 1 + r 6 with noise ε t ∼ N ( 0 , 0 . 25 ) for periods t = 0 , . . . , 50 ◮ subjects are paid according to the precision of their forecast 1 − 1 49 ( p t − p e t , h ) 2 , 0 × 1 � � e t , h = max 2 euro Mikhail Anufriev, Cars Hommes CeNDEF, University of Amsterdam Evolution of Market Heuristics

Learning Experiment Homogeneous Expectations Individual Predictions Model Other Experiments Conclusion Information Subjects know ◮ the environment (interest rate r and mean dividend ¯ y ) ◮ some qualitative information (positive relation between the forecasts and demand, higher demand should imply higher price) ◮ past prices and own forecasts Subjects do not know ◮ exact equilibrium equation ◮ exact demand schedule of themselves and others ◮ number and identity of other participants Mikhail Anufriev, Cars Hommes CeNDEF, University of Amsterdam Evolution of Market Heuristics

Learning Experiment Homogeneous Expectations Individual Predictions Model Other Experiments Conclusion Rational Benchmark 70 fundamental price price under rational expectations 65 If everybody predicts 60 fundamental price, Price 55 1 then 0.5 ε t 50 0 p t = p f + -0.5 1 + r 45 -1 0 10 20 30 40 50 40 0 10 20 30 40 50 Time Mikhail Anufriev, Cars Hommes CeNDEF, University of Amsterdam Evolution of Market Heuristics

Learning Experiment Homogeneous Expectations Individual Predictions Model Other Experiments Conclusion Price in the Experiment Group 2 Group 5 70 70 fundamental price experimental price fundamental price experimental price 65 65 60 60 Price Price 55 55 50 50 45 45 40 40 0 10 20 30 40 50 0 10 20 30 40 50 Group 1 Group 6 70 70 fundamental price experimental price fundamental price experimental price 65 65 60 60 Price Price 55 55 50 50 45 45 40 40 0 10 20 30 40 50 0 10 20 30 40 50 Group 4 Group 7 90 70 fundamental price experimental price fundamental price experimental price 80 65 70 60 60 Price Price 50 55 40 50 30 45 20 10 40 0 10 20 30 40 50 0 10 20 30 40 50 Mikhail Anufriev, Cars Hommes CeNDEF, University of Amsterdam Evolution of Market Heuristics

Learning Experiment Homogeneous Expectations Individual Predictions Model Other Experiments Conclusion 2 Groups with (Almost) Monotonic Convergence Group 2 Group 5 65 65 Price Price 55 55 45 45 65 65 55 55 Predictions Predictions 45 45 2 2 0 0 35 35 -2 -2 0 10 20 30 40 50 0 10 20 30 40 50 Mikhail Anufriev, Cars Hommes CeNDEF, University of Amsterdam Evolution of Market Heuristics