The Evolution of Portfolio Rules and the Capital Asset Pricing Model

The aim of this paper is to test the performance of the standard version of CAPM in an evolutionary framework. We imagine a heterogeneous population of long-lived agents who invest their wealth according to di¤erent portfolio rules and we ask what is the fate of those who happen to behave as prescribed by CAPM. In a complete securities’ market with aggregate uncertainty, we prove that traders who either “believe” in CAPM and use it as a rule of thumb, or are endowed with genuine mean-variance preferences, under some very weak conditions, vanish in the long run. We show that a su¢cient condition to drive CAPM or mean variance traders’ wealth shares to zero is that an investor endowed with a logarithmic utility function enters the market. We …nally check the robustness of our results allowing for di¤erent kinds of heterogeneity among traders. JEL Classi…cation C61, D81, G11 Keywords Evolution; portfolio rules; CAPM; Kelly criterion. Address for Correspondence Emanuela Sciubba, Lucy Cavendish College, CB3 0BU Cambridge, UK. E-mail: [email protected] ¤I am deeply indebted to Luca Anderlini for his helpful guidance. I also bene…ted from discussion with Robert Evans and Peter Sorensen. Useful comments came from participants to the St.John’s Theory Workshops, University of Cambridge, and to the Third International Conference on “Computation in Economics and Finance”, Stanford University. All remaining errors are mine.