On the Evolution of Investment Strategies and the Kelly Rule—A Darwinian Approach*

Abstract

This paper complements theoretical studies on the Kelly rule in evolutionary finance by studying a Darwinian model of selection and reproduction in which the diversity of investment strategies is maintained through genetic programming. We find that investment strategies which optimize long-term performance can emerge in markets populated by unsophisticated investors. Regardless whether the market is complete or incomplete and whether states are i.i.d. or Markov, the Kelly rule is obtained as the asymptotic outcome. With price-dependent rather than just state-dependent investment strategies, the market portfolio plays an important role as a protection against severe losses in volatile markets. In this paper, we pursue a Darwinian approach to the study of the evolution of investment strategies in financial markets with short-lived assets. The model comprises the two main processes, selection and reproduction, in a genetic programming framework. According to this approach, center stage is occupied by the population which embodies the investment skills of many individual strategies. Our investors are simple-minded and unsophisticated in the sense that they follow preprogrammed behavior rules which are the result of mutations and crossovers. This simplicity is a key factor, as it opens up the possibility of studying, in quite a realistic context, the validity of equilibrium predictions derived from theoretical models that impose strong assumptions on the market dynamics, as well as on individuals' rationality or learning behavior. Our approach complements these models by replacing their rationality assumptions with a Darwinian selection mechanism in