On the Evolution of Investment Strategies and the Kelly RuleA Darwinian Approach*
1 Norwegian School of Economics and Business Administration
2 University of Leeds
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.
JEL Classification: G11, G12, C63
* We are most grateful for helpful and constructive comments from an anonymous referee and from the editor, Peter Bossaerts. Thanks are also due to Jarle Møen for a helpful discussion. Financial support from Leeds University Business School and the National Centre of Competence in Research "Financial Valuation and Risk Management" is gratefully acknowledged.