The growth of relative wealth and the Kelly criterion
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We propose an evolutionary framework for optimal portfolio growth theory in which investors subject to environmental pressures allocate their wealth between two assets. By considering both absolute wealth and relative wealth between investors, we show that different investor behaviors survive in different environments. When investors maximize their relative wealth, the Kelly criterion is optimal only under certain conditions, which are identified. The initial relative wealth plays a critical role in determining the deviation of optimal behavior from the Kelly criterion regardless of whether the investor is myopic across a single time period or maximizing wealth over an infinite horizon. We relate these results to population genetics, and discuss testable consequences of these findings using experimental evolution.
KeywordsKelly criterion Portfolio optimization Adaptive Markets Hypothesis Evolutionary game theory
JEL ClassificationG11 G12 D03 D11
Research support from the MIT Laboratory for Financial Engineering and the University of Rochester is greatly acknowledged.
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