The Growth of Relative Wealth and the Kelly Criterion
24 Pages Posted: 6 Feb 2019 Last revised: 19 Oct 2021
Date Written: September 10, 2017
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, whether the investor is myopic across a single time period, or is maximizing wealth with an infinite horizon. We relate these results to population genetics, and discuss testable consequences of these findings using experimental evolution.
Keywords: Kelly Criterion, Portfolio Optimization, Adaptive Markets Hypothesis, Evolutionary Game Theory
JEL Classification: G11, G12, D03, D11
Suggested Citation: Suggested Citation