The Growth of Relative Wealth and the Kelly Criterion

Abstract

We propose an evolutionary framework for optimal portfolio growth theory in which investors allocate their wealth between two assets. By considering both absolute wealth and relative wealth between investors, we show that different investor behaviors survive under different environments. When investors maximize their relative wealth, the Kelly criterion is optimal only under certain identified conditions. It is shown that 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 infinite-horizon wealth.