The Kelly criterion in portfolio optimization: a decoupled problem

Zachariah Peterson

Abstract

The Kelly criterion is well known among gamblers and investors as a method for maximizing the returns one would expect to observe over long periods of betting or investing. This paper will demonstrate how the Kelly criterion can be incorporated into standard portfolio optimization models that include a risk function. The model developed here combines the risk and return functions into a single objective function using a risk parameter. This model is then solved for a portfolio of ten stocks from a major stock exchange using a differential evolution algorithm. Monte Carlo calculations are used to directly simulate and compare the average returns from the mean–variance and Kelly portfolios. The results show that the Kelly criterion can be used to calculate optimal returns and generate portfolios that are similar to those from the mean–variance model. The results also show that evolutionary algorithms can be successfully applied to solve this unique portfolio optimization problem.