On the Kelly Criterion in Stock Investment

Abstract

This paper examines the Kelly criterion in stock investment. In general, the Kelly criterion is the method of determining gambling stakes (investment portfolios) that maximizes the geometric mean return, i.e., the growth rate of wealth, and it is considered to be the criterion for maximizing the logarithmic expected utility function in economics. Thorp (1971, 2006) developed an approximate formula for optimal portfolios in stock investment based on the Kelly criterion. However, since this optimization problem seems to be a problem that cannot be solved analytically, strictly speaking, it is assumed that the solutions must be obtained by numerical calculation. This paper provides a method to estimate the optimal portfolio in stock investment based on the Kelly criterion using Monte Carlo simulation.

Keywords: Kelly Criterion, Fortune's Formula, Monte Carlo Simulation, Portfolio Optimization

JEL Classification: C61,D81,G11