Kelly Criterion for Multivariate Portfolios: A Model-Free Approach

Abstract

The Kelly criterion is a money management principle that beats any other approach in many respects. In particular, it maximizes the expected growth rate and the median of the terminal wealth. However, until recently application of the Kelly criterion to multivariate portfolios has seen little analysis. We briefly introduce the Kelly criterion and then present its multivariate version based only on the first and the second moments of the asset excess returns. Additionally, we provide a simple numerical algorithm to manage virtually arbitrarily large portfolios according to so-called fractional Kelly strategies.

Keywords: Kelly criterion, money management, multivariate portfolios, fractional Kelly strategies, analytic and numerical approximation, portfolio optimization on GPUs, CUDA

JEL Classification: C73, C61, D81, G11