Kelly Criterion for Multivariate Portfolios: A Model-Free Approach

15 Pages Posted: 2 May 2013 Last revised: 30 Sep 2014

Date Written: September 30, 2014


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

Suggested Citation

Nekrasov, Vasily, Kelly Criterion for Multivariate Portfolios: A Model-Free Approach (September 30, 2014). Available at SSRN: or

Vasily Nekrasov (Contact Author) ( email )



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