Generalized framework for applying the Kelly criterion to stock markets

TL;DR

This paper introduces a flexible mathematical framework for applying the Kelly criterion to stock markets, enabling efficient calculation of optimal investment fractions for various probability models and asset correlations.

Contribution

It provides a novel, generalizable method to compute Kelly fractions using moments, applicable to multiple stocks and different probability distributions.

Findings

Kelly fractions match known results for geometric Brownian motion.

Framework efficiently computes Kelly fractions for Gaussian and correlated assets.

Applicable to single stocks and portfolios with arbitrary probability models.

Abstract

We develop a general framework for applying the Kelly criterion to stock markets. By supplying an arbitrary probability distribution modeling the future price movement of a set of stocks, the Kelly fraction for investing each stock can be calculated by inverting a matrix involving only first and second moments. The framework works for one or a portfolio of stocks and the Kelly fractions can be efficiently calculated. For a simple model of geometric Brownian motion of a single stock we show that our calculated Kelly fraction agrees with existing results. We demonstrate that the Kelly fractions can be calculated easily for other types of probabilities such as the Gaussian distribution and correlated multivariate assets.