Tackling estimation risk in Kelly investing using options

TL;DR

This paper proposes a method to reduce estimation risk in Kelly investing by incorporating European options, resulting in more robust growth-optimal portfolios.

Contribution

It introduces a novel approach of using European options within the Kelly framework to mitigate estimation risk in portfolio optimization.

Findings

European options improve robustness to estimation errors

The method enhances growth rate stability

Portfolio performance is less sensitive to probability misestimations

Abstract

The Kelly criterion provides a general framework for optimizing the growth rate of an investment portfolio over time by maximizing the expected logarithmic utility of wealth. However, the optimality condition of the Kelly criterion is highly sensitive to accurate estimates of the probabilities and investment payoffs. Estimation risk can lead to greatly suboptimal portfolios. In a simple binomial model, we show that the introduction of a European option in the Kelly framework can be used to construct a class of growth optimal portfolios that are robust to estimation risk.