On Kelly Betting: Some Limitations

TL;DR

This paper critically examines the limitations of the Kelly Criterion, highlighting issues with approximations and drawdowns, and suggests future research directions for improving the theory.

Contribution

It provides specific examples of the Kelly Criterion's limitations, especially regarding Taylor approximations and wealth drawdowns, and proposes research directions for enhancement.

Findings

Illustrates difficulties with Taylor-style approximations

Quantifies issues related to wealth drawdowns

Suggests promising research directions for theory improvement

Abstract

The focal point of this paper is the so-called Kelly Criterion, a prescription for optimal resource allocation among a set of gambles which are repeated over time. The criterion calls for maximization of the expected value of the logarithmic growth of wealth. While significant literature exists providing the rationale for such an optimization, this paper concentrates on the limitations of the Kelly-based theory. To this end, we fill a void in published results by providing specific examples quantifying what difficulties are encountered when Taylor-style approximations are used and when wealth drawdowns are considered. For the case of drawdown, we describe some research directions which we feel are promising for improvement of the theory.