Analysis of Kelly-optimal portfolios

TL;DR

This paper explores Kelly's strategy for optimal asset portfolio construction, deriving analytical results for lognormal returns, and reveals that Kelly portfolios tend to include only a few assets, especially under certain conditions.

Contribution

It provides analytical insights into Kelly-optimal portfolios, showing their relation to Markowitz frontier and the phenomenon of portfolio condensation under specific assumptions.

Findings

Kelly-optimal portfolios align with the Markowitz Efficient Frontier under certain conditions.

Portfolio condensation occurs, with only a few assets included in the Kelly portfolio.

Analytical results describe the behavior of Kelly portfolios with small mean returns and volatilities.

Abstract

We investigate the use of Kelly's strategy in the construction of an optimal portfolio of assets. For lognormally distributed asset returns, we derive approximate analytical results for the optimal investment fractions in various settings. We show that when mean returns and volatilities of the assets are small and there is no risk-free asset, the Kelly-optimal portfolio lies on Markowitz Efficient Frontier. Since in the investigated case the Kelly approach forbids short positions and borrowing, often only a small fraction of the available assets is included in the Kelly-optimal portfolio. This phenomenon, that we call condensation, is studied analytically in various model scenarios.