Transaction fees and optimal rebalancing in the growth-optimal portfolio

TL;DR

This paper investigates how transaction fees influence the optimal rebalancing period in growth-optimal portfolios, revealing that fees can create an optimal rebalancing interval and that partial rebalancing can enhance long-term growth.

Contribution

It analytically derives the optimal rebalancing period considering transaction fees and demonstrates the benefits of partial rebalancing for portfolio growth.

Findings

Transaction fees can induce an optimal rebalancing period.

Partial rebalancing can outperform full rebalancing in growth optimization.

Analytical and numerical methods confirm the results across various return distributions.

Abstract

The growth-optimal portfolio optimization strategy pioneered by Kelly is based on constant portfolio rebalancing which makes it sensitive to transaction fees. We examine the effect of fees on an example of a risky asset with a binary return distribution and show that the fees may give rise to an optimal period of portfolio rebalancing. The optimal period is found analytically in the case of lognormal returns. This result is consequently generalized and numerically verified for broad return distributions and returns generated by a GARCH process. Finally we study the case when investment is rebalanced only partially and show that this strategy can improve the investment long-term growth rate more than optimization of the rebalancing period.