Computing optimal rebalance frequency for log-optimal portfolios in linear time

Sujit R. Das and Mukul Goyal

Quantitative Finance, 2015, vol. 15, issue 7, 1191-1204

Abstract: The pure form of log-optimal investment strategies are often considered to be impractical due to the inherent need for continuous rebalancing. It is however possible to improve investor log utility by adopting a discrete-time periodic rebalancing strategy. Under the assumptions of geometric Brownian motion for assets and approximate log-normality for a sum of log-normal random variables, we find that the optimum rebalance frequency is a piecewise continuous function of investment horizon. One can construct this rebalance strategy function, called the optimal rebalance frequency function , up to a specified investment horizon given a limited trajectory of the expected log of portfolio growth when the initial portfolio is never rebalanced. We develop the analytical framework to compute the optimal rebalance strategy in linear time, a significant improvement from the previously proposed search-based quadratic time algorithm.

Date: 2015
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DOI: 10.1080/14697688.2014.926020

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