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

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  • Sujit R. Das
  • Mukul Goyal

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.

Suggested Citation

  • Sujit R. Das & Mukul Goyal, 2015. "Computing optimal rebalance frequency for log-optimal portfolios in linear time," Quantitative Finance, Taylor & Francis Journals, vol. 15(7), pages 1191-1204, July.
    • Handle: RePEc:taf:quantf:v:15:y:2015:i:7:p:1191-1204
    DOI: 10.1080/14697688.2014.926020
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    References listed on IDEAS

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    1. Nicole Branger & Beate Breuer & Christian Schlag, 2010. "Discrete-time implementation of continuous-time portfolio strategies," The European Journal of Finance, Taylor & Francis Journals, vol. 16(2), pages 137-152.
    2. Sujit R. Das & Dmitri Kaznachey & Mukul Goyal, 2014. "Computing optimal rebalance frequency for log-optimal portfolios," Quantitative Finance, Taylor & Francis Journals, vol. 14(8), pages 1489-1502, January.
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    Cited by:

    1. Chung-Han Hsieh, 2021. "On Asymptotic Log-Optimal Buy-and-Hold Strategy," Papers 2103.04898, arXiv.org.
    2. Chung-Han Hsieh, 2020. "Necessary and Sufficient Conditions for Frequency-Based Kelly Optimal Portfolio," Papers 2004.12099, arXiv.org.

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