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Analysis of the rebalancing frequency in log-optimal portfolio selection

Author

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  • Daniel Kuhn
  • David Luenberger

Abstract

In a dynamic investment situation, the right timing of portfolio revisions and adjustments is essential to sustain long-term growth. A high rebalancing frequency reduces the portfolio performance in the presence of transaction costs, whereas a low rebalancing frequency entails a static investment strategy that hardly reacts to changing market conditions. This article studies a family of portfolio problems in a Black-Scholes type economy which depend parametrically on the rebalancing frequency. As an objective criterion we use log-utility, which has strong theoretical appeal and represents a natural choice if the primary goal is long-term performance. We argue that continuous rebalancing only slightly outperforms discrete rebalancing if there are no transaction costs and if the rebalancing intervals are shorter than about one year. Our analysis also reveals that diversification has a dual effect on the mean and variance of the portfolio growth rate as well as on their sensitivities with respect to the rebalancing frequency.

Suggested Citation

  • Daniel Kuhn & David Luenberger, 2010. "Analysis of the rebalancing frequency in log-optimal portfolio selection," Quantitative Finance, Taylor & Francis Journals, vol. 10(2), pages 221-234.
    • Handle: RePEc:taf:quantf:v:10:y:2010:i:2:p:221-234
    DOI: 10.1080/14697680802629400
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    Citations

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    Cited by:

    1. Soumik Pal & Ting-Kam Leonard Wong, 2013. "Energy, entropy, and arbitrage," Papers 1308.5376, arXiv.org, revised Jan 2016.
    2. Chung-Han Hsieh & John A. Gubner & B. Ross Barmish, 2018. "Rebalancing Frequency Considerations for Kelly-Optimal Stock Portfolios in a Control-Theoretic Framework," Papers 1807.05265, arXiv.org, revised Aug 2018.
    3. Igor V. EVSTIGNEEVY & Thorsten HENS & Klaus Reiner SCHENK-HOPPE, 2010. "An evolutionary financial market model with a risk-free asset," Swiss Finance Institute Research Paper Series 10-36, Swiss Finance Institute.
    4. W. Bahsoun & I. Evstigneev & L. Xu, 2011. "Almost sure Nash equilibrium strategies in evolutionary models of asset markets," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 73(2), pages 235-250, April.
    5. Napat Rujeerapaiboon & Daniel Kuhn & Wolfram Wiesemann, 2016. "Robust Growth-Optimal Portfolios," Management Science, INFORMS, vol. 62(7), pages 2090-2109, July.
    6. Chung-Han Hsieh, 2021. "On Asymptotic Log-Optimal Buy-and-Hold Strategy," Papers 2103.04898, arXiv.org.
    7. Chung-Han Hsieh & B. Ross Barmish & John A. Gubner, 2017. "Kelly Betting Can Be Too Conservative," Papers 1710.01786, arXiv.org.
    8. Sergei Belkov & Igor V. Evstigneev & Thorsten Hens, 2020. "An evolutionary finance model with a risk-free asset," Annals of Finance, Springer, vol. 16(4), pages 593-607, December.
    9. Chung-Han Hsieh, 2022. "On Solving Robust Log-Optimal Portfolio: A Supporting Hyperplane Approximation Approach," Papers 2202.03858, arXiv.org.
    10. Zhu, Bo & Zhang, Tianlun, 2021. "Long-term wealth growth portfolio allocation under parameter uncertainty: A non-conservative robust approach," The North American Journal of Economics and Finance, Elsevier, vol. 57(C).
    11. Chung-Han Hsieh & B. Ross Barmish & John A. Gubner, 2019. "The Impact of Execution Delay on Kelly-Based Stock Trading: High-Frequency Versus Buy and Hold," Papers 1907.08771, arXiv.org.
    12. Chung-Han Hsieh, 2020. "Necessary and Sufficient Conditions for Frequency-Based Kelly Optimal Portfolio," Papers 2004.12099, arXiv.org.
    13. Chung-Han Hsieh & B. Ross Barmish & John A. Gubner, 2018. "At What Frequency Should the Kelly Bettor Bet?," Papers 1801.06737, arXiv.org, revised Aug 2018.

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