IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2103.04898.html
   My bibliography  Save this paper

On Asymptotic Log-Optimal Buy-and-Hold Strategy

Author

Listed:
  • Chung-Han Hsieh

Abstract

In this paper, we consider a frequency-based portfolio optimization problem with $m \geq 2$ assets when the expected logarithmic growth (ELG) rate of wealth is used as the performance metric. With the aid of the notion called dominant asset, it is known that the optimal ELG level is achieved by investing all available funds on that asset. However, such an "all-in" strategy is arguably too risky to implement in practice. Motivated by this issue, we study the case where the portfolio weights are chosen in a rather ad-hoc manner and a buy-and-hold strategy is subsequently used. Then we show that, if the underlying portfolio contains a dominant asset, buy and hold on that specific asset is asymptotically log-optimal with a sublinear rate of convergence. This result also extends to the scenario where a trader either does not have a probabilistic model for the returns or does not trust a model obtained from historical data. To be more specific, we show that if a market contains a dominant asset, buy and hold a market portfolio involving nonzero weights for each asset is asymptotically log-optimal. Additionally, this paper also includes a conjecture regarding the property called high-frequency maximality. That is, in the absence of transaction costs, high-frequency rebalancing is unbeatable in the ELG sense. Support for the conjecture, involving a lemma for a weak version of the conjecture, is provided. This conjecture, if true, enables us to improve the log-optimality result obtained previously. Finally, a result that indicates a way regarding an issue about when should one to rebalance their portfolio if needed, is also provided. Examples, some involving simulations with historical data, are also provided along the way to illustrate the~theory.

Suggested Citation

  • Chung-Han Hsieh, 2021. "On Asymptotic Log-Optimal Buy-and-Hold Strategy," Papers 2103.04898, arXiv.org.
    • Handle: RePEc:arx:papers:2103.04898
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2103.04898
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. 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.
    2. Sergei Maslov & Yi-Cheng Zhang, 1998. "Optimal Investment Strategy for Risky Assets," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 1(03), pages 377-387.
    3. 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.
    4. Napat Rujeerapaiboon & Daniel Kuhn & Wolfram Wiesemann, 2016. "Robust Growth-Optimal Portfolios," Management Science, INFORMS, vol. 62(7), pages 2090-2109, July.
    5. 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.
    6. 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.
    7. Hakansson, Nils H, 1971. "On Optimal Myopic Portfolio Policies, With and Without Serial Correlation of Yields," The Journal of Business, University of Chicago Press, vol. 44(3), pages 324-334, July.
    8. Wu, Mu-En & Tsai, Hui-Huang & Chung, Wei-Ho & Chen, Chien-Ming, 2020. "Analysis of Kelly betting on finite repeated games," Applied Mathematics and Computation, Elsevier, vol. 373(C).
    9. Sergei Maslov & Yi-Cheng Zhang, 1998. "Optimal Investment Strategy for Risky Assets," Papers cond-mat/9801240, arXiv.org.
    10. Andrew W. Lo & H. Allen Orr & Ruixun Zhang, 2018. "The growth of relative wealth and the Kelly criterion," Journal of Bioeconomics, Springer, vol. 20(1), pages 49-67, April.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Chung-Han Hsieh, 2020. "Necessary and Sufficient Conditions for Frequency-Based Kelly Optimal Portfolio," Papers 2004.12099, arXiv.org.
    2. 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.
    3. Chung-Han Hsieh, 2022. "On Solving Robust Log-Optimal Portfolio: A Supporting Hyperplane Approximation Approach," Papers 2202.03858, arXiv.org.
    4. 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.
    5. Erik Aurell & Paolo Muratore-Ginanneschi, 1999. "Financial Friction and Multiplicative Markov Market Game," Papers cond-mat/9908253, arXiv.org.
    6. 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.
    7. Rubina Zadourian, 2024. "Model-based and empirical analyses of stochastic fluctuations in economy and finance," Papers 2408.16010, arXiv.org.
    8. Paolo Laureti & Matus Medo & Yi-Cheng Zhang, 2010. "Analysis of Kelly-optimal portfolios," Quantitative Finance, Taylor & Francis Journals, vol. 10(7), pages 689-697.
    9. Subbiah, Mohan & Fabozzi, Frank J., 2016. "Hedge fund allocation: Evaluating parametric and nonparametric forecasts using alternative portfolio construction techniques," International Review of Financial Analysis, Elsevier, vol. 45(C), pages 189-201.
    10. Sornette, Didier, 1998. "Large deviations and portfolio optimization," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 256(1), pages 251-283.
    11. E. Aurell & R. Baviera & O. Hammarlid & M. Serva & A. Vulpiani, 1998. "A general methodology to price and hedge derivatives in incomplete markets," Papers cond-mat/9810257, arXiv.org, revised Apr 1999.
    12. Napat Rujeerapaiboon & Daniel Kuhn & Wolfram Wiesemann, 2016. "Robust Growth-Optimal Portfolios," Management Science, INFORMS, vol. 62(7), pages 2090-2109, July.
    13. Hendrik J. Blok, 2000. "On the nature of the stock market: Simulations and experiments," Papers cond-mat/0010211, arXiv.org.
    14. Hsieh, Chung-Han, 2024. "On solving robust log-optimal portfolio: A supporting hyperplane approximation approach," European Journal of Operational Research, Elsevier, vol. 313(3), pages 1129-1139.
    15. E. Aurell & P. Muratore-Ginanneschi, 2002. "Growth-Optimal Strategies with Quadratic Friction Over Finite-Time Investment Horizons," Papers cond-mat/0211044, arXiv.org.
    16. Chung-Han Hsieh & B. Ross Barmish & John A. Gubner, 2017. "Kelly Betting Can Be Too Conservative," Papers 1710.01786, arXiv.org.
    17. Edward W. Piotrowski, "undated". "Problems with the Astumian's Paradox (in Polish)," Departmental Working Papers 121pl, University of Bialtystok, Department of Theoretical Physics.
    18. Mu-En Wu & Jia-Hao Syu & Chien-Ming Chen, 2022. "Kelly-Based Options Trading Strategies on Settlement Date via Supervised Learning Algorithms," Computational Economics, Springer;Society for Computational Economics, vol. 59(4), pages 1627-1644, April.
    19. 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).
    20. Arpan Jani, 2021. "An agent-based model of repeated decision making under risk: modeling the role of alternate reference points and risk behavior on long-run outcomes," Journal of Business Economics, Springer, vol. 91(9), pages 1271-1297, November.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:arx:papers:2103.04898. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.