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Analysis of Kelly-optimal portfolios

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  • Paolo Laureti
  • Matus Medo
  • Yi-Cheng Zhang

Abstract

We investigate the use of Kelly's strategy in the construction of an optimal portfolio of assets. For lognormally distributed asset returns, we derive approximate analytical results for the optimal investment fractions in various settings. We show that when mean returns and volatilities of the assets are small and there is no risk-free asset, the Kelly-optimal portfolio lies on Markowitz Efficient Frontier. Since in the investigated case the Kelly approach forbids short positions and borrowing, often only a small fraction of the available assets is included in the Kelly-optimal portfolio. This phenomenon, that we call condensation, is studied analytically in various model scenarios.
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  • Paolo Laureti & Matus Medo & Yi-Cheng Zhang, 2010. "Analysis of Kelly-optimal portfolios," Quantitative Finance, Taylor & Francis Journals, vol. 10(7), pages 689-697.
    • Handle: RePEc:taf:quantf:v:10:y:2010:i:7:p:689-697
    DOI: 10.1080/14697680902991619
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    2. Medo, Matús & Yeung, Chi Ho & Zhang, Yi-Cheng, 2009. "How to quantify the influence of correlations on investment diversification," International Review of Financial Analysis, Elsevier, vol. 18(1-2), pages 34-39, March.
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    Cited by:

    1. Tim Byrnes & Tristan Barnett, 2018. "Generalized Framework For Applying The Kelly Criterion To Stock Markets," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 21(05), pages 1-13, August.
    2. 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.
    3. Gruszka, Jarosław & Szwabiński, Janusz, 2020. "Best portfolio management strategies for synthetic and real assets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 539(C).
    4. Matus Medo & Chi Ho Yeung & Yi-Cheng Zhang, 2008. "How to quantify the influence of correlations on investment diversification," Papers 0805.3397, arXiv.org, revised Feb 2009.
    5. Sergey Kamenshchikov & Ilia Drozdov, 2016. "Fractal Optimization of Market Neutral Portfolio," Papers 1612.03698, arXiv.org, revised Dec 2016.
    6. Yoshiharu Sato, 2019. "Model-Free Reinforcement Learning for Financial Portfolios: A Brief Survey," Papers 1904.04973, arXiv.org, revised May 2019.
    7. Medo, Matús & Yeung, Chi Ho & Zhang, Yi-Cheng, 2009. "How to quantify the influence of correlations on investment diversification," International Review of Financial Analysis, Elsevier, vol. 18(1-2), pages 34-39, March.

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