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Generalized Framework For Applying The Kelly Criterion To Stock Markets

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  • TIM BYRNES

    (New York University Shanghai, 1555 Century Ave, Pudong, Shanghai 200122, P. R. China†State Key Laboratory of Precision Spectroscopy, School of Physical and Material Sciences, East China Normal University, Shanghai 200062, P. R. China‡NYU-ECNU Institute of Physics at NYU Shanghai, 3663 Zhongshan Road North, Shanghai 200062, P. R. China§National Institute of Informatics, 2-1-2 Hitotsubashi, Chiyoda-ku, Tokyo 101-8430, Japan¶Department of Physics, New York University, New York, NY 10003, USA)

  • TRISTAN BARNETT

    (New York University Shanghai, 1555 Century Ave, Pudong, Shanghai 200122, P. R. China†State Key Laboratory of Precision Spectroscopy, School of Physical and Material Sciences, East China Normal University, Shanghai 200062, P. R. China)

Abstract

We develop a general framework for applying the Kelly criterion to the stock market. By supplying an arbitrary probability distribution modeling the future price movement of a set of stocks, the Kelly fraction for investing each stock can be calculated by inverting a matrix involving only first and second moments. The framework works for one or a portfolio of stocks and the Kelly fractions can be efficiently calculated. For a simple model of geometric Brownian motion of a single stock we show that our calculated Kelly fraction agrees with existing results. We demonstrate that the Kelly fractions can be calculated easily for other types of probabilities such as the Gaussian distribution and correlated multivariate assets.

Suggested Citation

  • 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.
    • Handle: RePEc:wsi:ijtafx:v:21:y:2018:i:05:n:s0219024918500334
    DOI: 10.1142/S0219024918500334
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    References listed on IDEAS

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    1. E. O. Thorp, 2011. "Optimal Gambling Systems For Favorable Games," World Scientific Book Chapters, in: Leonard C MacLean & Edward O Thorp & William T Ziemba (ed.), THE KELLY CAPITAL GROWTH INVESTMENT CRITERION THEORY and PRACTICE, chapter 6, pages 61-80, World Scientific Publishing Co. Pte. Ltd..
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    5. Paolo Laureti & Matus Medo & Yi-Cheng Zhang, 2010. "Analysis of Kelly-optimal portfolios," Quantitative Finance, Taylor & Francis Journals, vol. 10(7), pages 689-697.
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    Cited by:

    1. Steven Y. K. Wong & Jennifer S. K. Chan & Lamiae Azizi, 2024. "Quantifying neural network uncertainty under volatility clustering," Papers 2402.14476, arXiv.org, revised Sep 2024.
    2. Vuko Vukcevic & Robert Keser, 2024. "Sizing the bets in a focused portfolio," Papers 2402.15588, arXiv.org.
    3. Richard Watt, 2025. "When Harry Met Kelly: An Overlooked Result in the Classical Theory of Optimal Capital Growth," Working Papers in Economics 25/08, University of Canterbury, Department of Economics and Finance.

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