IDEAS home Printed from https://ideas.repec.org/a/wsi/ijtafx/v21y2018i05ns0219024918500334.html
   My bibliography  Save this article

Generalized Framework For Applying The Kelly Criterion To Stock Markets

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.worldscientific.com/doi/abs/10.1142/S0219024918500334
    Download Restriction: Access to full text is restricted to subscribers
    File URL: https://libkey.io/10.1142/S0219024918500334?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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..
    2. Henry Allen Latane, 1959. "Criteria for Choice Among Risky Ventures," Journal of Political Economy, University of Chicago Press, vol. 67(2), pages 144-144.
    3. MacLean, Leonard C. & Sanegre, Rafael & Zhao, Yonggan & Ziemba, William T., 2004. "Capital growth with security," Journal of Economic Dynamics and Control, Elsevier, vol. 28(5), pages 937-954, February.
    4. Hiroshi Konno & Hiroaki Yamazaki, 1991. "Mean-Absolute Deviation Portfolio Optimization Model and Its Applications to Tokyo Stock Market," Management Science, INFORMS, vol. 37(5), pages 519-531, May.
    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.
    6. Sanford J. Grossman & Zhongquan Zhou, 1993. "Optimal Investment Strategies For Controlling Drawdowns," Mathematical Finance, Wiley Blackwell, vol. 3(3), pages 241-276, July.
    7. Levy, Haim, 1973. "Stochastic Dominance Among Log-Normal Prospects," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 14(3), pages 601-614, October.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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.

    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. Yong, Luo & Bo, Zhu & Yong, Tang, 2013. "Dynamic optimal capital growth with risk constraints," Economic Modelling, Elsevier, vol. 30(C), pages 586-594.
    2. Traian A. Pirvu & Gordan Zitkovic, 2007. "Maximizing the Growth Rate under Risk Constraints," Papers 0706.0480, arXiv.org.
    3. Sagara Dewasurendra & Pedro Judice & Qiji Zhu, 2019. "The Optimum Leverage Level of the Banking Sector," Risks, MDPI, vol. 7(2), pages 1-30, May.
    4. Scholz, Peter, 2012. "Size matters! How position sizing determines risk and return of technical timing strategies," CPQF Working Paper Series 31, Frankfurt School of Finance and Management, Centre for Practical Quantitative Finance (CPQF).
    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.
    6. Kaplanski, Guy & Kroll, Yoram, 2002. "VaR Risk Measures versus Traditional Risk Measures: an Analysis and Survey," MPRA Paper 80070, University Library of Munich, Germany.
    7. E. Babaei & I.V. Evstigneev & K.R. Schenk-Hoppé & M.V. Zhitlukhin, 2018. "Von Neumann-Gale Dynamics, Market Frictions, and Capital Growth," Economics Discussion Paper Series 1816, Economics, The University of Manchester.
    8. Ziemba, William, 2016. "A response to Professor Paul A. Samuelson's objections to Kelly capital growth investing," LSE Research Online Documents on Economics 119002, London School of Economics and Political Science, LSE Library.
    9. Traian A. Pirvu & Gordan Žitković, 2009. "Maximizing The Growth Rate Under Risk Constraints," Mathematical Finance, Wiley Blackwell, vol. 19(3), pages 423-455, July.
    10. Adam Borovička, 2022. "Stock portfolio selection under unstable uncertainty via fuzzy mean-semivariance model," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 30(2), pages 595-616, June.
    11. Robert C. Merton, 2006. "Paul Samuelson and Financial Economics," The American Economist, Sage Publications, vol. 50(2), pages 9-31, October.
    12. Gupta, Pankaj & Mittal, Garima & Mehlawat, Mukesh Kumar, 2013. "Expected value multiobjective portfolio rebalancing model with fuzzy parameters," Insurance: Mathematics and Economics, Elsevier, vol. 52(2), pages 190-203.
    13. Giovanni Bonaccolto & Massimiliano Caporin & Sandra Paterlini, 2018. "Asset allocation strategies based on penalized quantile regression," Computational Management Science, Springer, vol. 15(1), pages 1-32, January.
    14. Wojtek Michalowski & Włodzimierz Ogryczak, 2001. "Extending the MAD portfolio optimization model to incorporate downside risk aversion," Naval Research Logistics (NRL), John Wiley & Sons, vol. 48(3), pages 185-200, April.
    15. Neofytos Rodosthenous & Hongzhong Zhang, 2020. "When to sell an asset amid anxiety about drawdowns," Mathematical Finance, Wiley Blackwell, vol. 30(4), pages 1422-1460, October.
    16. Ogryczak, Wlodzimierz & Ruszczynski, Andrzej, 1999. "From stochastic dominance to mean-risk models: Semideviations as risk measures," European Journal of Operational Research, Elsevier, vol. 116(1), pages 33-50, July.
    17. Hongzhong Zhang, 2018. "Stochastic Drawdowns," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 10078, September.
    18. Zbigniew Palmowski & Joanna Tumilewicz, 2017. "Fair valuation of L\'evy-type drawdown-drawup contracts with general insured and penalty functions," Papers 1712.04418, arXiv.org, revised Feb 2018.
    19. Luisa Corrado & Marcus Miller & Lei Zhang, 2007. "Bulls, bears and excess volatility: can currency intervention help?," International Journal of Finance & Economics, John Wiley & Sons, Ltd., vol. 12(2), pages 261-272.
    20. Laura Alfaro & Nick Bloom & Paola Conconi & Harald Fadinger & Patrick Legros & Andrew F Newman & Raffaella Sadun & John Van Reenen, 2024. "Come Together: Firm Boundaries and Delegation," Journal of the European Economic Association, European Economic Association, vol. 22(1), pages 34-72.

    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:wsi:ijtafx:v:21:y:2018:i:05:n:s0219024918500334. 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: Tai Tone Lim (email available below). General contact details of provider: http://www.worldscinet.com/ijtaf/ijtaf.shtml .

    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.