IDEAS home Printed from https://ideas.repec.org/a/taf/quantf/v10y2010i7p689-697.html
   My bibliography  Save this article

Analysis of Kelly-optimal portfolios

Author

Listed:
  • 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.
(This abstract was borrowed from another version of this item.)

Suggested Citation

  • 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
    as

    Download full text from publisher

    File URL: http://www.tandfonline.com/doi/abs/10.1080/14697680902991619
    Download Restriction: Access to full text is restricted to subscribers.

    File URL: https://libkey.io/10.1080/14697680902991619?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 look for a different version below or search for a different version of it.

    Other versions of this item:

    References listed on IDEAS

    as
    1. Harry M. Markowitz, 2011. "Investment for the Long Run: New Evidence for an Old Rule," 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 35, pages 495-508, World Scientific Publishing Co. Pte. Ltd..
    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.
    3. L. C. MacLean & W. T. Ziemba & G. Blazenko, 1992. "Growth Versus Security in Dynamic Investment Analysis," Management Science, INFORMS, vol. 38(11), pages 1562-1585, November.
    4. 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.
    5. Matus Medo & Yury M. Pis'mak & Yi-Cheng Zhang, 2008. "Diversification and limited information in the Kelly game," Papers 0803.1364, arXiv.org, revised Jul 2008.
    6. 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.
    7. Eckhard Platen, 2006. "A Benchmark Approach To Finance," Mathematical Finance, Wiley Blackwell, vol. 16(1), pages 131-151, January.
    8. 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.
    9. Sergei Maslov & Yi-Cheng Zhang, 1998. "Optimal Investment Strategy for Risky Assets," Papers cond-mat/9801240, arXiv.org.
    10. Harry Markowitz, 1952. "Portfolio Selection," Journal of Finance, American Finance Association, vol. 7(1), pages 77-91, March.
    11. Marsili, Matteo & Maslov, Sergei & Zhang, Yi-Cheng, 1998. "Dynamical optimization theory of a diversified portfolio," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 253(1), pages 403-418.
    12. Andre F. Perold, 1984. "Large-Scale Portfolio Optimization," Management Science, INFORMS, vol. 30(10), pages 1143-1160, October.
    13. 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.
    14. William F. Sharpe, 1964. "Capital Asset Prices: A Theory Of Market Equilibrium Under Conditions Of Risk," Journal of Finance, American Finance Association, vol. 19(3), pages 425-442, September.
    15. Merton, Robert C, 1969. "Lifetime Portfolio Selection under Uncertainty: The Continuous-Time Case," The Review of Economics and Statistics, MIT Press, vol. 51(3), pages 247-257, August.
    16. Matteo Marsili & Sergei Maslov & Yi-Cheng Zhang, 1998. "Dynamical Optimization Theory of a Diversified Portfolio," Papers cond-mat/9801239, arXiv.org, revised Jan 1998.
    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. 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.

    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. Sornette, Didier, 1998. "Large deviations and portfolio optimization," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 256(1), pages 251-283.
    2. Arenas Parra, M. & Bilbao Terol, A. & Rodriguez Uria, M. V., 2001. "A fuzzy goal programming approach to portfolio selection," European Journal of Operational Research, Elsevier, vol. 133(2), pages 287-297, January.
    3. Leung, Pui-Lam & Ng, Hon-Yip & Wong, Wing-Keung, 2012. "An improved estimation to make Markowitz’s portfolio optimization theory users friendly and estimation accurate with application on the US stock market investment," European Journal of Operational Research, Elsevier, vol. 222(1), pages 85-95.
    4. Charfeddine, Lanouar & Najah, Ahlem & Teulon, Frédéric, 2016. "Socially responsible investing and Islamic funds: New perspectives for portfolio allocation," Research in International Business and Finance, Elsevier, vol. 36(C), pages 351-361.
    5. Levy, Haim & Levy, Moshe, 2021. "Stocks versus bonds for the long run when a riskless asset is available," Journal of Banking & Finance, Elsevier, vol. 133(C).
    6. Bai, Zhidong & Liu, Huixia & Wong, Wing-Keung, 2016. "Making Markowitz's Portfolio Optimization Theory Practically Useful," MPRA Paper 74360, University Library of Munich, Germany.
    7. Platen, Eckhard, 2006. "Portfolio selection and asset pricing under a benchmark approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 370(1), pages 23-29.
    8. Bai, Zhidong & Li, Hua & Wong, Wing-Keung, 2013. "The best estimation for high-dimensional Markowitz mean-variance optimization," MPRA Paper 43862, University Library of Munich, Germany.
    9. 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.
    10. Giofré, Maela, 2014. "Domestic investor protection and foreign portfolio investment," Journal of Banking & Finance, Elsevier, vol. 46(C), pages 355-371.
    11. Walter Murray & Howard Shek, 2012. "A local relaxation method for the cardinality constrained portfolio optimization problem," Computational Optimization and Applications, Springer, vol. 53(3), pages 681-709, December.
    12. Trabelsi, Mohamed Ali, 2010. "Choix de portefeuille: comparaison des différentes stratégies [Portfolio selection: comparison of different strategies]," MPRA Paper 82946, University Library of Munich, Germany, revised 01 Dec 2010.
    13. Lin, Wen-chang & Lu, Jin-ray, 2012. "Risky asset allocation and consumption rule in the presence of background risk and insurance markets," Insurance: Mathematics and Economics, Elsevier, vol. 50(1), pages 150-158.
    14. Mark Davis & SEBastien Lleo, 2008. "Risk-sensitive benchmarked asset management," Quantitative Finance, Taylor & Francis Journals, vol. 8(4), pages 415-426.
    15. Hubáček, Ondřej & Šír, Gustav, 2023. "Beating the market with a bad predictive model," International Journal of Forecasting, Elsevier, vol. 39(2), pages 691-719.
    16. David S. Jones & V. Vance Roley, 1981. "Bliss Points in Mean-Variance Portfolio Models," NBER Technical Working Papers 0019, National Bureau of Economic Research, Inc.
    17. Fang, Yong & Chen, Lihua & Fukushima, Masao, 2008. "A mixed R&D projects and securities portfolio selection model," European Journal of Operational Research, Elsevier, vol. 185(2), pages 700-715, March.
    18. Bilel Jarraya & Abdelfettah Bouri, 2013. "A Theoretical Assessment on Optimal Asset Allocations in Insurance Industry," International Journal of Finance & Banking Studies, Center for the Strategic Studies in Business and Finance, vol. 2(4), pages 30-44, October.
    19. Penaranda, Francisco, 2007. "Portfolio choice beyond the traditional approach," LSE Research Online Documents on Economics 24481, London School of Economics and Political Science, LSE Library.
    20. Eckhard Platen, 2011. "A Benchmark Approach to Investing and Pricing," 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 28, pages 409-426, World Scientific Publishing Co. Pte. Ltd..

    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:taf:quantf:v:10:y:2010:i:7:p:689-697. 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: Chris Longhurst (email available below). General contact details of provider: http://www.tandfonline.com/RQUF20 .

    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.