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Growth Versus Security in Dynamic Investment Analysis


Author Info

  • L. C. MacLean

    (School of Business Administration, Dalhousie University, Halifax, Nova Scotia, Canada B3H 1Z5)

  • W. T. Ziemba

    (Faculty of Commerce, University of British Columbia, Vancouver, British Columbia, Canada V6T 1Z2)

  • G. Blazenko

    (School of Business Administration, Simon Fraser University, Burnaby, British Columbia, Canada V5A 1S6)

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    This paper concerns the problem of optimal dynamic choice in discrete time for an investor. In each period the investor is faced with one or more risky investments. The maximization of the expected logarithm of the period by period wealth, referred to as the Kelly criterion, is a very desirable investment procedure. It has many attractive properties, such as maximizing the asymptotic rate of growth of the investor's fortune. On the other hand, instead of focusing on maximal growth, one can develop strategies based on maximum security. For example, one can minimize the ruin probability subject to making a positive return or compute a confidence level of increasing the investor's initial fortune to a given final wealth goal. This paper is concerned with methods to combine these two approaches. We derive computational formulas for a variety of growth and security measures. Utilizing fractional Kelly strategies, we can develop a complete tradeoff of growth versus security. The theory is applicable to favorable investment situations such as blackjack, horseracing, lotto games, index and commodity futures and options trading. The results provide insight into how one should properly invest in these situations.

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    Bibliographic Info

    Article provided by INFORMS in its journal Management Science.

    Volume (Year): 38 (1992)
    Issue (Month): 11 (November)
    Pages: 1562-1585

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    Handle: RePEc:inm:ormnsc:v:38:y:1992:i:11:p:1562-1585

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    Keywords: capital accumulation; fractional kelly strategies; effective growth-security tradeoff; blackjack; horseracing; lotto games; turn of the year effect;


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    Cited by:
    1. Victor Matheson & Kent Grote, 2004. "In Search of a Fair Bet in the Lottery," Working Papers 0401, College of the Holy Cross, Department of Economics.
    2. David Johnstone, 2007. "Economic Darwinism: Who has the Best Probabilities?," Theory and Decision, Springer, vol. 62(1), pages 47-96, February.
    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. Kent Grote & Victor Matheson, 2011. "The Economics of Lotteries: An Annotated Bibliography," Working Papers 1110, College of the Holy Cross, Department of Economics.
    5. Bin Li & Steven C. H. Hoi, 2012. "Online Portfolio Selection: A Survey," Papers 1212.2129,, revised May 2013.
    6. Daniel Lane & William Ziemba, 2004. "Jai Alai arbitrage strategies," The European Journal of Finance, Taylor & Francis Journals, vol. 10(5), pages 353-369.
    7. Grant, Andrew & Johnstone, David, 2010. "Finding profitable forecast combinations using probability scoring rules," International Journal of Forecasting, Elsevier, vol. 26(3), pages 498-510, July.
    8. 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).
    9. MacLean, Leonard & Zhao, Yonggan & Ziemba, William, 2006. "Dynamic portfolio selection with process control," Journal of Banking & Finance, Elsevier, vol. 30(2), pages 317-339, February.
    10. Andrea Beltratti & Andrea Consiglio & Stavros A. Zenios, 1998. "Scenario Modeling for the Management of International Bond Portfolios," Center for Financial Institutions Working Papers 98-20, Wharton School Center for Financial Institutions, University of Pennsylvania.
    11. Ryall, Richard & Bedford, Anthony, 2010. "An optimized ratings-based model for forecasting Australian Rules football," International Journal of Forecasting, Elsevier, vol. 26(3), pages 511-517, July.
    12. Dohi, T. & Tanaka, H. & Kaio, N. & Osaki, S., 1995. "Alternative growth versus security in continuous dynamic trading," European Journal of Operational Research, Elsevier, vol. 84(2), pages 265-278, July.
    13. Stutzer, Michael, 2003. "Portfolio choice with endogenous utility: a large deviations approach," Journal of Econometrics, Elsevier, vol. 116(1-2), pages 365-386.
    14. Blomvall, Jorgen & Lindberg, Per Olov, 2003. "Back-testing the performance of an actively managed option portfolio at the Swedish Stock Market, 1990-1999," Journal of Economic Dynamics and Control, Elsevier, vol. 27(6), pages 1099-1112, April.
    15. Roderick Bain & Donald Hausch & William Ziemba, 2006. "An application of expert information to win betting on the Kentucky Derby, 1981-2005," The European Journal of Finance, Taylor & Francis Journals, vol. 12(4), pages 283-301.


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