IDEAS home Printed from https://ideas.repec.org/a/inm/ormnsc/v38y1992i11p1562-1585.html
   My bibliography  Save this article

Growth Versus Security in Dynamic Investment Analysis

Author

Listed:
  • 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)

Abstract

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.

Suggested Citation

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

    Download full text from publisher

    File URL: http://dx.doi.org/10.1287/mnsc.38.11.1562
    Download Restriction: no

    Citations

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


    Cited by:

    1. David Johnstone, 2007. "Economic Darwinism: Who has the Best Probabilities?," Theory and Decision, Springer, vol. 62(1), pages 47-96, February.
    2. 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.
    3. Igor V. Evstigneev & Thorsten Hens & Klaus Reiner Schenk-Hoppé, 2008. "Evolutionary Finance," Swiss Finance Institute Research Paper Series 08-14, Swiss Finance Institute.
    4. Daniel Lane & William Ziemba, 2004. "Jai Alai arbitrage strategies," The European Journal of Finance, Taylor & Francis Journals, vol. 10(5), pages 353-369.
    5. 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.
    6. 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.
    7. Andrea Beltratti & Andrea Consiglio & Stavros Zenios, 1999. "Scenario modeling for the management ofinternational bond portfolios," Annals of Operations Research, Springer, vol. 85(0), pages 227-247, January.
    8. Kent R. Grote & Victor A. Matheson, 2006. "In Search of a Fair Bet in the Lottery," Eastern Economic Journal, Eastern Economic Association, vol. 32(4), pages 673-684, Fall.
    9. Bin Li & Steven C. H. Hoi, 2012. "Online Portfolio Selection: A Survey," Papers 1212.2129, arXiv.org, revised May 2013.
    10. 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.
    11. 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).
    12. Steven D. Moffitt & William T. Ziemba, 2018. "A Method for Winning at Lotteries," Papers 1801.02958, arXiv.org.
    13. D.J. Johnstone, 2015. "Information and the Cost of Capital in a Mean-Variance Efficient Market," Journal of Business Finance & Accounting, Wiley Blackwell, vol. 42(1-2), pages 79-100, January.
    14. Kent Grote & Victor Matheson, 2011. "The Economics of Lotteries: An Annotated Bibliography," Working Papers 1110, College of the Holy Cross, Department of Economics.
    15. 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.
    16. Michael A. H. Dempster & Igor V. Evstigneev & Klaus R. Schenk-hoppe, 2007. "Volatility-induced financial growth," Quantitative Finance, Taylor & Francis Journals, vol. 7(2), pages 151-160.
    17. Hwang, Joon Ho & Kim, Min-Su, 2015. "Misunderstanding of the binomial distribution, market inefficiency, and learning behavior: Evidence from an exotic sports betting market," European Journal of Operational Research, Elsevier, vol. 243(1), pages 333-344.
    18. 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.
    19. Giulio Bottazzi & Daniele Giachini, 2016. "Far from the Madding Crowd: Collective Wisdom in Prediction Markets," LEM Papers Series 2016/14, Laboratory of Economics and Management (LEM), Sant'Anna School of Advanced Studies, Pisa, Italy.
    20. Stutzer, Michael, 2003. "Portfolio choice with endogenous utility: a large deviations approach," Journal of Econometrics, Elsevier, vol. 116(1-2), pages 365-386.
    21. Bottazzi, Giulio & Giachini, Daniele, 2017. "Wealth and price distribution by diffusive approximation in a repeated prediction market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 471(C), pages 473-479.
    22. MacLean, Leonard C. & Zhao, Yonggan & Ziemba, William T., 2014. "Optimal capital growth with convex shortfall penalties," LSE Research Online Documents on Economics 59292, London School of Economics and Political Science, LSE Library.
    23. Steven D. Moffitt & William T. Ziemba, 2018. "Does it Pay to Buy the Pot in the Canadian 6/49 Lotto? Implications for Lottery Design," Papers 1801.02959, arXiv.org.
    24. MacLean, Leonard C. & Zhao, Yonggan & Ziemba, William T., 2016. "Optimal capital growth with convex shortfall penalties," LSE Research Online Documents on Economics 65486, London School of Economics and Political Science, LSE Library.
    25. 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.

    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:inm:ormnsc:v:38:y:1992:i:11:p:1562-1585. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Mirko Janc). General contact details of provider: http://edirc.repec.org/data/inforea.html .

    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.

    We have no references for this item. You can help adding them by using 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.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.