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A response to Professor Paul A. Samuelson's objections to Kelly capital growth investing

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  • Ziemba, William

Abstract

The Kelly Capital Growth Investment Strategy maximizes the expected utility of final wealth with a Bernoulli logarithmic utility function. In 1956 Kelly showed that static expected log maximization yields the maximum asymptotic long run growth. Good properties include minimizing the time to large asymptotic goals, maximizing the median, and being ahead on average after the first period. Bad properties include extremely large bets for short term favorable investment situations because the Arrow-Pratt risk aversion index is essentially zero. Paul Samuelson was a critic of this approach and I discuss his various points sent in letters he sent me and papers reprinted in MacLean, Thorp and Ziemba (2011). Samuelson's criticism is partially responsible for the current situation that most finance academics and professionals do not recommend Kelly strategies. I was asked to explain this to Fidelity Investments, a major Boston investment firm influenced by Samuelson at MIT. Should they be using Kelly and safer fractional Kelly strategies which blend cash with the full Kelly strategy? The points of Samuelson are theoretically correct and sharpen the theory. They caution users of this approach to be careful and understand the true characteristics of these investments including ways to lower the investment exposure. Samuelson's objections help us understand the theory better, but they do not detract from numerous valuable applications.

Suggested Citation

  • 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.
    • Handle: RePEc:ehl:lserod:119002
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    File URL: http://eprints.lse.ac.uk/119002/
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    References listed on IDEAS

    as
    1. William T Ziemba, 2012. "Calendar Anomalies and Arbitrage," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 8467.
    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. Merton, Robert C. & Samuelson, Paul A., 1974. "Fallacy of the log-normal approximation to optimal portfolio decision-making over many periods," Journal of Financial Economics, Elsevier, vol. 1(1), pages 67-94, May.
    4. Latane, Henry A., 1978. "The geometric-mean principle revisited : A reply," Journal of Banking & Finance, Elsevier, vol. 2(4), pages 395-398, December.
    5. 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.
    6. Leo Breiman, 1960. "Investment policies for expanding businesses optimal in a long‐run sense," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 7(4), pages 647-651, December.
    7. Paul A. Samuelson, 1970. "The Fundamental Approximation Theorem of Portfolio Analysis in terms of Means, Variances and Higher Moments," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 37(4), pages 537-542.
    8. Hakansson, Nils H, 1971. "On Optimal Myopic Portfolio Policies, With and Without Serial Correlation of Yields," The Journal of Business, University of Chicago Press, vol. 44(3), pages 324-334, July.
    9. Rubinstein, Mark, 1976. "The Strong Case for the Generalized Logarithmic Utility Model as the Premier Model of Financial Markets," Journal of Finance, American Finance Association, vol. 31(2), pages 551-571, May.
    10. Hakansson, Nils H., 1971. "Capital Growth and the Mean-Variance Approach to Portfolio Selection," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 6(1), pages 517-557, January.
    11. Leonard Maclean & William Ziemba & Yuming Li, 2005. "Time to wealth goals in capital accumulation," Quantitative Finance, Taylor & Francis Journals, vol. 5(4), pages 343-355.
    12. Edward O. Thorp, 2011. "The Kelly Criterion in Blackjack Sports Betting, and the Stock Market," 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 54, pages 789-832, World Scientific Publishing Co. Pte. Ltd..
    13. Rachel E S Ziemba & William T Ziemba, 2013. "Investing in the Modern Age," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 8793.
    14. 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..
    15. 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.
    16. MOSSIN, Jan, 1968. "Optimal multiperiod portfolio policies," LIDAM Reprints CORE 19, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    17. Luenberger, David G., 1993. "A preference foundation for log mean-variance criteria in portfolio choice problems," Journal of Economic Dynamics and Control, Elsevier, vol. 17(5-6), pages 887-906.
    18. Roll, Richard, 1973. "Evidence on the "Growth-Optimum" Model," Journal of Finance, American Finance Association, vol. 28(3), pages 551-566, June.
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    More about this item

    Keywords

    capital growth; log utility; risk aversion; long run wealth maximization;
    All these keywords.

    JEL classification:

    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions

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