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Article

How Does the Fortune’s Formula Kelly Capital
Growth Model Perform?

Leonard C. MacLean, Edward O. Thorp, Yonggan Zhao and William T. Ziemba
The Journal of Portfolio Management Summer 2011, 37 (4) 96-111; DOI: https://doi.org/10.3905/jpm.2011.37.4.096
Leonard C. MacLean
holds the Herbert Lam Chair in the School of Business at Dalhousie University in Halifax, NS, Canada.
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  • For correspondence: l.c.maclean@dal.ca
Edward O. Thorp
is the president of Edward O. Thorp and Associates, L.P., and a professor emeritus at the University of California in Irvine, CA.
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  • For correspondence: EOThorp@ix.netcom.com
Yonggan Zhao
holds the Canada Research Chair in the School of Business Administration at Dalhousie University in Halifax, NS, Canada.
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  • For correspondence: yonggan.zhao@dal.ca
William T. Ziemba
is the Alumni Professor of Financial Modeling and Stochastic Optimization (emeritus) at the University of British Columbia in Vancouver, BC, Canada, and a visiting professor at Oxford University in the UK, the ICMA Centre-University of Reading in the UK, and the University of Bergamo in Italy.
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  • For correspondence: wtzimi@mac.com
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Abstract

William Poundstone’s book, Fortune’s Formula, brought the Kelly capital growth criterion to the attention of investors. But how do full and fractional Kelly strategies perform in practice? The authors study three simple investment situations and simulate the behavior of these strategies over medium-term horizons using a large number of scenarios. The results show 1) the great superiority of full Kelly and close-to-full Kelly strategies over longer horizons in that they earn very large gains a large fraction of the time, 2) the very risky short-term performance of Kelly and high-fractional Kelly strategies, 3) a consistent trade-off of growth versus security as a function of the bet size determined by the various strategies, and 4) no matter how favorable the investment opportunities are, or how long the finite horizon is, a sequence of bad scenarios can lead to very poor final wealth outcomes with a loss of most of the investor’s initial capital. Hence, in practice, financial engineering is important for dealing with the short-term volatility and long-run situations in a sequence of bad scenarios. Properly used, however, the strategy has much to commend it, especially in trading with many repeated investments.

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The Journal of Portfolio Management: 37 (4)
The Journal of Portfolio Management
Vol. 37, Issue 4
Summer 2011
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How Does the Fortune’s Formula Kelly Capital
Growth Model Perform?
Leonard C. MacLean, Edward O. Thorp, Yonggan Zhao, William T. Ziemba
The Journal of Portfolio Management Jul 2011, 37 (4) 96-111; DOI: 10.3905/jpm.2011.37.4.096

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How Does the Fortune’s Formula Kelly Capital
Growth Model Perform?
Leonard C. MacLean, Edward O. Thorp, Yonggan Zhao, William T. Ziemba
The Journal of Portfolio Management Jul 2011, 37 (4) 96-111; DOI: 10.3905/jpm.2011.37.4.096
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  • Article
    • Abstract
    • THE SIMPLEST CASE
    • MOTIVATION FOR THIS ARTICLE
    • FRACTIONAL KELLY STRATEGIES: THE ZIEMBA AND HAUSCH EXPERIMENT
    • PROPORTIONAL INVESTMENT STRATEGIES: ALTERNATIVE EXPERIMENTS
    • CONCLUSION
    • ENDNOTES
    • REFERENCES
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