Response to Paul a Samuelson Letters and Papers on the Kelly Capital Growth Investment Strategy

27 Pages Posted: 13 Oct 2012  

William T. Ziemba

University of British Columbia (UBC) - Sauder School of Business

Date Written: August 24, 2012

Abstract

The Kelly Capital Growth Investment Strategy (KCGIS) is to maximize the expected utility of nal wealth with a logarithmic utility function. This approach dates to Bernoulli's 1738 suggestion of log as the utility function arguing that marginal utility was proportional to the reciprocal of current wealth. In 1956 Kelly showed that static expected log maximization yields the maximum asymptotic long run growth. Later, others added more good properties such as minimizing the time to large asymptotic goals, maximizing the median, and being ahead on average for the fi rst period. But there are bad properties as well such as extremely large bets for short term favorable investment situations because the Arrow-Pratt risk aversion index is near zero. Paul Samuelson was a critic of this approach and here we discuss his various points sent in letters to Ziemba and papers reprinted in the recent book, MacLean, Thorp and Ziemba (2010). Samuelson's opposition has prevented many fi nance academics and professionals from using Kelly strategies. For example, Ziemba was asked to explain this to Fidelity Investments, a major Boston investment fi rm close to and influenced by Samuelson at MIT. I agree that these points of Samuelson are correct and argue that they all make sense and caution users of this approach to be careful and understand the true characteristics of these investments including ways to lower the investment exposure.

Keywords: capital growth, log utility, risk aversion, long run growth

JEL Classification: C02, C61, G11

Suggested Citation

Ziemba, William T., Response to Paul a Samuelson Letters and Papers on the Kelly Capital Growth Investment Strategy (August 24, 2012). Available at SSRN: https://ssrn.com/abstract=2161068 or http://dx.doi.org/10.2139/ssrn.2161068

William T. Ziemba (Contact Author)

University of British Columbia (UBC) - Sauder School of Business ( email )

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Vancouver, BC V6T 1Z2
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HOME PAGE: http://williamtziemba.com

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