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

Ziemba, William (2016) A response to Professor Paul A. Samuelson's objections to Kelly capital growth investing. Systemic Risk Centre Discussion Papers (52). Systemic Risk Centre, The London School of Economics and Political Science, London, UK.

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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.

Item Type:	Monograph (Discussion Paper)
Official URL:	https://www.systemicrisk.ac.uk/
Additional Information:	© 2016 The Author
Divisions:	Systemic Risk Centre
Subjects:	H Social Sciences > HC Economic History and Conditions H Social Sciences > HG Finance
JEL classification:	C - Mathematical and Quantitative Methods > C0 - General > C02 - Mathematical Methods C - Mathematical and Quantitative Methods > C6 - Mathematical Methods and Programming > C61 - Optimization Techniques; Programming Models; Dynamic Analysis G - Financial Economics > G1 - General Financial Markets > G11 - Portfolio Choice; Investment Decisions
Date Deposited:	16 Jun 2023 10:03
Last Modified:	16 Sep 2023 00:01
URI:	http://eprints.lse.ac.uk/id/eprint/119002

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