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T he Kelly capital growth criterion, which maximizes the expected log of final wealth, provides the strategy that maximizes long-run wealth growth asymptotically for repeated investments over time. A shortcoming is its very risky short-term behavior because of log's essentially zero Arrow-Pratt absolute risk aversion, and consequently the large concentrated non-diversified investment bets that it suggests. Many investors, hedge funds, bank trading departments, and sports bettors use this criterion, and its seminal application is to a long sequence of favorable investment situations. Some of these applications are briefly surveyed later in this article.
Because I have a long history with Professor Paul A. Samuelson, starting with his articles in Ziemba and Vickson [1975, 2006], he wrote me from time to time on various topics. Samuelson was a critic of the Kelly theory, concerned with the Kelly criterion and how that affected its use in practice. Because of Samuelson's status as arguably the most important economist of the last century, people took note of the fact that he was objecting, even though they did not actually know what these objections were. As a consequence of this and other causes, the most important being the non-diversification and large investment wagers suggested, the Kelly strategy is not used much in the investment industry, except by investors looking for superior long-run performance. It is also not a standard topic in MBA finance courses.
My motivation for this article comes from two sources. First, Samuelson wrote me three letters on this topic, and his articles objecting to the Kelly criterion are reprinted in MacLean, Thorp, and Ziemba [2010]. I wanted to respond to these letters and his articles. The second reason for this article is an August 2011 request from Fidelity Investments, a multi-trillion-dollar investment firm in Boston, to explain Samuelson's objections to Kelly. Should they be using Kelly strategies? If so, when and with what caution? After a five-hour session on this and other topics, I think they were convinced to consider Kelly strategies and did understand the advantages and disadvantages.
The first letter was the correspondence of November 16, 2005 to Professor Elwyn Berlekamp,1 which Samuelson forwarded to me on December 13, 2006. Samuelson sent additional letters to me on May 17, 2007 and May 12,...