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.
