Can You Do Better Than Kelly in the Short Run?

The Kelly criterion, also known as the optimal growth or logarithmic utility strategy, is optimal, or near optimal, in a wide variety of settings when wealth grows purely multiplicatively. However, most of these optimality properties are over an infinite horizon or are asymptotic in nature. In this paper, we analyze some of the short-run properties of the Kelly strategy, and compare its performance to the dynamic state and time dependent policy that is optimal for maximizing the probability of achieving a given value, or outperforming another strategy, by a given fixed deadline.