Partial-Kelly Strategies and Expected Utility: Small-Edge Asymptotics

Partial-Kelly strategies, proposed because full-Kelly strategies that use log of fortune as utility were found to be too risky, are examined from the perspective of maximizing expected utility. The results are as follows: (1) there is no utility function that is independent of the risks it confronts and that exactly has partial-Kelly strategies as the optimal strategy; and (2) constant relative risk aversion utility, with the constant relative risk parameter equal to the reciprocal of the partial-Kelly parameter, is a good approximation to such a utility function, particularly when the investor's edge is small.