“KLICing” there and back again: Portfolio selection using the empirical likelihood divergence and Hellinger distance

Stutzer (2000, 2003) proposes the decay-rate maximizing portfolio selection rule wherein the investor selects the asset mix that maximizes the rate at which the probability of shortfall decays to zero. A close examination of this rule reveals that it ranks portfolios by computing the divergence, in the Kullback–Leibler sense, between the unweighted portfolio return distribution and a tilted distribution meaned at the predetermined target or benchmark rate of return selected by or imposed upon the investor. This result implies, in the IID case, that Stutzer's rules can be written as a benchmark constrained Kullback–Leibler-based optimization problem with an endogenous utility interpretation. Here we expand on this idea by introducing two closely related portfolio selection rules based on the empirical likelihood divergence and the Hellinger–Matusita distance. The first of these is the reversed Kullback–Leibler divergence and the second is proportional to the average of the two divergences. The theoretical and in-sample properties of the new criteria suggest them to be competitive with and in some cases better than existing methods, especially in terms of skewness preference.