Disparity, Shortfall, and Twice-Endogenous HARA Utility

We demonstrate that shortfall-minimizing portfolio selection based on the Cressie- Read family of divergence measures maps to the HARA family. This means that all HARA utility functions can be interpreted as “endogenous” in the sense described in Stutzer (2003), and that traditional HARA expected utility maximization has an analog to the behavioral notion that an investor seeks to organize their selection of assets to minimize the probability of realizing a return below some pre-determined target or benchmark rate. We show that not only do risk aversion parameters arise endogenously, given the choice set, but that the type of risk aversion, relative or constant, is also determined endogenously. We also connect this approach to portfolio selection to some topics in behavioral economics.