An analysis of heterogeneous utility benchmarks in a zero return environment

The utility of an investor should be based on an acceptable loss in the loss region and a target return in the gain region of a set of investment opportunities. The level of these benchmarks will unveil an opportunity cost, break-even effect, or indifference when the return of an investment equals zero. This condition has been arbitrarily assumed away for continuity and other simplification purposes over the past few decades. Historically, utility functions, Von Neumann–Morgenstern compliant and not, are constrained via a single target or reference point. This single target restriction coupled with the arbitrary zero-return assumption has ignored the important interpretation of this salient point on the utility curve as a proxy for the investor's current wealth. We propose a utility function using lower partial moments to describe the utility of losses and upper partial moments to describe the utility of gains.