Portfolio Performance Measure and a New Generalized Utility-Based N-Moment Measure

Most of the performance measures proposed in the financial and academic literature are subject to be gamed in an active management framework (Goetzmann et al., 2007). One of the main reasons of this drawback is due to an incomplete characterization by these measures of studied return distributions. We introduce a new flexible Generalized Utility-based N-moment measure of performance (GUN, in short), characterizing the whole return distribution, and thus hardly gamable. More precisely, it takes into account the first four moments of the return distribution and the associated sensitivities of the studied agent, reflecting his preferences and risk profile. The new performance measure is also well adapted for analyzing performance of hedge funds and more peculiarly in presence of derivative instruments associated with non-Gaussian return distributions