Higher-Moment Portfolio Theory

Abstract

A new portfolio theory takes into account the non-Gaussian properties of asset returns. The non-Gaussian properties of a portfolio are quantified by the so-called moments and cumulants of its distribution of returns. Generalizing the concept of efficient frontiers, the non-Gaussian efficient frontier depends on the chosen risk measure, corresponding to different orders or combinations of centered moments or cumulants. These extended formulas let investors analyze the conditions under which it is possible to have one's cake and eat it too, in order to construct a portfolio with both higher return and fewer major risks.