The anatomy of portfolio skewness and kurtosis

Abstract

This article re-examines portfolio higher moments, skewness and kurtosis, to see whether this information can be used to improve portfolio construction and to diagnose any mis-specification of models for portfolio returns. In common with most discussion of quantitative portfolio risk, we assume a linear factor model framework, and some empirical calculations using data from the components of the Dow Jones Industrial Index are carried out. The major insight that we glean from this exercise is that a well-diversified portfolio of skewed stocks can have a symmetric distribution unless we pay some attention to the third moment structure. These ideas are likely to have some potential application to fund of fund construction and the matching of bespoke portfolios to the risk attributes of high-net worth investors.