Moment Component Analysis: An Illustration with International Stock Markets

It is well known that non-normality plays an important role in asset and risk management.However, handling a large number of assets has long been a challenge.In this paper, we present a statistical technique that extends Principal ComponentAnalysis to higher moments such as skewness and kurtosis. This method allows usto identify factors that drive the co-skewness and co-kurtosis across assets. Thesefactors have interesting interpretations, for instance as hedges against increases involatility among certain assets. We illustrate this approach using 37 internationalstock indices sampled at weekly frequency, for a total of 763 observations. We assertthat both the co-skewness and co-kurtosis structures can be summarized with a smallnumber of factors. This method is both fast and able to handle large portfolios undernon-normality. Estimations using a rolling window reveal interesting commonalitiesover the business cycle.[...]