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 Component Analysis to higher moments such as skewness and kurtosis. This method allows us to identify factors that drive the co-skewness and co-kurtosis across assets. These factors have interesting interpretations, for instance as hedges against increases in volatility among certain assets. We illustrate this approach using 37 international stock indices sampled at weekly frequency, for a total of 763 observations. We assert that both the co-skewness and co-kurtosis structures can be summarized with a small number of factors. This method is both fast and able to handle large portfolios under non-normality. Estimations using a rolling window reveal interesting commonalities over the business cycle.