The Empirical Properties of Large Covariance Matrices

Our second paper also takes on an ambitious empirical study and challenges some commonly held notions. In this paper, Gilles Zumbach investigates the evolution of large covariance matrices. Having previously investigated volatility on the same datasets, Gilles turns to the joint problem of volatility and correlation. Certainly, one challenge in the study is to define meaningful ways to reduce the quantity of information, so that we can gain some intuition about how covariance evolves broadly. Gilles shows that the spectrum of the covariance matrix is actually quite static, with most of the interesting dynamics restricted to a small number of eigenvalues. This in itself would seem to support methods such as principal components analysis, where we concentrate on a small number of stable directions for correlation or covariance. Gilles's deeper investigation shows, however, that the directions associated with the important eigenvalues change quite a bit, supporting an approach where correlation and volatility are both dynamic quantities