How Predictable are Equity Covariance Matrices? Evidence from High Frequency Data for Four Markets

Most pricing and hedging models rely on the long run temporal stability of a sample covariance matrix. Using a large dataset of equity prices from four countries, the US, UK, Japan and Germany, we test the rolling stability of realized sample covariance matrices using two complementary approaches; a standard covariance equality test and a novel matrix loss function approach. Our results present a pessmistic outlook for equilibrium models that require the covariance of assets returns to mean revert in the long run. We find that whilst, a daily first order Wishart autoregression is the best covariance matrix generating candidate, this non-mean reverting process cannot capture all of the time series variation in the covariance generating process