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 USA, UK, Japan and Germany–we test the 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 pessimistic outlook for equilibrium models that require the covariance of assets returns to mean revert in the long run. We find that, while 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.