How predictable are equity covariance matrices? Evidence from high frequency data for four markets.

Abstract

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.