Covariance forecasting in equity markets

We compare the performance of popular covariance forecasting models in the context of a portfolio of major European equity indices. We find that models based on high-frequency data offer a clear advantage in terms of statistical accuracy. They also yield more theoretically consistent predictions from an empirical asset pricing perspective, and, lead to superior out-of-sample portfolio performance. Overall, a parsimonious Vector Heterogeneous Autoregressive (VHAR) model that involves lagged daily, weekly and monthly realised covariances achieves the best performance out of the competing models. A promising new simple hybrid covariance estimator is developed that exploits option-implied information and high-frequency data while adjusting for the volatility riskpremium. Relative model performance does not change during the global financial crisis, or, if a different forecast horizon, or, intraday sampling frequency is employed. Finally, our evidence remains robust when we consider an alternative sample of U.S. stocks.