Realized Factor Models for Vast Dimensional Covariance Estimation

We introduce a novel approach for estimating vast dimensional covariance matrices of asset returns by combining a linear factor model structure with the use of high- and low-frequency data. Specically, we propose the use of \liquid" factors { i.e. factors that can be observed free of noise at high frequency { to estimate the factor covariance matrix and idiosyncratic risk with high precision from intra-day data whereas the individual assets’ factor exposures are estimated from low frequency data to counter the impact of non-synchronicity between illiquid stocks and highly liquid factors. Our theoretical and simulation results illustrate that the performance of this \mixed-frequency" factor model is excellent: it compares favorably to the Hayashi and Yoshida (2005) covariance estimator (in a bi-variate setting) and the realized covariance estimator in the presence of market microstructure noise and non-synchronous trading. In empirical applications for the S&P500, S&P400 and S&P600 stock universes and using highly liquid ETFs as proxies for the Fama and French (1992) style and industry factors, we nd that the mixed-frequency factor model delivers better tracking errors and Value-at-Risk forecasts compared to the realized covariance. In contrast to the realized covariance the performance of the \mixed-frequency factor model" is robust across sampling frequencies and forecast weighting schemes.