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Realized Factor Models for Vast Dimensional Covariance Estimation

Roel Oomen

This paper develops 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. Specifically, 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 show 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 under realistic scenarios. In an empirical application for the S&P400, S&P500 and S&P600 stock universes and using highly liquid ETFs as proxies for the Fama and French (1992) style and industry factors, we find that the mixed-frequency factor model delivers a superior tracking error compared to the realized covariance. In contrast to the realized covariance the performance of the “mixed-frequency factor model” is robust across sampling frequencies, forecast weighting schemes and outperforms the 1/N portfolios recently advocated by DeMiguel et al. (2007). This is joint work with Karim Bannouh, Martin Martens, and Dick van Dijk all from Erasmus University Rotterdam.

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