Factor state–space models for high-dimensional realized covariance matrices of asset returns

We propose a dynamic factor state–space model for high-dimensional covariance matrices of asset returns. It makes use of observed risk factors and assumes that the latent integrated joint covariance matrix of the assets and the factors is observed through their realized covariance matrix with a Wishart measurement density. For the latent integrated covariance matrix of the assets we impose a strict factor structure allowing for dynamic variation in the covariance matrices of the factors and the residual components as well as in the factor loadings. This factor structure translates into a factorization of the Wishart measurement density which facilitates statistical inference based on simple Bayesian MCMC procedures making the approach scalable w.r.t. the number of assets. An empirical application to realized covariance matrices for 60 NYSE traded stocks using the Fama–French factors and sector-specific factors represented by Exchange Traded Funds (ETFs) shows that the model performs very well in- and out of sample.