  We propose a model to forecast large realized covariance matrices of returns,
applying it to the constituents of the S\&P 500 daily. To address the curse of
dimensionality, we decompose the return covariance matrix using standard
firm-level factors (e.g., size, value, and profitability) and use sectoral
restrictions in the residual covariance matrix. This restricted model is then
estimated using vector heterogeneous autoregressive (VHAR) models with the
least absolute shrinkage and selection operator (LASSO). Our methodology
improves forecasting precision relative to standard benchmarks and leads to
better estimates of minimum variance portfolios.
