Forecasting Large Realized Covariance Matrices: The Benefits of Factor Models and Shrinkage

Abstract

We propose a model to forecast very large realized covariance matrices of returns, applying it to the constituents of the S&P 500 on a daily basis. 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 estimated with the least absolute shrinkage and selection operator (LASSO). Our methodology improves forecasting precision relative to standard benchmarks and leads to better estimates of the minimum variance portfolios.

Keywords: realized covariance, factor models, shrinkage, Lasso, forecasting, portfolio allocation, big data

JEL Classification: C22