High Frequency Asset Factor Models: Applications to Covariance Estimation and Risk Management

Abstract

We document a striking block-diagonal pattern in the factor model residual covariances of the S&P 500 Equity Index constituents, after sorting the assets by their assigned Global Industry Classification Standard (GICS) codes. Cognizant of this structure, we propose combining a location-based thresholding approach based on sector inclusion with the Fama-French and SDPR sector Exchange Traded Funds (ETF's). We also introduce the integrated risk of continuously re-balanced optimal portfolio strategies. We find a first-order bias that causes risk forecasts based on optimized portfolios to systematically underestimate risk. We develop the closed-form correction for this underestimation.

An out-of-sample portfolio allocation study is also undertaken. We find that our simple and positive-definite covariance matrix estimator yields strong empirical results under a variety of factor models and thresholding schemes. Conversely, and somewhat surprisingly, we find that the Fama-French factor model is only suitable for covariance estimation when used in conjunction with our proposed thresholding technique.

Theoretically, we provide justification for the empirical results by jointly analyzing the in-fill and diverging dimension asymptotics. Moreover, we develop the central limit theory for the integrated risk of continuously rebalanced portfolio strategies.