| 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. |
