A Test of Covariance-Matrix Forecasting Methods

Abstract

Providing a more accurate covariance matrix forecast can substantially improve the performance of optimized portfolios. Using out-of-sample tests, in this article the author evaluates alternative covariance matrix-forecasting methods by looking at: (1) their forecast accuracy, (2) their ability to track the volatility of a minimum-variance portfolio, and (3) their ability to keep the volatility of a minimum-variance portfolio at a target level. The author finds large differences between the methods. The results suggest that shrinking the sample covariance matrix improves neither the forecast accuracy nor the performance of minimum-variance portfolios. In contrast, switching from the sample covariance matrix forecast to a multivariate generalized autoregressive conditional heteroskedasticity (GARCH) forecast reduces the forecasting error and portfolio tracking error by at least half. The findings also reveal that the exponentially weighted covariance matrix forecast performs only slightly worse than the multivariate GARCH forecast.