A Test of Covariance Matrix Forecasting Methods

Providing a more accurate covariance matrix forecast can substantially improve the performance of optimized portfolios. Using out-of-sample tests, in this paper, we evaluate alternative covariance matrix forecasting methods by looking at (1) their forecast accuracy, (2) their ability to track the volatility of the minimum-variance portfolio, and (3) their ability to keep the volatility of the minimum-variance portfolio at a target level. We find large differences between the methods. Our results suggest that shrinkage of 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 GARCH forecast reduces forecasting error and portfolio tracking error by at least half. Our findings also reveal that the exponentially weighted covariance matrix forecast performs only slightly worse than the multivariate GARCH forecast