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A Test of Covariance Matrix Forecasting Methods

7 Pages Posted: 20 Mar 2014 Last revised: 26 Mar 2015

Valeriy Zakamulin

University of Agder - School of Business and Law

Date Written: March 19, 2014


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.

Keywords: covariance matrix forecasting, minimum-variance portfolio optimization, sample covariance, covariance shrinkage, exponentially weighted covariance, multivariate GARCH, model comparison

JEL Classification: C30, C52, G11, G17

Suggested Citation

Zakamulin, Valeriy, A Test of Covariance Matrix Forecasting Methods (March 19, 2014). Journal of Portfolio Management, 215. Available at SSRN: or

Valeriy Zakamulin (Contact Author)

University of Agder - School of Business and Law ( email )

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