Scientific Beta

This paper compares 12 estimators of the covariance matrix: the sample covariance matrix, the identity matrix, the constant-correlation estimator, three estimators derived from an explicit factor model, three obtained from an implicit factor model, and three shrunk estimators. Following the literature, the comparison is conducted by computing the volatility of estimated Minimum Variance portfolios.

We compare 12 estimators of the covariance matrix: the sample covariance matrix, the identity matrix, the constant-correlation estimator, three estimators derived from an explicit factor model, three obtained from an implicit factor model, and three shrunk estimators. Following the literature, we conduct the comparison by computing the volatility of estimated Minimum Variance portfolios. We do this in two frameworks: first, an ideal situation where the true covariance matrix would be known, and second, a real-world situation where it is unknown. In each of these two cases, we perform the tests with and without short-sale constraints, and we assess the impact of the universe and sample sizes on the results. Our findings are in line with those of Ledoit and Wolf (2003), in that we confirm that in the absence of short-sale constraints, shrunk estimators lead, in general, to the lowest volatilities. With long-only constraints, however, their performance is similar to that of principal component estimators. Moreover, the latter estimators tend to imply lower levels of turnover, which is an important practical consideration.