When do improved covariance matrix estimators enhance portfolio optimization? An empirical comparative study of nine estimators

The use of improved covariance matrix estimators as an alternative to the sample estimator isconsidered an important approach for enhancing portfolio optimization. Here we empiricallycompare the performance of nine improved covariance estimation procedures using dailyreturns of 90 highly capitalized US stocks for the period 1997–2007. We find that theusefulness of covariance matrix estimators strongly depends on the ratio between theestimation period T and the number of stocks N, on the presence or absence of short selling,and on the performance metric considered. When short selling is allowed, several estimationmethods achieve a realized risk that is significantly smaller than that obtained with the samplecovariance method. This is particularly true when T/N is close to one. Moreover, manyestimators reduce the fraction of negative portfolio weights, while little improvement isachieved in the degree of diversification. On the contrary, when short selling is not allowedand T4N, the considered methods are unable to outperform the sample covariance in termsof realized risk, but can give much more diversified portfolios than that obtained withthe sample covariance. When T5N, the use of the sample covariance matrix and of thepseudo-inverse gives portfolios with very poor performance.