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The use of improved covariance matrix estimators as an alternative to thesample estimator is considered an important approach for enhancing portfoliooptimization. Here we empirically compare the performance of 9 improvedcovariance estimation procedures by using daily returns of 90 highlycapitalized US stocks for the period 1997-2007. We find that the usefulness ofcovariance matrix estimators strongly depends on the ratio between estimationperiod T and number of stocks N, on the presence or absence of short selling,and on the performance metric considered. When short selling is allowed,several estimation methods achieve a realized risk that is significantlysmaller than the one obtained with the sample covariance method. This isparticularly true when T/N is close to one. Moreover many estimators reduce thefraction of negative portfolio weights, while little improvement is achieved inthe degree of diversification. On the contrary when short selling is notallowed and T>N, the considered methods are unable to outperform the samplecovariance in terms of realized risk but can give much more diversifiedportfolios than the one obtained with the sample covariance. When T<N the useof the sample covariance matrix and of the pseudoinverse gives portfolios withvery poor performance.

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