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


  • Ester Pantaleo
  • Michele Tumminello
  • Fabrizio Lillo
  • Rosario Mantegna


The use of improved covariance matrix estimators as an alternative to the sample estimator is considered an important approach for enhancing portfolio optimization. Here we empirically compare the performance of nine improved covariance estimation procedures using daily returns of 90 highly capitalized US stocks for the period 1997-2007. We find that the usefulness of covariance matrix estimators strongly depends on the ratio between the estimation 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 estimation methods achieve a realized risk that is significantly smaller than that obtained with the sample covariance method. This is particularly true when T/N is close to one. Moreover, many estimators reduce the fraction of negative portfolio weights, while little improvement is achieved in the degree of diversification. On the contrary, when short selling is not allowed and T > N, the considered methods are unable to outperform the sample covariance in terms of realized risk, but can give much more diversified portfolios than that obtained with the sample covariance. When T < N, the use of the sample covariance matrix and of the pseudo-inverse gives portfolios with very poor performance.

Suggested Citation

  • Ester Pantaleo & Michele Tumminello & Fabrizio Lillo & Rosario Mantegna, 2011. "When do improved covariance matrix estimators enhance portfolio optimization? An empirical comparative study of nine estimators," Quantitative Finance, Taylor & Francis Journals, vol. 11(7), pages 1067-1080.
  • Handle: RePEc:taf:quantf:v:11:y:2011:i:7:p:1067-1080 DOI: 10.1080/14697688.2010.534813

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    3. Leonidas Sandoval Junior & Adriana Bruscato & Maria Kelly Venezuela, 2012. "Building portfolios of stocks in the S\~ao Paulo Stock Exchange using Random Matrix Theory," Papers 1201.0625,, revised Mar 2013.
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    7. Sandoval, Leonidas & Franca, Italo De Paula, 2012. "Correlation of financial markets in times of crisis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(1), pages 187-208.
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    11. Thilo A. Schmitt & Rudi Schäfer & Dominik Wied & Thomas Guhr, 2016. "Spatial dependence in stock returns: local normalization and VaR forecasts," Empirical Economics, Springer, vol. 50(3), pages 1091-1109, May.


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