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

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

Abstract

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 9 improved covariance estimation procedures by 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 estimation period 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 significantly smaller than the one 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 the one obtained with the sample covariance. When T

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  • Ester Pantaleo & Michele Tumminello & Fabrizio Lillo & Rosario N. Mantegna, 2010. "When do improved covariance matrix estimators enhance portfolio optimization? An empirical comparative study of nine estimators," Papers 1004.4272, arXiv.org.
  • Handle: RePEc:arx:papers:1004.4272
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    3. Eli Bouri & Andre Eid & Imad Kachacha, 2014. "The Dynamic Behaviour and Determinants of Linkages among Middle Eastern and North African Stock Exchanges," Economic Issues Journal Articles, Economic Issues, vol. 19(1), pages 1-22, March.
    4. Gautier Marti & Frank Nielsen & Miko{l}aj Bi'nkowski & Philippe Donnat, 2017. "A review of two decades of correlations, hierarchies, networks and clustering in financial markets," Papers 1703.00485, arXiv.org, revised Sep 2017.
    5. Gautier Marti & Frank Nielsen & Philippe Donnat & S'ebastien Andler, 2016. "On clustering financial time series: a need for distances between dependent random variables," Papers 1603.07822, arXiv.org.
    6. 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.
    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.
    8. Joel Bun & Jean-Philippe Bouchaud & Marc Potters, 2016. "Cleaning large correlation matrices: tools from random matrix theory," Papers 1610.08104, arXiv.org.
    9. 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, arXiv.org, revised Mar 2013.
    10. Elie I Bouri, 2013. "Correlation and Volatility of the MENA Equity Markets in Turbulent Periods, and Portfolio Implications," Economics Bulletin, AccessEcon, vol. 33(2), pages 1575-1593.
    11. repec:eee:apmaco:v:282:y:2016:i:c:p:187-203 is not listed on IDEAS

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