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Improved estimation of the covariance matrix of stock returns with an application to portofolio selection

Author

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  • Olivier Ledoit
  • Michael Wolf

Abstract

This paper proposes to estimate the covariance matrix of stock returns by an optimally weighted average of two existing estimators: the sample covariance matrix and single-index covariance matrix. This method is generally known as shrinkage, and it is standard in decision theory and in empirical Bayesian statistics. Our shrinkage estimator can be seen as a way to account for extra-market covariance without having to specify an arbitrary multi-factor structure. For NYSE and AMEX stock returns from 1972 to 1995, it can be used to select portfolios with significantly lower out-of-sample variance than a set of existing estimators, including multi-factor models.

Suggested Citation

  • Olivier Ledoit & Michael Wolf, 2001. "Improved estimation of the covariance matrix of stock returns with an application to portofolio selection," Economics Working Papers 586, Department of Economics and Business, Universitat Pompeu Fabra.
    • Handle: RePEc:upf:upfgen:586
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    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • G15 - Financial Economics - - General Financial Markets - - - International Financial Markets

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