TAILIEUCHUNG - Improved Estimation of the Covariance Matrix of Stock Returns With an Application to Portfolio Selection

This new strategy is supported by significant changes in Nokia’s leadership, operational structure and approach. Effective today, Nokia has a new leadership team with the commitment, competencies and innovative thinking needed in today’s dynamic environment. The Nokia Leadership Team, previously the Group Executive Board, will consist of the following members: Stephen Elop, Esko Aho, Juha Akras, Jerri DeVard, Colin Giles, Rich Green, Jo Harlow, Timo Ihamuotila, Mary McDowell, Kai Oistamo, Tero Ojanpera, Louise Pentland and Niklas Savander. Alberto Torres has stepped down from the management team, effective February 10 to pursue other interests outside the company. . | Improved Estimation of the Covariance Matrix of Stock Returns With an Application to Portfolio Selection Olivier Ledoit Equities Division Credit Suisse First Boston Michael Wolf Dept. of Economics and Business Universitat Pompeu Fabra November 2001 Michael Wolf Phone 34-93-542-2552 Fax 34-93-542-1749 E-mail . We wish to thank Andrew Lo John Heaton Bin Zhou Timothy Crack Bruce Lehmann Richard Michaud Richard Roll Pedro Santa-Clara and Jay Shanken for their feedback. Also the paper has benefited from seminar participants at MIT the NBER UCLA Washington University in Saint Louis Yale Chicago Wharton and UBC. All remaining errors are our own. Research of the second author supported by DGES grant BEC2001-1270. 1 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. JEL CLASSIFICATION NOS C13 C51 C61 G11 G15. KEY WORDS Covariance matrix estimation Factor models Portfolio selection Shrinkage method. 2 1 Introduction The objective of this paper is to estimate the covariance matrix of stock returns. This is a fundamental question in empirical Finance with implications for portfolio selection and for tests of asset pricing models such as the CAPM. The traditional estimator the sample covariance matrix is seldom used because it imposes too little structure. When the number of stocks N is of the same order of magnitude as the number of historical .

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