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\centerline{\bf STANFORD UNIVERSITY}
\centerline{\bf DEPARTMENT OF STATISTICS}
\centerline{\big DEPARTMENT SEMINAR}
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\centerline{ Sequoia Hall, Room 200}
\centerline{4:15 p.m., Thursday, August 15, 2002}


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\centerline{\sl Michael Wolf}
\centerline{\sl Dept. of Economics}
\centerline{\sl Universitat Pompeu Fabra, Spain}
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\centerline{\bf Improved Estimation of the Covariance Matrix of Stock Returns
With an Application to Portofolio Selection}

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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.


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