Dominance of a Class of Stein type Estimators for Optimal Portfolio Weights When the Covariance Matrix is Unknown |
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Authors: | Takuya Kinkawa Nobuo Shinozaki |
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Institution: | (1) Department of Statistics, European University Viadrina, 15230 Frankfurt (Oder), Germany |
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Abstract: | For the estimation problem of mean-variance optimal portfolio weights, several previous studies have proposed applying Stein
type estimators. However, few studies have addressed this problem analytically. Since the form of the loss function used in
this problem is not of the quadratic type commonly used in statistical studies, there have been some difficulties in showing
analytically the general dominance results. However, dominance results are given here of a class of Stein type estimators
for the mean-variance optimal portfolio weights when the covariance matrix is unknown and is estimated. The class of estimators
is broader than the one given in a previous study. The results we have obtained enable us to clarify conditions for some previously
proposed estimators in finance to have smaller risks than the estimator which we obtain by plugging in the sample estimates. |
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