On the existence of unbiased estimators for the portfolio weights obtained by maximizing the Sharpe ratio |
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Authors: | Wolfgang Schmid Taras Zabolotskyy |
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Affiliation: | (1) Department of Statistics, European University, PO Box 1786, 15207 Frankfurt (Oder), Germany |
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Abstract: | We consider the problem of estimating the portfolio weights obtained by maximizing the Sharpe ratio. Assuming that the underlying asset returns are independent and multivariate normally distributed, Okhrin and Schmid (J. Econom. 134:235–256, 2006) showed that the frequently used sample estimators of these weights do not have a first moment. This paper proves that an unbiased estimator of the Sharpe ratio portfolio weights does not exist at all. Moreover, we show that there is no asymptotically unbiased estimator of these weights within the family of estimators which are bounded by cylinder functions. |
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Keywords: | Optimal portfolio weights Unbiased estimator Asymptotically unbiased estimator Sharpe ratio optimal weights |
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