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On the existence of unbiased estimators for the portfolio weights obtained by maximizing the Sharpe ratio

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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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Authors and Affiliations

  1. Department of Statistics, European University, PO Box 1786, 15207, Frankfurt (Oder), Germany

    Wolfgang Schmid & Taras Zabolotskyy

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  1. Wolfgang Schmid
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  2. Taras Zabolotskyy
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Correspondence to Wolfgang Schmid.

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Schmid, W., Zabolotskyy, T. On the existence of unbiased estimators for the portfolio weights obtained by maximizing the Sharpe ratio. AStA 92, 29–34 (2008). https://doi.org/10.1007/s10182-008-0054-5

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  • DOI: https://doi.org/10.1007/s10182-008-0054-5

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