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The global minimum variance portfolio (GMVP) plays an important role in the Markowitz's mean-variance analysis. The usual assumption for studying the GMVP is the normality which is a symmetric model. In this paper, we study the influence of the skewness on the distributional properties of the estimated weights of optimal portfolios and on the corresponding inference procedures derived for the optimal portfolio weights assuming that the asset returns are normally distributed. It is shown that even a simple form of the skewness in the asset returns can dramatically influence the performance of optimal portfolios. In the empirical study, we apply our results to the real data of several stocks included into the Dow Jones index.

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