Robustness of the inference procedures for the global minimum variance portfolio weights in a skew-normal model

^†A brief version of this paper was presented at the third meeting of the Econometric Society of Thailand.

Abstract

In this paper, we study the influence of 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 skewness in the asset returns can dramatically influence the performance of the test on the structure of the global minimum variance portfolio. The results obtained can be applied in the small sample case as well. Moreover, we introduce an estimation procedure for the parameters of the skew-normal distribution that is based on the modified method of moments. A goodness-of-fit test for the matrix variate closed skew-normal distribution has also been derived. In the empirical study, we apply our results to real data of several stocks included in the Dow Jones index.

Keywords:

• asset pricing
• parameter uncertainty
• matrix variate skew-normal distribution
• global minimum variance portfolio
• statistical inference procedures

JEL Classification:

• C16
• C52
• G11
• G12
• G15

Acknowledgements

The authors thank the referees and the editor for their suggestions which have improved the presentation in this paper.

Notes

^† A brief version of this paper was presented at the third meeting of the Econometric Society of Thailand.