The distribution of the sample variance of the global minimum variance portfolio in elliptical models

Abstract

In this article, we consider the variance of the global minimum variance portfolio. Assuming a matrix variate elliptically contoured distribution for the portfolio asset returns, we give the exact distribution and the density of an estimator of the portfolio variance. These results have many useful applications. They permit statements about the performance of the estimator. Moreover, it is possible to derive confidence intervals and to construct a test for the hypothesis that the global minimum variance is less than or equal to a certain value. We illustrate our results in an empirical study dealing with the daily returns of three developed countries.

Keywords:

• Global minimum variance portfolio
• Asset allocation
• Matrix variate elliptically contoured distributions
• Stochastic representation