An exact test on structural changes in the weights of the global minimum variance portfolio

In the paper, a finite sample test is suggested for detecting changes in the composition of the global minimum variance portfolio. The exact density of the test statistic is calculated. It appears that under the null hypothesis of no change, it is independent of the parameters of the asset returns distribution. The testing procedure is implemented in a situation that is practically relevant. We show that ignoring the uncertainty about the estimated weights of the holding portfolio leads to misleading results, i.e. to a more frequent reallocation of the investor's wealth.