Statistical Estimation of Optimal Portfolios for non-Gaussian Dependent Returns of Assets

This paper discusses the asymptotic efficiency of estimators for optimal portfolios when returns are vector-valued non-Gaussian stationary processes. We give the asymptotic distribution of portfolio estimators ${\hat{g}}$ for non-Gaussian dependent return processes. Next we address the problem of asymptotic efficiency for the class of estimators ${\hat{g}}$ First, it is shown that there are some cases when the asymptotic variance of ${\hat{g}}$ under non-Gaussianity can be smaller than that under Gaussianity. The result shows that non-Gaussianity of X(t) does not always affect worse. Second, we give a necessary and sufficient condition for ${\hat{g}}$ to be asymptotically efficient when the return process is Gaussian, which shows that ${\hat{g}}$ is not asymptotically efficient generally. From this point of view we propose to use maximum likelihood type estimators for g, which are asymptotically efficient. We examine our approach numerically.