Statistical Estimation of Optimal Portfolios for Dependent Returns

Abstract

In this talk, we discuss 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 the returns does not always affect the efficiency badly. 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. Also we report that the results are extended to the case when the return processes are locally stationary (Joint work with Hiroshi Shiraishi).