Asymptotic behavior of the estimated weights and of the estimated performance measures of the minimum VaR and the minimum CVaR optimal portfolios for dependent data

In this paper we derive the asymptotic distributions of the estimated weights and of estimated performance measures of the minimum value-at-risk portfolio and of the minimum conditional value-at-risk portfolio assuming that the asset returns follow a strictly stationary process. It is proved that the estimated weights as well as the estimated performance measures are asymptotically multivariate normally distributed. We also present an asymptotic test for the weights and a joint test for the characteristics of both portfolios. Moreover, the asymptotic densities of the estimated performance measures are compared with the corresponding exact densities. It is shown that the asymptotic approximation performs well even for the moderate sample size. Copyright Springer-Verlag Berlin Heidelberg 2013