On the exact distribution of the estimated expected utility portfolio weights: Theory and applications

Abstract In this paper we consider the portfolio weights obtained by maximizing the expected quadratic utility function. The unknown parameters of the return process, the mean vector and the covariance matrix, are estimated by their sample counterparts. Assuming independent and multivariate normally distributed returns we derive the conditional density of the estimated weights given the mean vector of the asset returns and the unconditional density of the estimated weights. Moreover, the characteristic function of the estimated weights is calculated and it is used to determine the moments of higher order. Furthermore a test for the mean-variance efficiency is presented.