Title: Portfolio optimization by a bivariate functional of the mean and variance
Authors: Zinoviy Landsman - University of Haifa (Israel) [presenting]
Abstract: The focus is on the problem of maximization of a functional of the expected portfolio return and variance portfolio return in its most general form and the presentation of an explicit closed-form solution of the optimal portfolio selection. This problem is closely related to the expected utility maximization and the two-moment decision models. We show that the most-known risk measures, such as mean-variance, expected short-fall, Sharpe ratio, generalized Sharpe ratio and the recently introduced tail mean-variance, are special cases of this functional. The new results essentially generalize previous results concerning the maximization of a combination of the expected portfolio return and a function of the variance of portfolio return. The general mean-variance functional is not restricted to a concave function with a single optimal solution. Thus, we also provide optimal solutions to a fractional programming problem, that is arising in portfolio theory. The obtained analytic solution of the optimization problem allows us to conclude that all the optimization problems corresponding to the general functional have efficient frontiers belonging to the efficient frontier obtained for the mean-variance portfolio.