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Title: From multivariate to univariate: Projections of optimal portfolio selection problems Authors:  Tomer Shushi - Ben Gurion University of the Negev (Israel) [presenting]
Zinoviy Landsman - University of Haifa (Israel)
Udi Makov - University of Haifa (Israel)
Abstract: The focus is on the problem of maximization of the functional of expected portfolio return and variance portfolio return in its most general form. We present an explicit closed-form solution of the optimal portfolio selection. This problem is closely related to expected utility maximization and two-moment decision models. We show that most known risk measures, such as mean-variance, expected shortfall, 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 by the authors concerning the maximization of a combination of expected portfolio return and a function of the variance of portfolio return. Our 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 belonged to the efficient frontier obtained for the mean-variance portfolio.