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On the Tail Mean-Variance optimal portfolio selection
Authors:Zinoviy Landsman
Affiliation:Department of Statistics, University of Haifa, Mount Carmel, 31905 Haifa, Israel
Abstract:In the present paper we propose the Tail Mean-Variance (TMV) approach, based on Tail Condition Expectation (TCE) (or Expected Short Fall) and the recently introduced Tail Variance (TV) as a measure for the optimal portfolio selection. We show that, when the underlying distribution is multivariate normal, the TMV model reduces to a more complicated functional than the quadratic and represents a combination of linear, square root of quadratic and quadratic functionals. We show, however, that under general linear constraints, the solution of the optimization problem still exists and in the case where short selling is possible we provide an analytical closed form solution, which looks more “robust” than the classical MV solution. The results are extended to more general multivariate elliptical distributions of risks.
Keywords:Tail condition expectation   Tail variance   Tail Mean-Variance model   Optimal portfolio selection   Square root of quadratic functional   Elliptical family   Quartic equation
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