Elliptical Black-Litterman Portfolio Optimization

28 Pages Posted: 27 Mar 2017 Last revised: 29 Aug 2017

See all articles by Andrzej Palczewski

Andrzej Palczewski

University of Warsaw - Faculty of Mathematics, Informatics, and Mechanics

Jan Palczewski

University of Leeds - School of Mathematics

Date Written: July 10, 2017

Abstract

We extend the Black-Litterman framework beyond normality to general elliptical distributions of investor's views and asset returns and portfolio risk measured by CVaR. Unlike existing solutions, cf. Xiao and Valdez [Quant. Finan. 2015, 15:3, 509-519], the choice of distributions, with the first and second moment constant, has a significant effect on optimal portfolio weights in a way that cannot be achieved by appropriate reparametrisation of the classical Black-Litterman methodology. The posterior distribution, in general, is not in a parametric form and, therefore, we design efficient numerical algorithms for approximating it in order to compute optimal portfolio weights. Of independent interest are our results on equivalence of a variety of portfolio optimization problems for elliptical distributions with linear constraints in the sense that they select portfolios from the same efficient frontier. We further prove a mutual fund theorem in this broad framework.

Keywords: Black-Litterman, asset allocation, elliptical distribution

JEL Classification: G11, C11, C15, C61, C63

Suggested Citation

Palczewski, Andrzej and Palczewski, Jan, Elliptical Black-Litterman Portfolio Optimization (July 10, 2017). Available at SSRN: https://ssrn.com/abstract=2941483 or http://dx.doi.org/10.2139/ssrn.2941483

Andrzej Palczewski

University of Warsaw - Faculty of Mathematics, Informatics, and Mechanics ( email )

Banacha 2
Warsaw, 02-097
Poland

Jan Palczewski (Contact Author)

University of Leeds - School of Mathematics ( email )

Leeds, LS2 9JT
United Kingdom

HOME PAGE: http://www.maths.leeds.ac.uk/~jp

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