Equilibrium With Investors Using a Diversity of Deviation Measures

17 Pages Posted: 1 Aug 2007

See all articles by R. Tyrrell Rockafellar

R. Tyrrell Rockafellar

University of Washington - Department of Mathmatics

Stanislav P. Uryasev

University of Florida

Michael Zabarankin

Stevens Institute of Technology - Department of Mathematical Sciences

Date Written: October 26, 2005

Abstract

It has been argued that investors who optimize their portfolios with attention paid only to mean and standard deviation will all end up choosing some multiple of a certain master fund portfolio. Justification for the capital asset pricing model of classical portfolio theory, which relates individual assets to such a master fund, has come from this direction in particular. Attempts have been made to provide solid mathematical support by showing that the imputed behavior of investors is a consequence of price equilibrium in a market in which assets are traded subject to budget constraints, and optimization is carried out with respect to utility functions that depend only on mean and standard deviation.

In recent years, reliance on standard deviation has come under increasing criticism because of inconsistencies in its effect on portfolio references. One response has been to introduce generalized measures of deviation which lead to alternative master funds. The market implications of such extensions of theory have hitherto been unclear, but in this paper the existence of equilibrium is established in circumstances where nonstandard deviations are admitted. Equilibrium is guaranteed even when different investors use different measures of deviation and thereby end up with portfolios scaled from different master funds. Whether they employ the same measure or not, they may impose caps on deviation, which likewise may be different.

Keywords: financial equilibrium, portfolio analysis, generalized deviation measures

JEL Classification: C62, C68, D58, G11

Suggested Citation

Rockafellar, R. Tyrrell and Uryasev, Stanislav P. and Zabarankin, Michael, Equilibrium With Investors Using a Diversity of Deviation Measures (October 26, 2005). Available at SSRN: https://ssrn.com/abstract=1003870 or http://dx.doi.org/10.2139/ssrn.1003870

R. Tyrrell Rockafellar (Contact Author)

University of Washington - Department of Mathmatics ( email )

Box 354350
Seattle, WA 98195-4350
United States

Stanislav P. Uryasev

University of Florida ( email )

303 Weil Hall
Gainesville, FL 32611-6595
United States
352-392-3091 (Phone)
352-392-3537 (Fax)

HOME PAGE: http://www.ise.ufl.edu/uryasev/

Michael Zabarankin

Stevens Institute of Technology - Department of Mathematical Sciences ( email )

Hoboken, NJ 07030
United States

HOME PAGE: http://personal.stevens.edu/~mzabaran/

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