Variance Covariance Orders and Median Preserving

29 Pages Posted: 22 Apr 2009

See all articles by Fabio Trojani

Fabio Trojani

Swiss Finance Institute; University of Geneva

Semyon Malamud

Ecole Polytechnique Federale de Lausanne; Centre for Economic Policy Research (CEPR); Swiss Finance Institute

Date Written: March 24, 2009

Abstract

A random variable dominates another random variable with respect to the covariance order if the covariance of any two monotone increasing functions of this variable is smaller. We characterize completely the covariance order, give strong sufficient conditions for it, present a number of examples in concrete economic applications, and provide natural extensions for the multivariate context. In analogy to mean preserving spreads in standard stochastic dominance, we show that the covariance order is intimately linked to a comparison of median preserving spreads of random variables. Moreover, it arises naturally in a variety of important economic questions like, e.g., Hansen-Jagannathan stochastic discount factor bounds, the efficient portfolios implied by semi-variance optimization problems, or the measurement of macroeconomic inequality and dispersion in beliefs.

Keywords: variance, risk, median preserving spread, Hansen-Jagannathan bounds

JEL Classification: G11, C02, D00

Suggested Citation

Trojani, Fabio and Malamud, Semyon, Variance Covariance Orders and Median Preserving (March 24, 2009). Swiss Finance Institute Research Paper No. 09-13, Available at SSRN: https://ssrn.com/abstract=1392728 or http://dx.doi.org/10.2139/ssrn.1392728

Fabio Trojani

Swiss Finance Institute ( email )

c/o University of Geneva
40, Bd du Pont-d'Arve
CH-1211 Geneva 4
Switzerland

University of Geneva ( email )

Geneva, Geneva
Switzerland

Semyon Malamud (Contact Author)

Ecole Polytechnique Federale de Lausanne ( email )

Lausanne, 1015
Switzerland

Centre for Economic Policy Research (CEPR) ( email )

London
United Kingdom

Swiss Finance Institute

c/o University of Geneva
40, Bd du Pont-d'Arve
CH-1211 Geneva 4
Switzerland

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