Standardized Variables, Risks and Preference

Abstract

This paper examines the expected utility effects of adding one risk to another. In comparison to related works, it places fewer restrictions on utilities and more structure on risky asset returns. The paper, entailing little loss of generality, uses discrete variables defined on a common domain (hereafter standardized variables) to find sufficient conditions for either of two (dependent or independent) variables to dominate their sum in the second degree. It then finds (higher order) sufficient conditions for either of the variables to dominate their sum in the third degree. While utilities are only restricted to be increasing concave, the expected utility differences for the respective risk positions are the same as if the investors were respectively proper or standard risk averse (Pratt-Zeckhauser [1987], Kimball [1993]