Variance Vulnerability, Background Risks, and Mean-Variance Preferences

Author: Eichner T.  

Publisher: Springer Publishing Company

ISSN: 0926-4957

Source: The GENEVA PAPERS on Risk and Insurance Theory, Vol.28, Iss.2, 2003-01, pp. : 173-184

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Abstract

An agent with two-parameter, mean-variance preferences is called variance vulnerable if an increase in the variance of an exogenous, independent background risk induces the agent to choose a lower level of risky activities. Variance vulnerability resembles the notion of risk vulnerability in the expected utility (EU) framework. First, we characterize variance vulnerability in terms of two-parameter utility functions. Second, we identify the multivariate normal as the only distribution such that EU- and two-parameter approach are compatible when independent background risks prevail. Third, presupposing normality, we show that—analogously to risk vulnerability—temperance is a necessary, and standardness and convex risk aversion are sufficient conditions for variance vulnerability.