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Variance Vulnerability, Background Risks, and Mean-Variance Preferences

Author

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  • Thomas Eichner

    (VWL IV, FB 5, University of Siegen, Hölderlinstr. 3, 57068 Siegen, Germany, e-mail: eichner@vwl.wiwi.uni-siegen.de)

  • Andreas Wagener

    (Department of Economics, University of Vienna, Hohenstaufengasse 9, 1010 Vienna, Austria, e-mail: andreas.wagener@univie.ac.at)

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. The Geneva Papers on Risk and Insurance Theory (2003) 28, 173–184. doi:10.1023/A:1026396922206

Suggested Citation

  • Thomas Eichner & Andreas Wagener, 2003. "Variance Vulnerability, Background Risks, and Mean-Variance Preferences," The Geneva Risk and Insurance Review, Palgrave Macmillan;International Association for the Study of Insurance Economics (The Geneva Association), vol. 28(2), pages 173-184, December.
    • Handle: RePEc:pal:genrir:v:28:y:2003:i:2:p:173-184
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