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Variance Vulnerability, Background Risks, and Mean-Variance Preferences

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  • Thomas Eichner

    (VWL IV, FB 5, University of Siegen, H�lderlinstr. 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

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Bibliographic Info

Article provided by Palgrave Macmillan in its journal The Geneva Papers on Risk and Insurance Theory.

Volume (Year): 28 (2003)
Issue (Month): 2 (December)
Pages: 173-184

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Handle: RePEc:pal:genrir:v:28:y:2003:i:2:p:173-184

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Cited by:
  1. Guo, Xu & Wong, Wing-Keung & Zhu, Lixing, 2013. "An analysis of portfolio selection with multiplicative background risk," MPRA Paper 51331, University Library of Munich, Germany.
  2. Malevergne, Y. & Rey, B., 2009. "On cross-risk vulnerability," Insurance: Mathematics and Economics, Elsevier, vol. 45(2), pages 224-229, October.
  3. DENUIT, Michel M. & EECKHOUDT, Louis & MENEGATTI, Mario, . "Correlated risks, bivariate utility and optimal choices," CORE Discussion Papers RP -2272, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  4. Xu, Guo & Wing-Keung, Wong & Lixing, Zhu, 2013. "Comparisons and Characterizations of the Mean-Variance, Mean-VaR, Mean-CVaR Models for Portfolio Selection With Background Risk," MPRA Paper 51827, University Library of Munich, Germany.
  5. Thomas Eichner & Andreas Wagener, 2004. "Relative risk aversion, relative prudence and comparative statics under uncertainty: The case of (μ, σ)-preferences," Bulletin of Economic Research, Wiley Blackwell, vol. 56(2), pages 159-170, 04.
  6. Andreas Wagener, 2005. "Linear risk tolerance and mean-variance preferences," Economics Bulletin, AccessEcon, vol. 4(1), pages 1-8.
  7. Alghalith, Moawia & Guo, Xu & Wong, Wing-Keung & Zhu, Lixing, 2013. "Input Demand under Joint Energy and Output Prices Uncertainties," MPRA Paper 52368, University Library of Munich, Germany.
  8. Guo, Xu & Wong, Wing-Keung & Zhu, Lixing, 2013. "Two-moment decision model for location-scale family with background asset," MPRA Paper 43864, University Library of Munich, Germany.
  9. Eichner, Thomas & Wagener, Andreas, 2012. "Tempering effects of (dependent) background risks: A mean-variance analysis of portfolio selection," Journal of Mathematical Economics, Elsevier, vol. 48(6), pages 422-430.
  10. Thomas Eichner & Andreas Wagener, 2011. "Portfolio allocation and asset demand with mean-variance preferences," Theory and Decision, Springer, vol. 70(2), pages 179-193, February.
  11. Lin, Wen-chang & Lu, Jin-ray, 2012. "Risky asset allocation and consumption rule in the presence of background risk and insurance markets," Insurance: Mathematics and Economics, Elsevier, vol. 50(1), pages 150-158.
  12. Thomas Eichner & Andreas Wagener, 2005. "Notes and Comments: Measures of risk attitude: correspondences between mean-variance and expected-utility approaches," Decisions in Economics and Finance, Springer, vol. 28(1), pages 53-65, 06.
  13. Günter Franke & Richard C. Stapleton & Marti G. Subrahmanyam, 2005. "Incremental Risk Vulnerability," CoFE Discussion Paper 05-08, Center of Finance and Econometrics, University of Konstanz.
  14. Thomas Eichner, 2010. "Slutzky equations and substitution effects of risks in terms of mean-variance preferences," Theory and Decision, Springer, vol. 69(1), pages 17-26, July.
  15. Thomas Eichner & Andreas Wagener, 2004. "The Welfare State in a Changing Environment," International Tax and Public Finance, Springer, vol. 11(3), pages 313-331, 05.
  16. Bilancini, Ennio & D’Antoni, Massimo, 2012. "The desirability of pay-as-you-go pensions when relative consumption matters and returns are stochastic," Economics Letters, Elsevier, vol. 117(2), pages 418-422.

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