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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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    Citations

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    Cited by:

    1. Andreas Wagener, 2005. "Linear risk tolerance and mean-variance preferences," Economics Bulletin, AccessEcon, vol. 4(1), pages 1-8.
    2. 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;Associazione per la Matematica, vol. 28(1), pages 53-65, June.
    3. Thomas Eichner, 2008. "Mean Variance Vulnerability," Management Science, INFORMS, vol. 54(3), pages 586-593, March.
    4. Michel Denuit & Louis Eeckhoudt & Mario Menegatti, 2011. "Correlated risks, bivariate utility and optimal choices," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 46(1), pages 39-54, January.
    5. Matthias Pelster, 2015. "Marketable and non-hedgeable risk in a duopoly framework with hedging," Journal of Economics and Finance, Springer;Academy of Economics and Finance, vol. 39(4), pages 697-716, October.
    6. Fatma Lajeri-Chaherli, 2016. "On The Concavity And Quasiconcavity Properties Of ( Σ , Μ ) Utility Functions," Bulletin of Economic Research, Wiley Blackwell, vol. 68(3), pages 287-296, April.
    7. Xiaoxia Huang & Guowei Jiang, 2021. "Portfolio management with background risk under uncertain mean-variance utility," Fuzzy Optimization and Decision Making, Springer, vol. 20(3), pages 315-330, September.
    8. Soumyatanu Mukherjee & Sidhartha S Padhi, 2018. "Risk connectivity and risk mitigation: An analytical framework," Discussion Papers 2018-11, University of Nottingham, CREDIT.
    9. 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.
    10. Malevergne, Y. & Rey, B., 2009. "On cross-risk vulnerability," Insurance: Mathematics and Economics, Elsevier, vol. 45(2), pages 224-229, October.
    11. Xu Guo & Andreas Wagener & Wing-Keung Wong & Lixing Zhu, 2018. "The two-moment decision model with additive risks," Risk Management, Palgrave Macmillan, vol. 20(1), pages 77-94, February.
    12. 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.
    13. 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.
    14. 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, April.
    15. An, Galina & Becker, Charles M., 2013. "Uncertainty, Insecurity, and Emigration from Kazakhstan to Russia," World Development, Elsevier, vol. 42(C), pages 44-66.
    16. 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.
    17. 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.
    18. Moawia Alghalith & Xu Guo & Cuizhen Niu & Wing-Keung Wong, 2017. "Input Demand Under Joint Energy and Output Prices Uncertainties," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 34(04), pages 1-12, August.
    19. Xu Guo & Raymond H. Chan & Wing-Keung Wong & Lixing Zhu, 2019. "Mean–variance, mean–VaR, and mean–CVaR models for portfolio selection with background risk," Risk Management, Palgrave Macmillan, vol. 21(2), pages 73-98, June.
    20. 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.
    21. Subhadip Mukherjee & Soumyatanu Mukherjee & Tapas Mishra & Udo Broll & Mamata Parhi, 2021. "Spot exchange rate volatility, uncertain policies and export investment decision of firms: a mean-variance decision approach," The European Journal of Finance, Taylor & Francis Journals, vol. 27(8), pages 752-773, May.
    22. 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.
    23. Thomas Eichner & Andreas Wagener, 2004. "The Welfare State in a Changing Environment," International Tax and Public Finance, Springer;International Institute of Public Finance, vol. 11(3), pages 313-331, May.
    24. Soumyatanu Mukherjee & Sidhartha S. Padhi, 2022. "Sourcing decision under interconnected risks: an application of mean–variance preferences approach," Annals of Operations Research, Springer, vol. 313(2), pages 1243-1268, June.
    25. 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.

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