IDEAS home Printed from https://ideas.repec.org/a/inm/ormnsc/v54y2008i3p586-593.html
   My bibliography  Save this article

Mean Variance Vulnerability

Author

Listed:
  • Thomas Eichner

    (Department of Economics, University of Bielefeld, D-33615 Bielefeld, Germany)

Abstract

This paper transfers the concept of Gollier and Pratt's (Gollier, C., J. W. Pratt. 1996. Risk vulnerability and the tempering effect of background risk. Econometrica 64 1109-1123) risk vulnerability into mean variance preferences. Risk vulnerability is shown to be equivalent to the slope of the mean variance indifference curve being decreasing in mean and increasing in variance. Next, we introduce the notion of mean variance vulnerability to link the concepts of decreasing absolute risk aversion, risk vulnerability, properness, and standardness. All of the abovementioned concepts are characterized in terms of mean variance indifference curve properties and in terms of absolute risk measures.

Suggested Citation

  • Thomas Eichner, 2008. "Mean Variance Vulnerability," Management Science, INFORMS, vol. 54(3), pages 586-593, March.
  • Handle: RePEc:inm:ormnsc:v:54:y:2008:i:3:p:586-593
    DOI: 10.1287/mnsc.1070.0772
    as

    Download full text from publisher

    File URL: http://dx.doi.org/10.1287/mnsc.1070.0772
    Download Restriction: no

    File URL: https://libkey.io/10.1287/mnsc.1070.0772?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. Kimball, Miles S, 1990. "Precautionary Saving in the Small and in the Large," Econometrica, Econometric Society, vol. 58(1), pages 53-73, January.
    2. Peter H. Farquhar & Yutaka Nakamura, 1987. "Constant Exchange Risk Properties," Operations Research, INFORMS, vol. 35(2), pages 206-214, April.
    3. Fatma Lajeri-Chaherli, 2002. "More on Properness: The Case of Mean-Variance Preferences," The Geneva Risk and Insurance Review, Palgrave Macmillan;International Association for the Study of Insurance Economics (The Geneva Association), vol. 27(1), pages 49-60, June.
    4. Chamberlain, Gary, 1983. "A characterization of the distributions that imply mean--Variance utility functions," Journal of Economic Theory, Elsevier, vol. 29(1), pages 185-201, February.
    5. Eeckhoudt, Louis & Gollier, Christian & Schlesinger, Harris, 1996. "Changes in Background Risk and Risk-Taking Behavior," Econometrica, Econometric Society, vol. 64(3), pages 683-689, May.
    6. Kimball, Miles S, 1993. "Standard Risk Aversion," Econometrica, Econometric Society, vol. 61(3), pages 589-611, May.
    7. 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.
    8. Lars Tyge Nielsen, 1990. "Equilibrium in CAPM Without a Riskless Asset," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 57(2), pages 315-324.
    9. Fatma Lajeri-Chaherli, 2004. "Proper and Standard Risk Aversion in Two-Moment Decision Models," Theory and Decision, Springer, vol. 57(3), pages 213-225, November.
    10. Allingham, Michael, 1991. "Existence Theorems in the Capital Asset Pricing Model," Econometrica, Econometric Society, vol. 59(4), pages 1169-1174, July.
    11. Ormiston, Michael B & Schlee, Edward E, 2001. "Mean-Variance Preferences and Investor Behaviour," Economic Journal, Royal Economic Society, vol. 111(474), pages 849-861, October.
    12. Lars Tyge Nielsen & Fatma Lajeri, 2000. "Parametric characterizations of risk aversion and prudence," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 15(2), pages 469-476.
    13. J. Tobin, 1958. "Liquidity Preference as Behavior Towards Risk," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 25(2), pages 65-86.
    14. Lajeri-Chaherli, Fatma, 2003. "Partial derivatives, comparative risk behavior and concavity of utility functions," Mathematical Social Sciences, Elsevier, vol. 46(1), pages 81-99, August.
    15. Meyer, Jack, 1987. "Two-moment Decision Models and Expected Utility Maximization," American Economic Review, American Economic Association, vol. 77(3), pages 421-430, June.
    16. John S. Chipman, 1973. "The Ordering of Portfolios in Terms of Mean and Variance," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 40(2), pages 167-190.
    17. Pratt, John W & Zeckhauser, Richard J, 1987. "Proper Risk Aversion," Econometrica, Econometric Society, vol. 55(1), pages 143-154, January.
    18. Owen, Joel & Rabinovitch, Ramon, 1983. "On the Class of Elliptical Distributions and Their Applications to the Theory of Portfolio Choice," Journal of Finance, American Finance Association, vol. 38(3), pages 745-752, June.
    19. Gollier, Christian & Pratt, John W, 1996. "Risk Vulnerability and the Tempering Effect of Background Risk," Econometrica, Econometric Society, vol. 64(5), pages 1109-1123, September.
    20. Peter C. Fishburn & R. Burr Porter, 1976. "Optimal Portfolios with One Safe and One Risky Asset: Effects of Changes in Rate of Return and Risk," Management Science, INFORMS, vol. 22(10), pages 1064-1073, June.
    21. Thomas Eichner, 2005. "Comparative statics of properness in two-moment decision models," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 25(4), pages 1007-1012, June.
    22. Wagener, Andreas, 2002. "Prudence and risk vulnerability in two-moment decision models," Economics Letters, Elsevier, vol. 74(2), pages 229-235, January.
    23. David E. Bell, 1988. "One-Switch Utility Functions and a Measure of Risk," Management Science, INFORMS, vol. 34(12), pages 1416-1424, December.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. Thomas Eichner & Andreas Wagener, 2009. "Multiple Risks and Mean-Variance Preferences," Operations Research, INFORMS, vol. 57(5), pages 1142-1154, October.
    3. 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.
    4. 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.
    5. 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.
    6. Wagener, Andreas, 2003. "Comparative statics under uncertainty: The case of mean-variance preferences," European Journal of Operational Research, Elsevier, vol. 151(1), pages 224-232, November.
    7. 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.
    8. 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.
    9. Subhadip Mukherjee & Soumyatanu Mukherjee & Tapas Mishra & Udo Broll, 2019. "Export investment under uncertainty: a mean-variance decision analysis for Indian manufacturing exporters," Discussion Papers 2019-18, University of Nottingham, GEP.
    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. Eichner, Thomas, 2011. "Portfolio selection and duality under mean variance preferences," Insurance: Mathematics and Economics, Elsevier, vol. 48(1), pages 146-152, January.
    12. Lajeri-Chaherli, Fatma, 2003. "Partial derivatives, comparative risk behavior and concavity of utility functions," Mathematical Social Sciences, Elsevier, vol. 46(1), pages 81-99, August.
    13. Fatma Lajeri-Chaherli, 2004. "Proper and Standard Risk Aversion in Two-Moment Decision Models," Theory and Decision, Springer, vol. 57(3), pages 213-225, November.
    14. Christian Gollier & James Hammitt & Nicolas Treich, 2013. "Risk and choice: A research saga," Journal of Risk and Uncertainty, Springer, vol. 47(2), pages 129-145, October.
    15. Gollier Christian & Schlee Edward E, 2006. "Increased Risk-Bearing with Background Risk," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 6(1), pages 1-29, March.
    16. Udo Broll & Jack E. Wahl, 2004. "Optimal hedge ratio and elasticity of risk aversion," Economics Bulletin, AccessEcon, vol. 6(5), pages 1-7.
    17. Wagener, Andreas, 2002. "Prudence and risk vulnerability in two-moment decision models," Economics Letters, Elsevier, vol. 74(2), pages 229-235, January.
    18. Lajeri-Chaherli, Fatma, 2004. "Proper prudence, standard prudence and precautionary vulnerability," Economics Letters, Elsevier, vol. 82(1), pages 29-34, January.
    19. Berk, Jonathan B., 1997. "Necessary Conditions for the CAPM," Journal of Economic Theory, Elsevier, vol. 73(1), pages 245-257, March.
    20. Vergara, Marcos & Bonilla, Claudio A., 2021. "Precautionary saving in mean-variance models and different sources of risk," Economic Modelling, Elsevier, vol. 98(C), pages 280-289.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:inm:ormnsc:v:54:y:2008:i:3:p:586-593. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Chris Asher (email available below). General contact details of provider: https://edirc.repec.org/data/inforea.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.