IDEAS home Printed from https://ideas.repec.org/a/eee/insuma/v48y2011i1p146-152.html
   My bibliography  Save this article

Portfolio selection and duality under mean variance preferences

Author

Listed:
  • Eichner, Thomas

Abstract

This paper uses duality to analyze an investor's behavior in a n-asset portfolio selection problem when the investor has mean variance preferences. The indirect utility and wealth requirement functions are used to derive Roy's identity, Shephard's lemma and the Slutsky equation. In our simple Slutsky equation the income effect is characterized by decreasing absolute risk aversion (DARA) and the substitution effect is always positive [negative] with respect to an asset's holding if the asset's mean return [risk] increases. Substitution effect and income effect work in the same direction presupposed mean variance preferences display DARA.

Suggested Citation

  • Eichner, Thomas, 2011. "Portfolio selection and duality under mean variance preferences," Insurance: Mathematics and Economics, Elsevier, vol. 48(1), pages 146-152, January.
  • Handle: RePEc:eee:insuma:v:48:y:2011:i:1:p:146-152
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167-6687(10)00122-8
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Meyer, Jack & Ormiston, Michael B, 1994. "The Effect on Optimal Portfolios of Changing the Return to a Risky Asset: The Case of Dependent Risky Returns," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 35(3), pages 603-612, August.
    2. Guiso, Luigi & Jappelli, Tullio & Terlizzese, Daniele, 1996. "Income Risk, Borrowing Constraints, and Portfolio Choice," American Economic Review, American Economic Association, vol. 86(1), pages 158-172, March.
    3. Binswanger, Hans P, 1981. "Attitudes toward Risk: Theoretical Implications of an Experiment in Rural India," Economic Journal, Royal Economic Society, vol. 91(364), pages 867-890, December.
    4. 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.
    5. 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.
    6. Aivazian, Varouj, 1977. "The Demand for Assets under Conditions of Risk: Comment," Journal of Finance, American Finance Association, vol. 32(3), pages 927-929, June.
    7. 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.
    8. Ardeshir J. Dalal, 1983. "Comparative Statics and Asset Substitutability/Complementarity in a Portfolio Model: A Dual Approach," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 50(2), pages 355-367.
    9. Agnar Sandmo, 1977. "Portfolio Theory, Asset Demand and Taxation: Comparative Statics with Many Assets," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 44(2), pages 369-379.
    10. Carmen F. Menezes & X. Henry Wang, 2005. "Duality and the Slutsky income and substitution effects of increases in wage rate uncertainty," Oxford Economic Papers, Oxford University Press, vol. 57(3), pages 545-557, July.
    11. Chavas, Jean-Paul & Holt, Matthew T, 1996. "Economic Behavior under Uncertainty: A Joint Analysis of Risk Preferences and Technology," The Review of Economics and Statistics, MIT Press, vol. 78(2), pages 329-335, May.
    12. Levy, Haim, 1994. "Absolute and Relative Risk Aversion: An Experimental Study," Journal of Risk and Uncertainty, Springer, vol. 8(3), pages 289-307, May.
    13. 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.
    14. William F. Sharpe, 1964. "Capital Asset Prices: A Theory Of Market Equilibrium Under Conditions Of Risk," Journal of Finance, American Finance Association, vol. 19(3), pages 425-442, September.
    15. 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.
    16. Hadar, Josef & Seo, Tae Kun, 1990. "The Effects of Shifts in a Return Distribution on Optimal Portfolios," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 31(3), pages 721-736, August.
    17. Meyer, Jack, 1987. "Two-moment Decision Models and Expected Utility Maximization," American Economic Review, American Economic Association, vol. 77(3), pages 421-430, June.
    18. Menezes, Carmen F. & Henry Wang, X. & Bigelow, John P., 2005. "Duality and consumption decisions under income and price risk," Journal of Mathematical Economics, Elsevier, vol. 41(3), pages 387-405, April.
    19. Thomas Eichner, 2008. "Mean Variance Vulnerability," Management Science, INFORMS, vol. 54(3), pages 586-593, March.
    20. Levy, Haim, 1973. "The Demand for Assets Under Conditions of Risk," Journal of Finance, American Finance Association, vol. 28(1), pages 79-96, March.
    21. Carmen F. Menezes & X. Henry Wang, 2006. "Optimal Decisions With Linear Random Payoff," Manchester School, University of Manchester, vol. 74(3), pages 251-265, June.
    22. 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.
    23. Carmen F. Menezes & X. Henry Wang, 2005. "Duality, income and substitution effects for the competitive firm under price uncertainty," Managerial and Decision Economics, John Wiley & Sons, Ltd., vol. 26(4), pages 249-257.
    24. Mitchell, Douglas W & Douglas, Stratford M, 1997. "Portfolio Response to a Shift in a Return Distribution: The Case of n-Dependent Assets," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 38(4), pages 945-950, November.
    25. Thomas Eichner & Andreas Wagener, 2009. "Multiple Risks and Mean-Variance Preferences," Operations Research, INFORMS, vol. 57(5), pages 1142-1154, October.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Peng-Sheng You & Ming-Hsiang Chen & Ching-Hui (Joan) Su, 2021. "Travel agent’s tour selection and sightseeing bus schedule for group package tour planning," Tourism Economics, , vol. 27(1), pages 220-242, February.

    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. 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.
    2. 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.
    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. Thomas Eichner & Andreas Wagener, 2009. "Multiple Risks and Mean-Variance Preferences," Operations Research, INFORMS, vol. 57(5), pages 1142-1154, October.
    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. Thomas Eichner, 2008. "Mean Variance Vulnerability," Management Science, INFORMS, vol. 54(3), pages 586-593, March.
    7. Thomas Eichner & Rüdiger Pethig, 2015. "Efficient Management of Insecure Fossil Fuel Imports through Taxing Domestic Green Energy?," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 17(5), pages 724-751, October.
    8. 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.
    9. Padhi, Sidhartha S. & Mukherjee, Soumyatanu & Edwin Cheng, T.C., 2024. "Optimal investment decision for industry 4.0 under uncertainties of capability and competence building for managing supply chain risks," International Journal of Production Economics, Elsevier, vol. 267(C).
    10. 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.
    11. 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.
    12. 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.
    13. Thomas Eichner & Daniel Weinreich, 2015. "Welfare stigma and risk taking in the welfare state," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 44(2), pages 319-348, February.
    14. 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.
    15. Frank Schuhmacher & Hendrik Kohrs & Benjamin R. Auer, 2021. "Justifying Mean-Variance Portfolio Selection when Asset Returns Are Skewed," Management Science, INFORMS, vol. 67(12), pages 7812-7824, December.
    16. 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.
    17. Jean-Michel Courtault, 1992. "Les effets de substitution et de richesse de la théorie du portefeuille : une mise au point," Revue Économique, Programme National Persée, vol. 43(6), pages 983-1006.
    18. Douglas J. Hodgson & Oliver Linton & Keith Vorkink, 2002. "Testing the capital asset pricing model efficiently under elliptical symmetry: a semiparametric approach," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 17(6), pages 617-639, December.
    19. Schuhmacher, Frank & Auer, Benjamin R., 2014. "Sufficient conditions under which SSD- and MR-efficient sets are identical," European Journal of Operational Research, Elsevier, vol. 239(3), pages 756-763.
    20. Wing-Keung Wong & Chenghu Ma, 2008. "Preferences over location-scale family," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 37(1), pages 119-146, October.

    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:eee:insuma:v:48:y:2011:i:1:p:146-152. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/inca/505554 .

    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.