IDEAS home Printed from https://ideas.repec.org/a/eee/jetheo/v147y2012i3p1222-1246.html
   My bibliography  Save this article

Increases in risk aversion and the distribution of portfolio payoffs

Author

Listed:
  • Dybvig, Philip H.
  • Wang, Yajun

Abstract

Oliver Hart proved the impossibility of deriving general comparative static properties in portfolio weights. Instead, we derive new comparative statics for the distribution of payoffs: A is less risk averse than B iff Aʼs payoff is always distributed as Bʼs payoff plus a non-negative random variable plus conditional-mean-zero noise. If either agent has nonincreasing absolute risk aversion, the non-negative part can be chosen to be constant. The main result also holds in some incomplete markets with two assets or two-fund separation, and in multiple periods for a mixture of payoff distributions over time (but not at every point in time).

Suggested Citation

  • Dybvig, Philip H. & Wang, Yajun, 2012. "Increases in risk aversion and the distribution of portfolio payoffs," Journal of Economic Theory, Elsevier, vol. 147(3), pages 1222-1246.
    • Handle: RePEc:eee:jetheo:v:147:y:2012:i:3:p:1222-1246
    DOI: 10.1016/j.jet.2011.11.009
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S002205311100161X
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jet.2011.11.009?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
    ---><---

    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. Dybvig, Philip H. & Liu, Hong, 2010. "Lifetime consumption and investment: Retirement and constrained borrowing," Journal of Economic Theory, Elsevier, vol. 145(3), pages 885-907, May.
    2. Machina, Mark J, 1982. ""Expected Utility" Analysis without the Independence Axiom," Econometrica, Econometric Society, vol. 50(2), pages 277-323, March.
    3. Rothschild, Michael & Stiglitz, Joseph E., 1972. "Addendum to "increasing risk: I. A definition"," Journal of Economic Theory, Elsevier, vol. 5(2), pages 306-306, October.
    4. Oliver D. Hart, 1975. "Some Negative Results on the Existence of Comparative Statics (Properties) in Portfolio Theory," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 42(4), pages 615-621.
    5. Stephen A. Ross, 2005. "Mutual Fund Separation in Financial Theory—The Separating Distributions," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 10, pages 309-356, World Scientific Publishing Co. Pte. Ltd..
    6. Ross, Stephen A, 1981. "Some Stronger Measures of Risk Aversion in the Small and the Large with Applications," Econometrica, Econometric Society, vol. 49(3), pages 621-638, May.
    7. Rothschild, Michael & Stiglitz, Joseph E., 1970. "Increasing risk: I. A definition," Journal of Economic Theory, Elsevier, vol. 2(3), pages 225-243, September.
    8. Machina, Mark J., 1989. "Comparative statics and non-expected utility preferences," Journal of Economic Theory, Elsevier, vol. 47(2), pages 393-405, April.
    9. Kihlstrom, Richard E & Romer, David & Williams, Steve, 1981. "Risk Aversion with Random Initial Wealth," Econometrica, Econometric Society, vol. 49(4), pages 911-920, June.
    10. Levy, Haim & Hanoch, Giora, 1970. "Relative Effectiveness of Efficiency Criteria for Portfolio Selection," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 5(1), pages 63-76, March.
    11. Cass, David & Stiglitz, Joseph E., 1970. "The structure of investor preferences and asset returns, and separability in portfolio allocation: A contribution to the pure theory of mutual funds," Journal of Economic Theory, Elsevier, vol. 2(2), pages 122-160, June.
    12. Cox, John C. & Huang, Chi-fu, 1991. "A variational problem arising in financial economics," Journal of Mathematical Economics, Elsevier, vol. 20(5), pages 465-487.
    13. Dybvig, Philip H & Ingersoll, Jonathan E, Jr, 1982. "Mean-Variance Theory in Complete Markets," The Journal of Business, University of Chicago Press, vol. 55(2), pages 233-251, April.
    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. Elie Bouri & Rangan Gupta & Chi keung marco Lau & David Roubaud, 2021. "Risk aversion and Bitcoin returns in extreme quantiles," Economics Bulletin, AccessEcon, vol. 41(3), pages 1374-1386.
    2. Dejian Tian & Weidong Tian, 2016. "Comparative statics under κ-ambiguity for log-Brownian asset prices," International Journal of Economic Theory, The International Society for Economic Theory, vol. 12(4), pages 361-378, December.
    3. Elie Bouri & Rangan Gupta & Chi Keung Marco Lau & David Roubaud, 2019. "Risk Aversion and Bitcoin Returns in Normal, Bull, and Bear Markets," Working Papers 201927, University of Pretoria, Department of Economics.
    4. Soo Hong Chew & Jacob S. Sagi, 2022. "A critical look at the Aumann-Serrano and Foster-Hart measures of riskiness," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 74(2), pages 397-422, September.
    5. Bernard, Carole & Chen, Jit Seng & Vanduffel, Steven, 2015. "Rationalizing investors’ choices," Journal of Mathematical Economics, Elsevier, vol. 59(C), pages 10-23.

    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. Kimball, Miles S, 1993. "Standard Risk Aversion," Econometrica, Econometric Society, vol. 61(3), pages 589-611, May.
    2. Franke, Gunter & Stapleton, Richard C. & Subrahmanyam, Marti G., 1998. "Who Buys and Who Sells Options: The Role of Options in an Economy with Background Risk," Journal of Economic Theory, Elsevier, vol. 82(1), pages 89-109, September.
    3. Franke, Günter & Stapleton, Richard C. & Subrahmanyam, Marti G., 1995. "Who buys and who sells options: The role and pricing of options in an economy with background risk," Discussion Papers, Series II 253, University of Konstanz, Collaborative Research Centre (SFB) 178 "Internationalization of the Economy".
    4. Gelles, Gregory M. & Mitchell, Douglas W., 2002. "Increasingly mean-seeking utility functions and n-asset portfolios," The Quarterly Review of Economics and Finance, Elsevier, vol. 42(5), pages 911-919.
    5. Henri Loubergé, 1998. "Risk and Insurance Economics 25 Years After," The Geneva Papers on Risk and Insurance - Issues and Practice, Palgrave Macmillan;The Geneva Association, vol. 23(4), pages 540-567, October.
    6. Chiu, W. Henry, 2019. "Comparative statics in an ordinal theory of choice under risk," Mathematical Social Sciences, Elsevier, vol. 101(C), pages 113-123.
    7. White, Lucy, 2006. "Prudence in Bargaining: The Effect of Uncertainty on Bargaining Outcomes," CEPR Discussion Papers 5822, C.E.P.R. Discussion Papers.
    8. Ramaswami, Bharat & Roe, Terry L., 1989. "Incompleteness in Insurance: An Analysis of the Multiplicative Case," Bulletins 7492, University of Minnesota, Economic Development Center.
    9. Alain Chateauneuf & Ghizlane Lakhnati & Eric Langlais, 2016. "On the precautionary motive for savings and prudence in the rank-dependent utility framework," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 61(1), pages 169-182, January.
    10. Gollier, Christian & Schlesinger, Harris, 2002. "Changes in risk and asset prices," Journal of Monetary Economics, Elsevier, vol. 49(4), pages 747-760, May.
    11. Günter Franke & Harris Schlesinger & Richard C. Stapleton, 2006. "Multiplicative Background Risk," Management Science, INFORMS, vol. 52(1), pages 146-153, January.
    12. AJ A. Bostian & Christoph Heinzel, 2018. "Comparative precautionary saving under higher-order risk and recursive utility," The Geneva Risk and Insurance Review, Palgrave Macmillan;International Association for the Study of Insurance Economics (The Geneva Association), vol. 43(1), pages 95-114, May.
    13. 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.
    14. Merton, Robert, 1990. "Capital market theory and the pricing of financial securities," Handbook of Monetary Economics, in: B. M. Friedman & F. H. Hahn (ed.), Handbook of Monetary Economics, edition 1, volume 1, chapter 11, pages 497-581, Elsevier.
    15. Henk Keffert & Nikolaus Schweizer, 2024. "Stochastic Monotonicity and Random Utility Models: The Good and The Ugly," Papers 2409.00704, arXiv.org.
    16. Dachraoui, Kais & Dionne, Georges, 2001. "Stochastic dominance and optimal portfolio," Economics Letters, Elsevier, vol. 71(3), pages 347-354, June.
    17. Octave Jokung, 2013. "Changes in multiplicative background risk and risk-taking behavior," Theory and Decision, Springer, vol. 74(1), pages 127-149, January.
    18. Timo Kuosmanen, 2004. "Efficient Diversification According to Stochastic Dominance Criteria," Management Science, INFORMS, vol. 50(10), pages 1390-1406, October.
    19. Liu, Liqun & Meyer, Jack, 2013. "Substituting one risk increase for another: A method for measuring risk aversion," Journal of Economic Theory, Elsevier, vol. 148(6), pages 2706-2718.
    20. Geiger, Gebhard, 2002. "On the statistical foundations of non-linear utility theory: The case of status quo-dependent preferences," European Journal of Operational Research, Elsevier, vol. 136(2), pages 449-465, January.

    More about this item

    Keywords

    Risk aversion; Portfolio theory; Stochastic dominance; Complete markets; Two-fund separation;
    All these keywords.

    JEL classification:

    • D33 - Microeconomics - - Distribution - - - Factor Income Distribution
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions

    Statistics

    Access and download statistics

    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:jetheo:v:147:y:2012:i:3:p:1222-1246. 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/622869 .

    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.