IDEAS home Printed from https://ideas.repec.org/p/arx/papers/1306.2728.html
   My bibliography  Save this paper

Mean-Variance and Expected Utility: The Borch Paradox

Author

Listed:
  • David Johnstone
  • Dennis Lindley

Abstract

The model of rational decision-making in most of economics and statistics is expected utility theory (EU) axiomatised by von Neumann and Morgenstern, Savage and others. This is less the case, however, in financial economics and mathematical finance, where investment decisions are commonly based on the methods of mean-variance (MV) introduced in the 1950s by Markowitz. Under the MV framework, each available investment opportunity ("asset") or portfolio is represented in just two dimensions by the ex ante mean and standard deviation $(\mu,\sigma)$ of the financial return anticipated from that investment. Utility adherents consider that in general MV methods are logically incoherent. Most famously, Norwegian insurance theorist Borch presented a proof suggesting that two-dimensional MV indifference curves cannot represent the preferences of a rational investor (he claimed that MV indifference curves "do not exist"). This is known as Borch's paradox and gave rise to an important but generally little-known philosophical literature relating MV to EU. We examine the main early contributions to this literature, focussing on Borch's logic and the arguments by which it has been set aside.

Suggested Citation

  • David Johnstone & Dennis Lindley, 2013. "Mean-Variance and Expected Utility: The Borch Paradox," Papers 1306.2728, arXiv.org.
  • Handle: RePEc:arx:papers:1306.2728
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/1306.2728
    File Function: Latest version
    Download Restriction: no

    References listed on IDEAS

    as
    1. Baron, David P, 1977. "On the Utility Theoretic Foundations of Mean-Variance Analysis," Journal of Finance, American Finance Association, vol. 32(5), pages 1683-1697, December.
    2. Borch, Karl, 1978. "Portfolio theory is for risk lovers," Journal of Banking & Finance, Elsevier, vol. 2(2), pages 179-181, August.
    3. M. S. Feldstein, 1969. "Mean-Variance Analysis in the Theory of Liquidity Preference and Portfolio Selection," Review of Economic Studies, Oxford University Press, vol. 36(1), pages 5-12.
    4. D. J. Johnstone, 2012. "Log-optimal economic evaluation of probability forecasts," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 175(3), pages 661-689, July.
    5. Meyer, Jack, 1977. "Choice among distributions," Journal of Economic Theory, Elsevier, vol. 14(2), pages 326-336, April.
    6. Björn Hagströmer & Richard G. Anderson & Jane M. Binner & Thomas Elger & Birger Nilsson, 2008. "Mean-Variance Versus Full-Scale Optimization: Broad Evidence For The Uk," Manchester School, University of Manchester, vol. 76(s1), pages 134-156, September.
    7. Liu, Liping, 2004. "A new foundation for the mean-variance analysis," European Journal of Operational Research, Elsevier, vol. 158(1), pages 229-242, October.
    8. L. Eeckhoudt & C. Gollier & H. Schlesinger, 2005. "Economic and financial decisions under risk," Post-Print hal-00325882, HAL.
    9. Borch, Karl, 1973. "Expected utility expressed in terms of moments," Omega, Elsevier, vol. 1(3), pages 331-343, June.
    10. Barone, Luca, 2008. "Bruno de Finetti and the case of the critical line's last segment," Insurance: Mathematics and Economics, Elsevier, vol. 42(1), pages 359-377, February.
    11. Markowitz, Harry M, 1991. " Foundations of Portfolio Theory," Journal of Finance, American Finance Association, vol. 46(2), pages 469-477, June.
    12. Sarnat, Marshall, 1974. "A Note on the Implications of Quadratic Utility for Portfolio Theory," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 9(04), pages 687-689, September.
    13. Björn Hagströmer & Richard G. Anderson & Jane M. Binner & Thomas Elger & Birger Nilsson, 2007. "Mean-variance vs. full-scale optimization: broad evidence for the U.K," Working Papers 2007-016, Federal Reserve Bank of St. Louis.
    14. Borch, Karl, 1979. "Equilibrium in capital markets," Economics Letters, Elsevier, vol. 2(2), pages 175-179.
    Full references (including those not matched with items on IDEAS)

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    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:arx:papers:1306.2728. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (arXiv administrators). General contact details of provider: http://arxiv.org/ .

    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 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.

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

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.