Mean-Variance and Expected Utility: The Borch Paradox
AbstractThe 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.
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Bibliographic InfoPaper provided by arXiv.org in its series Papers with number 1306.2728.
Date of creation: Jun 2013
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Publication status: Published in Statistical Science 2013, Vol. 28, No. 2, 223-237
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This paper has been announced in the following NEP Reports:
- NEP-ALL-2013-06-16 (All new papers)
- NEP-HPE-2013-06-16 (History & Philosophy of Economics)
- NEP-UPT-2013-06-16 (Utility Models & Prospect Theory)
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- Bj�Rn Hagstr�Mer & 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, University of Manchester, vol. 76(s1), pages 134-156, 09.
- Baron, David P, 1977. "On the Utility Theoretic Foundations of Mean-Variance Analysis," Journal of Finance, American Finance Association, American Finance Association, vol. 32(5), pages 1683-97, December.
- Feldstein, Martin S, 1969. "Mean-Variance Analysis in the Theory of Liquidity Preference and Portfolio Selection," Review of Economic Studies, Wiley Blackwell, Wiley Blackwell, vol. 36(105), pages 5-12, January.
- Markowitz, Harry M, 1991.
" Foundations of Portfolio Theory,"
Journal of Finance, American Finance Association,
American Finance Association, vol. 46(2), pages 469-77, June.
- Markowitz, Harry M., 1990. "Foundations of Portfolio Theory," Nobel Prize in Economics documents, Nobel Prize Committee 1990-1, Nobel Prize Committee.
- Meyer, Jack, 1977. "Choice among distributions," Journal of Economic Theory, Elsevier, Elsevier, vol. 14(2), pages 326-336, April.
- Liu, Liping, 2004. "A new foundation for the mean-variance analysis," European Journal of Operational Research, Elsevier, Elsevier, vol. 158(1), pages 229-242, October.
- Borch, Karl, 1978. "Portfolio theory is for risk lovers," Journal of Banking & Finance, Elsevier, Elsevier, vol. 2(2), pages 179-181, August.
- Sarnat, Marshall, 1974. "A Note on the Implications of Quadratic Utility for Portfolio Theory," Journal of Financial and Quantitative Analysis, Cambridge University Press, Cambridge University Press, vol. 9(04), pages 687-689, September.
- Hagströmer, Björn & Anderson, Richard G. & Binner, Jane & Elger, Thomas & Nilsson, Birger, 2007.
"Mean-Variance vs. Full-Scale Optimization: Broad Evidence for the UK,"
Working Papers, Lund University, Department of Economics
2008:1, Lund University, Department of Economics.
- 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, Federal Reserve Bank of St. Louis 2007-016, Federal Reserve Bank of St. Louis.
- D. J. Johnstone, 2012. "Log-optimal economic evaluation of probability forecasts," Journal of the Royal Statistical Society Series A, Royal Statistical Society, Royal Statistical Society, vol. 175(3), pages 661-689, 07.
- Borch, Karl, 1979. "Equilibrium in capital markets," Economics Letters, Elsevier, Elsevier, vol. 2(2), pages 175-179.
- Borch, Karl, 1973. "Expected utility expressed in terms of moments," Omega, Elsevier, Elsevier, vol. 1(3), pages 331-343, June.
- 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.
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