General linear formulations of stochastic dominance criteria
AbstractWe develop and implement linear formulations of general Nth order stochastic dominance criteria for discrete probability distributions. Our approach is based on a piece-wise polynomial representation of utility and its derivatives and can be implemented by solving a relatively small system of linear inequalities. This approach allows for comparing a given prospect with a discrete set of alternative prospects as well as for comparison with a polyhedral set of linear combinations of prospects. We also derive a linear dual formulation in terms of lower partial moments and co-lower partial moments. An empirical application to historical stock market data suggests that the passive stock market portfolio is highly inefficient relative to actively managed portfolios for all investment horizons and for nearly all investors. The results also illustrate that the mean–variance rule and second-order stochastic dominance rule may not detect market portfolio inefficiency because of non-trivial violations of non-satiation and prudence.
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Bibliographic InfoArticle provided by Elsevier in its journal European Journal of Operational Research.
Volume (Year): 230 (2013)
Issue (Month): 2 ()
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Web page: http://www.elsevier.com/locate/eor
Stochastic dominance; Utility theory; Non-satiation; Risk aversion; Prudence; Temperance;
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- Kimball, Miles S, 1993.
"Standard Risk Aversion,"
Econometric Society, vol. 61(3), pages 589-611, May.
- Lizyayev, Andrey & Ruszczyński, Andrzej, 2012. "Tractable Almost Stochastic Dominance," European Journal of Operational Research, Elsevier, vol. 218(2), pages 448-455.
- Timo Kuosmanen, 2004. "Efficient Diversification According to Stochastic Dominance Criteria," Management Science, INFORMS, vol. 50(10), pages 1390-1406, October.
- Bali, Turan G. & Demirtas, K. Ozgur & Levy, Haim & Wolf, Avner, 2009. "Bonds versus stocks: Investors' age and risk taking," Journal of Monetary Economics, Elsevier, vol. 56(6), pages 817-830, September.
- Linton, Oliver & Maasoumi, Esfandiar & Whang, Yoon-Jae, 2003.
"Consistent Testing for Stochastic Dominance under General Sampling Schemes,"
SFB 373 Discussion Papers
2003,31, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
- Oliver Linton & Esfandiar Maasoumi & Yoon-Jae Whang, 2005. "Consistent Testing for Stochastic Dominance under General Sampling Schemes," Review of Economic Studies, Oxford University Press, vol. 72(3), pages 735-765.
- Oliver Linton & Esfandiar Maasoumi & Yoon-Jae Whang, 2003. "Consistent testing for stochastic dominance under general sampling schemes," LSE Research Online Documents on Economics 2208, London School of Economics and Political Science, LSE Library.
- Meyer, Jack, 1977. "Choice among distributions," Journal of Economic Theory, Elsevier, vol. 14(2), pages 326-336, April.
- David B. Brown & Enrico De Giorgi & Melvyn Sim, 2012. "Aspirational Preferences and Their Representation by Risk Measures," Management Science, INFORMS, vol. 58(11), pages 2095-2113, November.
- Bawa, Vijay S. & Lindenberg, Eric B., 1977. "Capital market equilibrium in a mean-lower partial moment framework," Journal of Financial Economics, Elsevier, vol. 5(2), pages 189-200, November.
- Bawa, Vijay S., 1975. "Optimal rules for ordering uncertain prospects," Journal of Financial Economics, Elsevier, vol. 2(1), pages 95-121, March.
- Banz, Rolf W., 1981. "The relationship between return and market value of common stocks," Journal of Financial Economics, Elsevier, vol. 9(1), pages 3-18, March.
- Fama, Eugene F & French, Kenneth R, 1988. "Permanent and Temporary Components of Stock Prices," Journal of Political Economy, University of Chicago Press, vol. 96(2), pages 246-73, April.
- Kopa, Miloš & Post, Thierry, 2009. "A Portfolio Optimality Test Based on the First-Order Stochastic Dominance Criterion," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 44(05), pages 1103-1124, October.
- Benartzi, Shlomo & Thaler, Richard H, 1995.
"Myopic Loss Aversion and the Equity Premium Puzzle,"
The Quarterly Journal of Economics,
MIT Press, vol. 110(1), pages 73-92, February.
- Shlomo Benartzi & Richard H. Thaler, 1993. "Myopic Loss Aversion and the Equity Premium Puzzle," NBER Working Papers 4369, National Bureau of Economic Research, Inc.
- Levy, H & Markowtiz, H M, 1979. "Approximating Expected Utility by a Function of Mean and Variance," American Economic Review, American Economic Association, vol. 69(3), pages 308-17, June.
- Hanoch, G & Levy, Haim, 1969. "The Efficiency Analysis of Choices Involving Risk," Review of Economic Studies, Wiley Blackwell, vol. 36(107), pages 335-46, July.
- Garry F. Barrett & Stephen G. Donald, 2003. "Consistent Tests for Stochastic Dominance," Econometrica, Econometric Society, vol. 71(1), pages 71-104, January.
- Hadar, Josef & Russell, William R, 1969. "Rules for Ordering Uncertain Prospects," American Economic Review, American Economic Association, vol. 59(1), pages 25-34, March.
- Lozano, Sebastián & Gutiérrez, Ester, 2008. "Data envelopment analysis of mutual funds based on second-order stochastic dominance," European Journal of Operational Research, Elsevier, vol. 189(1), pages 230-244, August.
- Thierry Post, 2003. "Empirical Tests for Stochastic Dominance Efficiency," Journal of Finance, American Finance Association, vol. 58(5), pages 1905-1932, October.
- Meyer, Jack, 1977. "Second Degree Stochastic Dominance with Respect to a Function," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 18(2), pages 477-87, June.
- Haim Shalit & Shlomo Yitzhaki, 1994. "Marginal Conditional Stochastic Dominance," Management Science, INFORMS, vol. 40(5), pages 670-684, May.
- Post, Thierry, 2008. "On the dual test for SSD efficiency: With an application to momentum investment strategies," European Journal of Operational Research, Elsevier, vol. 185(3), pages 1564-1573, March.
- Ray D. Nelson & Rulon D. Pope, 1991. "Bootstrapped Insights into Empirical Applications of Stochastic Dominance," Management Science, INFORMS, vol. 37(9), pages 1182-1194, September.
- Fishburn, Peter C., 1974. "Convex stochastic dominance with continuous distribution functions," Journal of Economic Theory, Elsevier, vol. 7(2), pages 143-158, February.
- Hadar, Josef & Seo, Tae Kun, 1988. "Asset Proportions in Optimal Portfolios," Review of Economic Studies, Wiley Blackwell, vol. 55(3), pages 459-68, July.
- Moshe Leshno & Haim Levy, 2002. "Preferred by "All" and Preferred by "Most" Decision Makers: Almost Stochastic Dominance," Management Science, INFORMS, vol. 48(8), pages 1074-1085, August.
- Mehra, Rajnish & Prescott, Edward C., 1985.
"The equity premium: A puzzle,"
Journal of Monetary Economics,
Elsevier, vol. 15(2), pages 145-161, March.
- Bawa, Vijay S, et al, 1985. " On Determination of Stochastic Dominance Optimal Sets," Journal of Finance, American Finance Association, vol. 40(2), pages 417-31, June.
- Pavlo R. Blavatskyy, 2010. "Modifying the Mean-Variance Approach to Avoid Violations of Stochastic Dominance," Management Science, INFORMS, vol. 56(11), pages 2050-2057, November.
- Donald Meyer & Jack Meyer, 2005. "Relative Risk Aversion: What Do We Know?," Journal of Risk and Uncertainty, Springer, vol. 31(3), pages 243-262, December.
- Guo, Xu & Post, Thierry & Wong, Wing-Keung & Zhu, Lixing, 2013. "Moment Conditions for Almost Stochastic Dominance," MPRA Paper 51725, University Library of Munich, Germany.
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