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On the Third Order Stochastic Dominance for Risk-Averse and Risk-Seeking Investors

  • Chan, Raymond H.
  • Clark, Ephraim
  • Wong, Wing-Keung

This paper studies some properties of stochastic dominance (SD) for risk-averse and risk-seeking investors, especially for the third order SD (TSD). We call the former ascending stochastic dominance (ASD) and the latter descending stochastic dominance(DSD). We first discuss the basic property of ASD and DSD linking the ASD and DSD of the first three orders to expected-utility maximization for risk-averse and risk-seeking investors. Thereafter, we prove that a hierarchy exists in both ASD and DSD relationships and that the higher orders of ASD and DSD cannot be replaced by the lower orders of ASD and DSD. Furthermore, we study conditions in which third order ASD preferences will be 'the opposite of' or 'the same as' their counterpart third order DSD preferences. In addition, we construct examples to illustrate all the properties developed in this paper. The theory developed in this paper provides investors with tools to identify first, second, and third order ASD and DSD prospects and thus they could make wiser choices on their investment decision.

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Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 42676.

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Date of creation: 16 Nov 2012
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Handle: RePEc:pra:mprapa:42676
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  1. Dominic Gasbarro & Wing-Keung Wong & J. Kenton Zumwalt, 2007. "Stochastic Dominance Analysis of iShares," The European Journal of Finance, Taylor & Francis Journals, vol. 13(1), pages 89-101.
  2. Man-Chung Ng, 2000. "A Remark on Third Degree Stochastic Dominance," Management Science, INFORMS, vol. 46(6), pages 870-873, June.
  3. Wing-Keung Wong, 2007. "Stochastic Dominance and Mean-Variance Measures of Profit and Loss for Business Planning and Investment," Finance Working Papers 21922, East Asian Bureau of Economic Research.
  4. Rothschild, Michael & Stiglitz, Joseph E., 1971. "Increasing risk II: Its economic consequences," Journal of Economic Theory, Elsevier, vol. 3(1), pages 66-84, March.
  5. Hadar, Josef & Russell, William R., 1971. "Stochastic dominance and diversification," Journal of Economic Theory, Elsevier, vol. 3(3), pages 288-305, September.
  6. Thierry Post & Haim Levy, 2005. "Does Risk Seeking Drive Stock Prices? A Stochastic Dominance Analysis of Aggregate Investor Preferences and Beliefs," Review of Financial Studies, Society for Financial Studies, vol. 18(3), pages 925-953.
  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. Fong, Wai Mun & Lean, Hooi Hooi & Wong, Wing Keung, 2008. "Stochastic dominance and behavior towards risk: The market for Internet stocks," Journal of Economic Behavior & Organization, Elsevier, vol. 68(1), pages 194-208, October.
  9. Anderson, Gordon, 2004. "Toward an empirical analysis of polarization," Journal of Econometrics, Elsevier, vol. 122(1), pages 1-26, September.
  10. Fong, Wai Mun & Wong, Wing Keung & Lean, Hooi Hooi, 2005. "International momentum strategies: a stochastic dominance approach," Journal of Financial Markets, Elsevier, vol. 8(1), pages 89-109, February.
  11. Post, Thierry & Versijp, Philippe, 2007. "Multivariate Tests for Stochastic Dominance Efficiency of a Given Portfolio," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 42(02), pages 489-515, June.
  12. Jun-ya Gotoh & Hiroshi Konno, 2000. "Third Degree Stochastic Dominance and Mean-Risk Analysis," Management Science, INFORMS, vol. 46(2), pages 289-301, February.
  13. Moshe Levy & Haim Levy, 2002. "Prospect Theory: Much Ado About Nothing?," Management Science, INFORMS, vol. 48(10), pages 1334-1349, October.
  14. John S. Hammond, III, 1974. "Simplifying the Choice between Uncertain Prospects Where Preference is Nonlinear," Management Science, INFORMS, vol. 20(7), pages 1047-1072, March.
  15. 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.
  16. Menezes, C & Geiss, C & Tressler, J, 1980. "Increasing Downside Risk," American Economic Review, American Economic Association, vol. 70(5), pages 921-32, December.
  17. Michel Le Breton & Eugenio Peluso, 2009. "Third-degree stochastic dominance and inequality measurement," Journal of Economic Inequality, Springer, vol. 7(3), pages 249-268, September.
  18. Wing-Keung Wong & Chenghu Ma, 2005. "Preferences over Meyer’s Location-Scale Family," Departmental Working Papers wp0506, National University of Singapore, Department of Economics.
  19. Vijay S. Bawa & Eric B. Lindenberg & Lawrence C. Rafsky, 1979. "An Efficient Algorithm to Determine Stochastic Dominance Admissible Sets," Management Science, INFORMS, vol. 25(7), pages 609-622, July.
  20. Whitmore, G A, 1970. "Third-Degree Stochastic Dominance," American Economic Review, American Economic Association, vol. 60(3), pages 457-59, June.
  21. Fishburn, Peter C., 1974. "Convex stochastic dominance with continuous distribution functions," Journal of Economic Theory, Elsevier, vol. 7(2), pages 143-158, February.
  22. Thorlund-Petersen, Lars, 2001. "Third-degree stochastic dominance and axioms for a convex marginal utility function," Mathematical Social Sciences, Elsevier, vol. 41(2), pages 167-199, March.
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