IDEAS home Printed from https://ideas.repec.org/p/pra/mprapa/42676.html
   My bibliography  Save this paper

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

Author

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

Abstract

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.

Suggested Citation

  • Chan, Raymond H. & Clark, Ephraim & Wong, Wing-Keung, 2012. "On the Third Order Stochastic Dominance for Risk-Averse and Risk-Seeking Investors," MPRA Paper 42676, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:42676
    as

    Download full text from publisher

    File URL: https://mpra.ub.uni-muenchen.de/42676/1/MPRA_paper_42676.pdf
    File Function: original version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Fishburn, Peter C., 1974. "Convex stochastic dominance with continuous distribution functions," Journal of Economic Theory, Elsevier, vol. 7(2), pages 143-158, February.
    2. Whitmore, G A, 1970. "Third-Degree Stochastic Dominance," American Economic Review, American Economic Association, vol. 60(3), pages 457-459, June.
    3. Davies James & Hoy Michael, 1994. "The Normative Significance of Using Third-Degree Stochastic Dominance in Comparing Income Distributions," Journal of Economic Theory, Elsevier, vol. 64(2), pages 520-530, December.
    4. Hadar, Josef & Russell, William R., 1971. "Stochastic dominance and diversification," Journal of Economic Theory, Elsevier, vol. 3(3), pages 288-305, September.
    5. 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 477-487, June.
    6. 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.
    7. G. Hanoch & H. Levy, 1969. "The Efficiency Analysis of Choices Involving Risk," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 36(3), pages 335-346.
    8. 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.
    9. Thierry Post & Haim Levy, 2005. "Does Risk Seeking Drive Stock Prices? A Stochastic Dominance Analysis of Aggregate Investor Preferences and Beliefs," The Review of Financial Studies, Society for Financial Studies, vol. 18(3), pages 925-953.
    10. Moshe Levy & Haim Levy, 2013. "Prospect Theory: Much Ado About Nothing?," World Scientific Book Chapters, in: Leonard C MacLean & William T Ziemba (ed.), HANDBOOK OF THE FUNDAMENTALS OF FINANCIAL DECISION MAKING Part I, chapter 7, pages 129-144, World Scientific Publishing Co. Pte. Ltd..
    11. Menezes, C & Geiss, C & Tressler, J, 1980. "Increasing Downside Risk," American Economic Review, American Economic Association, vol. 70(5), pages 921-932, December.
    12. 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.
    13. Rudi Zagst & Julia Kraus, 2011. "Stochastic dominance of portfolio insurance strategies," Annals of Operations Research, Springer, vol. 185(1), pages 75-103, May.
    14. Michel Le Breton & Eugenio Peluso, 2009. "Third-degree stochastic dominance and inequality measurement," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 7(3), pages 249-268, September.
    15. Jun-ya Gotoh & Hiroshi Konno, 2000. "Third Degree Stochastic Dominance and Mean-Risk Analysis," Management Science, INFORMS, vol. 46(2), pages 289-301, February.
    16. 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.
    17. 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.
    18. 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(2), pages 489-515, June.
    19. Anderson, Gordon, 2004. "Toward an empirical analysis of polarization," Journal of Econometrics, Elsevier, vol. 122(1), pages 1-26, September.
    20. Rothschild, Michael & Stiglitz, Joseph E., 1970. "Increasing risk: I. A definition," Journal of Economic Theory, Elsevier, vol. 2(3), pages 225-243, September.
    21. 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.
    22. Wong, Wing-Keung, 2007. "Stochastic dominance and mean-variance measures of profit and loss for business planning and investment," European Journal of Operational Research, Elsevier, vol. 182(2), pages 829-843, October.
    23. 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.
    24. Rothschild, Michael & Stiglitz, Joseph E., 1971. "Increasing risk II: Its economic consequences," Journal of Economic Theory, Elsevier, vol. 3(1), pages 66-84, March.
    25. Man-Chung Ng, 2000. "A Remark on Third Degree Stochastic Dominance," Management Science, INFORMS, vol. 46(6), pages 870-873, June.
    26. Leigh Tesfatsion, 1976. "Stochastic Dominance and the Maximization of Expected Utility," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 43(2), pages 301-315.
    27. Wong, Wing-Keung, 2007. "Stochastic dominance and mean-variance measures of profit and loss for business planning and investment," European Journal of Operational Research, Elsevier, vol. 182(2), pages 829-843, October.
    28. 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.
    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. Xu, Guo & Wing-Keung, Wong & Lixing, Zhu, 2013. "Almost Stochastic Dominance for Risk-Averse and Risk-Seeking Investors," MPRA Paper 51744, University Library of Munich, Germany.
    2. Hoang, Thi-Hong-Van & Wong, Wing-Keung & Zhu, Zhenzhen, 2015. "Is gold different for risk-averse and risk-seeking investors? An empirical analysis of the Shanghai Gold Exchange," Economic Modelling, Elsevier, vol. 50(C), pages 200-211.
    3. Chia-Lin Chang & Michael McAleer & Wing-Keung Wong, 2018. "Management Information, Decision Sciences, and Financial Economics: A Connection," Tinbergen Institute Discussion Papers 18-004/III, Tinbergen Institute.
    4. Abdelbari El Khamlichi & Thi Hong Van Hoang & Wing‐keung Wong, 2016. "Is Gold Different for Islamic and Conventional Portfolios? A Sectorial Analysis," Post-Print hal-02964594, HAL.
    5. Qiao, Zhuo & Wong, Wing-Keung & Fung, Joseph K.W., 2013. "Stochastic dominance relationships between stock and stock index futures markets: International evidence," Economic Modelling, Elsevier, vol. 33(C), pages 552-559.
    6. Hoang, Thi-Hong-Van & Lean, Hooi Hooi & Wong, Wing-Keung, 2015. "Is gold good for portfolio diversification? A stochastic dominance analysis of the Paris stock exchange," International Review of Financial Analysis, Elsevier, vol. 42(C), pages 98-108.
    7. Sheung-Chi Chow & Ma. Rebecca Valenzuela & Wing-Keung Wong, 2016. "New Tests for Richness and Poorness:A Stochastic Dominance Analysis of Income Distributions in Hong Kong," Monash Economics Working Papers 25-16, Monash University, Department of Economics.

    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. Chan, Raymond H. & Clark, Ephraim & Wong, Wing-Keung, 2016. "On the Third Order Stochastic Dominance for Risk-Averse and Risk-Seeking Investors with Analysis of their Traditional and Internet Stocks," MPRA Paper 75002, University Library of Munich, Germany.
    2. Raymond H. Chan & Ephraim Clark & Xu Guo & Wing-Keung Wong, 2020. "New development on the third-order stochastic dominance for risk-averse and risk-seeking investors with application in risk management," Risk Management, Palgrave Macmillan, vol. 22(2), pages 108-132, June.
    3. W. Wong & R. Chan, 2008. "Prospect and Markowitz stochastic dominance," Annals of Finance, Springer, vol. 4(1), pages 105-129, January.
    4. Hooi Hooi Lean & Michael McAleer & Wing-Keung Wong, 2010. "Market Efficiency of Oil Spot and Futures: A Stochastic Dominance Approach," CIRJE F-Series CIRJE-F-705, CIRJE, Faculty of Economics, University of Tokyo.
    5. Lean, H.H. & McAleer, M.J. & Wong, W.-K., 2010. "Investor preferences for oil spot and futures based on mean-variance and stochastic dominance," Econometric Institute Research Papers EI 2010-37, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    6. Chia-Lin Chang & Michael McAleer & Wing-Keung Wong, 2018. "Decision Sciences, Economics, Finance, Business, Computing, and Big Data: Connections," Tinbergen Institute Discussion Papers 18-024/III, Tinbergen Institute.
    7. Chia-Lin Chang & Michael McAleer & Wing-Keung Wong, 2018. "Decision Sciences, Economics, Finance, Business, Computing, And Big Data: Connections," Advances in Decision Sciences, Asia University, Taiwan, vol. 22(1), pages 36-94, December.
    8. Chia-Lin Chang & Michael McAleer & Wing-Keung Wong, 2018. "Big Data, Computational Science, Economics, Finance, Marketing, Management, and Psychology: Connections," JRFM, MDPI, vol. 11(1), pages 1-29, March.
    9. Chia-Lin Chang & Michael McAleer & Wing-Keung Wong, 2016. "Management science, economics and finance: A connection," Documentos de Trabajo del ICAE 2016-07, Universidad Complutense de Madrid, Facultad de Ciencias Económicas y Empresariales, Instituto Complutense de Análisis Económico.
    10. Chia-Lin Chang & Michael McAleer & Wing-Keung Wong, 2018. "Big Data, Computational Science, Economics, Finance, Marketing, Management, and Psychology: Connections," Journal of Risk and Financial Management, MDPI, Open Access Journal, vol. 11(1), pages 1-29, March.
    11. Hooi Hooi Lean & Michael McAleer & Wing-Keung Wong, 2013. "Risk-averse and Risk-seeking Investor Preferences for Oil Spot and Futures," Documentos de Trabajo del ICAE 2013-31, Universidad Complutense de Madrid, Facultad de Ciencias Económicas y Empresariales, Instituto Complutense de Análisis Económico, revised Aug 2013.
    12. Zhidong Bai & Hua Li & Michael McAleer & Wing-Keung Wong, 2015. "Stochastic dominance statistics for risk averters and risk seekers: an analysis of stock preferences for USA and China," Quantitative Finance, Taylor & Francis Journals, vol. 15(5), pages 889-900, May.
    13. Kai-Yin Woo & Chulin Mai & Michael McAleer & Wing-Keung Wong, 2020. "Review on Efficiency and Anomalies in Stock Markets," Economies, MDPI, vol. 8(1), pages 1-51, March.
    14. Lean, Hooi Hooi & McAleer, Michael & Wong, Wing-Keung, 2015. "Preferences of risk-averse and risk-seeking investors for oil spot and futures before, during and after the Global Financial Crisis," International Review of Economics & Finance, Elsevier, vol. 40(C), pages 204-216.
    15. Broll, Udo & Wong, Wing-Keung & Wu, Mojia, 2013. "Banking Firm and Two-Moment Decision Making," MPRA Paper 51687, University Library of Munich, Germany.
    16. Ephraim Clark & Zhuo Qiao & Wing-Keung Wong, 2016. "Theories Of Risk: Testing Investor Behavior On The Taiwan Stock And Stock Index Futures Markets," Economic Inquiry, Western Economic Association International, vol. 54(2), pages 907-924, April.
    17. Xu, Guo & Wing-Keung, Wong & Lixing, Zhu, 2013. "Almost Stochastic Dominance for Risk-Averse and Risk-Seeking Investors," MPRA Paper 51744, University Library of Munich, Germany.
    18. Wong, Wing-Keung, 2007. "Stochastic dominance and mean-variance measures of profit and loss for business planning and investment," European Journal of Operational Research, Elsevier, vol. 182(2), pages 829-843, October.
    19. Lam, Kin & Lean, Hooi Hooi & Wong, Wing-Keung, 2016. "Stochastic Dominance and Investors’ Behavior towards Risk: The Hong Kong Stocks and Futures Markets," MPRA Paper 74386, University Library of Munich, Germany.
    20. Egozcue, Martin & Wong, Wing-Keung, 2010. "Gains from diversification on convex combinations: A majorization and stochastic dominance approach," European Journal of Operational Research, Elsevier, vol. 200(3), pages 893-900, February.

    More about this item

    Keywords

    Third order stochastic dominance; ascending stochastic dominance; descending stochastic dominance; expected-utility maximization; risk averters; risk seekers;
    All these keywords.

    JEL classification:

    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics

    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:pra:mprapa:42676. 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: Joachim Winter (email available below). General contact details of provider: https://edirc.repec.org/data/vfmunde.html .

    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.