IDEAS home Printed from https://ideas.repec.org/a/inm/ormnsc/v46y2000i2p289-301.html
   My bibliography  Save this article

Third Degree Stochastic Dominance and Mean-Risk Analysis

Author

Listed:
  • Jun-ya Gotoh

    () (Department of Industrial Engineering and Management, Tokyo Institute of Technology, Tokyo, Japan)

  • Hiroshi Konno

    () (Department of Industrial Engineering and Management, and Center for Research in Advanced Financial Technologies, Tokyo Institute of Technology, Tokyo, Japan)

Abstract

In their recent article, Ogryczak and Ruszczy\'nski (1999) proved that those portfolios associated with the efficient frontiers generated by mean-lower semi-standard deviation model and mean- (lower semi-)absolute deviation model are efficient in the sense of second degree stochastic dominance. This rather surprising result reveals the importance of lower partial risk models in portfolio analysis. In this paper, we extend the results of Ogryczak and Ruszczy\'nski for second degree stochastic dominance to third degree stochastic dominance. We show that portfolios on a significant portion of the efficient frontier generated by mean-lower semi-skewness model are efficient in the sense of third degree stochastic dominance. Also, we prove that the portfolios generated by mean-variance-skewness model are semi-efficient in the sense of third degree stochastic dominance.

Suggested Citation

  • Jun-ya Gotoh & Hiroshi Konno, 2000. "Third Degree Stochastic Dominance and Mean-Risk Analysis," Management Science, INFORMS, vol. 46(2), pages 289-301, February.
  • Handle: RePEc:inm:ormnsc:v:46:y:2000:i:2:p:289-301
    DOI: 10.1287/mnsc.46.2.289.11928
    as

    Download full text from publisher

    File URL: http://dx.doi.org/10.1287/mnsc.46.2.289.11928
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Fishburn, Peter C, 1977. "Mean-Risk Analysis with Risk Associated with Below-Target Returns," American Economic Review, American Economic Association, vol. 67(2), pages 116-126, March.
    2. John C. Cox & Jonathan E. Ingersoll Jr. & Stephen A. Ross, 2005. "A Theory Of The Term Structure Of Interest Rates," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 5, pages 129-164, World Scientific Publishing Co. Pte. Ltd..
    3. G. Hanoch & H. Levy, 1969. "The Efficiency Analysis of Choices Involving Risk," Review of Economic Studies, Oxford University Press, vol. 36(3), pages 335-346.
    4. Vijay S. Bawa, 1982. "Research Bibliography---Stochastic Dominance: A Research Bibliography," Management Science, INFORMS, vol. 28(6), pages 698-712, June.
    5. Ogryczak, Wlodzimierz & Ruszczynski, Andrzej, 1999. "From stochastic dominance to mean-risk models: Semideviations as risk measures," European Journal of Operational Research, Elsevier, vol. 116(1), pages 33-50, July.
    6. Yitzhaki, Shlomo, 1982. "Stochastic Dominance, Mean Variance, and Gini's Mean Difference," American Economic Review, American Economic Association, vol. 72(1), pages 178-185, March.
    7. Harry Markowitz, 1952. "Portfolio Selection," Journal of Finance, American Finance Association, vol. 7(1), pages 77-91, March.
    8. Hiroshi Konno & Hiroaki Yamazaki, 1991. "Mean-Absolute Deviation Portfolio Optimization Model and Its Applications to Tokyo Stock Market," Management Science, INFORMS, vol. 37(5), pages 519-531, May.
    9. Haim Levy, 1992. "Stochastic Dominance and Expected Utility: Survey and Analysis," Management Science, INFORMS, vol. 38(4), pages 555-593, April.
    10. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
    11. Porter, R Burr, 1974. "Semivariance and Stochastic Dominance: A Comparison," American Economic Review, American Economic Association, vol. 64(1), pages 200-204, March.
    12. Hull, John C & White, Alan D, 1987. "The Pricing of Options on Assets with Stochastic Volatilities," Journal of Finance, American Finance Association, vol. 42(2), pages 281-300, June.
    Full references (including those not matched with items on IDEAS)

    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. Ogryczak, Wlodzimierz & Ruszczynski, Andrzej, 1999. "From stochastic dominance to mean-risk models: Semideviations as risk measures," European Journal of Operational Research, Elsevier, vol. 116(1), pages 33-50, July.
    2. Schuhmacher, Frank & Auer, Benjamin R., 2014. "Sufficient conditions under which SSD- and MR-efficient sets are identical," European Journal of Operational Research, Elsevier, vol. 239(3), pages 756-763.
    3. Mansini, Renata & Ogryczak, Wlodzimierz & Speranza, M. Grazia, 2014. "Twenty years of linear programming based portfolio optimization," European Journal of Operational Research, Elsevier, vol. 234(2), pages 518-535.
    4. Wojtek Michalowski & Włodzimierz Ogryczak, 2001. "Extending the MAD portfolio optimization model to incorporate downside risk aversion," Naval Research Logistics (NRL), John Wiley & Sons, vol. 48(3), pages 185-200, April.
    5. Nowak, Maciej, 2004. "Preference and veto thresholds in multicriteria analysis based on stochastic dominance," European Journal of Operational Research, Elsevier, vol. 158(2), pages 339-350, October.
    6. Thierry Chauveau & Sylvain Friederich & Jérôme Héricourt & Emmanuel Jurczenko & Catherine Lubochinsky & Bertrand Maillet & Christophe Moussu & Bogdan Négréa & Hélène Raymond-Feingold, 2004. "La volatilité des marchés augmente-t-elle ?," Revue d'Économie Financière, Programme National Persée, vol. 74(1), pages 17-44.
    7. Levy, Moshe, 2009. "Almost Stochastic Dominance and stocks for the long run," European Journal of Operational Research, Elsevier, vol. 194(1), pages 250-257, April.
    8. Heller, Yuval & Schreiber, Amnon, 0. "Short-term investments and indices of risk," Theoretical Economics, Econometric Society.
    9. Branda, Martin, 2013. "Diversification-consistent data envelopment analysis with general deviation measures," European Journal of Operational Research, Elsevier, vol. 226(3), pages 626-635.
    10. Lim, Terence & Lo, Andrew W. & Merton, Robert C. & Scholes, Myron S., 2006. "The Derivatives Sourcebook," Foundations and Trends(R) in Finance, now publishers, vol. 1(5–6), pages 365-572, April.
    11. Schmid Friedrich & Trede Mark, 2000. "Stochastic Dominance in German Asset Returns: Empirical Evidence from the 1990s / Stochastische Dominanz von Renditen deutscher Aktien: Eine empirische Untersuchung für die 90er Jahre," Journal of Economics and Statistics (Jahrbuecher fuer Nationaloekonomie und Statistik), De Gruyter, vol. 220(3), pages 315-326, June.
    12. Alessandra Carleo & Francesco Cesarone & Andrea Gheno & Jacopo Maria Ricci, 2017. "Approximating exact expected utility via portfolio efficient frontiers," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 40(1), pages 115-143, November.
    13. Janne Gustafsson & Ahti Salo, 2005. "Contingent Portfolio Programming for the Management of Risky Projects," Operations Research, INFORMS, vol. 53(6), pages 946-956, December.
    14. 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.
    15. Amita Sharma & Sebastian Utz & Aparna Mehra, 2017. "Omega-CVaR portfolio optimization and its worst case analysis," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 39(2), pages 505-539, March.
    16. Andrey Lizyayev, 2010. "Stochastic Dominance Efficiency Analysis of Diversified Portfolios: Classification, Comparison and Refinements," Tinbergen Institute Discussion Papers 10-084/2, Tinbergen Institute.
    17. Dentcheva, Darinka & Ruszczynski, Andrzej, 2006. "Portfolio optimization with stochastic dominance constraints," Journal of Banking & Finance, Elsevier, vol. 30(2), pages 433-451, February.
    18. Sergio Ortobelli Lozza, 2001. "The classification of parametric choices under uncertainty: analysis of the portfolio choice problem," Theory and Decision, Springer, vol. 51(2), pages 297-328, December.
    19. Kaplanski, Guy & Kroll, Yoram, 2002. "VaR Risk Measures versus Traditional Risk Measures: an Analysis and Survey," MPRA Paper 80070, University Library of Munich, Germany.
    20. Amita Sharma & Aparna Mehra, 2017. "Financial analysis based sectoral portfolio optimization under second order stochastic dominance," Annals of Operations Research, Springer, vol. 256(1), pages 171-197, September.

    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:inm:ormnsc:v:46:y:2000:i:2:p:289-301. 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: (Matthew Walls). General contact details of provider: https://edirc.repec.org/data/inforea.html .

    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.