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Third Degree Stochastic Dominance and Mean-Risk Analysis

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  • 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)

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    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.

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    File URL: http://dx.doi.org/10.1287/mnsc.46.2.289.11928
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    Bibliographic Info

    Article provided by INFORMS in its journal Management Science.

    Volume (Year): 46 (2000)
    Issue (Month): 2 (February)
    Pages: 289-301

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    Handle: RePEc:inm:ormnsc:v:46:y:2000:i:2:p:289-301

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    Keywords: mean-risk analysis; second and third degree stochastic dominance; lower partial risk; lower semi-skewness; absolute deviation; mean-variance-skewness model;

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    Cited by:
    1. Wing-Keung Wong & Raymond H. Chan, 2005. "Prospect and Markowitz Stochastic Dominance," Departmental Working Papers wp0505, National University of Singapore, Department of Economics.
    2. 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.
    3. Walter Briec & Kristiaan Kerstens, 2009. "Portfolio Selection in Multidimensional General and Partial Moment Space," Working Papers 2009-ECO-08, IESEG School of Management.
    4. Gonzalo, J. & Olmo, J., 2008. "Testing Downside Risk Efficiency Under Market Distress," Working Papers 08/11, Department of Economics, City University London.
    5. Branda, Martin, 2013. "Diversification-consistent data envelopment analysis with general deviation measures," European Journal of Operational Research, Elsevier, vol. 226(3), pages 626-635.
    6. Clasen, Christian & Griess, Verena C. & Knoke, Thomas, 2011. "Financial consequences of losing admixed tree species: A new approach to value increased financial risks by ungulate browsing," Forest Policy and Economics, Elsevier, vol. 13(6), pages 503-511, July.
    7. 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.

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