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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
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    File URL: http://dx.doi.org/10.1287/mnsc.46.2.289.11928
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    References listed on IDEAS

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    Citations

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    Cited by:

    1. W. Wong & R. Chan, 2008. "Prospect and Markowitz stochastic dominance," Annals of Finance, Springer, vol. 4(1), pages 105-129, January.
    2. Knoke, Thomas, 2008. "Mixed forests and finance -- Methodological approaches," Ecological Economics, Elsevier, vol. 65(3), pages 590-601, April.
    3. Albrecht, Peter, 2003. "Risk measures," Papers 03-01, Sonderforschungsbreich 504.
    4. 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.
    5. Gonzalo, Jesús & Olmo, José, 2008. "Testing downside risk efficiency under market distress," UC3M Working papers. Economics we084321, Universidad Carlos III de Madrid. Departamento de Economía.
    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, 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.
    8. 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.
    9. Hildebrandt, Patrick & Knoke, Thomas, 2011. "Investment decisions under uncertainty--A methodological review on forest science studies," Forest Policy and Economics, Elsevier, vol. 13(1), pages 1-15, January.
    10. Branda, Martin, 2013. "Diversification-consistent data envelopment analysis with general deviation measures," European Journal of Operational Research, Elsevier, vol. 226(3), pages 626-635.
    11. 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.
    12. Thierry Post & Milos Kopa, 2015. "Portfolio Choice based on Third-degree Stochastic Dominance, With an Application to Industry Momentum," Koç University-TUSIAD Economic Research Forum Working Papers 1527, Koc University-TUSIAD Economic Research Forum.
    13. repec:eee:ecoser:v:16:y:2015:i:c:p:1-12 is not listed on IDEAS
    14. 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.
    15. 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.
    16. Briec, Walter & Kerstens, Kristiaan, 2010. "Portfolio selection in multidimensional general and partial moment space," Journal of Economic Dynamics and Control, Elsevier, vol. 34(4), pages 636-656, April.
    17. Clark, Ephraim & Kassimatis, Konstantinos, 2014. "Exploiting stochastic dominance to generate abnormal stock returns," Journal of Financial Markets, Elsevier, vol. 20(C), pages 20-38.
    18. Bruni, Renato & Cesarone, Francesco & Scozzari, Andrea & Tardella, Fabio, 2017. "On exact and approximate stochastic dominance strategies for portfolio selection," European Journal of Operational Research, Elsevier, vol. 259(1), pages 322-329.
    19. 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.
    20. Martin Branda & Miloš Kopa, 2014. "On relations between DEA-risk models and stochastic dominance efficiency tests," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 22(1), pages 13-35, March.

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