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A Portfolio Optimality Test Based on the First-Order Stochastic Dominance Criterion

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  • Kopa, Miloš
  • Post, Thierry

Abstract

Existing approaches to testing for the efficiency of a given portfolio make strong parametric assumptions about investor preferences and return distributions. Stochastic dominance-based procedures promise a useful nonparametric alternative. However, these procedures have been limited to considering binary choices. In this paper we take a new approach that considers all diversified portfolios and thereby introduce a new concept of first-order stochastic dominance (FSD) optimality of a given portfolio relative to all possible portfolios. Using our new test, we show that the U.S. stock market portfolio is significantly FSD nonoptimal relative to benchmark portfolios formed on market capitalization and book-to-market equity ratios. Without appealing to parametric assumptions about the return distribution, we conclude that no nonsatiable investor would hold the market portfolio in the face of the attractive premia of small caps and value stocks.

Suggested Citation

  • Kopa, Miloš & Post, Thierry, 2009. "A Portfolio Optimality Test Based on the First-Order Stochastic Dominance Criterion," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 44(5), pages 1103-1124, October.
    • Handle: RePEc:cup:jfinqa:v:44:y:2009:i:05:p:1103-1124_99
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    Cited by:

    1. Levy, Moshe, 2022. "An inter-temporal CAPM based on First order Stochastic Dominance," European Journal of Operational Research, Elsevier, vol. 298(2), pages 734-739.
    2. Fang, Yi & Niu, Hui & Lin, Yuen, 2023. "Ex-ante Valuation based on Prospect Theory," MPRA Paper 116386, University Library of Munich, Germany.
    3. Andrey Lizyayev, 2012. "Stochastic dominance efficiency analysis of diversified portfolios: classification, comparison and refinements," Annals of Operations Research, Springer, vol. 196(1), pages 391-410, July.
    4. Jesus Gonzalo & Jose Olmo, 2014. "Conditional Stochastic Dominance Tests In Dynamic Settings," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 55(3), pages 819-838, August.
    5. Topaloglou, Nikolas & Tsionas, Mike G., 2020. "Stochastic dominance tests," Journal of Economic Dynamics and Control, Elsevier, vol. 112(C).
    6. repec:prg:jnlpep:v:preprint:id:649:p:1-27 is not listed on IDEAS
    7. repec:stn:sotoec:1311 is not listed on IDEAS
    8. Umut Ugurlu & Oktay Tas & Celal Barkan Guran & Aysun Guran, 2018. "SSD Efficiency at Multiple Data Frequencies: Application on the OECD Countries," Prague Economic Papers, Prague University of Economics and Business, vol. 2018(2), pages 169-195.
    9. Fang, Yi & Post, Thierry, 2017. "Higher-degree stochastic dominance optimality and efficiency," European Journal of Operational Research, Elsevier, vol. 261(3), pages 984-993.
    10. Thierry Post & Miloš Kopa, 2017. "Portfolio Choice Based on Third-Degree Stochastic Dominance," Management Science, INFORMS, vol. 63(10), pages 3381-3392, October.
    11. Chen, Andrew N.K. & Wang, Shin-Yun & Yu, Po-Lung, 2014. "Evaluating multi-criteria ratings of financial investment options," International Review of Economics & Finance, Elsevier, vol. 31(C), pages 46-58.
    12. Anderson, Ronald C. & Reeb, David M. & Zhang, Yuzhao & Zhao, Wanli, 2013. "The efficacy of regulatory intervention: Evidence from the distribution of informed option trading," Journal of Banking & Finance, Elsevier, vol. 37(11), pages 4337-4352.
    13. Post, Thierry & Kopa, Miloš, 2013. "General linear formulations of stochastic dominance criteria," European Journal of Operational Research, Elsevier, vol. 230(2), pages 321-332.
    14. Kolokolova, Olga & Le Courtois, Olivier & Xu, Xia, 2022. "Is the index efficient? A worldwide tour with stochastic dominance," Journal of Financial Markets, Elsevier, vol. 59(PB).
    15. Dupačová, Jitka & Kopa, Miloš, 2014. "Robustness of optimal portfolios under risk and stochastic dominance constraints," European Journal of Operational Research, Elsevier, vol. 234(2), pages 434-441.

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