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Second-order stochastic dominance constrained portfolio optimization: Theory and computational tests

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  • Kallio, Markku
  • Dehghan Hardoroudi, Nasim

Abstract

Due to the definition of second-order stochastic dominance (SSD) in terms of utility theory, portfolio optimization with SSD constraints is of major practical interest. We contribute to the field in two ways: first, we present a self-contained theory with some new results and new proofs of known results; second, we perform a set of tests for computational efficiency. We provide new and simple arguments for the formulation of SSD constraints in a mathematical programming framework. For many individuals, an SSD constraint may seem too severe wherefore various relaxations (ASSD), have been proposed. We introduce yet another relaxation, directional SSD, where a candidate portfolio is admissible if a step from the benchmark in the direction of the candidate yields a dominating portfolio. Optimal step size depends on individual preferences reflected by the objective function. We compare computational efficiency of seven approaches for SD constrained portfolio problems, including SSD and ASSD constrained cases.

Suggested Citation

  • Kallio, Markku & Dehghan Hardoroudi, Nasim, 2018. "Second-order stochastic dominance constrained portfolio optimization: Theory and computational tests," European Journal of Operational Research, Elsevier, vol. 264(2), pages 675-685.
    • Handle: RePEc:eee:ejores:v:264:y:2018:i:2:p:675-685
    DOI: 10.1016/j.ejor.2017.06.067
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    as
    1. Bawa, Vijay S., 1975. "Optimal rules for ordering uncertain prospects," Journal of Financial Economics, Elsevier, vol. 2(1), pages 95-121, March.
    2. Bawa, Vijay S, et al, 1985. "On Determination of Stochastic Dominance Optimal Sets," Journal of Finance, American Finance Association, vol. 40(2), pages 417-431, June.
    3. Iñaki R. Longarela, 2016. "A Characterization of the SSD-Efficient Frontier of Portfolio Weights by Means of a Set of Mixed-Integer Linear Constraints," Management Science, INFORMS, vol. 62(12), pages 3549-3554, December.
    4. Csaba I. Fábián & Gautam Mitra & Diana Roman & Victor Zverovich & Tibor Vajnai & Edit Csizmás & Olga Papp, 2011. "Portfolio Choice Models Based on Second-Order Stochastic Dominance Measures: An Overview and a Computational Study," International Series in Operations Research & Management Science, in: Marida Bertocchi & Giorgio Consigli & Michael A. H. Dempster (ed.), Stochastic Optimization Methods in Finance and Energy, edition 1, chapter 0, pages 441-469, Springer.
    5. repec:bla:jfinan:v:58:y:2003:i:5:p:1905-1932 is not listed on IDEAS
    6. Haim Levy, 1992. "Stochastic Dominance and Expected Utility: Survey and Analysis," Management Science, INFORMS, vol. 38(4), pages 555-593, April.
    7. 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.
    8. Benjamin Armbruster & Erick Delage, 2015. "Decision Making Under Uncertainty When Preference Information Is Incomplete," Management Science, INFORMS, vol. 61(1), pages 111-128, January.
    9. 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.
    10. Ilia Tsetlin & Robert L. Winkler & Rachel J. Huang & Larry Y. Tzeng, 2015. "Generalized Almost Stochastic Dominance," Operations Research, INFORMS, vol. 63(2), pages 363-377, April.
    11. Scaillet, Olivier & Topaloglou, Nikolas, 2010. "Testing for Stochastic Dominance Efficiency," Journal of Business & Economic Statistics, American Statistical Association, vol. 28(1), pages 169-180.
    12. James P. Quirk & Rubin Saposnik, 1962. "Admissibility and Measurable Utility Functions," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 29(2), pages 140-146.
    13. 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.
    14. Thierry Post, 2003. "Empirical Tests for Stochastic Dominance Efficiency," Journal of Finance, American Finance Association, vol. 58(5), pages 1905-1931, October.
    15. Moshe Leshno & Haim Levy, 2002. "Preferred by "All" and Preferred by "Most" Decision Makers: Almost Stochastic Dominance," Management Science, INFORMS, vol. 48(8), pages 1074-1085, August.
    16. Dentcheva, Darinka & Ruszczynski, Andrzej, 2006. "Portfolio optimization with stochastic dominance constraints," Journal of Banking & Finance, Elsevier, vol. 30(2), pages 433-451, February.
    17. 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.
    18. James E. Hodder & Jens Carsten Jackwerth & Olga Kolokolova, 2015. "Improved Portfolio Choice Using Second-Order Stochastic Dominance," Review of Finance, European Finance Association, vol. 19(4), pages 1623-1647.
    19. Hadar, Josef & Russell, William R, 1969. "Rules for Ordering Uncertain Prospects," American Economic Review, American Economic Association, vol. 59(1), pages 25-34, March.
    20. Lizyayev, Andrey & Ruszczyński, Andrzej, 2012. "Tractable Almost Stochastic Dominance," European Journal of Operational Research, Elsevier, vol. 218(2), pages 448-455.
    21. Post, Thierry, 2008. "On the dual test for SSD efficiency: With an application to momentum investment strategies," European Journal of Operational Research, Elsevier, vol. 185(3), pages 1564-1573, March.
    22. Haim Shalit & Shlomo Yitzhaki, 1994. "Marginal Conditional Stochastic Dominance," Management Science, INFORMS, vol. 40(5), pages 670-684, May.
    23. Timo Kuosmanen, 2001. "Stochastic Dominance Efficiency Tests under Diversification," Finance 0105001, University Library of Munich, Germany.
    24. Rockafellar, R. Tyrrell & Uryasev, Stanislav, 2002. "Conditional value-at-risk for general loss distributions," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1443-1471, July.
    25. Andrzej Ruszczynski & Robert J. Vanderbei, 2003. "Frontiers of Stochastically Nondominated Portfolios," Econometrica, Econometric Society, vol. 71(4), pages 1287-1297, July.
    26. 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.
    27. Timo Kuosmanen, 2004. "Efficient Diversification According to Stochastic Dominance Criteria," Management Science, INFORMS, vol. 50(10), pages 1390-1406, October.
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    2. Sree Vinutha Venkataraman & S. V. D. Nageswara Rao, 2023. "Stochastic dominance algorithms with application to mutual fund performance evaluation," International Journal of Finance & Economics, John Wiley & Sons, Ltd., vol. 28(1), pages 681-698, January.
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    7. Wei-Han Liu & Jow-Ran Chang & Guo-Jun Yang, 2024. "An improved criterion for almost marginal conditional stochastic dominance," Review of Quantitative Finance and Accounting, Springer, vol. 62(3), pages 1251-1290, April.
    8. Liesiö, Juuso & Xu, Peng & Kuosmanen, Timo, 2020. "Portfolio diversification based on stochastic dominance under incomplete probability information," European Journal of Operational Research, Elsevier, vol. 286(2), pages 755-768.

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