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Robustness of optimal portfolios under risk and stochastic dominance constraints

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  • Dupačová, Jitka
  • Kopa, Miloš

Abstract

Solutions of portfolio optimization problems are often influenced by a model misspecification or by errors due to approximation, estimation and incomplete information. The obtained results, recommendations for the risk and portfolio manager, should be then carefully analyzed. We shall deal with output analysis and stress testing with respect to uncertainty or perturbations of input data for static risk constrained portfolio optimization problems by means of the contamination technique. Dependence of the set of feasible solutions on the probability distribution rules out the straightforward construction of convexity-based global contamination bounds. Results obtained in our paper [Dupačová, J., & Kopa, M. (2012). Robustness in stochastic programs with risk constraints. Annals of Operations Research, 200, 55–74.] were derived for the risk and second order stochastic dominance constraints under suitable smoothness and/or convexity assumptions that are fulfilled, e.g. for the Markowitz mean–variance model. In this paper we relax these assumptions having in mind the first order stochastic dominance and probabilistic risk constraints. Local bounds for problems of a special structure are obtained. Under suitable conditions on the structure of the problem and for discrete distributions we shall exploit the contamination technique to derive a new robust first order stochastic dominance portfolio efficiency test.

Suggested Citation

  • 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.
  • Handle: RePEc:eee:ejores:v:234:y:2014:i:2:p:434-441
    DOI: 10.1016/j.ejor.2013.06.018
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    References listed on IDEAS

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    1. Jitka Dupacova & Jan PolIvka, 2007. "Stress testing for VaR and CVaR," Quantitative Finance, Taylor & Francis Journals, vol. 7(4), pages 411-421.
    2. Lizyayev, Andrey & Ruszczyński, Andrzej, 2012. "Tractable Almost Stochastic Dominance," European Journal of Operational Research, Elsevier, vol. 218(2), pages 448-455.
    3. Harry Markowitz, 1952. "Portfolio Selection," Journal of Finance, American Finance Association, vol. 7(1), pages 77-91, March.
    4. 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(05), pages 1103-1124, October.
    5. Stoyan Stoyanov & Svetlozar Rachev & Frank Fabozzi, 2013. "Sensitivity of portfolio VaR and CVaR to portfolio return characteristics," Annals of Operations Research, Springer, vol. 205(1), pages 169-187, May.
    6. 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.
    7. Timo Kuosmanen, 2004. "Efficient Diversification According to Stochastic Dominance Criteria," Management Science, INFORMS, vol. 50(10), pages 1390-1406, October.
    8. Philippe Artzner & Freddy Delbaen & Jean-Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228.
    9. Georg Pflug & David Wozabal, 2007. "Ambiguity in portfolio selection," Quantitative Finance, Taylor & Francis Journals, vol. 7(4), pages 435-442.
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    Cited by:

    1. repec:spr:annopr:v:260:y:2018:i:1:d:10.1007_s10479-016-2387-x is not listed on IDEAS
    2. repec:eee:ejores:v:261:y:2017:i:3:p:984-993 is not listed on IDEAS
    3. Balbás, Alejandro & Balbás, Raquel & Balbás, Beatriz, 2016. "Coherent Pricing," INDEM - Working Paper Business Economic Series 22932, Instituto para el Desarrollo Empresarial (INDEM).
    4. Post, Thierry, 2016. "Standard Stochastic Dominance," European Journal of Operational Research, Elsevier, vol. 248(3), pages 1009-1020.
    5. Branda, Martin, 2015. "Diversification-consistent data envelopment analysis based on directional-distance measures," Omega, Elsevier, vol. 52(C), pages 65-76.
    6. Escudero, Laureano F. & Garín, María Araceli & Merino, María & Pérez, Gloria, 2016. "On time stochastic dominance induced by mixed integer-linear recourse in multistage stochastic programs," European Journal of Operational Research, Elsevier, vol. 249(1), pages 164-176.
    7. Balbás, Alejandro & Balbás, Raquel & Balbás, Beatriz, 2016. "VaR as the CVaR sensitivity : applications in risk optimization," INDEM - Working Paper Business Economic Series id-16-01, Instituto para el Desarrollo Empresarial (INDEM).
    8. repec:eee:ejores:v:262:y:2017:i:1:p:299-305 is not listed on IDEAS
    9. repec:eee:ecmode:v:64:y:2017:i:c:p:60-71 is not listed on IDEAS
    10. Allen, D.E. & Powell, R.J. & Singh, A.K., 2016. "Take it to the limit: Innovative CVaR applications to extreme credit risk measurement," European Journal of Operational Research, Elsevier, vol. 249(2), pages 465-475.
    11. repec:eee:ejores:v:264:y:2018:i:2:p:675-685 is not listed on IDEAS

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