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Robust optimization of conditional value at risk and portfolio selection


  • Quaranta, Anna Grazia
  • Zaffaroni, Alberto


This paper deals with a portfolio selection model in which the methodologies of robust optimization are used for the minimization of the conditional value at risk of a portfolio of shares. Conditional value at risk, being in essence the mean shortfall at a specified confidence level, is a coherent risk measure which can hold account of the so called "tail risk" and is therefore an efficient and synthetic risk measure, which can overcome the drawbacks of the most famous and largely used VaR. An important feature of our approach consists in the use of techniques of robust optimization to deal with uncertainty, in place of stochastic programming as proposed by Rockafellar and Uryasev. Moreover we succeeded in obtaining a linear robust copy of the bi-criteria minimization model proposed by Rockafellar and Uryasev. We suggest different approaches for the generation of input data, with special attention to the estimation of expected returns. The relevance of our methodology is illustrated by a portfolio selection experiment on the Italian market.

Suggested Citation

  • Quaranta, Anna Grazia & Zaffaroni, Alberto, 2008. "Robust optimization of conditional value at risk and portfolio selection," Journal of Banking & Finance, Elsevier, vol. 32(10), pages 2046-2056, October.
  • Handle: RePEc:eee:jbfina:v:32:y:2008:i:10:p:2046-2056

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    References listed on IDEAS

    1. Philippe Artzner & Freddy Delbaen & Jean-Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228.
    2. Carlo Acerbi & Dirk Tasche, 2001. "Expected Shortfall: a natural coherent alternative to Value at Risk," Papers cond-mat/0105191,
    3. 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.
    4. Kondor, Imre & Pafka, Szilard & Nagy, Gabor, 2007. "Noise sensitivity of portfolio selection under various risk measures," Journal of Banking & Finance, Elsevier, vol. 31(5), pages 1545-1573, May.
    5. Matthew Pritsker, 2001. "The hidden dangers of historical simulation," Finance and Economics Discussion Series 2001-27, Board of Governors of the Federal Reserve System (U.S.).
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    Cited by:

    1. Lotfi, Somayyeh & Zeniosn, Stravros A., 2016. "Equivalence of Robust VaR and CVaR Optimization," Working Papers 16-03, University of Pennsylvania, Wharton School, Weiss Center.
    2. Balbás, Alejandro & Balbás, Beatriz & Balbás, Raquel, 2010. "CAPM and APT-like models with risk measures," Journal of Banking & Finance, Elsevier, vol. 34(6), pages 1166-1174, June.
    3. Selim Mankaï & Khaled Guesmi, 2015. "Robust Portfolio Protection: A Scenarios-based Approach," Bankers, Markets & Investors, ESKA Publishing, issue 138, pages 30-44, September.
    4. Jing Li & Mingxin Xu, 2013. "Optimal Dynamic Portfolio with Mean-CVaR Criterion," Risks, MDPI, Open Access Journal, vol. 1(3), pages 1-29, November.
    5. repec:spr:annopr:v:247:y:2016:i:2:d:10.1007_s10479-015-1909-2 is not listed on IDEAS
    6. repec:spr:annopr:v:237:y:2016:i:1:d:10.1007_s10479-015-1822-8 is not listed on IDEAS
    7. repec:ipg:wpaper:2014-394 is not listed on IDEAS
    8. repec:eee:asieco:v:52:y:2017:i:c:p:32-44 is not listed on IDEAS
    9. Ferstl, Robert & Weissensteiner, Alex, 2011. "Asset-liability management under time-varying investment opportunities," Journal of Banking & Finance, Elsevier, vol. 35(1), pages 182-192, January.
    10. Boubaker, Heni & Sghaier, Nadia, 2013. "Portfolio optimization in the presence of dependent financial returns with long memory: A copula based approach," Journal of Banking & Finance, Elsevier, vol. 37(2), pages 361-377.
    11. David McInerney & Robert Lempert & Klaus Keller, 2012. "What are robust strategies in the face of uncertain climate threshold responses?," Climatic Change, Springer, vol. 112(3), pages 547-568, June.
    12. Cerqueti, Roy & Quaranta, Anna Grazia & Ventura, Marco, 2016. "Innovation, imitation and policy inaction," Technological Forecasting and Social Change, Elsevier, vol. 111(C), pages 22-30.
    13. Ansaripoor, Amir H. & Oliveira, Fernando S. & Liret, Anne, 2014. "A risk management system for sustainable fleet replacement," European Journal of Operational Research, Elsevier, vol. 237(2), pages 701-712.
    14. Víctor Adame-García & Fernando Fernández-Rodríguez & Simón Sosvilla-Rivero, 2017. "“Resolution of optimization problems and construction of efficient portfolios: An application to the Euro Stoxx 50 index"," IREA Working Papers 201702, University of Barcelona, Research Institute of Applied Economics, revised Feb 2017.
    15. Xu, Qifa & Zhou, Yingying & Jiang, Cuixia & Yu, Keming & Niu, Xufeng, 2016. "A large CVaR-based portfolio selection model with weight constraints," Economic Modelling, Elsevier, vol. 59(C), pages 436-447.
    16. Chan, Timothy C.Y. & Mahmoudzadeh, Houra & Purdie, Thomas G., 2014. "A robust-CVaR optimization approach with application to breast cancer therapy," European Journal of Operational Research, Elsevier, vol. 238(3), pages 876-885.
    17. You, Leyuan & Daigler, Robert T., 2010. "Is international diversification really beneficial?," Journal of Banking & Finance, Elsevier, vol. 34(1), pages 163-173, January.
    18. Pflug, Georg Ch. & Pichler, Alois & Wozabal, David, 2012. "The 1/N investment strategy is optimal under high model ambiguity," Journal of Banking & Finance, Elsevier, vol. 36(2), pages 410-417.
    19. Ghahtarani, Alireza & Najafi, Amir Abbas, 2013. "Robust goal programming for multi-objective portfolio selection problem," Economic Modelling, Elsevier, vol. 33(C), pages 588-592.
    20. repec:eee:eneeco:v:70:y:2018:i:c:p:516-524 is not listed on IDEAS
    21. Wang, Ching-Ping & Huang, Hung-Hsi, 2016. "Optimal insurance contract under VaR and CVaR constraints," The North American Journal of Economics and Finance, Elsevier, vol. 37(C), pages 110-127.
    22. Víctor M. Adame-García & Fernando Fernández-Rodríguez & Simón Sosvilla-Rivero, "undated". "Portfolios in the Ibex 35 index: Alternative methods to the traditional framework, a comparative with the naive diversification in a pre- and post- crisis context," Documentos de Trabajo del ICAE 2015-07, Universidad Complutense de Madrid, Facultad de Ciencias Económicas y Empresariales, Instituto Complutense de Análisis Económico, revised Jun 2015.
    23. repec:spr:annopr:v:249:y:2017:i:1:d:10.1007_s10479-016-2279-0 is not listed on IDEAS
    24. Selim Mankaï, 2014. "Data-Driven Robust Optimization with Application to Portfolio Management," Working Papers 2014-104, Department of Research, Ipag Business School.
    25. Chen, Zhiping & Wang, Yi, 2008. "Two-sided coherent risk measures and their application in realistic portfolio optimization," Journal of Banking & Finance, Elsevier, vol. 32(12), pages 2667-2673, December.


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