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Robust optimization of conditional value at risk and portfolio selection

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  • Quaranta, Anna Grazia
  • Zaffaroni, Alberto

Abstract

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.

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Bibliographic Info

Article provided by Elsevier in its journal Journal of Banking & Finance.

Volume (Year): 32 (2008)
Issue (Month): 10 (October)
Pages: 2046-2056

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Handle: RePEc:eee:jbfina:v:32:y:2008:i:10:p:2046-2056

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Web page: http://www.elsevier.com/locate/jbf

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Keywords: Coherent risk measures Conditional value at risk Robust optimization;

References

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  1. Carlo Acerbi & Dirk Tasche, 2001. "Expected Shortfall: a natural coherent alternative to Value at Risk," Papers cond-mat/0105191, arXiv.org.
  2. 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.).
  3. Philippe Artzner & Freddy Delbaen & Jean-Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228.
  4. 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.
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Cited by:
  1. Selim Mankaï, 2014. "Data-Driven Robust Optimization with Application to Portfolio Management," Working Papers 2014-104, Department of Research, Ipag Business School.
  2. Jing Li & Mingxin Xu, 2013. "Optimal Dynamic Portfolio with Mean-CVaR Criterion," Risks, MDPI, Open Access Journal, vol. 1(3), pages 119-147, November.
  3. 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.
  4. 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.
  5. Selim Mankaï & Khaled Guesmi, 2014. "Robust Portfolio Protection: A Scenarios-Based Approach," Working Papers 2014-394, Department of Research, Ipag Business School.
  6. Ghahtarani, Alireza & Najafi, Amir Abbas, 2013. "Robust goal programming for multi-objective portfolio selection problem," Economic Modelling, Elsevier, vol. 33(C), pages 588-592.
  7. 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.
  8. You, Leyuan & Daigler, Robert T., 2010. "Is international diversification really beneficial?," Journal of Banking & Finance, Elsevier, vol. 34(1), pages 163-173, January.
  9. 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.
  10. 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.

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