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Robust portfolio optimization with copulas

Author

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  • Kakouris, Iakovos
  • Rustem, Berç

Abstract

Conditional Value at Risk (CVaR) is widely used in portfolio optimization as a measure of risk. CVaR is clearly dependent on the underlying probability distribution of the portfolio. We show how copulas can be introduced to any problem that involves distributions and how they can provide solutions for the modeling of the portfolio. We use this to provide the copula formulation of the CVaR of a portfolio. Given the critical dependence of CVaR on the underlying distribution, we use a robust framework to extend our approach to Worst Case CVaR (WCVaR). WCVaR is achieved through the use of rival copulas. These rival copulas have the advantage of exploiting a variety of dependence structures, symmetric and not. We compare our model against two other models, Gaussian CVaR and Worst Case Markowitz. Our empirical analysis shows that WCVaR can asses the risk more adequately than the two competitive models during periods of crisis.

Suggested Citation

  • Kakouris, Iakovos & Rustem, Berç, 2014. "Robust portfolio optimization with copulas," European Journal of Operational Research, Elsevier, vol. 235(1), pages 28-37.
  • Handle: RePEc:eee:ejores:v:235:y:2014:i:1:p:28-37
    DOI: 10.1016/j.ejor.2013.12.022
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    References listed on IDEAS

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    1. Rustem, Berc & Becker, Robin G. & Marty, Wolfgang, 2000. "Robust min-max portfolio strategies for rival forecast and risk scenarios," Journal of Economic Dynamics and Control, Elsevier, vol. 24(11-12), pages 1591-1621, October.
    2. Chan, Joshua C.C. & Kroese, Dirk P., 2010. "Efficient estimation of large portfolio loss probabilities in t-copula models," European Journal of Operational Research, Elsevier, vol. 205(2), pages 361-367, September.
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    7. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
    8. Ling Hu, 2006. "Dependence patterns across financial markets: a mixed copula approach," Applied Financial Economics, Taylor & Francis Journals, vol. 16(10), pages 717-729.
    9. 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. repec:eee:ejores:v:267:y:2018:i:2:p:765-777 is not listed on IDEAS
    2. repec:eee:ejores:v:277:y:2019:i:3:p:1046-1059 is not listed on IDEAS
    3. repec:eee:ejores:v:262:y:2017:i:2:p:720-732 is not listed on IDEAS
    4. Reboredo, Juan C. & Tiwari, Aviral Kumar & Albulescu, Claudiu Tiberiu, 2015. "An analysis of dependence between Central and Eastern European stock markets," Economic Systems, Elsevier, vol. 39(3), pages 474-490.
    5. Banciu, M. & Ødegaard, F., 2016. "Optimal product bundling with dependent valuations: The price of independence," European Journal of Operational Research, Elsevier, vol. 255(2), pages 481-495.
    6. Bekiros, Stelios & Hernandez, Jose Arreola & Hammoudeh, Shawkat & Nguyen, Duc Khuong, 2015. "Multivariate dependence risk and portfolio optimization: An application to mining stock portfolios," Resources Policy, Elsevier, vol. 46(P2), pages 1-11.
    7. repec:bap:journl:170303 is not listed on IDEAS
    8. Hayette Gatfaoui, 2018. "Diversifying portfolios of U.S. stocks with crude oil and natural gas: A regime-dependent optimization with several risk measures," Papers 1811.02382, arXiv.org.
    9. Atskanov, Isuf, 2015. "Dynamic optimization of an investment portfolio on European stock markets using pair copulas," Applied Econometrics, Publishing House "SINERGIA PRESS", vol. 40(4), pages 84-105.
    10. repec:eee:quaeco:v:69:y:2018:i:c:p:56-69 is not listed on IDEAS
    11. Fernandes, Betina & Street, Alexandre & Valladão, Davi & Fernandes, Cristiano, 2016. "An adaptive robust portfolio optimization model with loss constraints based on data-driven polyhedral uncertainty sets," European Journal of Operational Research, Elsevier, vol. 255(3), pages 961-970.
    12. repec:eee:finlet:v:21:y:2017:i:c:p:190-200 is not listed on IDEAS

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