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Stability analysis of portfolio management with conditional value-at-risk


  • Michal Kaut
  • Hercules Vladimirou
  • Stein W. Wallace
  • Stavros A. Zenios


We examine the stability of a portfolio management model based on the conditional value-at-risk (CVaR) measure; the model controls risk exposure of international investment portfolios. We use a moment-matching method to generate discrete distributions (scenario sets) of asset returns and exchange rates so that their statistical properties match corresponding values estimated from historical data. First, we establish that the scenario generation procedure does not bias the results of the optimization program, and we determine the required number of scenarios to attain stable solutions. We then investigate the sensitivity of the CVaR model to mis-specifications in the statistics of stochastic parameters: mean, standard deviation, skewness, kurtosis, as well as correlations. The results are most sensitive to estimation errors in the means of the stochastic parameters (asset returns and currency exchange rates). Mis-specifications in the standard deviation, skewness and correlations of the random parameters also have considerable impact on the solutions. The effect of mis-specifications in the values of kurtosis, although less than that of the other statistics, is still not negligible.

Suggested Citation

  • Michal Kaut & Hercules Vladimirou & Stein W. Wallace & Stavros A. Zenios, 2007. "Stability analysis of portfolio management with conditional value-at-risk," Quantitative Finance, Taylor & Francis Journals, vol. 7(4), pages 397-409.
  • Handle: RePEc:taf:quantf:v:7:y:2007:i:4:p:397-409
    DOI: 10.1080/14697680701483222

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    References listed on IDEAS

    1. Tasche, Dirk, 2002. "Expected shortfall and beyond," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1519-1533, July.
    2. Acerbi, Carlo & Tasche, Dirk, 2002. "On the coherence of expected shortfall," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1487-1503, July.
    3. Topaloglou, Nikolas & Vladimirou, Hercules & Zenios, Stavros A., 2002. "CVaR models with selective hedging for international asset allocation," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1535-1561, July.
    4. Norbert Jobst & Stavros A. Zenios, 2001. "The Tail that Wags the Dog: Integrating Credit Risk in Asset Portfolios," Center for Financial Institutions Working Papers 01-24, Wharton School Center for Financial Institutions, University of Pennsylvania.
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    Cited by:

    1. Topaloglou, Nikolas & Vladimirou, Hercules & Zenios, Stavros A., 2011. "Optimizing international portfolios with options and forwards," Journal of Banking & Finance, Elsevier, vol. 35(12), pages 3188-3201.
    2. Pier Francesco Procacci & Tomaso Aste, 2018. "Forecasting market states," Papers 1807.05836,, revised May 2019.
    3. Lotfi, Somayyeh & Zeniosn, Stravros A., 2016. "Equivalence of Robust VaR and CVaR Optimization," Working Papers 16-03, University of Pennsylvania, Wharton School, Weiss Center.
    4. Michal Kaut & Stein Wallace, 2011. "Shape-based scenario generation using copulas," Computational Management Science, Springer, vol. 8(1), pages 181-199, April.
    5. Staino, Alessandro & Russo, Emilio, 2015. "A moment-matching method to generate arbitrage-free scenarios," European Journal of Operational Research, Elsevier, vol. 246(2), pages 619-630.
    6. Anne Pedersen & Alex Weissensteiner & Rolf Poulsen, 2013. "Financial planning for young households," Annals of Operations Research, Springer, vol. 205(1), pages 55-76, May.
    7. Nader Azad & Georgios Saharidis & Hamid Davoudpour & Hooman Malekly & Seyed Yektamaram, 2013. "Strategies for protecting supply chain networks against facility and transportation disruptions: an improved Benders decomposition approach," Annals of Operations Research, Springer, vol. 210(1), pages 125-163, November.
    8. Shanshan Guo & Lei Zhao & Xiaowei Xu, 2016. "Impact of supply risks on procurement decisions," Annals of Operations Research, Springer, vol. 241(1), pages 411-430, June.
    9. Elçin Çetinkaya & Aurélie Thiele, 2016. "A moment matching approach to log-normal portfolio optimization," Computational Management Science, Springer, vol. 13(4), pages 501-520, October.
    10. Wang, Xin & Fagerholt, Kjetil & Wallace, Stein W., 2018. "Planning for charters: A stochastic maritime fleet composition and deployment problem," Omega, Elsevier, vol. 79(C), pages 54-66.
    11. Fadda, Edoardo & Perboli, Guido & Tadei, Roberto, 2019. "A progressive hedging method for the optimization of social engagement and opportunistic IoT problems," European Journal of Operational Research, Elsevier, vol. 277(2), pages 643-652.
    12. Fodstad, Marte & Midthun, Kjetil T. & Tomasgard, Asgeir, 2015. "Adding flexibility in a natural gas transportation network using interruptible transportation services," European Journal of Operational Research, Elsevier, vol. 243(2), pages 647-657.
    13. Lotfi, Somayyeh & Zenios, Stavros A., 2018. "Robust VaR and CVaR optimization under joint ambiguity in distributions, means, and covariances," European Journal of Operational Research, Elsevier, vol. 269(2), pages 556-576.
    14. Richard Gerlach & Zudi Lu & Hai Huang, 2013. "Exponentially Smoothing the Skewed Laplace Distribution for Value‐at‐Risk Forecasting," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 32(6), pages 534-550, September.
    15. Gambella, Claudio & Maggioni, Francesca & Vigo, Daniele, 2019. "A stochastic programming model for a tactical solid waste management problem," European Journal of Operational Research, Elsevier, vol. 273(2), pages 684-694.
    16. Jörgen Blomvall & Jonas Ekblom, 2018. "Corporate hedging: an answer to the “how” question," Annals of Operations Research, Springer, vol. 266(1), pages 35-69, July.
    17. Nonthachote Chatsanga & Andrew J. Parkes, 2017. "Two-Stage Stochastic International Portfolio Optimisation under Regular-Vine-Copula-Based Scenarios," Papers 1704.01174,
    18. Jamie Fairbrother & Amanda Turner & Stein Wallace, 2015. "Scenario generation for single-period portfolio selection problems with tail risk measures: coping with high dimensions and integer variables," Papers 1511.04935,, revised Apr 2017.
    19. 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.
    20. Schütz, Peter & Westgaard, Sjur, 2018. "Optimal hedging strategies for salmon producers," Journal of Commodity Markets, Elsevier, vol. 12(C), pages 60-70.


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