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

Author

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

Abstract

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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    Citations

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    1. repec:spr:annopr:v:241:y:2016:i:1:d:10.1007_s10479-013-1422-4 is not listed on IDEAS
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    6. Lotfi, Somayyeh & Zeniosn, Stravros A., 2016. "Equivalence of Robust VaR and CVaR Optimization," Working Papers 16-03, University of Pennsylvania, Wharton School, Weiss Center.
    7. Nonthachote Chatsanga & Andrew J. Parkes, 2017. "Two-Stage Stochastic International Portfolio Optimisation under Regular-Vine-Copula-Based Scenarios," Papers 1704.01174, arXiv.org.
    8. 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.
    9. Michal Kaut & Stein Wallace, 2011. "Shape-based scenario generation using copulas," Computational Management Science, Springer, vol. 8(1), pages 181-199, April.
    10. 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.
    11. 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, arXiv.org, revised Apr 2017.

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