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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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    References listed on IDEAS

    as
    1. Acerbi, Carlo & Tasche, Dirk, 2002. "On the coherence of expected shortfall," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1487-1503, July.
    2. 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.
    3. 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.
    4. Jarque, Carlos M. & Bera, Anil K., 1980. "Efficient tests for normality, homoscedasticity and serial independence of regression residuals," Economics Letters, Elsevier, vol. 6(3), pages 255-259.
    5. Norbert J. Jobst & Stavros A. Zenios, 2001. "The Tail that Wags the Dog: Integrating Credit Risk in Asset Portfolios," Journal of Risk Finance, Emerald Group Publishing Limited, vol. 3(1), pages 31-43, April.
    6. Tasche, Dirk, 2002. "Expected shortfall and beyond," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1519-1533, July.
    7. 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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