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Portfolio Diversification and Value at Risk Under Thick-Tailedness

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  • Rustam Ibragimov

Abstract

We present a unified approach to value at risk analysis under heavy-tailedness using new majorization theory for linear combinations of thick-tailed random variables that we develop. Among other results, we show that the stylized fact that portfolio diversification is always preferable is reversed for extremely heavy-tailed risks or returns. The stylized facts on diversification are nevertheless robust to thick-tailedness of risks or returns as long as their distributions are not extremely long-tailed. We further demonstrate that the value at risk is a coherent measure of risk if distributions of risks are not extremely heavy-tailed. However, coherency of the value at risk is always violated under extreme thick-tailedness. Extensions of the results to the case of dependence, including convolutions of a-symmetric distributions and models with common stochs are provided.

Suggested Citation

  • Rustam Ibragimov, 2005. "Portfolio Diversification and Value at Risk Under Thick-Tailedness," Harvard Institute of Economic Research Working Papers 2086, Harvard - Institute of Economic Research.
    • Handle: RePEc:fth:harver:2086
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    Cited by:

    1. Rustam Ibragimov & Johan Walden, 2011. "Value at risk and efficiency under dependence and heavy-tailedness: models with common shocks," Annals of Finance, Springer, vol. 7(3), pages 285-318, August.
    2. Ankudinov, Andrei & Ibragimov, Rustam & Lebedev, Oleg, 2017. "Sanctions and the Russian stock market," Research in International Business and Finance, Elsevier, vol. 40(C), pages 150-162.
    3. Ibragimov Marat & Khamidov Rufat, 2010. "Heavy-Tailedness and Volatility in Emerging Foreign Exchange Markets: Theory and Empirics," EERC Working Paper Series 10/06e, EERC Research Network, Russia and CIS.
    4. Alfred Galichon, 2010. "The Var At Risk," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 13(04), pages 503-506.
    5. Xavier Gabaix & Parameswaran Gopikrishnan & Vasiliki Plerou & H. Eugene Stanley, 2006. "Institutional Investors and Stock Market Volatility," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 121(2), pages 461-504.
    6. Ibragimov, Rustam & Jaffee, Dwight & Walden, Johan, 2011. "Diversification disasters," Journal of Financial Economics, Elsevier, vol. 99(2), pages 333-348, February.
    7. Walden, Johan & Ibragimov, Rustam, 2008. "Portfolio Diversification under Local and Moderate Deviations from Power Laws," Scholarly Articles 2640586, Harvard University Department of Economics.
    8. KANAMURA Takashi, 2018. "Diversification Effect of Commodity Futures on Financial Markets," Discussion papers 18019, Research Institute of Economy, Trade and Industry (RIETI).
    9. Ibragimov, Rustam & Walden, Johan, 2007. "The limits of diversification when losses may be large," Scholarly Articles 2624460, Harvard University Department of Economics.
    10. Christian Gourieroux & Wei Liu, 2006. "Sensitivity Analysis of Distortion Risk Measures," Working Papers 2006-33, Center for Research in Economics and Statistics.
    11. Ibragimov, Rustam, 2007. "Efficiency of linear estimators under heavy-tailedness: convolutions of [alpha]-symmetric distributions," Scholarly Articles 2623749, Harvard University Department of Economics.
    12. Asche, Frank & Dahl, Roy Endre & Oglend, Atle, 2013. "Value-at-Risk: Risk assessment for the portfolio of oil and gas producers," UiS Working Papers in Economics and Finance 2013/3, University of Stavanger.

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