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The Limits of Diversification When Losses May Be Large


  • Rustam Ibragimov
  • Johan Walden


Recent results in value at risk analysis show that, for extremely heavy-tailed risks with unbounded distribution support, diversification may increase value at risk, and that, generally, it is difficult to construct an appropriate risk measure for such distributions. We further analyze the limitations of diversification for heavy-tailed risks. We provide additional insight in two ways. First, we show that similar nondiversification results are valid for a large class of risks with bounded support, as long as the risks are concentrated on a sufficiently large interval. The required length of the support depends on the number of risks available and on the degree of heavy-tailedness. Second, we relate the value at risk approach to more general risk frameworks. We argue that in financial markets where the number of assets is limited compared with the (bounded) distributional support of the risks, unbounded heavy-tailed risks may provide a reasonable approximation. We suggest that this type of analysis may have a role in explaining various types of market failures in markets for assets with possibly large negative outcomes.

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  • Rustam Ibragimov & Johan Walden, 2006. "The Limits of Diversification When Losses May Be Large," Harvard Institute of Economic Research Working Papers 2104, Harvard - Institute of Economic Research.
  • Handle: RePEc:fth:harver:2104

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    References listed on IDEAS

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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. Baur, Dirk G. & McDermott, Thomas K., 2010. "Is gold a safe haven? International evidence," Journal of Banking & Finance, Elsevier, vol. 34(8), pages 1886-1898, August.
    3. Chernobai, Anna & Yildirim, Yildiray, 2008. "The dynamics of operational loss clustering," Journal of Banking & Finance, Elsevier, vol. 32(12), pages 2655-2666, December.
    4. Riccetti, Luca & Russo, Alberto & Gallegati, Mauro, 2013. "Leveraged network-based financial accelerator," Journal of Economic Dynamics and Control, Elsevier, vol. 37(8), pages 1626-1640.
    5. Ibragimov, Rustam, 2008. "Heavy-tailedness and threshold sex determination," Statistics & Probability Letters, Elsevier, vol. 78(16), pages 2804-2810, November.
    6. Chollete, Loran, 2011. "A Model of Endogenous Extreme Events," UiS Working Papers in Economics and Finance 2012/2, University of Stavanger.
    7. Chang, Carolyn W. & Chang, Jack S.K. & Lu, WeLi, 2010. "Pricing catastrophe options with stochastic claim arrival intensity in claim time," Journal of Banking & Finance, Elsevier, vol. 34(1), pages 24-32, January.
    8. Chirok Han & Jin Seo Cho & Peter C. B. Phillips, 2011. "Infinite Density at the Median and the Typical Shape of Stock Return Distributions," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 29(2), pages 282-294, April.
    9. Markwat, Thijs & Kole, Erik & van Dijk, Dick, 2009. "Contagion as a domino effect in global stock markets," Journal of Banking & Finance, Elsevier, vol. 33(11), pages 1996-2012, November.
    10. Ibragimov, Rustam & Walden, Johan, 2007. "The limits of diversification when losses may be large," Journal of Banking & Finance, Elsevier, vol. 31(8), pages 2551-2569, August.
    11. Ibragimov, Rustam & Jaffee, Dwight & Walden, Johan, 2011. "Diversification disasters," Journal of Financial Economics, Elsevier, vol. 99(2), pages 333-348, February.
    12. Chollete, Lorán & de la Peña, Victor & Lu, Ching-Chih, 2011. "International diversification: A copula approach," Journal of Banking & Finance, Elsevier, vol. 35(2), pages 403-417, February.
    13. Walden, Johan & Ibragimov, Rustam, 2008. "Portfolio Diversification under Local and Moderate Deviations from Power Laws," Scholarly Articles 2640586, Harvard University Department of Economics.
    14. Chollete, Loran & Pena, Victor de la & Lu, Ching-Chih, 2009. "International Diversification: A Copula Approach," UiS Working Papers in Economics and Finance 2009/27, University of Stavanger.
    15. Ibragimov, Rustam & Walden, Johan, 2007. "The limits of diversification when losses may be large," Scholarly Articles 2624460, Harvard University Department of Economics.
    16. Chollete, Loran & de la Pena , Victor & Lu, Ching-Chih, 2009. "International Diversification: An Extreme Value Approach," UiS Working Papers in Economics and Finance 2009/26, University of Stavanger.
    17. Annaert, Jan & Osselaer, Sofieke Van & Verstraete, Bert, 2009. "Performance evaluation of portfolio insurance strategies using stochastic dominance criteria," Journal of Banking & Finance, Elsevier, vol. 33(2), pages 272-280, February.
    18. Ibragimov, Rustam & Walden, Johan, 2008. "Portfolio diversification under local and moderate deviations from power laws," Insurance: Mathematics and Economics, Elsevier, vol. 42(2), pages 594-599, April.
    19. Akhter Mohiuddin Rather, 2012. "Portfolio selection using mean-risk model and mean-risk diversification model," International Journal of Operational Research, Inderscience Enterprises Ltd, vol. 14(3), pages 324-342.
    20. Degen, Matthias & Lambrigger, Dominik D. & Segers, Johan, 2010. "Risk concentration and diversification: Second-order properties," Insurance: Mathematics and Economics, Elsevier, vol. 46(3), pages 541-546, June.
    21. Chollete, Lorán, 2008. "The Propagation of Financial Extremes: An Application to Subprime Market Spillovers," Discussion Papers 2008/2, Norwegian School of Economics, Department of Business and Management Science.
    22. 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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