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The Limits of Diversification When Losses May Be Large

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  • Rustam Ibragimov
  • Johan Walden

Abstract

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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Bibliographic Info

Paper provided by Harvard - Institute of Economic Research in its series Harvard Institute of Economic Research Working Papers with number 2104.

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Date of creation: 2006
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Handle: RePEc:fth:harver:2104

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Cited by:
  1. Chirok Han & Jin Seo Cho & Peter C. B. Phillips, 2009. "Infinite Density at the Median and the Typical Shape of Stock Return Distributions," Discussion Paper Series 0914, Institute of Economic Research, Korea University.
  2. 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.
  3. 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.
    • Markwat, T.D. & Kole, H.J.W.G. & Dijk, D.J.C. van, 2008. "Contagion as Domino Effect in Global Stock Markets," Research Paper ERS-2008-071-F&A, Erasmus Research Institute of Management (ERIM), ERIM is the joint research institute of the Rotterdam School of Management, Erasmus University and the Erasmus School of Economics (ESE) at Erasmus Uni.
  4. Dirk G. Baur & Thomas K. McDermott, . "Is gold a safe haven? International evidence," The Institute for International Integration Studies Discussion Paper Series iiisdp310, IIIS.
  5. Chernobai, Anna & Yildirim, Yildiray, 2008. "The dynamics of operational loss clustering," Journal of Banking & Finance, Elsevier, vol. 32(12), pages 2655-2666, December.
  6. 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.
  7. 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.
  8. Luca RICCETTI & Alberto RUSSO & Mauro GALLEGATI, 2011. "Leveraged Network-Based Financial Accelerator," Working Papers 371, Universita' Politecnica delle Marche (I), Dipartimento di Scienze Economiche e Sociali.
  9. Paolo Tasca & Stefano Battiston, . "Diversification and Financial Stability," Working Papers CCSS-11-001, ETH Zurich, Chair of Systems Design.
  10. 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.
  11. Chollete, Lorán, 2008. "The Propagation of Financial Extremes: An Application to Subprime Market Spillovers," Discussion Papers 2008/2, Department of Finance and Management Science, Norwegian School of Economics.
  12. Walden, Johan & Ibragimov, Rustam, 2008. "Portfolio Diversification under Local and Moderate Deviations from Power Laws," Scholarly Articles 2640586, Harvard University Department of Economics.
  13. 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.
  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. 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.
  16. Ibragimov, Rustam & Jaffee, Dwight & Walden, Johan, 2011. "Diversification disasters," Journal of Financial Economics, Elsevier, vol. 99(2), pages 333-348, February.
  17. 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.
  18. 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.
  19. Chollete, Loran, 2011. "A Model of Endogenous Extreme Events," UiS Working Papers in Economics and Finance 2012/2, University of Stavanger.
  20. Walden, Johan & Ibragimov, Rustam, 2007. "The limits of diversification when losses may be large," Scholarly Articles 2624460, Harvard University Department of Economics.

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