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Portfolio diversification under local and moderate deviations from power laws

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  • Ibragimov, Rustam
  • Walden, Johan
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    Abstract

    This paper analyzes portfolio diversification for nonlinear transformations of heavy-tailed risks. It is shown that diversification of a portfolio of convex functions of heavy-tailed risks increases the portfolio's riskiness if expectations of these risks are infinite. In contrast, for concave functions of heavy-tailed risks with finite expectations, the stylized fact that diversification is preferable continues to hold. The framework of transformations of heavy-tailed risks includes many models with Pareto-type distributions that exhibit local or moderate deviations from power tails in the form of additional slowly varying or exponential factors. The class of distributions under study is therefore extended beyond the stable class.

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    Bibliographic Info

    Article provided by Elsevier in its journal Insurance: Mathematics and Economics.

    Volume (Year): 42 (2008)
    Issue (Month): 2 (April)
    Pages: 594-599

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    Handle: RePEc:eee:insuma:v:42:y:2008:i:2:p:594-599

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    Web page: http://www.elsevier.com/locate/inca/505554

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    References

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    1. Phillips, Peter C.B. & Magdalinos, Tassos, 2007. "Limit theory for moderate deviations from a unit root," Journal of Econometrics, Elsevier, vol. 136(1), pages 115-130, January.
    2. Y. Malevergne & D. Sornette, 2003. "VaR-Efficient Portfolios for a Class of Super- and Sub-Exponentially Decaying Assets Return Distributions," Papers physics/0301009, arXiv.org.
    3. An, Mark Yuying, 1995. "Logconcavity versus Logconvexity: A Complete Characterization," Working Papers 95-03, Duke University, Department of Economics.
    4. Eugene F. Fama, 1965. "Portfolio Analysis in a Stable Paretian Market," Management Science, INFORMS, vol. 11(3), pages 404-419, January.
    5. Peter C.B. Phillips, 1986. "Regression Theory for Near-Integrated Time Series," Cowles Foundation Discussion Papers 781R, Cowles Foundation for Research in Economics, Yale University, revised Jan 1987.
    6. 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.
    7. Silverberg, Gerald & Verspagen, Bart, 2007. "The size distribution of innovations revisited: An application of extreme value statistics to citation and value measures of patent significance," Journal of Econometrics, Elsevier, vol. 139(2), pages 318-339, August.
    8. Walden, Johan & Ibragimov, Rustam, 2007. "The limits of diversification when losses may be large," Scholarly Articles 2624460, Harvard University Department of Economics.
    9. 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.
    10. Jansen, Dennis W & de Vries, Casper G, 1991. "On the Frequency of Large Stock Returns: Putting Booms and Busts into Perspective," The Review of Economics and Statistics, MIT Press, vol. 73(1), pages 18-24, February.
    11. F. M. Scherer & Dietmar Harhoff & J, rg Kukies, 2000. "Uncertainty and the size distribution of rewards from innovation," Journal of Evolutionary Economics, Springer, vol. 10(1), pages 175-200.
    12. Benoit Mandelbrot, 1963. "The Variation of Certain Speculative Prices," The Journal of Business, University of Chicago Press, vol. 36, pages 394.
    13. McCulloch, J Huston, 1997. "Measuring Tail Thickness to Estimate the Stable Index Alpha: A Critique," Journal of Business & Economic Statistics, American Statistical Association, vol. 15(1), pages 74-81, January.
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    Cited by:
    1. Moore, Kyle & Sun, Pengei & de Vries, Casper G. & Zhou, Chen, 2013. "The drivers of downside equity tail risk," MPRA Paper 45591, University Library of Munich, Germany.
    2. Moore, Kyle & Sun, Pengfei & de Vries, Casper G. & Zhou, Chen, 2013. "The cross-section of tail risks in stock returns," MPRA Paper 45592, University Library of Munich, Germany.
    3. 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.
    4. Zhou, Chen, 2010. "Dependence structure of risk factors and diversification effects," Insurance: Mathematics and Economics, Elsevier, vol. 46(3), pages 531-540, June.
    5. Embrechts, Paul & Puccetti, Giovanni, 2010. "Bounds for the sum of dependent risks having overlapping marginals," Journal of Multivariate Analysis, Elsevier, vol. 101(1), pages 177-190, January.
    6. Chen Zou, 2009. "Dependence structure of risk factors and diversification effects," DNB Working Papers 219, Netherlands Central Bank, Research Department.
    7. Ibragimov, Rustam, 2014. "On the robustness of location estimators in models of firm growth under heavy-tailedness," Journal of Econometrics, Elsevier, vol. 181(1), pages 25-33.

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