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Portfolio Diversification Under Local, Moderate and Global Deviations From Power Laws


  • Rustam Ibragimov
  • Johan Walden


This paper focuses on the analysis of portfolio diversification for a wide class of nonlinear transformations of heavy-tailed risks. We show that diversification of a portfolio of nonlinear transformations of thick-tailed risks increases riskiness if expectations of these functions are infinite. In addition, coherency of the value at risk measure is always violated for such portfolios. On the contrary, for nonlinearly transformed heavy-tailed risks with finite expectations, the stylized fact that diversification is preferable continues to hold. Moreover, in the latter setting, the value of risk is a coherent measure of risk. The framework of transformations of long-tailed random variables includes many models with Pareto-type distributions that exhibit local, moderate and global deviations from power tails in the form of additional slowly varying or exponential factors. This leads to a refined understanding of under what distributional assumptions diversification increases riskiness.

Suggested Citation

  • Rustam Ibragimov & Johan Walden, 2006. "Portfolio Diversification Under Local, Moderate and Global Deviations From Power Laws," Harvard Institute of Economic Research Working Papers 2116, Harvard - Institute of Economic Research.
  • Handle: RePEc:fth:harver:2116

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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. Chen Zou, 2009. "Dependence structure of risk factors and diversification effects," DNB Working Papers 219, Netherlands Central Bank, Research Department.
    3. 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.
    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. Walden, Johan & Ibragimov, Rustam, 2008. "Portfolio Diversification under Local and Moderate Deviations from Power Laws," Scholarly Articles 2640586, Harvard University Department of Economics.
    6. Kyle Moore & Pengfei Sun & Casper de Vries & Chen Zhou, 2013. "Shape Homogeneity and Scale Heterogeneity of Downside Tail Risk," Working Papers 13-13, Chapman University, Economic Science Institute.

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