期刊名称：HIER Discussion Paper Series / Harvard Institute of Economic Research
出版年度：2006
卷号：2006
出版社：Harvard Institute of Economic Research
摘要：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.
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