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Value-at-Risk Diversification of $\alpha$-stable Risks: The Tail-Dependence Puzzle

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  • Umberto Cherubini
  • Paolo Neri

Abstract

We consider the problem of risk diversification of $\alpha$-stable heavy tailed risks. We study the behaviour of the aggregated Value-at-Risk, with particular reference to the impact of different tail dependence structures on the limits to diversification. We confirm the large evidence of sub-additivity violations, particularly for risks with low tail index values and positive dependence. So, reinsurance strategies are not allowed to exploit diversification gains, or only a very limited amount of them. Concerning the impact of tail dependence, we find the peculiar results that for high tail dependence levels the limits to diversification are uniformly lower for all the levels of dependence, and for all levels of $\alpha

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  • Umberto Cherubini & Paolo Neri, 2017. "Value-at-Risk Diversification of $\alpha$-stable Risks: The Tail-Dependence Puzzle," Papers 1704.07235, arXiv.org.
    • Handle: RePEc:arx:papers:1704.07235
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    References listed on IDEAS

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    3. Embrechts, Paul & Neslehová, Johanna & Wüthrich, Mario V., 2009. "Additivity properties for Value-at-Risk under Archimedean dependence and heavy-tailedness," Insurance: Mathematics and Economics, Elsevier, vol. 44(2), pages 164-169, April.
    4. Ibragimov, Rustam & Prokhorov, Artem, 2016. "Heavy tails and copulas: Limits of diversification revisited," Economics Letters, Elsevier, vol. 149(C), pages 102-107.
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