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Portfolio Diversification and Value At Risk Under Thick-Tailedness

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  • Rustam Ibragimov

Abstract

We present a unified approach to value at risk analysis under heavy-tailedness using new majorization theory for linear combinations of thick-tailed random variables that we develop. Among other results, we show that the stylized fact that portfolio diversification is always preferable is reversed for extremely heavy-tailed risks or returns. The stylized facts on diversification are nevertheless robust to thick-tailedness of risks or returns as long as their distributions are not extremely long-tailed. We further demonstrate that the value at risk is a coherent measure of risk if distributions of risks are not extremely heavy-tailed. However, coherency of the value at risk is always violated under extreme thick-tailedness. Extensions of the results to the case of dependence, including convolutions of alpha-symmetric distributions and models with common shocks are provided.

Suggested Citation

  • Rustam Ibragimov, 2005. "Portfolio Diversification and Value At Risk Under Thick-Tailedness," Yale School of Management Working Papers amz2386, Yale School of Management, revised 01 Aug 2005.
  • Handle: RePEc:ysm:somwrk:amz2386
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    File URL: http://icfpub.som.yale.edu/publications/2386
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    Cited by:

    1. KANAMURA Takashi, 2018. "Diversification Effect of Commodity Futures on Financial Markets," Discussion papers 18019, Research Institute of Economy, Trade and Industry (RIETI).

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