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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 a-symmetric distributions and models with common stochs are provided.

Suggested Citation

  • Rustam Ibragimov, 2005. "Portfolio Diversification and Value at Risk Under Thick-Tailedness," Harvard Institute of Economic Research Working Papers 2086, Harvard - Institute of Economic Research.
    • Handle: RePEc:fth:harver:2086
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