Portfolio Diversification and Value At Risk Under Thick-Tailedness
AbstractWe 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.
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Bibliographic InfoPaper provided by Yale School of Management in its series Yale School of Management Working Papers with number amz2386.
Date of creation: 01 May 2005
Date of revision: 01 Aug 2005
value at risk; coherent measures of risk; heavy-tailed risks; portfolios; riskiness; diversification; risk bonds;
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