Portfolio Diversification and Value at Risk Under Thick-Tailedness

23 Pages Posted: 9 May 2005

See all articles by Rustam Ibragimov

Rustam Ibragimov

Harvard University - Department of Economics

Date Written: October 2004

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.

Keywords: value at risk, coherent measures of risk, heavy-tailed risks, portfolios, riskiness, diversification, risk bonds

JEL Classification: G11

Suggested Citation

Ibragimov, Rustam, Portfolio Diversification and Value at Risk Under Thick-Tailedness (October 2004). Yale ICF Working Paper No. 05-10, Harvard Institute of Economic Research Discussion Paper No. 2086, Available at SSRN: https://ssrn.com/abstract=721109

Rustam Ibragimov (Contact Author)

Harvard University - Department of Economics ( email )

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