Portfolio Diversification and Value At Risk Under Thick-Tailedness
Portfolio Diversification and Value At Risk Under Thick-Tailedness
Ibragimov, Rustam, "Portfolio Diversification and Value At Risk Under Thick-Tailedness" (October 2004). Yale ICF Working Paper No. 05-10 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. Go to article
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Facts on MBA
France has initiated one-year MBA programs, with INSEAD MBA pioneering this formula in 1959. Most of the Grandes Ecoles also offer respected MBA programs, including ESCP-EAP (the oldest business school in the world, founded in Paris in 1819), ESSEC, HEC, EM-Lyon and EDHEC. University-based French business schools have created since then (mostly in the 1990s) their own 12 to 24-month MBA programs, but with a much lower emphasis on internationalization and diversity.
Executive Master of Business Administration (EMBA) programs were first established for senior executives by the University of Chicago in 1943 and are now offered by many school worldwide.
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