Portfolio Diversification and Value At Risk Under Thick-Tailedness

Rustam Ibragimov

Yale School of Management Working Papers from Yale School of Management

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 (search for similar items in EconPapers)
Date: 2005-05-01, Revised 2005-08-01
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://repec.som.yale.edu/icfpub/publications/2386.pdf (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:ysm:wpaper:amz2386

Access Statistics for this paper

More papers in Yale School of Management Working Papers from Yale School of Management Contact information at EDIRC.
Bibliographic data for series maintained by ().