Value at Risk Under Dependence and Heavy-Tailedness: Models with Common Shocks

38 Pages Posted: 10 Oct 2007

See all articles by Rustam Ibragimov

Rustam Ibragimov

Harvard University - Department of Economics

Johan Walden

University of California, Berkeley - Finance Group

Date Written: October 2007

Abstract

This paper presents an analysis of diversification and portfolio value at risk for heavy-tailed dependent risks in models with multiple common shocks. We show that, in the framework of value at risk comparisons, diversification is optimal for moderately heavy-tailed dependent risks with common shocks and finite first moments, provided that the model is balanced, i.e., that all the risks are available for portfolio formation. However, diversification is inferior in balanced extremely heavy-tailed risk models with common factors. Finally, in several unbalanced dependent models, diversification is optimal, even though there is extreme heavy-tailedness in common shocks or in idiosyncratic parts of the risks.

Suggested Citation

Ibragimov, Rustam and Walden, Johan, Value at Risk Under Dependence and Heavy-Tailedness: Models with Common Shocks (October 2007). Harvard Institute of Economic Research Discussion Paper No. 2139, Available at SSRN: https://ssrn.com/abstract=1020281 or http://dx.doi.org/10.2139/ssrn.1020281

Rustam Ibragimov (Contact Author)

Harvard University - Department of Economics ( email )

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HOME PAGE: http://www.economics.harvard.edu/faculty/ibragimov/ibragimov.html

Johan Walden

University of California, Berkeley - Finance Group ( email )

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HOME PAGE: http://www.haas.berkeley.edu/faculty/walden.html

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