The Limits of Diversification When Losses May Be Large

36 Pages Posted: 3 Feb 2006

See all articles by Rustam Ibragimov

Rustam Ibragimov

Harvard University - Department of Economics

Johan Walden

University of California, Berkeley - Finance Group

Date Written: February 2006


Recent results in value at risk analysis show that, for extremely heavy-tailed risks with unbounded distribution support, diversification may increase value at risk, and that, generally, it is difficult to construct an appropriate risk measure for such distributions. We further analyze the limitations of diversification for heavy-tailed risks. We provide additional insight in two ways. First, we show that similar nondiversification results are valid for a large class of risks with bounded support, as long as the risks are concentrated on a sufficiently large interval. The required length of the support depends on the number of risks available and on the degree of heavy-tailedness. Second, we relate the value at risk approach to more general risk frameworks. We argue that in financial markets where the number of assets is limited compared with the (bounded) distributional support of the risks, unbounded heavy-tailed risks may provide a reasonable approximation. We suggest that this type of analysis may have a role in explaining various types of market failures in markets for assets with possibly large negative outcomes.

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

JEL Classification: G11

Suggested Citation

Ibragimov, Rustam and Walden, Johan, The Limits of Diversification When Losses May Be Large (February 2006). Harvard Institute of Economic Research Discussion Paper No. 2104, Available at SSRN: or

Rustam Ibragimov (Contact Author)

Harvard University - Department of Economics ( email )

Littauer Center
1805 Cambridge St.
Cambridge, MA 02138
United States
617-496-4795 (Phone)
617-495-7730 (Fax)


Johan Walden

University of California, Berkeley - Finance Group ( email )

545 Student Services Building, #1900
2220 Piedmont Avenue
Berkeley, CA 94720
United States
(510) 643-0547 (Phone)


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