Leitura do Dia - THE LIMITS OF DIVERSIFICATION WHEN LOSSES MAY BE LARGE

THE LIMITS OF DIVERSIFICATION WHEN LOSSES MAY BE LARGE∗
Rustam Ibragimov Johan Waldenb
Department of Economics, Harvard University, Cambridge, MA 02138, USA
Haas School of Business, University of California at Berkeley, Berkeley, CA 94720, USA

ABSTRACT
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 markets for risky assets where the number of assets is limited compared with
the (bounded) distribution 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.