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 t