On page 396 Sweeting explains that "VaR can be used to aggregate all types of risk, not just market risk" but then on page 397 he explains that because it is not subadditive it is not appropriate to aggregate. I think I am missing something subtle so please could someone explain?! Thanks
I think the subtlety lies in the second half of the sentence on page 396: "VAR also enables the aggregation of risks taking account of the ways in which risk factors are associated with each other." To me this is saying that to ascertain the VaR at the aggregate level, correlations must be allowed for. This then agrees with the statement on page 397, which is saying that it is not possible to determine VaR at the aggregate level by simple summation of the VaR of the constituent departments. Make sense?
I think you can probably take the Sweeting text literally. He's saying that it is possible to aggregate all types of risk using VaR but it may not be appropriate for some types. It can give particularly counterintuitive results where you have risks such as counterparty default risk, which have a high probability of being zero and a small probability of resulting in huge losses. It's a bit like saying you can use linear regression to model any situation where you have two real-valued variables, one dependent on the other. That doesn't necessarily mean it's an appropriate technique in every such situation.
