The process of decomposition and aggregation of credit risks involves more judgment than that required for market risk. As a general rule of thumb the better the relationship between the likelihood of a default occurring and the factor the lower down the decomposition tree it should be.
The following two schematic diagrams show possible decomposition and aggregation levels for a bank’s retail loan book and its corporate exposures. The first level of aggregation is that of borrower rating.
The equivalent of VAR must be estimated for each exposure at each borrower and at the lowest level. Historic correlation coefficients should be applied as we move up the tree although at the higher levels where correlations start to become weaker and less reliable it is probably better to simply make a policy decision as to whether to treat these as independent or assume perfect positive correlation.