# A technical note on the allocation of risk capital in credit

## Jan W. Kwiatkowski

#### Abstract

ABSTRACT

A methodology for computing and allocating risk capital for portfolios of defaultable exposures has been described by Kwiatkowski and Burridge. Risk capital is defined as the conditional expected shortfall over some threshold (percentile level) of the loss distribution. The methodology uses the recursive algorithm of Andersen, Sidenius and Basu for computing the loss distribution of a portfolio, the constituents of which may, in general, have stochastic losses given default. The recursion is reversed to compute the contributions of the individual constituents. In general, the computation time is dominated by the reversal of the recursion. In this paper it is shown how, using the same formulation, the computation of the individual contributions (the "allocation") may be considerably accelerated, to the extent that the computation time is dominated by the computation of the loss distribution.