JUSTIFICATION OF PER-UNIT RISK CAPITAL ALLOCATION IN PORTFOLIO CREDIT RISK MODELS

Risk capital allocation is based on the assumption that the risk of a homogeneous portfolio is scaled up and down with the portfolio size. In this article we show that this assumption is true for large portfolios, but has to be revised for small ones. On basis of numerical examples we calculate the minimum portfolio size that is necessary to limit the error of gradient risk capital allocation and the resulting error in a portfolio optimization algorithm or pricing strategy. We show the dependency of this minimum portfolio size on different parameters like the probability of default and on the credit risk model that is used.