This article reviews the literature on techniques of credit risk models, multiperiod risk measurement, and capital allocation, and gives a tutorial on applying these techniques to credit portfolios with a focus on practical aspects. The effects of the choice of considered loss process concerning the handling of write-offs and matured assets or rating migration are displayed, and the impact on portfolio optimization decisions is discussed. We highlight the trade-off between short-term and long-term profitability and allude to the practical challenges of an application of multi-period risk measurement. Keywords risk capital • credit risk • multi-period risk • Conditionally Independent Defaults • Copula models • capital allocation • risk contribution JEL Classification D81 • G21

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 dependence of this minimum portfolio size on different parameters like the probability of default and on the credit risk model that is used.

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