Abstract
A portfolio of non-performing loans needs economic capital. We present two models for forecasting the non-performing portfolio's loss and derive the probability distribution. In the first model, the loss for each loan is a Gaussian random variable, and the risk determinants are the portfolio concentration, as well as systematic and idiosyncratic risk. Our second model allows for diversification with a performing portfolio, because an investor typically owns a combination of performing and non-performing loans. This model is a mixture model. For both models, formulae for the economic capital and the fair contribution of a single loan are given. We calibrate the models with times series data and a benchmark portfolio. Our main finding is that the credit portfolio risk of non-performing loans depends on the volatility of economic activity, on the granularity of the portfolio and on the performing portfolio. Finally, we compare the economic capital charges for non-performing loans from our models with the regulatory capital charges of Basel II. The main difference is that our capital charges are sensitive to economic activity volatility, whereas the regulatory ones are not.
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