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Economic Capital for Nonperforming Loans

by Rafael Weißbach of the Universität Rostock, and
Carsten von Lieres und Wilkau of the WestLB AG

March 2010

Abstract: A portfolio of nonperforming loans requires economic capital. We present two models for forecasting the portfolio loss and its probability distribution. In the first model, the loss for each nonperforming loan entails a change in provision over the risk horizon. The risk determinants are the single-name concentration, measured by the Herfindahl-Hirschmann index, as well as a systematic factor and the idiosyncratic risk. Our second model allows for interportfolio diversification with a portfolio of performing loans because banks typically own both performing and nonperforming loans. In this model, the nonperforming loan is identified with its systematic risk. Both models allow for closed-form expressions of economic capital and for the capital charge of the single loan. We calibrate the macroeconomic model parameters statistically with a loss panel; the microeconomic parameters depend on the portfolio. The portfolio risk for nonperforming loans mainly depends on the volatility of the systematic economic factor. The dependence becomes more pronounced when interportfolio diversification is taken into account. The magnitude of interportfolio diversification is also marked. Finally, we calculate regulatory capital charges according to Basel II for past-due loans. The regulatory charges are on average smaller than our economic charges and, additionally, take the volatility of economic activity into account only implicitly.

JEL Classification: C51, G11, G18, G33.

Keywords: Economic capital, Regulatory capital, Nonperforming loan, Recovery, Loss given default.

Published in: Financial Markets and Portfolio Management, Vol. 24, No. 1, (March 2010), pp. 67-85.

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