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Modeling the Loss Distribution

by Sudheer Chava of Texas A&M University,
Catalina Stefanescu of the London Business School, and
Stuart Turnbull of the University of Houston

April 21, 2008

Abstract: This paper focuses on modeling and predicting the loss distribution for credit risky assets such as bonds or loans. We directly model the two components of loss -- the default probabilities and the recovery rates given default, and capture the dependence between them through shared covariates. Using an extensive default and recovery data set, we demonstrate the limitations of standard metrics of prediction performance which are based on the relative ordinal rankings of default probabilities. We use different approaches for assessing model performance, including a measure based on the actual magnitude of default probabilities that is more suitable for validating the loss distribution. We show that these approaches allow differentiation of default and recovery models which have virtually identical performance under standard metrics. We elucidate the impact of the choice of default and recovery models on the loss distribution through extensive out-of-sample testing. We document that the specification of the default model has a major impact on the predicted loss distribution, while the specification of the recovery model is less important. Further, we analyze the dependence between the default probabilities and recovery rates predicted out-of-sample. We show that they are negatively correlated, and that the magnitude of the correlation varies with the seniority class, the industry and the credit cycle.

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