Modeling the Loss Distribution

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. ∗Sudheer Chava: Mays School of Business at Texas A&M University. Email: [email protected]. Catalina Stefanescu: London Business School. Email: [email protected]. Stuart Turnbull: Bauer College of Business at University of Houston. Email: [email protected]. We are grateful to Alexander McNeil, Amiyatosh Purnanandam, Tyler Shumway, Matthew Spiegel (the Editor), Raman Uppal, seminar participants at the Bank of England, ETH Zürich, the Federal Reserve Board (Washington), McGill University, Rice University, York University, conference participants at BMBF Münich, Derivatives, Securities and Risk Management Conference (FDIC), and the INFORMS 2007 Annual Meeting, as well as to two anonymous referees for helpful comments which greatly improved the paper. All remaining errors are our own.