Modeling Banks’ Probability of Default

Abstract

The unprecedented financial crisis of 2008-2009 has called attention to limitations of existing methods for estimating the default risk of financial intuitions. Over the past decade, we have had considerable success at predicting default and credit relative value using Merton-type structural models and Hybrid Probability of Default models. However, generating accurate model-based estimates of default probabilities (PDs) for financial firms has proven difficult. To address this need, I built and tested a time-adaptive statistical model that predicts the default probabilities of banks. The model is a logistic regression whose input variables are selected based on their past effectiveness at predicting bank failures and whose inclusion in the model and weights are to be updated quarterly. Model performance at discriminating between defaults and non-defaults was evaluated for horizons of one to five years using a sequence of annual walk-forward out-of-sample tests from 1992 to 2012. I tested the ability of the model to predict absolute default rates out to five years and, except for underestimating the high bank default rates during the credit crisis, the models perform well at estimating the annual bank default rates. Because most default models provide little benefit over agency ratings for low-rated credits, I examined the performance of the model to Kroll agency ratings only for those banks rated above single-B-minus or above single-C-minus. Although default predictions from agency ratings fall off rapidly for banks rated at or above single-B and single-C, the time-adaptive statistical model predictions deteriorate far less. Accuracy at predicting bank defaults using agency ratings decreases to near chance at a prediction horizon of five years, but the time-adaptive statistical model continues to perform well above chance at all horizons. I also present a detailed analysis of the contributions of financial variables to model outputs by year (2000-2012) and tenor (1-5 years) and evaluate the consistency of variable contributions over time. The model performs favorably at predicting defaults, even relative to the best non-financial corporate default models, with a 97% accuracy ratio (AR) at one year prior to default, and decreasing, but still above-chance predictive power out to five years. I find that banks’ quality of assets and return on equity are most important for predicting near term defaults, giving way at longer horizons to operating income and the yield on earning assets.