Confidence Intervals for Probabilities of Default

by Samuel Hanson of the Federal Reserve Bank of New York, and
Til Schuermann of the Federal Reserve Bank of New York

July 19, 2005

Abstract: In this paper we conduct a systematic comparison of confidence intervals around estimated probabilities of default (PD) using several analytical approaches as well as parametric and nonparametric bootstrap methods. We do so for two different PD estimation methods, cohort and duration (intensity), with 22 years of credit ratings data. We find that the bootstrapped intervals for the duration based estimates are relatively tight when compared to either analytic or bootstrapped intervals around the less efficient cohort estimator. We show how the large differences between the point estimates and confidence intervals of these two estimators are consistent with non-Markovian migration behaviour. Surprisingly, even with these relatively tight confidence intervals, it is impossible to distinguish notch-level PDs for investment grade ratings, e.g. a PDAA- from a PDA+. However, once the speculative grade barrier is crossed, we are able to distinguish quite cleanly notch-level estimated PDs. Conditioning on the state of the business cycle helps: it is easier to distinguish adjacent PDs in recessions than in expansions.

JEL Classification: G21, G28, C16.

Keywords: Risk management, credit risk, bootstrap.

Published in: Journal of Banking & Finance, Vol. 30, No. 8, (August 2006), pp. 2281-2301.

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