Estimating Probabilities of Default
by Til Schuermann of the Federal Reserve Bank of New York, and
Abstract: We conduct a systematic comparison of confidence intervals around estimated probabilities of default (PD), using several analytical approaches from large-sample theory and bootstrapped small-sample confidence intervals. We do so for two different PD estimation methods--cohort and duration (intensity)--using twenty-two years of credit ratings data. We find that the bootstrapped intervals for the duration-based estimates are surprisingly tight when compared with the more commonly used (asymptotic) Wald interval. We find that even with these relatively tight confidence intervals, it is impossible to distinguish notch-level PDs for investment grade ratings--for example, a PDAA- from a PDA+. However, once the speculative grade barrier is crossed, we are able to distinguish quite cleanly notch-level estimated default probabilities. Conditioning on the state of the business cycle helps; it is easier to distinguish adjacent PDs in recessions than in expansions.