Estimating Probabilities of Default

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 PDAAfrom 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. Correspondence to Til Schuermann, Research and Market Analysis Group, Federal Reserve Bank of New York (e-mail: [email protected]). The authors thank Joshua Rosenberg, Marc Saidenberg, and seminar participants at the Federal Reserve Bank of New York for their insightful comments. The authors assume responsibility for any remaining errors. The views expressed in this paper are those of the authors and do not necessarily reflect the position of the Federal Reserve Bank of New York or the Federal Reserve System.