Re-Mapping Credit Ratings

Abstract

Rating agencies report ordinal ratings in discrete classes. We question the market's implicit assumption that agencies define their classes on identical scales, e.g., that AAA by Standard & Poor's is equivalent to Aaa by Moody's. To this end, we develop a non-parametric method to estimate the relation between rating scales for pairs of raters. For every rating class of one rater this, scale relation identifies the extent to which it corresponds to any rating class of another rater, and hence enables a rating-class specific re-mapping of one agency's ratings to another's. Our method is based purely on ordinal co-ratings to obviate error-prone estimation of default probabilities and the disputable assumptions involved in treating ratings as metric data. It estimates all rating classes' relations from a pair of raters jointly, and thus exploits the information content from ordinality.We find evidence against the presumption of identical scales for the three major rating agencies Fitch, Moody's and Standard & Poor's, provide the relations of their rating classes and illustrate the importance of correcting for scale relations in benchmarking.

A Bayesian inference model for the credit rating scale

“…Related to the topic of accuracy and the rating scale, the empirical result of Cantor and Packer (1997) suggests that differences in ratings between agencies are a consequence of the difference of default frequencies associated with the same rating letter on the rating scale. Related to that, Eisl et al (2013) address the issue that the market treats the different scales of the CRAs as the same. Furthermore, their empirical results highlight that the implicit assumption of the market that the ordinal rating scales are identical does in general not hold.…”