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.