Re-mapping credit ratings

Rating agencies report ordinal ratings in discrete classes . We question the market's implicit assumption that agencies define their classe s 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 o ne rater this, scale relation identifies the extent to which it corresponds to any rating cl ass 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 di sputable assumptions involved in treating ratings as metric data. It estimates al l rating classes' relations from a pair of raters jointly, and thus exploits the i nformation 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.