A Theory of Credit Rating Criteria

We propose a theory for rating financial securities in the presence of structural maximization by the issuer in a market with investors who rely on credit rating. Two types of investors, simple investors who price tranches solely based on the ratings and modelbased investors who use the rating information to calibrate models, are considered. Concepts of self-consistency and information gap are proposed to study different rating criteria. In particular, the expected loss criterion used by Moody's satisfies self-consistency, but the probability of default criterion used by Standard & Poor's does not. Moreover, the probability of default criterion typically has a higher information gap than the expected loss criterion. Empirical evidence in the post-Dodd-Frank period is consistent with our theoretical implications. We show that a set of axioms based on self-consistency leads to a tractable representation for all self-consistent rating criteria, which can also be extended to incorporate economic scenarios. New examples of self-consistent and scenario-based rating criteria are suggested.