Credit coordinate ratings with corresponding credit rating agencies and regulations

This paper develops a coordinate rating for Credit Rating Agencies (CRAs) in the rating market. We first show that there is a necessary condition for the restructured sub-portfolios to have no-arbitrage principle for coordinate ratings. The coordinate rating is not only a natural extension of a single rating, but also reduces the rating bias and increases the rating accuracy. We solve the voluntary-disclosure decision problem for the issuer in terms of coordinate ratings. Furthermore, we show that the complexities of sub-portfolios do reduce the incentive to shop for the coordinate rating by comparing it with the incentive to shop for a single rating. The correlation among sub-portfolios also affect the incentive to shop in the coordinate rating. We advocate four principles for the credit rating system, from adapting coordinate ratings and reducing conflicts of interest to encouraging competition among CRAs and ensuring incentive alignment. We also build a model with disapproval correlation among CRAs and show that the probability of the joint disapproval is extremely sensitive to the disapproval correlation, even though the correlation may be very small in absolute value. Under an approval arrangement from the regulator in terms of the default rate within a CRA, we show that there exists a sub-game perfect equilibrium in which both approved CRAs provide correct coordinate ratings.