Tranching and Rating

Abstract

In this paper we analyze the arbitrage gains from marketing structured debt securities at yields that reflect only the credit ratings of ratings agencies. The credit ratings considered include one that is based on default probabilities, corresponds to the credit ratings of Standard and Poor's, and one that is based on expected default losses, corresponds to the ratings of Moody's. For both rating systems, we find general conditions under which single and multiple tranche securitisations will yield an arbitrage gain. The conditions depend on the risk characteristics of the collateral relative to those of the typical firm for which the bond ratings apply. We then consider the gains both from choosing the collateral against which the debt securities are written, and from dividing the debt into tranches with different priority. We derive general results and characterize the gains for examples that are based on the CAPM and the Merton (1974) debt pricing model. We show that the arbitrage gains under both rating systems are highest when the systematic risk of the collateral is high and the total risk is low relative to that of the typical firm. In all cases we find significant additional gains to multi-tranching, which is consistent with the fact that there were 5.58 tranches in the average securitisation in the US in 2003. The arbitrage gains from multiple tranches are significantly higher when the securities are valued using S&P ratings than when they are valued using Moody's ratings. Our analysis highlights the limitations of current credit rating systems which reflect characteristics of the total risk of fixed income securities, neglecting portfolio considerations. If ratings are to be used for valuation then it is important that they reflect the systematic risk of the securities.