Collateralized debt obligations, CDOs, are credit risk products backed by a pool of debt obligations. Over recent years, CDOs have become an important part of the global fixed income market. In this paper, we first describe the overview of CDOs. Then we introduce how rating agencies - Moody’s, S&P and Fitch - determine the rating of a CDO tranche. Each of them has their own methodologies, some are similar and some are different. Next, we construct two synthetic CDOs with one is high premium portfolio and the other is low premium portfolio. Put the required information into S&P’s and Fitch’s rating software and compare these results. Finally, we use these result to make some short discussions about rating arbitrage.