Constant Proportion Debt Obligations: A Postmortem Analysis of Rating Models

In its complexity and its vulnerability to market volatility, the constant proportion debt obligation (CPDO) might be viewed as the poster child for the excesses of financial engineering in the credit market. This paper examines the CPDO as a case study in model risk in the rating of complex structured products. We demonstrate that the models used by Standard and Poor's (S&P) and Moody's fail in-sample specification tests even during the precrisis period and in particular understate the kurtosis of spread changes. Because stochastic volatility is the most natural explanation for the excess kurtosis, we estimate an extended version of the S&P model with stochastic volatility and find that the volatility-of-volatility is large and significant. An implication is that agency model-implied probabilities of attaining high spread levels were biased downward, which in turn biased the rating upward. We conclude with larger lessons for the rating of complex products and for modeling credit risk in general. <i>This paper was accepted by Wei Xiong, finance.</i>