Constant Proportion Debt Obligations (CPDOs): modeling and risk analysis

Abstract

Constant Proportion Debt Obligations (CPDOs) are structured credit derivatives that generate high coupon payments by dynamically leveraging a position in an underlying portfolio of investment-grade index default swaps. CPDO coupons and principal notes received high initial credit ratings from the major rating agencies, based on complex models for the joint transition of ratings and spreads for all names in the underlying portfolio. We propose a parsimonious model for analysing the performance of CPDO strategies using a top-down approach that captures the essential risk factors of the CPDO. Our approach allows us to compute default probabilities, loss distributions and other tail risk measures for the CPDO strategy and analyse the dependence of these risk measures on various parameters describing the risk factors. We find that the probability of the CPDO defaulting on its coupon payments can be made arbitrarily small—and thus the credit rating arbitrarily high—by increasing leverage, but the ratings obtained strongly depend on assumptions on the credit environment (high spread or low spread). More importantly, CPDO loss distributions are found to exhibit a wide range of tail risk measures inside a given rating category, suggesting that credit ratings are insufficient performance indicators for such complex leveraged strategies. A worst-case scenario analysis indicates that CPDO strategies have a high exposure to persistent spread-widening scenarios and that CPDO ratings are shown to be quite unstable during the lifetime of the strategy.

Keywords:

• Credit risk
• Applications to credit risk
• Credit derivatives
• Affine term structure models

JEL Classification :

• G1
• G13

Acknowledgements

We thank Michel Crouhy, William Morokoff, William Dellal and Eric Raiten for helpful comments.