Cumulative accuracy profile curves for correlating collateralized debt obligations to systematic factors

We present a methodology to calibrate the correlation to be used when paper issued by a collateralized debt obligation (CDO) is included in a general credit portfolio of corporate bonds. We extend a version of the CreditMetrics credit risk framework to model portfolios holding debt issued by CDOs. We then create Lorenz or cumulative accuracy profile curves that plot the cumulative default frequency against the loss percentile of simulated portfolio values for a CDO tranche, and also for corporate bonds with known correlations to a systematic risk factor. CDO bonds are then assigned the correlation of the corporate bond whose Lorenz/cumulative accuracy profile curve is closest to the CDO’s curve in L2 distance. We use the technique to explore various model scenarios in which a portfolio of corporate bonds from firms participating in systemically correlated industries is generated via Monte Carlo simulation. We discuss the sensitivity of intraportfolio CDO correlation to factors such as the rating quality of the general investment portfolio and that of the CDO’s portfolio. We find very high levels of correlation to a systematic risk factor for the CDOs in most of the modeled scenarios.