In the previous chapter, we provided the basic foundation for understanding default correlation. In this chapter, we explore the determination of historical default correlations and the problems inherent in empirical default correlation. We then compare different approaches of incorporating default correlation into portfolio credit analysis. Finally, we recommend the approach that makes the most direct use of historical data and is easiest to understand.

With enough data—and one very strong assumption that we discuss in detail later—we can calculate *historic default correlations*. The default correlation formula was given in Chapter 13 (as equation (13.5)) and is reproduced below as equation (14.1):

To compute, say, the default correlation of two B-rated companies over one year, we set *P*(A) and *P*(B) in equation (14.1) for the default correlation equal to the historic average 1-year default rate for B-rated companies. The remaining variable in equation (14.1) is the joint probability of default, *P*(A and B). We compute *P*(A and B) by first counting the number of companies rated B at the beginning of a year that subsequently defaulted over that particular year. We then calculate all possible *pairs* of such defaulting B-rated companies. If *X* is the number of B-rated companies defaulting in a year, ...

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