Credit Rating Dynamics and Markov Mixture Models

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Abstract
Credit migration matrices are cardinal inputs to many risk management applications; their accurate estimation is therefore critical. We explore two approaches: cohort and two variants of duration - one imposing, the other relaxing time homogeneity - and the resulting differences, both statistically through matrix norms and economically using a credit portfolio model. We propose a new metric for comparing these matrices based on singular values and apply it to credit rating histories of S&P rated U.S. firms from 1981-2002. We show that the migration matrices have been increasing in "size" since the mid-1990s, with 2002 being the "largest" in the sense of being the most dynamic. We develop a testing procedure using bootstrap techniques to assess statistically the differences between migration matrices as represented by our metric. We demonstrate that it can matter substantially which estimation method is chosen: economic credit risk capital differences implied by different estimation techniques can be as large as differences between economic regimes, recession vs. expansion. Ignoring the efficiency gain inherent in the duration methods by using the cohort method instead is more damaging than imposing a (possibly false) assumption of time homogeneity.

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