Metrics for Comparing Credit Migration Matrices

Yusuf Jafry and Til Schuermann

Center for Financial Institutions Working Papers from Wharton School Center for Financial Institutions, University of Pennsylvania

Abstract: Credit migration or transition matrices, which characterize the expected changes in credit quality of obligors, are cardinal inputs to applications such as asset pricing and risk management. We propose a new metric for comparing these matrices (a mobility index) by first subtracting the identity matrix, focusing the analysis on the dynamics, and then taking the average of the singular values for the resulting matrix. This yields a metric which has an intuitively-appealing “size” related to the average probability of migration of the original matrix. We also propose a new mobility index performance criterion which is particularly relevant for credit migration matrices, namely that it be distribution discriminatory, i.e. sensitive to the distribution of off-diagonal probability mass. We demonstrate the advantages of the proposed metric over more traditional cell-by-cell distance metrics and eigenvalue-based mobility indices. We then apply these metrics to credit rating histories of S&P rated U.S. obligors from 1981-2001.

Keywords: credit migration matrix; matrix norm; mobility indices; singular values; risk management (search for similar items in EconPapers)
JEL-codes: C13 C41 G20 (search for similar items in EconPapers)
Date: 2003-03
New Economics Papers: this item is included in nep-fin and nep-rmg
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Citations: View citations in EconPapers (6)

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