Metrics for Comparing Credit Migration Matrices

Wharton Financial Institutions Center Working Paper No. 03-09

43 Pages Posted: 9 May 2003

See all articles by Yusuf Jafry

Yusuf Jafry

Massachusetts Institute of Technology (MIT)

Til Schuermann

Oliver Wyman

Date Written: March 2003

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

JEL Classification: C13, C41, G20

Suggested Citation

Jafry, Yusuf and Schuermann, Til, Metrics for Comparing Credit Migration Matrices (March 2003). Wharton Financial Institutions Center Working Paper No. 03-09. Available at SSRN: https://ssrn.com/abstract=394020 or http://dx.doi.org/10.2139/ssrn.394020

Yusuf Jafry

Massachusetts Institute of Technology (MIT) ( email )

50 Memorial Drive
Cambridge, MA 02139-4307
United States

Til Schuermann (Contact Author)

Oliver Wyman ( email )

1166 6th Avenue
New York City, NY
United States

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