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Metrics for Comparing Credit Migration Matrices

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  • Yusuf Jafry
  • Til Schuermann

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.

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Bibliographic Info

Paper provided by Wharton School Center for Financial Institutions, University of Pennsylvania in its series Center for Financial Institutions Working Papers with number 03-09.

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Date of creation: Mar 2003
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Handle: RePEc:wop:pennin:03-09

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Keywords: credit migration matrix; matrix norm; mobility indices; singular values; risk management;

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References

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  1. Geweke, John & Marshall, Robert C & Zarkin, Gary A, 1986. "Mobility Indices in Continuous Time Markov Chains," Econometrica, Econometric Society, vol. 54(6), pages 1407-23, November.
  2. Robert B. Israel & Jeffrey S. Rosenthal & Jason Z. Wei, 2001. "Finding Generators for Markov Chains via Empirical Transition Matrices, with Applications to Credit Ratings," Mathematical Finance, Wiley Blackwell, vol. 11(2), pages 245-265.
  3. Anil Bangia & Francis X. Diebold & Til Schuermann, 2000. "Ratings Migration and the Business Cycle, With Application to Credit Portfolio Stress Testing," Center for Financial Institutions Working Papers 00-26, Wharton School Center for Financial Institutions, University of Pennsylvania.
  4. Shorrocks, A F, 1978. "The Measurement of Mobility," Econometrica, Econometric Society, vol. 46(5), pages 1013-24, September.
  5. Til Schuermann & Yusuf Jafry, 2003. "Measurement and Estimation of Credit Migration Matrices," Center for Financial Institutions Working Papers 03-08, Wharton School Center for Financial Institutions, University of Pennsylvania.
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Cited by:
  1. Til Schuermann & Yusuf Jafry, 2003. "Measurement and Estimation of Credit Migration Matrices," Center for Financial Institutions Working Papers 03-08, Wharton School Center for Financial Institutions, University of Pennsylvania.
  2. Sumon Bhaumik & John S. Landon-Lane, 2007. "Directional Mobility of Ratings," William Davidson Institute Working Papers Series wp900, William Davidson Institute at the University of Michigan.
  3. Phillips, Jill & Katchova, Ani L., 2004. "Credit Score Migration Analysis Of Farm Businesses: Conditioning On Business Cycles And Migration Trends," 2004 Annual meeting, August 1-4, Denver, CO 20136, American Agricultural Economics Association (New Name 2008: Agricultural and Applied Economics Association).
  4. Narcisa Kadlcakova & Joerg Keplinger, 2004. "Credit Risk and Bank Lending in the Czech Republic," Working Papers 2004/06, Czech National Bank, Research Department.
  5. Jongeneel, Roelof A. & Tonini, Axel, 2008. "Dairy Quota and Farm Structural Change: A Case Study on the Netherlands," 107th Seminar, January 30-February 1, 2008, Sevilla, Spain 6692, European Association of Agricultural Economists.
  6. Zhang, Tianwei & Katchova, Ani L., 2005. "Credit Risk Migration Analysis of Illinois Farm Business: Possible Impacts of Farm Business Cycle," 2005 Annual meeting, July 24-27, Providence, RI 19292, American Agricultural Economics Association (New Name 2008: Agricultural and Applied Economics Association).

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