Time Series Properties of a Rating System based on Financial Ratios

by Ulrich Krüger of Deutsche Bundesbank,
Martin Stötzel of the Universität Karlsruhe, and
Stefan Trück of the Universität Karlsruhe

November 23, 2005

Abstract: This paper provides an overview on classical and new methods for testing time series properties of migration matrices. It is well known that due to cyclical behavior of the economy transition matrices for many credit portfolios cannot be considered to be constant through time. Further, transition matrices are dependent on the used rating methodology. We investigate the changes in migrations of an extensive rating system based on financial ratios. Our findings are time-inhomogeneity, second-order Markov behavior, a tendency for "rating equalization" and vast effects of migration behavior on risk figures like expected shortfall and VaR. We further illustrate how changes in migration matrices can be related to macroeconomic factors.

JEL Classification: C13, G20, G33.

Keywords: Reduced Form Models, Rating Transitions, Markov Property, Internal Rating Systems, Time Homogeneity, Matrix Norms.

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