Directional mobility of debt ratings

In this paper we describe a method to decompose a well-known measure of debt ratings mobility into it's directional components. We show, using sovereign debt ratings as an example, that this directional decomposition allows us to better understand the underlying characteristics of debt ratings migration and, for the case of the data set used, that the standard Markov chain model is not homogeneous in either the time or cross-sectional dimensions. We find that the directional decomposition also allows us to sign the change in quality of debt over time and across sub-groups of the population.