Rating Migrations: The Effect of History and Time

Abstract

We use the Cox proportional hazard model to investigate the probability of rating transitions using data for the period 1986 to 2005. Variables that capture rating history and the current rating significantly affect the probability of a rating transition. Different models are required for upgrades and downgrades, but the evidence consistently shows a tendency for history to repeat itself. Longer lagged durations in ratings tend to lead to longer subsequent durations and rating changes exhibit momentum. In addition to lagged duration and the direction of the lagged rating change, other significant variables are the rate of prior rating changes, the firm's first ever rating, the time elapsed since that first rating, and having a period of being unrated. There is also evidence of interactions between the time spent in a rating grade and the main effect variables. The extent of these time interactions is greater for downgrades than for upgrades. The nature of the interaction is that the impact of the rating history variables diminishes as the time spent in the current rating gets bigger. The time interaction for the current rating diminishes the impact of the current rating for downgrades and intensifies it for upgrades.

Keywords: Event study, survival analysis, proportional hazard, time-varying covariates, rating migration, rating history, non-Markovian behaviors