Jun 27

Credit migration matrix

by David Harper, CFA, FRM, CIPM

Rating agencies publish credit migration matrices (a.k.a., transition tables). In the EditGrid below, you can see Standard & Poor's 2007 Global transition table. You read the table by starting at the first column on the left. For example, if you go to the first column, look down to the row that starts at BBB. This is the lowest investment-grade rating; the equivalent in Moody's scheme is Baa (and technically both can go one minor notch lower. Specifically, the lowest investment grade is BBB- for S&P and Baa3 for Moody's).

Then look at the row that is labeled BBB. The cells in the row sum to 1.0 (100%). Each cell gives the probability of a migration to another rating within the single one-year period:

It is interesting to connect the table to some of Gujarati's terms in the FRM assigned Essentials of Econometrics:

The row is an empirical distribution, as opposed to a parametric distribution. Unlike a normal or binomial distribution, this distribution is historically informed. It is a bit "messy," and not parametrically smooth
It is also probability mass function (PMF): for any given rating, there are nine possible discrete outcomes (where the mode, of course, is the starting rating). PMF for discrete variables, PDF for continuous variables.
The probabilities in a given cell are conditional probabilities. For example, consider the 3.81% probability cell above. This is P(A | starts at BBB) or "probability of upgrade to A conditional on rating starts the year at BBB."

Finally, note that if we assume Markovian independence (no serial correlation) from year-to-year, it is easy to generate a cumulative transition matrix: we simply multiply the matrix by itself. IF M is the one-year matrix, then a four-year cumulative matrix is given by M^4.