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Credit ratings, the universal language of risk, are "opinions" issued by rating agencies about the credit worthiness of corporate, municipal, and sovereign borrowers. The agencies say ratings are simply rankings of creditworthiness, that is, ratings are measured on a so-called ordinal scale. The agencies carefully avoid claiming that credit ratings predict probabilities of default. However, they publish detailed default studies, which show historical ratings migration and default experience as a function of the initial rating and time horizon.
Analysts and risk managers routinely use default study data as estimates of default probabilities. In practice, people assume that a rating pretty much matches to a probability of default. Probabilities of default fluctuate with economic cycles, so the general practice is to use the long-term average default rate for each rating category as a proxy for the rating on a "ratio scale." We will generally adopt this practice.
DEFAULT RATES INCREASE EXPONENTIALLY OVER RATING LEVELS
Our analysis of default studies reveals a striking pattern: default probability increases approximately exponentially as credit ratings decline. In other words, the logarithm of default probability is a straight-line function of the credit rating. This is strikingly analogous with logarithmic laws related to human perception (e.g., the "Weber-Fechner" law), and is consistent with credit ratings being "opinions" or perceptions. This property of credit ratings can be used to estimate default probabilities when default studies are insufficiently robust from a statistical viewpoint.
S&P says: "the rating describes the general creditworthiness of a company, city, or country that issues debt. The Standard and Poor's company rates how likely a debt will be repaid. The ratings are for information only. They are not investment recommendations nor do they predict the probability of default."
The definitions shown in Exhibit 1 are frustratingly qualitative. However, rating agencies do publish "default studies" (Ou et al. 2016 and Vazza et al. 2016) (regularly published by rating agencies since the 1980s), which show actual default rates for various rating categories and the "ratings migration" or transition matrixes. Exhibit 2 shows the default rates, over a 1-year horizon, as published by Moody's and S&P.
Exhibit 1
S&P Ratings Scale for Long-Term Bonds
[Figure omitted. See PDF]
Exhibit 2
Corporate 1-Year Default Probabilities by Credit Rating
[Figure omitted. See PDF]
These default...
