Credit Ratings, Default Probabilities, and Logarithms

Abstract

Analysis of rating agency global default studies reveals an interesting property of credit ratings: The logarithm of the probability of default is a linear function of the rating. On a semi-log chart, where the rating is on the horizontal axis and the probability of default on the vertical, the relationship is an upwardly sloping straight line. At any point on the rating scale, a rating downgrade by one rating category implies risk is approximately multiplied by a constant factor (around 3).

These findings suggest credit ratings follow the so-called Weber–Fechner law of psychophysics, which states that the perception of a phenomenon is proportional to the logarithm of the underlying stimulus. Credit ratings are effectively perceptions of risk, behaving like other human perceptions. This property of credit ratings can be used to estimate probabilities of default when default studies are absent, incomplete, or insufficiently robust, as is often the case in emerging markets.