Why Credit Rating Grades Often Use Unequal PD Ranges
Summary
The document asks why credit rating grades can span different widths of probability of default (PD). Its example mapping assigns relatively narrow PD intervals to stronger grades and wider intervals to weaker grades, and raises the possibility that a PD difference at the riskier end may matter less in practical investment decisions. The listed mapping is presented as one author's scheme, not as a universal standard; the source table also appears to contain a boundary inconsistency, so its specific values should be treated cautiously.
The response offers a statistical and practical rationale for grading on a logarithmic or roughly multiplicative scale, where PD may rise by a similar proportion between adjacent grades. Such spacing can distribute observations across grades more evenly, align with logistic regression approaches, and reflect that distinctions among very low default probabilities may be more informative than equal absolute differences among high probabilities. It suggests recalibration may change PD values while retaining an older grade structure. No formal derivation or empirical comparison is provided.
Key ideas
- Credit rating grades may cover unequal PD intervals, with wider ranges at riskier grades.
- The example mapping is an individual scheme rather than a universal rating standard.
- Multiplicative or logarithmic spacing can support a more even distribution across grades.
- Logistic regression based grading is compatible with a logarithmic PD scale.
- The explanation is conceptual and gives no formal statistical test.
Tags
Full text
# Why do rating grades have different PD ranges? # Why do rating grades have different PD ranges? The following shows link how to map a PD to a S&P rating: | S&P Rating | PD range [%] | | AAA | [0-0.05) | | AA | [0.05-0.09) | | A | [0.09-0.23) | | BBB | [0.23-1.16) | | BB | [1.16-5.44) | | B | [5.44-4.21) | | CCC | [14.21-) | I know that this mapping only is what the writer of this paper have come up with, but it shows a general trend I have observed by working with credit risk for many years. Bad risk grades do most often have wider PD ranges than better risk grades. In this table the PD range in B is from 5.44 % to 14.21 % but it for A is 0.09 % to 0.23 %. Is there a mathematical/statistical reason for that, or it is only practical. With practical I mean that there probably is not so big difference between a PD of 7 or 10 % when you are going to invest in a corporate. ## Answer by PalimPalim (score 1) https://quant.stackexchange.com/a/79889 Rating grades are normally based on a logarithmic scale. If we develop a rating scale for a bank's internal use it is common that pd doubles or increase by 50% from rating class to rating class. This is not the case for the scale you are referring to, but it might have been like this when the model was first developped. During recalibration they might have stuck with the logic for assigning rating classes and simply updated the corresponding pds. Having rating classes on a logistic scale makes sense for multiple reasons. - We want to have a fairly uniform distribution over the rating classes, i.e. if all observations fall into one rating class it is not very helpful. A logistic scale makes this much more likely than a uniform scale. - Normally grade assignement involves some form of logistic regression, so a logistic scale is natural. - It is much easer to distinguish someone with a PD of 0.1% from someone with a 5% PD than 95% to 99.9%. Classes reflect the level of information/ certainty which is higher for lower PDs.
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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.