Treating Credit Ratings as Ordinal Data in Empirical Models
Summary
Credit ratings from agencies can be ranked, but assigning numerical scores does not make the gaps between rating levels quantitatively equal. The document explains that ratings are ordinal: their order is meaningful, while the distance between adjacent categories is not established. Consequently, comparisons such as greater than or less than are justified, and a median can describe central tendency, but arithmetic operations on arbitrary scores need caution.
For empirical analysis, it recommends methods that respect the data type. Ordered logit or ordered probit can model an ordinal dependent variable, while dummy variables can represent rating categories used as predictors. A different approach is to map ratings to cardinal values using observed default probabilities, potentially refined with rating transition probabilities over a chosen period. Such mappings depend on the sample period and modeling choices; no universal conversion scale is established in the discussion.
Key ideas
- Agency ratings provide rank order but do not define equal numerical distances between categories.
- Arbitrary numeric encodings can misrepresent differences between rating levels.
- Ordered logit or ordered probit models can be used when ratings are the ordinal outcome.
- Dummy variables can represent rating categories used as predictors.
- Default probabilities and transition probabilities offer possible data-based cardinal mappings.
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Full text
# Standardized numerical values for ratings # Standardized numerical values for ratings Is there a standardized way of transforming the ratings of any of the major ratings agencies (S&P, Moody's, Fitch) to a numerical value. Ideally, it might be possible to create a similar scale for all of them. I just found some academic papers, which just assigned numerical values, i.e. 1 for AAA and 22 for D. Just interested if there are conventions on how to convert the ratings. Additionally, it would help comparing the impact of ratings in empirical studies. I found some documents by ESMA, which are outlining their mappings approach. "Mapping of Standard & Poor’s Ratings Services’credit assessments under the Standardised Approach" - Link to Report In their approach the mapping is the following: ## Answer by skoestlmeier (score 3) https://quant.stackexchange.com/a/44074 Mapping ordinal data to interval data is arbitrarily. The ranking of rating agencies is ordinal data, so only comparing operators `>` or `<` can be applied. The data can be sorted and as a central tendency, you can calculate the median. The main aspect of ordinal data is that it allows for rank order but it does not allow for the relative degree of difference between them. E.g. the difference between the rankings AAA and AA may not equal the difference between BBB and BB. Your figure shows this explicitly by assigning different rankings the same (arbitrary) numerical value. Comparing the impact of ratings is still possible however, by applying ordinal regression instead of a linear regression, if the dependent variable is in ordinal data. Commonly used models for this are ordered logit or ordered probit models. If the independent variable is in ordinal data, you may use dummy variables to control for their impact in a regression. ## Answer by AlRacoon (score 1) https://quant.stackexchange.com/a/44076 One possible approach to mapping these ordinal measures into cardinal measures is to use something like average default probabilities of each of the ratings over the period in question. One can perhaps enhance the mapping by using transition probabilities of each rating into the other ratings over the period to take into account the distribution of ratings for each entity.
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