Recently there has been a spate of bad news in the Credit Rating agency space. A link posted by Vivek suggests that these cos have let us down.
However, a little bit of Bayes type probabilistic thinking would have led to a surprising finding perhaps tempering the blame game a little bit - not completely though.
Even if the rating agency is very accurate in giving a good rating to companies that won’t default, there is a reasonably high chance that cos who defaulted had a good rating
The question is thus, given that a company has defaulted, what is the probability that it had an excellent rating?
Turns out that, that probability is 9%. That means that ~10% of all the defaults will probably have good credit ratings.
Data collected from CRISIL Default Study report 2018 contains the necessary data that we can plug into a Bayes type analysis.
Data source : https://www.crisil.com/content/dam/crisil/our-analysis/publications/default-study/CRISIL-Default-Study-2018.pdf
As per CRISIL, the overall default rate is 4.4%
They have given CDR (Cumulative Default Rate) data only uptil 3 years but on page 19 they mention the average time to default for AAA rated instruments as 177 months. But since there is no data beyond 3 years I will take 3 years.
The crux is this, “Good” ratings are those which are in the “A” category ( AAA,AA and A) and Bad ratings are the ones in the B&C category ( BBB,BB,B and C).
To cut a long story short, based on the data above suggests 1.1% default within 3 years even for the rockstars ( that itself is disturbing)
Here is the probability distribution. I have assumed a 50:50 split between the bad rating and good ratings.
| Item | Default | No Default | Total |
|---|---|---|---|
| Bad Rating | 10.0% | 90.0% | 50.0% |
| Good Rating | 1.0% | 99.0% | 50.0% |
| Total | 5.5% | 94.5% | 100.00% |
Bayes theorem says that
P(Good Rating given that you have Defaulted) = P(Good Rating)* P(Default given that you have a Good Rating)/P(Default)
OR
0.5*0.01/0.055 = 9%
Even though credit ratings agencies are generally very good at assigning ratings given and 99% of AAA rated cos dont default , the probability that a co which has defaulted with good credit ratings is still ~10%
For Bayes, one could possibly go to ( a good source as well)
Best
Bheeshma