Heatmaps for Comparing Credit Rating Stability Across Years
Summary
The document proposes a heatmap for showing how often obligors remain in each credit rating class from one period to the next. Ratings occupy one axis and time intervals the other; color represents the proportion that kept the same rating. This puts many rating classes and periods into one view, avoiding the clutter of separate line charts while retaining the individual categories.
The example uses MATLAB to map rating and time indices to the stability proportions, display them as a surface viewed from above, and add axis labels and a color scale. It also suggests limiting the number of colors to make the display easier to distinguish. The example data are randomly generated, so they demonstrate plotting mechanics rather than provide evidence about real rating behavior. The note does not discuss uncertainty, sample sizes, or how to choose color breaks; those choices matter when comparing stability across classes or periods.
Key ideas
- A heatmap can display rating classes against time intervals, with color encoding the proportion of obligors that retain their rating.
- Putting all classes in one plot can reduce clutter while preserving rating-level detail.
- A color scale and clear axis labels help readers interpret the stability values.
- The example uses simulated values and does not establish empirical patterns.
Tags
Full text
# Visualising credit rating stability
# Visualising credit rating stability
I am looking for a way to visualize credit rating stability results.
Some background: Per rating class (e.g. AAA, AA+, AA, AA-, A+, ...), I look at the percentage of obligors that keep their rating from one year to the other. E.g. if in rating class BBB, I have 100 counterparts at `t`, and, of these 100, only 85 remained in rating class BBB at time `t+1`, the percentage of obligors that keep their rating from `t` to `t+1` is 85%.
Doing so, I get a table like:
```
t to t+1 t+1 to t+2 ... t+n-1 to t+n
AAA 80% 90% ... 85%
AA+ 75% 92% ... 85%
...
Caa 60% 55% ... 67%
```
To visualize this, I tried line graphs for each of the rating classes, but this way I end up with way too many graphs; it becomes very messy. I thought about grouping the ratings into broader classes but I lose some information this way.
Does anyone know about a good visualization technique for this kind of problem?
## Answer by phdstudent (score 5, accepted)
https://quant.stackexchange.com/a/38932
One option to do it is a heatmap. Not sure which software are you using, but in matlab it is extremely simple to do and powerful to tweak.
Below an example. Let's assume there are 30 periods $t$ to $t+30$ and 21 ratings.
Then you could run:
```
rating = {'Aaa'; 'Aa1';'Aa2';'Aa3';'A1';'A2';'A3';'Baa1';'Baa2';'Baa3';'Ba1';'Ba2';'Ba3';'B1';'B2';'B3';'Caa1';'Caa2';'Caa3';'Ca';'C';}
ratingindex = (1:size(rating,1));
t = [1:30]';
prop = rand(size(rating,1),size(t,1));
[X, Y] = meshgrid(t,ratingindex);
[Xq,Yq,Vq] = griddata(t,ratingindex,prop,X,Y);
surf(Xq, Yq, Vq)
view(2);
xlabel('Time')
ylabel('rating')
colorbar
title('Probability of keeping rating')
```
The output would be:
Where the colors indicate probabilities. The $x-axis$ has the time and the $y-axis$ the ratings. For easiness I have categorized the ratings in 1 to 10 instead of the AAA, AA+, etc. But you can easily change the appearance of the axis.
Following the comment below, you can easily have less colors in the plot. Just add: `colormap(lines(n))` for `n` colors. For n=3 the output would look as follows:
Further, persistence in ratings should help with disciplining the output.Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.