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Answer: Spearman correlation
A is correct. The credit ratings are **ordinal** and the relationship between the two agencies’ ratings is **nonlinear**, as suggested by the scatter plot. Spearman correlation is the appropriate measure because it captures **monotonic relationships** between ordinal variables. B, C, and D are incorrect because Pearson correlation, correlation matrices, and covariance are designed for **linear** relationships between continuous variables.
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A credit risk manager is in charge of credit risk analysis of large corporates at Bank XYZ. The manager is in possession of credit ratings provided by two rating agencies, X and Y, for 30 companies the manager oversees. The ratings are classified into four categories:
| Rating categories | Description |
|---|---|
| 1 | High investment grade |
| 2 | Mid investment grade |
| 3 | Low investment grade |
| 4 | Non-investment grade |
The manager plots the rating categories from the two agencies as shown below:
Rating - Agency Y
5 |
4 | * *
3 | * *
2 | * *
1 | * *
0 |________________________________________
0 1 2 3 4 5
Rating - Agency X
Rating - Agency Y
5 |
4 | * *
3 | * *
2 | * *
1 | * *
0 |________________________________________
0 1 2 3 4 5
Rating - Agency X
Which of the following statistical measures could best help the manager approximate the link between rating categories from the two agencies?
A
Spearman correlation
B
Pearson correlation
C
Structured correlation matrix
D
Covariance
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