Explanation:
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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