Explanation:
At the end of year 1, there is a 5% chance of default and an 80% chance that the firm will maintain a Baa rating. In year 2, there is a 5% chance of default if the firm was rated Baa after 1 year (80% × 5% = 4%). There is a 0% chance of default if the firm was rated Aaa after 1 year (10% × 0% = 0%). Also, there is a 15% chance of default if the firm was rated Caa after 1 year (5% × 15% = 0.75%). The probability of default is 5% from year 1 plus 4.75% chance of default from year 2 (i.e., 4% + 0% + 0.75%) for a total probability of default over a 2-year period of 9.75%.
(Book 4, Module 50.2, LO 50.h)
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Question 83
Given the following 1-year transition matrix, what is the probability that a Baa-rated firm will default over a 2-year period?
| Rating From | Rating To | |||
|---|---|---|---|---|
| Aaa | Baa | Caa | Default | |
| Aaa | 90% | 10% | 0% | 0% |
| Baa | 10% | 80% | 5% | 5% |
| Caa | 1% | 4% | 80% | 15% |
A
5.00%.
B
9.75%.
C
14.50%.
D
20.00%.
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