
Explanation:
The defaults shown are cumulative. As such,
P(Default in year 3) = Cumulated default rate up to year 3 − Cumulated default rate up to year 2
= 36.908 − 27.867 = 9.041%
Note: Marginal probability is an unconditional PD from the perspective of today. It is not the PD conditioned on forward survival.
Q.3051 From the given below what is the probability of a bond rated Caa or below defaulting during the third year?
Average cumulative default rates (%), 1970-2012, from Moody's.
| Term (years): | 1 | 2 | 3 | 4 | 5 | 7 | 10 | 15 | 20 |
|---|---|---|---|---|---|---|---|---|---|
| Aaa | 0.000 | 0.013 | 0.013 | 0.037 | 0.106 | 0.247 | 0.503 | 0.935 | 1.104 |
| Aa | 0.022 | 0.069 | 0.139 | 0.256 | 0.383 | 0.621 | 0.922 | 1.756 | 3.135 |
| A | 0.063 | 0.203 | 0.414 | 0.625 | 0.870 | 1.441 | 2.480 | 4.255 | 6.841 |
| Baa | 0.177 | 0.495 | 0.894 | 1.369 | 1.877 | 2.927 | 4.740 | 8.628 | 12.483 |
| Ba | 1.112 | 3.083 | 5.424 | 7.934 | 10.189 | 14.117 | 19.708 | 29.172 | 36.321 |
| B | 4.051 | 9.608 | 15.216 | 20.134 | 24.613 | 32.747 | 41.947 | 52.217 | 58.084 |
| Caa – C | 16.448 | 27.867 | 36.908 | 44.128 | 50.366 | 58.302 | 69.483 | 79.178 | 81.248 |
A
36.908%
B
9.041%
C
52.124%
D
45.949%
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