What is the probability that it would have defaulted within 6 months?

The probability of default of a security over a 1 year period is 3%.

What is the probability that it would have defaulted within 6 months?
A . 98.49%
B . 3.00%
C . 1.51%
D . 17.32%

View Answer

Answer: C

Explanation:

The question is asking for the probability of default over a 6 month period when the probability of annual default is known. If we let the 6 month probability of defaut be ‘d’, then the probability of survival at the end of 1 year would be (1 – d)^2. This we know is equal to 1 – 3% = 0.97. Therefore we can calculate ‘d’ to be equal to 1.51%. Choice ‘c’ is the correct answer, the others are incorrect.

Note that an exam question may ask for probability of the security having survived after 6 months, in which case the answer might be 1 – 1.51%. Also note that such questions will always require you to use the probability of survival (1 – probability of default) for doing the calculations. That is because the probabilities of survival can be multiplied over periods of time, but not probabilities of default as the first default in any period is the ‘game-over’ event after which neither survival nor defaults mean anything. Therefore you generally always have to get the probability of survival till a point in time, and use that for any other calculations.