If the cumulative default probabilities of default for years 1 and 2 for a portfolio of credit risky assets is 5% and 15% respectively, what is the marginal probability of default in year 2 alone?

If the cumulative default probabilities of default for years 1 and 2 for a portfolio of credit risky assets is 5% and 15% respectively, what is the marginal probability of default in year 2 alone?
A . 15.79%
B . 10.53%
C . 10.00%
D . 11.76%

View Answer

Answer: B

Explanation:

One way to think about this question is this: we are provided with two pieces of information: if the portfolio is worth $100 to start with, it will be worth $95 at the end of year 1 and $85 at the end of year 2.

What it is asking for is the probability of default in year 2, for the debts that have survived year 1. This probability is $10/$95 = 10.53%. Choice ‘b’ is the correct answer.

Note that marginal probabilities of default are the probabilities for default for a given period, conditional on survival till the end of the previous period. Cumulative probabilities of default are probabilities of default by a point in time, regardless of when the default occurs. If the marginal probabilities of default for periods 1, 2… n are p1, p2…pn, then cumulative probability of default can be calculated as Cn = 1 – (1 – p1)(1-p2)…(1-pn). For this question, we can calculate the probability of default for year 2 as [1 – (1 – 5%)(1 – 10.53%)] = 15%.