[ 2009 FRM Sample Exam ] Quantitative Analysis Q23

lalamei

 

23. A portfolio consists of 17 uncorrelated bonds, each rated B. The 1-year marginal default probability of each bond is 5.93%. Assuming an even spread of default probability over the year for each of the bonds, what is the probability of exactly 2 bonds defaulting in the first month?

A. 0.0325%

B. 0.325%

C. 0.024%

D. 0.24%

lalamei

 

Correct answer is Bfficeffice" />

Given a 1-year marginal default rate of 5.93%, the 1-month marginal default rate is 1 ? (1 ? 0.0593)(1/12) = 0.00508.

The number of combinations of 2 bonds from 17 bonds is 17*16/2, and so the probability of exactly 2 bonds defaulting in the first month is:

(17*16/2) * (0.00508)2 * (1 ? 0.00508)15 = 0.325%