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Whats the difference between probability of default and marginal probability of default. Was trying the below

45. 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%

ANSWER: B

2006 FRM Practice Exams 39

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%

45. 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%

ANSWER: B

2006 FRM Practice Exams 39

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%

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