Question

You are looking at a Baa bond. The cumulative default rate at 2 years is 0.504% 0.00504) and at 3 years is 0.906% (0.00906). (4 points) a. what is the 2-year survival rate? b. what is the 3-year survival rate? C. what is the marginal probability of default during the 3rd year? __

Answer 1

Answer-

Given

Cumulative default rate at 2 years = 0.504 %
Cumulative default rate at 3 years = 0.906 %

a)

2nd year survival rate = ( 1 - cumulative probability of default at 2nd year)

= ( 1 - 0.504 % ) = ( 1 - 0.00504) = 0.99496 = 99.496 %  

b)

3rd year survival rate = ( 1 - cumulative probability of default at 3rd year)

= ( 1 - 0.906 %) = ( 1 - 0.00906) = 0.99094 = 99.094 %

c)

The marginal probability of default in 3rd year

it can be calculated either ways

=cumulative probability of default at 3rd year - cumulative probability of default at 2nd year
= 0.906 % - 0.504 %
= 0.402 % = 0.00402

(OR)

( 1 - cumulative probability of default at 2nd year) x ( 1 - probability of default in year 3 ) = ( 1 - cumulative probability of default at 3rd year)

0.99496 x ( 1 - probability of default in year 3 ) = 0.99094

( 1 - probability of default in year 3 ) = 0.99094 / 0.99494
( 1 - probability of default in year 3 ) = 0.9959797

probability of default in year 3 = 1 - 0.9959797
probability of default in year 3 = 0.0040203

Therefore marginal probability of default in year 3 = 0.0040203 = 0.40203 %