GARP.FRM.PQ.P2 GARP Mock Exam 2022 Part II - Q 29 Probability

[yukoc100]

Hey everyone,

I am having a hard time with the following task:

Question:
Q 29
A risk analyst estimates that the hazard rate for a company is 0.12 per year. Assuming a constant hazard rate model, what is the probability that the company will survive in the first year and then default before the end of the second year?

A. 8.9% B. 10.0% C. 11.3% D. 21.3%

Answer:
B is correct.

The joint probability of survival up to time t and default over (t, t+ τ) is:

P[t* > t ∩ t* < t+τ] = 1-e-λ(t+ τ)-(1-e-λt) = e-λt(1-e-λτ)

The joint probability of survival the first year and defaulting in the second year is:

P[t* > 1 ∩ t* < 1+1] = e-0.12*1(1-e-0.12*1) = 10.03%

My approach:
My solution was C (11.3%).
My approach is: default in t2 (10%) / survival in t1 (88%)

This approach is also from Schweser. Did GARP make a mistake here?


Thanks in advance!

 

[David Harper CFA FRM]

HI @yukoc100 GARP is correct. If the question were instead "What is the conditional probability of default during the second year?" then the answer would be 10.03% / (1 - 0.12*1) = 11.3%. But the questions asks for the joint (aka, unconditional) probability of default during the 2nd year, such that the correct answer indeed is 10.0293%, rounded to 10.0%. See https://forum.bionicturtle.com/thre...ginal-probability-of-default.22771/post-77917