GARP Sample Exam Question #6 (Credit Risk - Implied Default Probability)

[Robert Paterson]

Question 6 Sample Exam Question at the end of the GARP Credit Risk seems intuitive but the answer seems incomplete. See below for details.

Question:
Suppose that you want to estimate the implied default probability for a BB-rated discount corporate bond.

• The T-bond (a risk free bond) yields 12% per year
• The 1-year BB rated discount bond yields 15.8% per year.
• The 2-year BB rated discount bond yields 18% per year.

If the recovery rate on a BB-rated bond is expected to be 0%, and the marginal default probability in year one is 5%, which of the following is the best estimate of the risk neutral probability that the BB-rated discount bond defaults within the next two years?

A. 6.85%
B. 3.28%
C. 9.91%
D. 10.41%

The answer given by GARP is:
C
Explanation (by GARP): (1-.012)^2 = PD * (1+.18)^2 --> PD = 9.91%

There response seems incomplete. I start with the following (slightly more comprehensive and complete?) equation:
(1+r)^t = (1-PD) *(1+y)^t + (PD * R)
Where:
r = yield of risk free asset
y = yield of risky asset
R = Recovery rate

I set up as follows:
(1-.012)^2 = (1 - PD) * (1+.18)^2 + (PD * 0)
--> (1-.012)^2 / * (1+.18)^2 = (1 - PD)
--> PD = 1 - [(1-.012)^2 / * (1+.18)^2] = 9.91%

Two questions:
1) Anyone else have a similar observation?
2) Is the formula employed correct? (looked through GARP materials and could not confirm but formula makes intuitive sense).

Thanks -
Rob

 

[David Harper CFA FRM]

Hi @Robert Paterson

Yes, we had some discussion about this question a few years ago at https://forum.bionicturtle.com/threads/question-12-bb-rated-bond-credit.2145/page-2#post-20632
I think upshot is that GARP did intend to show your solution, it's just a typo; not a perfect question (also as I recall this assumption "marginal default probability in year one is 5%" wasn't used and, in fact, maybe didn't reconcile ...). Thanks!

 

[Robert Paterson]

Thanks, David!