2013 GARP Practice Exam Q8

[harvey]

Hi David,

This is my first time post question here.

Consider a 1-year maturity zero coupon bond with a face value of USD1,000,000 and a 0% recovery rate issued by Company A. The bond is currently trading at 80% of face value. Assuming the excess spread only captures credit risk and that the risk-free rate is 5% per annum, the risk-neutral 1-year probability of default on Company A is closest to which of the following?

A. 2%
B. 14%
C. 16%
D. 20%

I used the following equation but got a wrong answer:
e^-(r+s)t=e^-rt [ e^-(pt) * 1 +(1-e^-(p*t)) * RR] where r is the risk-free rate, p is the risk-neutral prob, s is the credit spread and RR is the recovery rate
I solved the equation and got p = 20% but the correct answer is C (16%)

The solution provides the following two equations but I have never seen those formulas in Schweser Notes:

1. 1+r = (1-p) * (1+y) + pR where p is the probability of default and R is the recovery rate
2. If RR=0, 1+r=(1-p) * (1+y) - (1-p)*(FV/MV) where MV is the market value and FV is the face value

I wonder why there would be such two equations for this question and I would like to understand when we should use those two equations and when we should use the one that I originally apply for.

Thank you very much!

 

[ShaktiRathore]

hi,
to find risk neutral PD use,
FV*(1-PD)/(1+rf)=FV/(1+rf+s)
=>1+rf+s=(1+rf)/(1-PD)
=>1+rf+s-(1+rf)=(1+rf)/(1-PD)-(1+rf)
=>s=(1+rf)/(1-PD)-(1+rf)...1
This is the risk neutral PD. At this PD i would recover FV*(1-PD) of the FV this is the credit risk captured by s the credit spread.
get the credit spread from , .8FV=FV/(1+.05+s)=>1.05+s=1.25=>s=.20...2
s=20% so that 1 becomes,
.20=(1.05)/(1-PD)-(1.05)
=>1.25=(1.05)/1-PD
=>1-PD=1.05/1.25
=>PD=1-(1.05/1.25)=.20/1.25=.2*(.8)=.16 or 16%
[the other form of PD is given by PD=Credit spread/(1-RR) just remember this is not the risk neutral PD.]
thanks

 

[harvey]

Thanks a lot !!