2 approaches to this question?

[qin841121]

Suppose the rate on 1-year zero-coupon corporate bonds is 13.5% and the implied
probability of default is 3.96%. Assume LGD is 100%. Based on the given
information, the 1-year T-bill rate is closest to:
A. 4.49%.
B. 9.00%.
C. 6.74%.
D. 6.00%.

I am able to solve using one method and get 9%.

May I know why I cannot use another method to solve it?
spread=edf*Lgd
spread=3.96
13.5-3.96=9.54%.

 

[troubleshooter]

I think the reason for this is the real world vs. risk neutral probability. PD of 3.96% is risk neutral probability, which when you use in the following formula, you get r = 9%

FV/(1+y) = FV*(1-PD)/(1+r) ; Note: Recovery Rate = 0

The Real world probability should be higher than 3.96%, hence the actual spread should be greater than 3.96% (spread = PD * LGD), where LGD = 1. This is why you are seeing a risk free rate higher than 9%, when you use underestimated spread as 3.96%.

 

[Robert Morris]

Hi troubleshooter,

I'd come across this in the Test bank questions from the Handbook. Is there a foolproof way of telling which method the the question is expecting to be used?

Quick estimate: spread = LGD * PD

Long real-world: FV/(1+y) = FV *(1-PD)/(1+Rf) + FV*(1-LGD)*PD/(1+Rf)

which simplifying gives (I think!): LGD*PD*(1+y) = (1+y) - (1+Rf) = spread