Implied default probabilty

[nanchary]

David:

Please help me in solving the following questions...

1) The US Government Bond Zero Curve give a 1-year semiannual yield of 4
percent, on the same basis a corporate security has a yield of 5
percent.

What is the market implied 1-year default probability of the corporate
security. The recovery rate is 88.6 percent?

a) 0.974%.
b) 1.000%.
c) 9.000%.
d) 0.184%

Convert the semiannual yield to annual yield and use 1-p=1-(1+i)/(1+k)
And answer is a, here I am not using recovery rate..
I can also solve the above by: solve following equation for p (default
prob):

1.04 = (1-p)*1.05 + p*0.886*1.05

You get 8.54% and I see 9% as close answer.


Thanks,
Narendar

 

[David Harper CFA FRM]

Narendar,

It's a bad question, I don't know source but I'd disregard it. First, to ask about "a 1 year semiannual yield of 4%" is confusing; is that an 8% bond-equivalent yield? If so, the question would just refer to a "1 year yield of 8%" as the 'semiannual' only confuses.

But you wouldn't get this question because it requires solving for the PD given the spread, where here is spread given PD:

http://learn.bionicturtle.com/images/forum/probdefaultwithrecovery.jpg

The correct answer is 15.95%, which doesn't seem to be an option (i.e., that is what i get for 1 - P when i solve for P above given a spread of 2% [10% - 8%] where P = prob of repayment). If the question meant to use six-month period, then the answer is 16% (= 1- 0.9165^2 where 0.9165 is the p given a spread of 1% [5%-4%]).

The answer starts with p = [1+i]/[1+k] which is correct when there is no recovery. With recovery, you can't use this formula because you are solving for PD and that would be circular!

David