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Specific Question on implied default from market prices

Thread starter #1
David, Hope you don't mind if If ask some specific questions (from previous FRM exams) (As you mentioned, some of the questions are quite weird to say the least).

The yield on a zero-coupon Treasury bond with a one-year maturity is currently 6% per annum. The Treasury zero-coupon yield curve is assumed to be flat. The spread over Treasuries for an AA-rated corporate bond with a maturity of three years is 70 basis points. What is the expected of loss from default as a percentage of the non-default value for the corporate bond?
a. 1.278
b. 1.763
c. 2.078
d. 2.215

The Answer is supposed to be C (2.078)
PV (spread) - exp(-0.007) X 3 = .97219. The expected loss is 1- PV(spread) = .02078

What is the theory behind this? - the same as what Saunders gives as p= probability of payment = (1+i)/(1+k), and the probability of default as 1-p. except that it is compounded continously (CC) here and for three years.

But expected loss can't be equated as probability of default!!!. This is weird or am I confused?

I have also noticed that FRM questions liberally and freely assume CC with out mentioning it. If we solve the above using the (1+i/1+k) approach, we get answers close by but not the exact answer, which leaves us more confused than before

Thanks as always


David Harper CFA FRM

David Harper CFA FRM
Staff member

I don't mind, I am just as troubled by this as you are. It is misleading to be giving these examples. I'm adding this to my list, and although it won't help this year, I've asked for a call with head of GARP because I've collected too many exceptions (I have already sent them many discrepancies this year.) I have a related concern (this year especially) around compounding conventions for bond pricing (i.e., annual vs. semi-annual, which I think has been loosely treated). So, yea, i see what they are doing here:

Prob repayment (p) = exp(6% x 3)/exp (6.7% x 3) = exp([6% x 3] -[6.7% x 3]) = 97.92%

But i would *not* have done that. I would have done, as you suggest:

p = [1+6%]/[1+6.7%] = 99.34% --> 99.34% ^ 3 = 98.04% is the cumulative probability of no default --> 1 - 98.04% = 1.96% is cumulative prob of default.

To use CC here is perhaps elegant but inconsistent with everything I've read (incl. Fabozzi); e.g., if you can do this here, then you can use CC to solve for implied forward rates but I've not seen that ??!!

Agreed also on confusion re: expected loss. I mean, if given the spread and given the prob of repayment (p), you could solve for the implied recovery rate, but that's not applicable. So, I don't really understand even the language of the question....confused me too!

Thread starter #3

Thanks a lot.

We often tend to assume that GARP/FRM questions are "great"while the problem lies with "us" (lack of understanding).

If these kind of questions are frequent, they can have an adverse impact on our confidence during the exam.

Hopefully, GARP has improved.