difficulty with CLN question

[southeuro]

Dear David,

I’ve have struggling with the following question from FRM practice and past exams. Appreciate your kind help on this!

On CLN valuation

A three-year, credit-linked note (CLN) with underlying company Z has a LIBOR + 60 bps semi-annual coupon. The face value of the CLN is USD 100. LIBOR is 5% for all maturities. The current three-year CDS spread for company Z is 90 bps. The fair value for the CLN is closet to
a. USD 100.00
b. USD 111.05
c. USD 101.65
d. USD 99.19

Much appreciated!

 

[hamu4ok]

well if you use your BAII Plus calculator:
N=6, i/Y=2.5 (Annual Libor 5% / 2); PMT = + 2.8 (100*5.6%/2); FV=+100
CPT PV=101.6524 which is close to C.
however this valuation does not take into account credit risk of default of referenced counterparty (+ and perhaps the counterparty that issued CLN). Here we need to compute CVA = EPE* spread= 101.65 * 0.9% =0.91
that is the fair value of CLN should be PV of expected cashflows = 101.65 - CVA 0.91 = 100.74
but there are no such answer (the closest would be A), which means that probably I am wrong, or CVA adjustment is not required?
#southeuro what is the correct answer?

 

[southeuro]

the answer is d. But thanks to your answer I think I get it now. They use the spread of 90bps right at the beginning. ie.

N=6, i/Y=2.95 (Libor 5 + spread of 90bps % / 2 = 2.95); PMT = + 2.8 (100*5.6%/2); FV=+100
PV --> 99.19

I am not sure when to make the CVA adjustment (and how? do we add or subtract? you subtracted) and when to take the spread at the beginning.
My guess is that the spread intrinsically includes the risks so we don't do a separate CVA calculation. We would do that calculation only if there's a change after the start of the contract to reflect those changes. Your thoughts?

 

[hamu4ok]

the answer is d. But thanks to your answer I think I get it now. They use the spread of 90bps right at the beginning. ie.

N=6, i/Y=2.95 (Libor 5 + spread of 90bps % / 2 = 2.95); PMT = + 2.8 (100*5.6%/2); FV=+100
PV --> 99.19

I am not sure when to make the CVA adjustment (and how? do we add or subtract? you subtracted) and when to take the spread at the beginning.
My guess is that the spread intrinsically includes the risks so we don't do a separate CVA calculation. We would do that calculation only if there's a change after the start of the contract to reflect those changes. Your thoughts?

Both methods should give the same results, but adjusting the discount rate seems here more easier and quicker (besides I guess I got it EPE all wrong).

On the other hand, another question arises, if fair value of CLN is less than par value 99.19 < 100 (= negative NPV), then it makes no sense for investors to invest into such product on negative net return! They should demand higher return to compensate for the risks inherent in such products (etc. double default if there is wrong way risk present).

 

[southeuro]

yep good catch, and that seems to be the point of that question apparently!

 

[frmexam]

David/All
My thoughts were like this
i might be wrong but cannot convince myself about the flaw in this thinking
Net payment would be about 30 basis points every 6 months, so if i calculate PV@libor of 30 basis points in 6m, 1y, 1.5y, 2y.. 3y and then subtract from 100. Shouldn't this lead to the correct answer

 

[David Harper CFA FRM]

Hi @frmexam

I can't find this question, if anybody can point me to the source (I think @hamu4ok makes an excellent point ...). In the meantime, given the implication of the answer given (i.e., the value of the CLN is essentially treated as a bond paying L+60 when the discount rate is L+90, your approach (if I understand you correctly) should work if you:

• compute each net payment = 100*(5.9%-5.6%)/2 = $0.15
• PV this stream, note I give a zero to FV = -PV(5.9%/2, 6, $0.15, 0) = $0.8139; i.e., the stream of six net coupons, $0.15, discounted at L+90
• Then 100 - 0.8139 = $99.186. I hope that helps, thanks,