2013 GARP practice exam P2 question 6

[cotton]

for this question, why can't we use formula: spread=pd * lgd?
if yes, then spread=5% * 25%=125bp, instead of the answer 390bp.

I know the formula above is an approximation, but the question is how we know when to use it and when not to?

 

[David Harper CFA FRM]

Hi cotton,

Interesting! At first glance, I think you should be able to use your approximation: 125 is too far away from 390 bps. Something may be wrong with the question (checking now .... I don't instantly see the reason for the difference, frankly ), but normally your approximation would be much closer.

More generally, you would know to use the exact equality (i.e., PV of premiums = PV of expected payoff) simply because the question gives you all of the necessary parameters; e.g., the approximation would not require the riskfree rate assumption, nor really even the term of the contract (certainly not the accrual payment assumption).

Your approximation is called for when you are only given the limited information (i.e., given 2 params, find the third) and can settle for a mere approximation. I notice the question hints at exactness, too, with atypical lack of dispersion among the answers:
a) 380 basis points
b) 385 basis points
c) 390 basis points
d) 400 basis points

i.e., we should not expect that approximation to arbitrage between 5 bps differences

thanks (i'll post up if/when i figure out why such a big, suspicious difference between 125 and 390) thanks,

 

[David Harper CFA FRM]

Hi cotton,

Okay, I missed this, too, when I first read it. From the question: "Lin Ping is valuing a 1-year credit default swap (CDS) contract which will pay the buyer 75% of the face value
of a bond issued by Xiao Corp. immediately after a default by Xiao."

The protection buyer will pay 75% because that is the loss net of recovery (CDS seller is "making whole" the protection buyer): the recovery assumption is 25% not 75%.

So, your approximation works nicely: as R = 25% and LGD = 75%, S = PD*LGD = 5%*75% = 375 bps
... normally, pretty good. Alas, the question gives too many nearby false options. Thanks,

 

[cotton]

thanks David for the reply.

thanks David for the reply.

"Lin Ping is valuing a 1-year credit default swap (CDS) contract which will pay the buyer 75% of the face value of a bond issued by Xiao Corp. immediately after a default by Xiao."
The protection seller will pay the buyer 75% in the event of default. so 75% is recovery rate, then lgd=25%. Am I missing anything?

 

[southeuro]

what i am not sure of, is why we assign probabilities to the spread payments…. and if we do, why assign probability of default for the first term, and the 1 - PD for the 2nd term?

any help would be appreciated! thanks

ps. yep I also like this approximation although doesn't work in this case.

 

[southeuro]

OK I guess I get it -- the question says the default can occur only at mid-point so we have to weigh the 1st payment with the default probability and the second with no default probability (since if it were to occur it would have prior to first term)… Am I right in this line of reasoning?

 

[prebhan27]

Hi @David Harper CFA FRM CIPM,
I am still not sure about the premium leg term: s*[0.5d(0.5)*PD+d(1)(1-PD)]
Does the part with 0.5d(0.5)*PD mean that, if in half a year there is a default you still get the accrued premium, which is half ot the premium (Therefore *0.5 at the beginning of the term)? And the part with d(1)(1-PD) means, if there is no default you get the full premium at the end of the year?
Could you explain that in a bit more detail?
Thank you in advance for your help!

 

[David Harper CFA FRM]

Hi @prebhan27 You are basically correct, I think. I don't want to defend the numeric values in the question (it's not mine), but the equation looks okay to me. As you know the fundamental CDS equality is simply: PV(payments by the protection buyer) = PV(contingent payoff by protection seller). The protection buyer will pay the spread premium regardless, but if the reference defaults then the protection buyer pays the accrued premium. In this case, it's only one year, so it's either

• pay the full premium with probability = (1-pd); i.e., survival
• or, pay the premium accrued over half the year (* 0.5); i.e., default

The protection buyer's calculation needs to include the full 100% probability, which is both the probability of survival and the probability of default. The protection seller only needs the default probability term simply because the seller pays zero in the case of survival. So the term, 0.5*d[0.5]*π + d[1.0]*(1-π), is conceptually correct because we need to include the premium(s) paid weighted by both survival and default scenarios. I hope that explains!

 

[prebhan27]

Thanks for your answer @David Harper CFA FRM CIPM. It explains it very well. When I first solved the question, I found it difficult to think about the accrued premium, if there is a default after half the year. How is that in practice, does the CDS seller really get the accrued premium after half the year, if there is a annual premium payment ?

 

[enjofaes]

 

[enjofaes]

It's a bit weird:
Premium leg gets spread payment and accrual
So spread*(0.5*df_0.5*PD + df_1*(1-PD)) reflecting the default payment in half a year and the survival accrual (term is new for me in this context)??

Payment leg = contingent payment which makes sense. 0.75*d_0.5 * PD

 

[enjofaes]

It's a bit weird:
Premium leg gets spread payment and accrual
So spread*(0.5*df_0.5*PD + df_1*(1-PD)) reflecting the default payment in half a year and the survival accrual.. NVM I below and it made sense

Hi @prebhan27 You are basically correct, I think. I don't want to defend the numeric values in the question (it's not mine), but the equation looks okay to me. As you know the fundamental CDS equality is simply: PV(payments by the protection buyer) = PV(contingent payoff by protection seller). The protection buyer will pay the spread premium regardless, but if the reference defaults then the protection buyer pays the accrued premium. In this case, it's only one year, so it's either

• pay the full premium with probability = (1-pd); i.e., survival
• or, pay the premium accrued over half the year (* 0.5); i.e., default

The protection buyer's calculation needs to include the full 100% probability, which is both the probability of survival and the probability of default. The protection seller only needs the default probability term simply because the seller pays zero in the case of survival. So the term, 0.5*d[0.5]*π + d[1.0]*(1-π), is conceptually correct because we need to include the premium(s) paid weighted by both survival and default scenarios. I hope that explains!

Payment leg = contingent payment which makes sense. 0.75*d_0.5 * PD