PD & expected loss

[higaurav]

Hi David,

I have taken this Q from the practice set 2007...

A company has been offered a USD 5 million term loan to be fully repaid only at maturity
2 years later. The bank estimates that it will recover only 55% of its exposure if the
borrower defaults and that the likelihood of that happening is 0.1%. What is the bank’s
expected loss one year later?
a. USD 2,750
b. USD 2,250 (answer)
c. USD 1,375
d. USD 1,125

here it mentions that maturity is at end therefor period doesn't matter, I am little confused...as in our credit risk portion, we have not used the same method for zero coupon bonds..and calculated the marginal PD at the end of the year. I was getting C as I calculated marginal PD

Rgrds,
OM

 

[David Harper CFA FRM]

Hi OM,

I *totally* empathize; i think your answer is absolutely good: marginal PD = 1 - SQRT(1 - 0.1% cumulative PD). Uggg. The question is imprecise to say "the likelihood of that happening is 0.1%." Ambiguous. Ugg, plus your approach has an answer.

Well, first, these practice questions are imperfect, i would hope the actual would not word this way. Second, sometimes you can "know too much." Since the question has EL, it's probably good to reflexively associate EL with (PD/EDF)(LGD/1-recovery)(EAD/AE) esp since there is no mention of marginal/cumulative. But that's mere pedagogy, I think you have an appeal case

David

 

[higaurav]

Thanks David, even my learning going through this question is that better not to think too much some times..

 

[Johannes]

Hi David,

can you please outline how you derive answer C? I do not get it.

Thanks,

Johannes

 

[David Harper CFA FRM]

Hi Johannes,

OM applied the thinking in the A. Saunders loan reading, where cumulative probability of default (i.e., default during any year in a multi-year period) = 1 -(marginal probability of repayment in year 1)*(marginal probability of repayment in year 2)*....(p in year n). So, if p = prob or repayment, then p^n = cumulative probability of repayment (i.e., repay every year). The only other outcome is non repayment in some year, so cumulative PD = 1 - p^n.

Or, p = (1 - PD)^(1/n) so that 1-p = marginal PD = 1 - (1-cumulative PD)^(1/2) = 1 - SQRT(1-cumulative PD)
Here is, 1 - SQRT(1-0.1%) = .05%. So that $5 MM EAD * .05% PD * 45% LGD = $1,125

So that approach depends on reading the 0.1% as a cumulative PD instead of what the question means (a marginal PD). But given the phrasing, IMO, OM's approach is just as sensible.

David

 

[Johannes]

Hi David,

thanks for your answer, but you calculate now $1,125, which is answer D and not C as OM calculated. I am getting a bit confused now. I understand your answer, but how did OM derive answer C then? And does this imply that C is incorrect?

Thanks a lot,

Johannes

 

[David Harper CFA FRM]

Hi Johannes,

OM initialy used 55% for the LGD:
($5 MM)(.05%)(55%) = $1,375 but that is incorrect because 55% is the recovery rate. 1-55% = 45% is the expected loss given default (LGD). So, yes, sorry for the confusion, (C) is incorrect and (D) has justification under this Saunders-inspired alternative. OM's appeal case is denied on a technicality, after all

But please don't let this take you off track. The question clearly expects: EL = EAD*PD*LGD. (B) is the answer because (B) is the most straightforward approach.

Please consider this alternative a kind of over-thinking, where (D), IMO, is certainly valid. We still do want to understand Saunders' cumulative/marginal PD concepts.

David

 

[higaurav]

Hi David /Johannes,

Thanks for pointing that out, I agree that was the calculation error ...

OM

 

[higaurav]

Hi David,

Practice set has confused once again .. Now this is Q26 given in the 2006 Test1. The reason for confusion is that the solution to this questions uses exactly what we were discussing in our last thread above for different Q from practice set ( same concept but different solution). Now confusion is that to consider which method to be correct - use maturity or not to use maturity in the calculation of expected loss? I hope you can throw some light on this. (BTW, do you think actual exam also have so much of ambiguity in questions ? )

26. Which of the following loans has the lowest credit risk?
Loan 1 Year Probability
of Default
Loss Give
Default
Remaining Term in
Months
a. 1.99% 60% 3
b. 0.90% 70% 9
c. 1.00% 75% 6
d. 0.75% 50% 12
ANSWER: A
The 1 year probability of default needs to be adjusted to the remaining term using
the formula [(1-d_month)12 = (1-d_annual)]. We multiply the monthly PD with the
loss given default (LGD) to get the expected percentage loss (EL%):
Loan 1 Year PD LGD Remaining Term PD to Maturity EL %
A 1.99% 60% 3 0.50% 0.301%
B 0.90% 70% 9 0.68% 0.473%
C 1.00% 75% 6 0.50% 0.376%
D 0.75% 50% 12 0.75% 0.375%
As shown, loan A has the lowest EL%.
Reference: Measuring and Managing Credit Risk, De Servigny and Renault,

 

[David Harper CFA FRM]

Hi OM,

I agree the phrasing is imprecise and leads to uncertain approach. It would be better for the question to say:

Given annual cumulative PD of 1.99%, LGD = 60%, and 3 months remaining in term, and further assuming the monthly marginal PD is constant, what is the EL?

That would lead us to use: cumulative PD = 1 - (monthly marginal PD)^months

Given: monthly marginal prob of repay = (1-1.99%)^(1/12) = 0.998326 monthly marginal prob of repay (p)
So, 3 month cumulative PD = 1 - (0.998326)^3 = 0.501%
and 0.501% 3 month cumulative PD * 60% LGD = .301% EL

Re: do you think actual exam also have so much of ambiguity in questions? I honestly don't know what the exam will contain, I sincerely hope not.

David

 

[higaurav]

Thanks David !!

 

[ritao]

Hi David,

I want to estimate the PD of corporate obligors under Basel II IRB approach.
I f I have the rating of each obligor, u have mentioned that I can combine this with a transition matrix, but I didn't get it, a transition matrix of what? and can I find this matrix somewhere?
Another thing, is it appropriate to calculate 1-y PD as the number of defaulted obligor during a year over the total number of obligors at the beginning of this year; and after finding the average probability by rating grade? and where can I use in this process the transition matrix you were talking about?
As I'm still junior in this domain, I would appreciate if you could help me.
Thank you.

Ritao

 

[[email protected]]

David,

In above mail chain
26. Which of the following loans has the lowest credit risk?
Loan 1 Year Probability
of Default
Loss Give
Default
Remaining Term in
Months

whether this question above i.e concept of cumulative/marginal PD of default relates to l1.

I thought for L1 the only formula we need t understand is EL = EAD*PD*LGD. Please correct me, if I m wrong.

Thanks a lot
snigdha

 

[David Harper CFA FRM]

Hi snigdha,

Yes, technically you are correct, this would fall under L2 not L1. Please note the sample question PRE-DATES the FRM split into L1/L2 so you can't read anything into there selection vis a vis the exam's two levels.
... however, given that GARP is a bit loose sometimes (questions vis-a-vis assignments) and given that they like to query PD, personally I would still familiarize (after all, L1 does include some related credit risk concepts).

Hope that helps, good luck! David