unexpected loss

[[email protected]]

hi David,
can you please help me to solve this question? i picked from Kaplan schweser, thanks

John Clayburn is trying to parameterize a credit risk model for his employer, Syacmoor Bank. Based on a large sample of loans, he has estimated a default frequency of 12%. John knows that this is a necessary input to calculate the unexpected loss. Which of the following is closestto the standard deviation of Sycamoor’s default frequency?


A) 35%.
B) 88%.
C) 12%.
D)
11%.

 

[David Harper CFA FRM]

Hi baffour,

the answers given are bunkish, but i've failed you if you can't take a first swipe
i'll give you a hint: EDF/PD is a Bernouilli random variable (default with p = 12%, no default with 1-p). You tell me the rest, don't let me down, my professional reputation is on the line... thanks, David

 

[Addy]

Great...

So, p = 12% and q = 88%..

Variance of bernoulli is : p x q = .12 x .88 = 10.56 % or 11 % is the answer..

 

[David Harper CFA FRM]

but question asks for standard deviation, so need to SQRT[p*(1-1p)], so i get ~32.5%. The answers are unusual, GARP won't do that, the FRM will include the actual answer. Thanks, David

 

[Hend Abuenein]

But the question asks for the standard deviation, Azfar, not the variance.
Stdv would be sqrt of 10.56% which is 0.3249
Which is not in the choices? Or am I wrong somewhere?

 

[Hend Abuenein]

But they didn't include a few actual answers in May David
.
.
.
We replied # 4 and #5 simultaneously here

 

[David Harper CFA FRM]

Hend, thanks, in the May exam, they used "nearest to" when it was not a case simply of rounding? Like this question above, it's rather silly to give 35% when answer is 32.5%.

Historically GARP did not do this. If they did it in May 2011, then I stand corrected (I assume it's not b/c the question is mistaken. It's another reason i think this would be bad exam methodology; the answer should be accountable to a specific result).

Thanks for an update w.r.t May 2011, i missed that feedback if that was the case. Thanks, David

 

[Hend Abuenein]

You're welcome. Let's hope they don't repeat that in November, not for the sake of their professionalism as much as the sake of our cognitive concentration It was a bad experience having us loop over bad answer choices like that.

 

[David Harper CFA FRM]

Agreed, i am currently preparing 2012 feedback based on their draft AIMs, so I will be sure to include this point (it won't help for Saturday of course) ... but "nearest to" questions like the above (IMO) have dubious methodological (psychometric) justification. i think cognitive is exactly the right word choice, it makes little sense to make the candidate jump throw the hoop to do the question, then ask them to perform the additional task of identifying nearest to. (in itself, when fractions, decimals, origin or negatives are involved, this can become non-trivial). Thanks Hend!

 

[[email protected]]

hi David
this is the answer i got for solving the question.
variance = EDF × (1 − EDF) = (0.12) × (1 − 0.12) = 0.1056. Thus, standard deviation of default frequency (0.1056)0.5 = 0.32496.

the options given made me confuse, although i believe i am correct.
i just wanted to find out if you will use a different method.

regards

 

[[email protected]]

oh sorry, emphasis was on closest to. hahahahaha, please dont fail me yet for choosing option A.
hahahahahaaaaa

 

[David Harper CFA FRM]

Baffour,

I see you wrote the correct: "variance = EDF × (1 − EDF) = (0.12) × (1 − 0.12) = 0.1056. Thus, standard deviation of default frequency (0.1056)0.5 = 0.32496."

Thank you, I was nervous as my honor was on the line
While i may not be a proud man, i am today at least not a broken man .... Cheers! David

 

[[email protected]]

David at times i face such problems and i want to find out if there are other alternatives in getting the exact answer or an answer which is extremely closer to the options provided in terms of rounding up. in my opinon i deem closest to as used in the quetion as the nearest whole number which could be 33%.
although i knew my steps were right.

 

[David Harper CFA FRM]

Barrour, yes, i absolutely sincerely understand. I hope my lame attempts at humor, enabled a bit by fatigue, did not given any offense or come at your offense, sorry!. I am the first person to tell you: the simplest problems give the worst kind of trouble.

Earlier this week i spent 2 hours on this same issue of Bernouilli, doubting myself on whether i can apply E[XY] = E[X]*E[Y] + covariance(X,Y) to two Bernouillis, see Q #6.
http://forum.bionicturtle.com/threads/l1-t2-202-variance-of-sum-of-random-variables.4967/

Thanks, David

 

[BioNerd]

so same for LGD too, right? The variance of LGD will be LGD*RR. If LGD, EDF and exposure are given, Unexpected Loss can be calculated.

 

[David Harper CFA FRM]

it's tempting but, no. Variance of EDF is EDF*(1-EDF) only because default is a Bernouill http://en.wikipedia.org/wiki/Bernoulli_distribution which has an ultra-simple variance. But loss/recovery is not 0/1. Quite the opposite LGD is considered difficult to parameterize. Popular is a beta distributions, so would need to use beta's variance in that case. For FRM, variance (LGD) will always be provided due to it's nature

UL is found in assigned Ong Ch 5 & 6:
Unexpected loss (%) = SQRT[EDF * variance(LGD) + LGD^2 * variance(EDF)]
.. in which case, you will always be provided variance(LGD)

 

[BioNerd]

That makes sense. Thanks much!