GARP Practice Exams Part 2 - Query on some questions

[papillonring]

Hi I have some queries on some questions in the GARP practice exams:

Ques 28
Is there some error in the answer? The answer provided is b) KMV's PortfolioManager. The question is asking which model builds on transition probabilities determined by marco factors but the explaination says that Credit PortfolioView does exactly that.

Ques 30
Could you please advise why statement iii is invalid?
The explanation says that asset correlation tends to be higher in in times of stress. From what I understand in statement iii, it is stating that we will not get extreme values by simulating historical data from stable period - this sounds in line with the explanation. I may have misunderstood the statement. Please advise?

Ques 38
Could you please advise why statement ii is not associated to this option? Is it possible to have negative gamma in a digital call option? If so, when will it be negative (i.e. OTM, ATM or ITM?)?

 

[David Harper CFA FRM]

Hi Papillion,

#28. You are correct, GARP intended correct answer to be B. CreditPortfolioView
See http://forum.bionicturtle.com/viewthread/2555/

#30. I think you are rightly confused; I have missed this mistake (this, too, is GARP's original) and this appears to be the first that anybody has noticed. Statement (iii) reads:
"With non-normal distributions, the use of correlations estimated using historical data from a stable period may not adequately capture how extreme returns for one type of risk are related to extreme returns of another type of risk."
… I do not see how this is false as explained ("asset correlations tend to be higher in times of stress"). The given answer makes no sense to me, either. The only argument I see for a false is the awkward logic of the assertion (non-normal > stable > extreme tail = 3 concepts ?!)

The problem with the statement is that it conflates:
* non-normal distributions: Dows says correlation is flawed for non-elliptical;
* stable period versus ?
* extreme tail dependence: correlation flawed in favor of dependence
So, I agree with your interpretation and would add: you could further argue it is also true by saying that correlation is not good for (i) non-normal and (ii) extreme tail dependence. All in, I would have said this statement is very true in the way that it awkwardly reinforces THREE separate LIMITATIONS of (linear) correlations!

#38. This is a tough, IMO unfair question. The gamma of a binary in-the-money is negative: the delta of binary ~= gamma of vanilla option, so delta is slightly decreasing ITM (the key is that the binary is capped … once in the money, there is no more moneyness to gain … meanwhile the long binary holder is short volatility [iii. negative vega]).
i.e.., see http://en.wikipedia.org/wiki/Binary_option (I am not sure there is a proper FRM source): "Since a binary call is a mathematical derivative of a vanilla call with respect to strike, the price of a binary call has the same shape as the delta of a vanilla call, and the delta of a binary call has the same shape as the gamma of a vanilla call." If you follow that, then just visualize the right-hand side of a vanilla call option GAMMA chart (i.e., decreasing with higher stock price) which approximates the binary delta (decreasing with tangent slope--rate of change--negative). So this answer does look correct

David

 

[papillonring]

Many thanks for your quick response, David.

1 more question and this is about VAR delta normal calculation.

In the previous part 1 FRM exams, I was taught to use the following formula to calculate delta normal VaR (caveat: I was not in bionic turtle for Part 1 but I did come across one of your old lectures that mentioned this formula):

E(R) - std dev x z = VaR


However, in part 2 FRM, Dowd Chapter 3 recommended the following formula for normal distribution:

-E(R) + std dev x z = VaR

I am slightly confused here. Which is the right one?
Could you please advise which formula should I use in my Part 2 FRM exams? Will there be cases when I need to alternate between formulas for different kind of questions?

 

[David Harper CFA FRM]

Papillonring,

That's right, the first was employed a few years ago (author Culp), but you will do fine to only and always use the second:
Dowd's -E(R) + std dev * z = VaR
Which, to give further comfort, is the same as Jorion's syntax: Jorion's absolute VaR = std dev * z - E(R)

(it has never really mattered for the exam, as you know, the difference is only the +/- signage and it is NOT in GARP's nature to try and stump you on this minor, semantic point ... e.g., they won't look for a -$15 VaR when the other correct is $15. They aren't lame like that.)

I have only used Dowd's for 2+years b/c we found it more robust to the liquidity extension: if you use the first, then you have to remember to subtract the liquidity cost (LC) which is not helpful...
... but the Dowd's is robust b/c you ADD LC to increase the VaR, just like we are told to do (FWIW).

David

 

[papillonring]

I see! Interesting about the liquidity cost! Thanks!

 

[[email protected]]

About the VaR, does GARP calculate it as
VaR = std dev * z

in Question 17 of this practice exam?

It says the VaR will decrease with 0.4581 after the trade.
I set up a spreadsheet which gave me a reduction of 0.4569 (probably GARP rounds intermediately).

https://spreadsheets.google.com/ccc?key=0Aoj_aQ1vMhKidElwR1J2NmRRYWJxNEFqQVpHdzhCdEE&hl=en&authkey=CPr9wqAF

 

[David Harper CFA FRM]

Hi mrbombastico,

In our paid member area, we have this question annotated with XLS, and where we get the same answer as you. Here is my XLS @ http://db.tt/WFaoJK8

My follow-up (17.2) referenced the problem of this question, it is flawed for assuming relative VaR without saying. Incorporating the return with an absolute VaR would be defensible, even more correct really. (This feedback does go to GARP). My 17.2 FWIW:

17.2 The question assumes (and should make explicit the assumption) a relative VaR. What is the relative daily VaR?
Relative VaR is loss relative to the future expected value.
Absolute VaR is the loss relative to zero; in this case, postive drift (return) offsets the loss.
Absolute VaR is the best (most encompassing) VaR and the most robust (robust to modifications like liquidity-adjustments) formula is given by Dowd:
Absolute VaR = -drift*delta_time + volatility * deviate * SQRT(delta_time)
... for short periods (daily) we often assume drift = 0. If drift = 0, absolute VaR = relative VaR

David