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# FRM Level 2 , Nov 2012 : Post what you remember here

#### klartxt

##### New Member
There was a question on finding a min variance position. corr coeff , and standard deviations were given. I tried using -(Corr*SD1/SDP) . Got an answer of -30? Anyone remembers this?

Also, for 28, i got the answer as LIBOR+118. Anyone got the same answer?
Wasn't that the question with more than 2 assets with same standard deviation and correlation? if so, you had to use stddev x (1/n + (1-1/n) x corrcoeff).

#### Level2WaitingForResults

##### New Member
Duration of IO strip - Was it -20? (For PO they gave it as 25 if i remember correctly)

#### klartxt

##### New Member
I remember this questions. I actually got a higher sharp ratio for asset A but was in a real hurry. I remember something like 0.33 for A vs. 0.28 to B. Didn't have much time to spend on this one...
i checked several times - pretty sure that B had the higher Sharpe Ratio and that the choices given incorrectly specified the assets in regards to which one had the higher Sharpe and which one the higher Info Ratio. But in the heat of the test (and not being able to drink without wasting time by having to leave the room for that) I could be wrong.
Any further comments from the community?

Also, on the Rusnak question: one had to choose between Roy being an incompetent supervisor FOR THE PROP GROUP (when in fact he concentrated on int.rate derivatives and did have knowledge there) or Rusnak using the inexperience of the TRADING CONTROL GROUP (which isn't exactly what it was called - but the function is a control function. And he did use their inexperience). Not sure if one can precisely answer that question with the choices given...

#### Level2WaitingForResults

##### New Member
Wasn't that the question with more than 2 assets with same standard deviation and correlation? if so, you had to use stddev x (1/n + (1-1/n) x corrcoeff).
i dont fully remember the question. But they had diff standard deviations i think.

#### roierez@gmail.com

##### New Member
IO duration - guessed it would be the highest negative number for counter the PO duration.
Rusnak - wen't with "used the inexperience of treasury control"
Hedging - I just calculated the variance of the portfolio. I think I answered -120 (it also made common sense).

#### fnctkaa

##### New Member
for 1), which actually asked to assume 252 days/yr (not 250), if i recall correctly, you divide by square rt of 252 to get one-day, then multiply by sq rt of 10.
for 8) the lognormal,loggamma and GPD are for severity, not frequency. Typical for frequency distributions are Poisson and neg. binomial. I think one of those was a possible and the right answer.
for 1) i know the formula,,,,,i was doing the same as what u said,,,,,but my calculated answer was not one of the four choices
something similiar happened 4 to 5 times on other questions about VaRs.

any ideas on the remainings that i have mentioned?
thank you

#### Level2WaitingForResults

##### New Member
IO duration, i thought it should be negative but less than that of PO (coz for pass through, Interest part starts high reduces as time passes - So, thought IO should have lesser duration than PO. Not sure)

##### New Member
There was a question where i think GARP made a mistake: they asked whether one wanted to add A or B to a portfolio. Choices were
a) Asset A because highest excess return
b) Asset A because highest Sharpe Ratio (this not a correct choice because Asset B Sharpe-Ratio was higher)
c) Asset ? because highest Info Ratio (also incorrect because the other asset had the higher Info Ratio)
d) Asset B because lower volatility
This left me with choosing A for its higher return or B for its lower volatility - but Garp gave no indication whether we have a risk averse investor or any other hint whether one should prefer return or lower volatility.
The only 3 ways I could think of to answer this question correctly (assuming Garp made no mistake) are:

1) Notice that the benchmarks return was given as 7% OVER THE PAST YEAR while the returns given in the table were EXPECTED RETURNS FOR THE NEXT YEAR. That being the case, you could not really compute an excess return (or an information ratio - but that was the wrong way around anyway), so choice d) was the only choice you could be left with (choosing asset B for the lower volatility).

2) Also possible would be that Garp expected you to remember that excess returns / Beta for each asset should be the same to optimize a portfolio (usually its excess return / MVAR. Excess return / Beta is a step before and also valid). Hence, even when you cannot calculate excess return, you can use the (return minus risk free) over beta as a proxy and you would choose the asset with the higher ratio - not sure which one of the two assets would have benn the right one then.

3) one could possibly calculate excess return by finding the return of the benchmark by knowing that the betas were 0.8 and 0.9. Don't those Betas imply that in risking markets the returns of A and B are lower than the benchmark?

However, I think that is asking for way too much interpretation and around-the-corner thinking than Garp would intend. Therefore, I think they made a mistake. They probably wanted you to calculate the Sharpe Ratio and choose Asset B for having the higher ratio but did not properly give that as an answer choice.
This was one of the shitty questions I encountered....I chose A after spending significant time...Like this question, there were two sentences/ a compound sentence in each option..Hence one part of the sentence may be true and the other part may be false.....So essentially we are working with more than 4 options...And regarding questions like which of the following are correct? There are two correct options in many cases and one is more correct than other....I mean one option will always be correct and the other option can be correct in certain scenario...I would be better off if GARP tests on quants rather than nitpicking on some theoretical statement in the corner of the material......

##### Member
ES is not easy to interpret...it is clearly mentioned in Schweser...I put Standard deviation instead! it's confusing...

#### nageshtheone

##### Member
Guys, does anyone remember the Type 1 error calculation. I guess it was 3/15 =0.2 Please correct me if I am wrong.

#### nageshtheone

##### Member

Good point about percentages. I put absolute as well but agree now it's wrong...imagine the numbers were ridiculous like

$1, 1M, 5M, 10M but bank A had$1 of total assets (e.g. all their assets pledged as collateral) but the other banks had 1B of assets

just because the fourth one has 10M floating out as collateral doesn't make them most vulnerable...the bank with the biggest piece of their assets floating out there is worse off.

grrr...I hate getting "easy" ones like that wrong
Do you remember the Type 1 error calculation. I guess it was 3/15 =0.2 Please correct me if I am wrong.​

#### Frm_Indonesia

##### New Member
IO duration - guessed it would be the highest negative number for counter the PO duration.
Rusnak - wen't with "used the inexperience of treasury control"
Hedging - I just calculated the variance of the portfolio. I think I answered -120 (it also made common sense).
But I thinks variance can't negative, how do you think?

#### roierez@gmail.com

##### New Member
The variance isn't negative but the position is (meaning short 120 of that security). I could be wrong of course but since we're discussing a hedge it should be negative

##### New Member
Can we use 1/T ln(D/F) -Risk free rate to calculate credit spread...i used this formula and got 5. sth answer. i dint use recovery rate. can anyboy confirm on this?

#### kuch2r

##### New Member
ES is not easy to interpret...it is clearly mentioned in Schweser...I put Standard deviation instead! it's confusing...
As far as I remember the question was about coherence risk measure that is easy to interpret and definitely standard deviation is a wrong answer as it does not fulfill the axiom of translation invariance.

#### klartxt

##### New Member
Roierez - you are right on the hedging question. You needed more of the hedging instrument than you had in the underlying so 30 or -30 were not valid choices. -120 is correct since you need a short position in the hedging instrument to counter your long position in the underlying. Though I hedge everyday at work I, me idiot chose +120

Regarding the question with the banks and potential liquidity problems when haircuts are increased: haircuts are always a percentage of the value, so of course you had to use percentages. The bank with the least amount of assets not yet pledged as a percentage would be the one most likely to run into problems.

Regarding the asian option - someone had mentioned using 43 ending price (vs. fixed strike of 40) to determine that the option is in-the-money: Nope, asian price option (call) here would use an average stock price of 41.5 i think, which is still in-the-money I would say, so I chose delta = 1. But, I think others who posted here are right: asian options will have a delta of 0 close to expiration, no matter what the price. Not sure why, but anyway -damn!.

Yes, "Type I Noise-To-Signal-Ratio" was 3 / 15 = 0.2, I believe. You weren't actually asked to calculate the Type I error but the NSR Type I (=Noise to Signal Ratio = Noise / Signals = False alarms / Signals = Type II error / 1-(Type I error) = 3/15)

Anyone any ideas regarding the question above, why one would choose Asset B with low volatilty or Asset A with high excess return to be added to the portfolio? I thought of 3 ways to solve that question (above) but cannot really imagine that GARP would require us to do that much interpretation...

#### klartxt

##### New Member
As far as I remember the question was about coherence risk measure that is easy to interpret and definitely standard deviation is a wrong answer as it does not fulfill the axiom of translation invariance.
Hey kuch2r, I also chose ES since stddev is not translation invariant and VaR does not necessarily fulfill the subadditivity requirement for a coherent measure. However, if I recall correctly, the Schweser Notes just 1 to 3 pages (bottom) or so further in that topic, say that stddev and VaR are special cases of coherent measures or something like that. And, as others have said, it was written in the Notes that ES is not easy to understand... I'm guessing that Garp wanted to hear ES, but it is not all clear . . .

#### Level2WaitingForResults

##### New Member
Roierez - you are right on the hedging question. You needed more of the hedging instrument than you had in the underlying so 30 or -30 were not valid choices. -120 is correct since you need a short position in the hedging instrument to counter your long position in the underlying. Though I hedge everyday at work I, me idiot chose +120

Regarding the question with the banks and potential liquidity problems when haircuts are increased: haircuts are always a percentage of the value, so of course you had to use percentages. The bank with the least amount of assets not yet pledged as a percentage would be the one most likely to run into problems.

Regarding the asian option - someone had mentioned using 43 ending price (vs. fixed strike of 40) to determine that the option is in-the-money: Nope, asian price option here would have an average price of 41.5 i think, which is still in-the-money I would say, so I chose delta = 1. But, I think others who posted here are right: asian options will have a delta of 0 close to expiration, no matter what the price. Not sure why, but anyway -damn!.

Yes, "Type I Noise-To-Signal-Ratio" was 3 / 15 = 0.2, I believe. You weren't actually asked to calculate the Type I error but the NSR Type I (=Noise to Signal Ratio = Noise / Signals = False alarms / Signals = Type II error / 1-(Type I error) = 3/15)

Anyone any ideas regarding the question above, why one would choose Asset B with low volatilty or Asset A with high excess return to be added to the portfolio? I thought of 3 ways to solve that question (above) but cannot really imagine that GARP would require us to do that much interpretation...
On Hedging question, -120 would be correct if the corr coeff was 1 (i.e. they were perfectly corr).But in the question they had given corr coeff, Sd1, SD2. So, it should be (corr coeff)*SD2/SD1 which gives 30 and as you mentioned, since iti s a short positon. it brings -30. Isnt that right?

#### klartxt

##### New Member
hmm - you may be right. I remember not getting to a value of either (+/-) 30 or 120 but the hedging instrument had the lower volatility, right? So I figured you would need more of the hedging instrument for any correlation above zero. After your last comment I'm not so sure anymore - so someone else should reply in order to potentially correct what i said... Anyway, given correlation coeff and both std deviations, it should have been easy to calculate beta - and the hedge ratio, right? And beta would have been positive but lower than 1 when correlation is above zero and std dev is lower in the hedging instrument, or not? However, couldn't get to either (+/-) 30 or to (+/-) 120...