FRM EXAM 2009 - Practice Question # 2

[al66440]

Hi David, i am having problem with the attached problem on the 2009 practice question.
It is probably some silly mistake on my side, but wanted to catch it is too late.
Your help and guidance will be greatly appreciated.
Thanks,
Alex

2. An investment bank uses the Exponentially Weighted Moving Average (EWMA) technique with lambda of 0.9 to model the daily volatility of a security. The current estimate of the daily volatility Is 1.5%. The closing price of the security is USD20 yesterday and USD18 today. Using continuously- compounded returns, what is the updated estimate of the volatility?
a. 5.44%
b. 3.62%
C. 2.96%
d. 1.31%
CORRECT: B
The current return of the security is = In (18/20) = -10.536%.

Using an EWMA model, the updated volatility is given as:
V(t) = (Iambda ((V[ t-1]^2) +(1-lambda)*(current return^2))^0.5
=(0.9 *((0.015^2)+(1-0.9)*(-0.10536^2))^0.5
=3.62%
INCORRECfl A — Forgets to square the volatility terms
INCORRECfl C— Forgets to square the volatility terms and to take the square root of the resulting variance, then miscalculates conversion to percentage.
INCORRECT: 0— Forgets to take the square root of the variance, then miscalculates conversion to percentage.
Reference: Hull, Chapter 21.

 

[David Harper CFA FRM]

Hi Alex,

You are close, you just have the weights reversed. The answer give (B) looks correct to me: lambda * [most recent variance] whereas you have lambda weighting the most recent return^2. Easy to confuse. The lambda is typically 80% - 90% or above; it is "persistence" and the series is more persistent than reactive; if the high lambda weighted the most recent return^2, the volatility would itself by highly volatile (reacting abruptly with each new day's information). The [most recent variance] mathematically contains all of the information about the prior returns in the time series, so another way to think about this is, along the lines of: we give the higher weight to the term that contains the most information about the series, the rest (1-lambda) is weight for "merely" the most recent piece of information. To illustrate extreme error of lamda*return^2, imagine lambda = 1, then the volatility estimate is simply today's 1-day volatility with a total forgetting of the past. It is maybe easier to entertain lambda = 1 under the correct lambda* [recent variance]: not distracted by today's event, but a total remembrance of the past. Hope this helps..David

 

[al66440]

Hey David,
Looks like the have an extra parenthesis in answer sheet and threw me off.
Thanks,
Alex

V(t) = {Iambda ( (V[ t-1]^2) +(1-lambda)*(current return^2)}^0.5

 

[hsuwang]

Hello,
I'm just wondering if this practice exam is something that's available from the BT website. Thanks!

 

[David Harper CFA FRM]

Hi Jack,

I asked: we are not allowed to distribute the document per se (bummer). But do you think it would be useful to blog out the exam's questions but one question at a time (e.g., like we are doing for certain end-of-chapter readings; e.g., http://www.bionicturtle.com/wiki/Amenc.04.01/)...like I was doing with prior exams (e.g., http://www.bionicturtle.com/learn/article/extreme_value_theory_0903_practice_frm_market/). So, in this way, the practice exam will be manually reconstructed & structured into our wiki. Let me know if you think it would be helpful, I can't really tell if blog questions are used -- except maybe they will be used near to the exam, in which case we will tag/structure them...thanks, David

 

[hsuwang]

Hello David,
Just to clarify, you said the practice exam questions can't be distributed, so is it published by GARP or some other sources that can be purchased? I think it's the source of the practice questions that I'm more curious about because I have no idea that there's a 09' practice exam out already. Thanks!

 

[David Harper CFA FRM]

Jack - Yes GARP sells @ http://www.garpdigitallibrary.org/display/product.asp?pid=2145 David

 

[hsuwang]

Oh my god, thanks for the lighting fast reply! LOL

 

[hsuwang]

Oh ok, I think it's the 08' practice exam. I was just curious because in the original post it says 2009 practice exam, which surprised me because I didn't think GARP would have the 09' ready this soon.

 

[David Harper CFA FRM]

it's 2009, the pub date is incorrect, but it's ready - David