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# GARP.2011.PQ.P1FRM 2011 Practice exam part 1/exam 2 question 24 (garp11-p1-24)

#### [email protected]

##### New Member

Question:

Sam Neil, the new quantitative analyst, has been asked by portfolio manager to calculate the portfolio 1-day VAR measure based on the past 100 trading days. What will this be if worst 5 losses in the past 100 trading days are 316m, 385m, 412m, 422m,485m in USD?

The question asks what is the 1 day 98% VAR based on past 100 trading days. To my understanding the answer is the 98 observation (ranked from best to worst observation) ==> 422m USD.

However, the answer sheet indicates that the answer is "422 is the 2nd worse loss corresponding to 98% VAR. 422/sqrt(100) = 42.2 is the 1-day var." is this the correct answer, if yes why do we need to factor the 98 observation by sqrt of the number of observations?

Thank very much

Tzvi

#### David Harper CFA FRM

##### David Harper CFA FRM
Staff member
Subscriber
Hi Tzvi,

I agree with you and so do several others ... we submitted this as an error to GARP (but it did not display on the errata. Uggh.) I think the question was somehow trying to require scaling down from 100-day VaR to a 1-day VaR, but the question phrasing simply does not set this up. There is no way I see to read it such that the /SQRT(100) is warranted. So, 422 is better

(actually, my full quibble is that, if we want to go by the assigned Down, then $412 is correct. For 98th %ile, we should use the 3rd worst; i.e., 2/100 = 2% in the discrete loss tail. But if we don't want to go by Dowd, then 412 is okay, 422 is okay, and any interpolation of between the two is okay). Hope that helps, David #### Ruolin ##### New Member Hi David, you answered this question both here and at http://www.bionicturtle.com/forum/t...sk-var-definition-and-methods-valuation.4151/ By "the question phrasing simply does not set this up", do you mean that the question should have asked students to answer the 100-day VaR first, and then explicitly assume the i.i.d. and normal distribution of the portifolio loss, before question students what the 1-day VaR is? Because as your 2012 Practice Questions "P1.T4" Question 29.2, choice "d" says (which is a correct statement), once the underlying variables are i.i.d., normal, then the VaR can be scaled by time. =================================================================== David's 2012 Practice Question P1.T4 Question 29.2: "Your colleague reports a 95% one-day VaR of$1.4 mil for a equties portfolio. If we assume 250 trading days in a year, each of the following is a valid conclusion EXCEPT which of the following is FALSE?

a) If the VaR is accurate, we expect a daily loss in excess of $1.4 million to occur on about 12 or 13 days (12.5) during year b) If the return distribution is normal, then we can assume the VaR is sub-additive c) This is a parametric VaR and therefore cannot characterize a heavy-tailed distribution d) If the returns are i.i.d. normal, we can scale to a 10-day VaR with$1.4*SQRT (10)=\$4.3 mil 95% 10-day VaR

===================================================================

Scaling volatility by the square root of time, under an i.i.d. assumption, is particularly stated in your 2012 T2 study note (page 24), could you say something about the scaling of VaR (e.g. and i.i.d assumption AND a normal distribution)?

Additionally, about the choice b of Question 29.2 I quoted above, you said in the answer that "b is true". Nowhere in your T4 study note or T4 video said that VaR is sub-additive under a normal distribution (the T4 study note gives an example how VaR is not sub-additive), but is VaR being sub-additive under "normal distribution" something that we should just know/remember? (And by now you might have guessesd: I did not purchase the Kevin Dowd book to check about this).

Thanks.