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Value at risk (VAR)

jlahuerta

Member
Subscriber
A new quantitative analyst, has been asked by the porfolio manager to calculated the portfloio 1 day 98pct value at risk measure beased on the past 100 trading days, what will this be if the worst 5 losses in the past 100 trading days are 316M, 385m, 412M, 422m & 485 M in USD?
Which be the correct answer?

Thanks

Flashback

Active Member
98 pct VaR meaning that 2 % of worst losses are considered. Thus, 0.02(100) = 2.
This might be the second worst loss among the above, thus it is -422 M.
Another approach might be it is second +1 the worst, meaning that exactly it would be the third one, -412 M.
The last approach, it would be an average between the second and the third one, (422 + 412/2) = 417M.

Since, in the literature, we have 3 different approaches, it might be confusing which one to use.
My experience in GARP's mocks taken thus far, would be - go with the first approach, thus the second worst loss, you wouldn't miss.

David Harper CFA FRM

David Harper CFA FRM
Staff member
Subscriber
@jlahuerta @Flashback makes an excellent point that three different approaches are possible, but this is a revision of an older flawed practice question (see https://www.bionicturtle.com/forum/...-part-1-exam-2-question-24-garp11-p1-24.4488/)

... but the best modern answer follows Dowd's approach (who is assigned in P1.T4 and therefore should be the default) and that would be the third worst among 100; i.e., 100*2% + 1 = 3rd worst.

This choice locates the full 2.0% tail "outside" the VaR quantile and would be consistent with a statements such as "we are 98% confident that [or "on 98% of days"] the daily loss will not exceed 412m" or equivalently "on 2.0% of days, we expect the loss to be greater than 412m." The latter is consistent with Jorion's P(L > VaR) ≤ 1 - c; in this case, P(L > 412m) ≤ (1-0.98). Notice that if we instead selected the 2nd worst loss (i.e, 422), it would be consistent with a slightly different definition: P(L 422m) ≤ (1-0.98) ≥ 2.0%. Ironically, Dowd's calculation is consistent with Jorion's definition (despite the fact that Jorion would select the 2nd worst)!

Please don't get me wrong: I absolutely agree with @Flashback that there exist three valid approaches ... however, we spent no small amount of time educating GARP on why the best exam-type answer is the one consistent with the author assigned (ie, Dowd). Thanks!