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GARP.FRM.PQ.P2 Important Difference in Information Ratio Formula (garp16-p2-72)


Well-Known Member
Fully understood, @David Harper CFA FRM.

I totally see your point that:

IR = α/TE could be confusing as candidates may think in regression language and want to dissect alpha from the regression equation instead of simply comparing the returns of the actively managed portfolio versus its benchmark.

Yes indeed, notationally

IR = α/TE = R(p) - R(b)/TE

should be used.

In case you need the Lhabitant book as a reference to back things up, I can send it over.

Litterman uses the same quite opaque terminology saying:
"A useful way to assess the risk/ reward trade-off is with the information ratio,
defined as active return per unit of active risk
(or active return divided by tracking


New Member
Many thanks @David Harper CFA FRM @emilioalzamora1 for your detailed and prompt answers. Very sorry for the LATE acknowledgement. I shall go and read up various references after the exam.

David, for my own clarity, may I please check in your excellent Nov 7, 2017 YouTube video that:

1. active information ratio is the one described by Jorion (in Chapter 17 of his book "Value at Risk"), as "the expected tracking error divided by the volatility of the expected tracking error" (given that what he calls tracking error would be seen as "active return" by most practitioners).

2. the residual information ratio is the one described by Grinold & Kahn in Chapter 14 of their book.

AND based on the exchanges above, there is INDEED a "third" version of information ratio, which would be "active return divided by tracking error". Whilst this definition "may be" the one most commonly used by practitioners, it is NOT in the FRM syllabus.

Sorry for labouring over this, and thank you very much again,


David Harper CFA FRM

David Harper CFA FRM
Staff member
Hi @Galaxy Yes, I agree with your (1) and (2) but question: how is your third different from your (1) exactly? i.e., if "active active return divided by tracking error" assumes TE = σ(active return), then it's the same as (1), yes? If TE is something different, then I agree it's a 3rd, but i'm not sure how it fits in as a viable third. Thanks!
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Active Member
IR = Ra / σa (active return / active risk) whereas Ra = Rp - Rb and σa is deviation of portfolio excess return from benchmark return.

In addition, by Fundamental Law IR = IC sqrt Breadth meaning that higher IR, as a measure of success of asset manager is a function of:
- security selection skill
- active bets
Thus, mediocre skilled managers to catch up with superior skilled colleagues must increase the number of active investments within period.
Bets should be unbiased (aka not concentrated in one rapidly growing sector).
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New Member
Hi @david harper, thanks very much for your answers. I shall come back after the exam - don't want to be burning up your valuable time during this crucial period. Thank you for your materials again, Galaxy


New Member
Hi @David Harper CFA FRM, I apologize but I do not understand the "Pr[-1.96 < Z < 1.96] ~= 95%" part. Why is it 1.96? Since, it is 5%, shouldn't it be 1.645 instead? According to me, shouldn't it be a 97.5% case, instead of a 95%?


@farahm Please note that, in May of this year, I both submitted a correction to this question (credit to Kenji who first spotted it https://www.bionicturtle.com/forum/threads/2016-frm-part-ii-practice-exam-q-a.9350/#post-40449) and further challenged it conceptually (based on its requiring more knowledge than found in the assignment; specifically, it requires additional Grinold, IMO). The answer to your specific question is likely simpler than you expect. Firstly, the question is utilizing Grinold's σ(refined α) = σ(α) * IC, based on σ(refined α) = σ(α) * IC * z-score but where score ~ N(0,1).

So the correct solution should read: the standard deviation (std) of the alphas = Residual Risk (volatility) * Information Coefficient (IC) = 0.18 * 0.09 = 0.0162 is the standard deviation of the alpha (versus 2.0%).

Then, to your question about the 5.0%, that's simply based on about two standard deviations including about 95% of the normal distribution: Pr[-1.96 < Z < 1.96] ~= 95%. In the incorrect version where σ(scaled α) = 2%, about 5% should be outside the +/- 2*2% interval; in the corrected version, about 5% should be outside the +/- 1.62%*2 interval. I still think the question has deeper problems, but I hope that helps.

David Harper CFA FRM

David Harper CFA FRM
Staff member
Hi @RushilChulani GARP 2016 P2.Q72 above is looking for a two-sided rejection regions when it asks "how many stocks have an alpha greater than 4.0% or less than 4.0%." Under the (mistaken, I think) original version of the question, the standard deviation of the alpha was meant to be about σ(α) ~2.0% such that the question is looking for how many stocks have an alpha outside the two-sided confidence interval given by µ - 1.96*σ(α) ≤ X ≤ µ + 1.96*σ(α); in this case, µ - 1.96*2.0% ≤ X ≤ µ + 1.96*2.0% -- > and where µ=0% that's a two-sided confidence interval: -4.0% ≤ X ≤ 4.0%. Of course, Pr(Z > 1.96) = 2.5%, but Pr (-1.96 < Z < +1.96) = 5.0% because there is 2.5% in each left/right rejection region.

If the question instead were to ask something like "roughly how many stocks have an alpha greater than 3.3%?", then notice we have a one-sided question and we can observe that's equivalent to Pr(Z > 0% + 3.3%/2.0%) = Pr(Z > 1.645) = 5.0%. That would be one-sided. Thanks,