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# Information Ratio

#### Atin

##### Consultant
Hi David,

I am struggling with information ratio concepts: I looked at the tabular example in the video and understood most of it with the exception of Information ratio. Could you please share the calculation details for both approaches - alpha and active return?
- When Tracking error is not given, what did you consider as the benchmark?
- For calculating vol(portfolio return - benchmark return), should I use the var(A-B) formula and compute the results?
- What is the basic difference in both - alpha and active return - approaches (sorry, might be a very basic question)?

Please help!

Thanks much,

#### Atin

##### Consultant
Hi David,

In continuation to my above question regarding IR, for P1.T1.32.1, I am wondering why 10%-8% (the active return) should not be taken?
(Adding question details for quick reference:
32.1 Make the following assumptions:
• Riskfree rate is 3%
• The benchmark is the market (i.e., CAPM) and the benchmark return was 8%
• Portfolio beta is 1.2
• Portfolio return was 10%
• Tracking error was 10%
• Minimum acceptable return (MAR) was 2%
• Downside deviation was 5%
What is the information ratio?
a. 0.10
b. 0.20
c. 0.30
d. 0.40
)
Based on the updates related to IR (https://www.bionicturtle.com/forum/threads/l1-t1-32-tracking-error-sharpe-sortino.3465/page-2):

IR = active return/TE
IR = alpha/TE (as per GARP this should no longer be considered)

So, for the question in reference, should the answer be .2 instead?

Please help at your earliest convenience!

Thank you so much!

#### David Harper CFA FRM

##### David Harper CFA FRM
Staff member
Subscriber
Hi @Atin

In regard to 32.1, yes, I agree that 0.20 is a valid answer (the question predated our current understanding which is reflected in this confirmed correspondence with garp: http://www.bionicturtle.com/forum/threads/information-ratio-definition.5554/). I neglected to update 32.1 in the revision, which I will do ASAP. As you demonstrate, the reality is the question is imprecise by merely asking for the "information ratio" without further clarification, such that your 0.20 is arguably the best answer because it makes the most common assumption that tracking error is active risk and matches this denominator with active return. So, I agree (+1 star). Thank you! In regard to the prior questions:
• Could you please share the calculation details for both approaches - alpha and active return? active return is just the difference between portfolio and benchmark (e.g., index); alpha excludes beta contributions. For example, assume Rf = 2%, market return (is benchmark/index) = 6%, and portfolio with beta of 1.50 returns 9.0%. Active return = 9% - 6% = 3%; alpha = 9% - [(6%-2%)*1.5] - 2% = 1.0%; i.e., pure skill or security selection
• When Tracking error is not given, what did you consider as the benchmark? In my opinion, that needs to be defined; e.g., can be market index, can be constructed benchmark, can be paper portfolio (we did this as consultants). To me, a "benchmark" is anything composition, in theory, that reflects the beta (common factor) exposures.
• For calculating vol(portfolio return - benchmark return), should I use the var(A-B) formula and compute the results? Only if the correlation/covariance is a robust parameter, which is realistically uncommon. This is a formula which makes sense really only as a ex ante measure of active risk because it implies we have prior knowledge about the correlation. But imo tracking error and information ration are really meant to be ex post measures that utilize actual return data. (But again, the math is solid, so it's a fine exercise)
• What is the basic difference in both - alpha and active return - approaches (sorry, might be a very basic question)? To me, per the last GARP correspondence and their flexibility--i.e., either active/active or residual/residual but not active/residual--the key is simply ratio consistency; i.e., the denominator is standard deviation is what's in the numerator. In theory, the alpha/residual is superior (and therefore different!) because it isolates on the results of security selection ("skill"); under that view, the weaknesses of the active/active approach is that it commingles skill with common factor (beta) exposures). I hope that helps, thanks,

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#### Atin

##### Consultant
Thank you so much David for the detailed explanation! Things are quite clear now #### tornellFRM

##### New Member
hi @David Harper CFA FRM ,
Can you explain the 32.1? I thought that according to GARP the IR=active return/TE which in this case the active return is 10%-8% but the answer refers to IR=alpha/TE. Can you indicate which is the best definition for IR? Thanks

#### RajivBoolell

##### Member
Subscriber
Hello @tornellFRM - GARP is (unnecessarily) ambiguous on IR. This is extensively discussed here.

Staff member
Subscriber