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Different formulas for Information Ratio


I have noticed that there are two formulas for the Information Ratio.

The 1st from topic 2.5 = (E(Rp) - Rbenchmark) / Tracking Error Porfolio

The 2nd from topic 4.5 = Information Coefficient * Breath^(1/2)++

Are this formula equivalent? Do they calculate the same value if we are given the correct inputs?

Thanks for your help

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Hi, Ibazer,

I got the same question and felt frustrated.

My conclusion is that they are the same thing - that is:

(E(Rp) - Rbenchmark) / Tracking Error Portfolio =  Information Coefficient * Breadth^(1/2)++

You can get the left side of the equation and breadth by using objective data. Then you can calculate Information Coefficient, which is what you really want to know.

Imagine you are a CIO of a pension fund and want to know the skill level (= IC) of a fund manager, which is not readily observable. You can estimate it by plugging the fund manager’s observable alpha (excess return over benchmark), TE (standard deviation of alpha) and BR (number of securities traded) into the above formula.

Please correct me if my understanding is wrong. 

You are correct in that the two formulas are equivalent; however, your explanation RE: the CIO is slightly flawed.  Excess return is not the same thing as alpha, in either the ex-post or ex-ante definitions.  Additionally, the breadth is not so simply the number of securities traded; rather, it is the number of independent active bets made within the portfolio during the period in question. However, per your logic, one could estimate the IC given all the correct inputs as described above.  With respect to how they’ll ask you on the exam, i’m fairly certain they’ll either use one method or the other to test your knowledge in lieu of setting each other equal…although, there’s always a first for everything :)

ya don't know what ya don't know until ya know it.

Thanks for the correction, govt/cheese.

I suppose the correct definition of alpha is “excess return over benchmark adjusted to the portfolio’s beta risk.

I agree with your precise definition of the breadth.