Information Ratio.

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In the 2010-1-foundations pdf, on page 32 you give the formula for information ratio which is difference in expected return over tracking error, but in the page after it you give an example, but you calculated the IR as alpha/TE. However, alpha is not the difference in expected return, since you have to take beta into consideration.

So which way is correct?

 

[David Harper CFA FRM]

Hi chugangc,

You are exactly right, the difference is due to the difference in GARP's assignments: Amenc (taking a less sophisticated/precise approach, does not seem count the beta exposures in introducing) versus Grinold (who does use a precise definition of alpha). Tracking error (TE) is even more difficult, as Jorion complicates by calling our TE by TEV.

I would like to give you a "correct answer" and I am (loudly) lobbying GARP to settle some key definitional inconsistencies, including alpha and tracking error. The problem is that we can find a precedent (source) for (actually) three IRs, depending on the source:

* active return/active risk (how Amenc seems to be interpreted and, unfortunately, how GARP seems to test; i.e., no accounting for beta)
* residual return/active risk (Grinold's stated definition, technically, where Grinold has TE = StdDev (active return) but notice this is not ratio "consistent" and therefore has a problem IMO [e.g., can be distorted via beta exposures]
* residual return/residual risk. My preferred definition because (i) is ratio consistent and (ii) finds support in BOTH Grinold and Amenc (it's true, if you read carefully both actually use this!...)

Frankly, the underlying issue is that GARP, in practical terms, has not seemed to test/practice for the distinction between active versus residual return/risk; e.g., most recently, GARP has tended to treat alpha (incorrectly) like an active return, unless it is a test of Jensen's alpha (which is a correct alpha! (ex post) Alpha is ultimately a regression intercept, and therefore "net of" beta exposures). Ergo, in the meantime, until they arbitrate, I tend to use #3 above as the truest definition of IR. But for exam purposes, it seem like #1 (active/active) will work, too.

David

 

[[email protected]]

Hi David:

I have read through a few threads on this topic and know that you favor Grinold's definition of IR. I too like his rigorous mathematics (I found only two typos in his first 6 chapters). But I am now leaning towards Jorion's definition. Please see my reason in the attached.

Please kindly comment on my thought. Thanks. Pichet