BT Presentation on Information Ratio

[notjusttp]

Hi David,

I was going thru the BT presentation 1.a.ii on Information ratio and had a doubt on reviewing slides 62 and 63.

1) In Slide 62 the numerator for Information ratio is taken as E(Rp)- E(Rb)

2) In Slide 63 the numerator for Information ratio is taken straightaway as Jenson alpha

In slide 63 if you take the explanation given in slide 62 then Numerator should become ( 14%-10% = 4%) since in absence of information about benchmark return the same can be assumed as market return( for eg S&P 500). The answers would differ significantly based on numerator taken.

Can you pls clarify how to handle this situation in exam if we have both the answers in the 4 options given.

Thanks and Rgds
Amit

 

[David Harper CFA FRM]

Hi Amit,

It's a good observation, it's sort of why i did the example as shown: to highlight that alpha is the numberator in IR.

First, i agree with you, and as a practical matter on the exam, it's a function of the benchmark given, so if the example were to say "return of benchmark = 10%" and "portfolio return = 14%" and, lacking any other information, you would be forced to assume alpha = 4% ... but that would be a weak question in regard to Infomation ratio because it does not give the beta...

...but we have a beta of 1.5 here, and therefore alpha = 14% - (6% * 1.5) - 4% = 1%
...it would be incorrect to use here alpha = 4%. 14% - 10% is the "active" return (Grinold's term) but we want the "residual" return (residual = alpha and accounts for the beta). Where alpha (residual) = 10% portfolio's excess return - 1.5 beta * market's excess return of 6% = 1%.

the p 62. is notation from assigned Amenc, so I see your point (i.e., portfolio return - benchmark return) but this just puts the burden on the definition of benchmark, and in this regard, the Grinold is more precise. We want to use:

IR = alpha / tracking error = E[residual return] / tracking error

David

 

[notjusttp]

David,

thats a cool explanation..so we have to always take the residual and not active return as alpha..For alpha to unveil beta should be given....cheers..Amit