Tracking error

[Kavita.bhangdia]

Hi David,
Information ratio = Alpha / volatility of tracking error.

Jorion defines tracking error as active return -benchmark return

But that is not how bodie defines it.
Am I right??

Kavita

 

[David Harper CFA FRM]

HI @Kavita.bhangdia Yes, you are correct, but GARP is aware (see https://forum.bionicturtle.com/threads/information-ratio-definition.5554/ ) since 2012. I really pushed hard for years on this, to be honest (there were three different approaches, actually!). Nowadays, for our purposes, IR had two definitions:

• IR = alpha/residual risk; the more technical; eg,, Grinold
• IR = active return/TE; the more common; e.g., Jorion

Either is what I call "ratio consistent" which means the denominator is simply the standard deviation of the numerator. For this reason, Bodie's definition is not useful to us, if I am correct in interpreting Bodie's IR as the ratio-inconsistent alpha/TE.

As evidence of GARP's healthy approach, here is from GARP's own 2016 P1.99.A (see below): "The information ratio may be calculated by either a comparison of the residual return to residual risk or the excess return [dh: i.e., active return] to tracking error [dh: i.e., active risk]." By "excess return" they obviously refer to return relative to the benchmark. I prefer that "excess return" always refer to "excess above the risk-free rate," but in practice we do see "excess return" also referring to "relative to the benchmark" (and the Rf is a special case). I would also note that while IR has two versions, I think everybody is fairly consistent that TE is active risk. (although, alas, Jorion actually refers to active risk as "tracking error volatility" but GARP/FRM never fell for that!). I hope that helps!

 

[Kavita.bhangdia]

Thanks David.. they just dont seem to make anything easy for us.. do they?

Regards,
Kavita