Definition of "benchmark" in information ratio

[wrongsaidfred]

Hi David,

When finding the information ratio in the example, why is the benchmark return 13%? When I think of benchmark, I think of the S&P 500 or Russell 3000. If the market return is 10%, shouldn’t this be the benchmark return?

It seems like 13% is more like the predicted return from the CAPM. Is this what is referred to as "the benchmark"? If so, are there other cases where this meaning of benchmark also holds?

Any explanation would be greatly appreciated.

Thanks,
Mike

 

[David Harper CFA FRM]

Hi Mike,

I can't quite get GARP to standardize on this particular terminology (no kidding, I have listed it specifically for the last three years), so technically, it is currently the case that the question needs to define. But, as a default, I do agree with you about the default meaning of "benchmark". However, the current definitional dilemma is actually that the information ratio (IR) can be defined in two ways:
residual return / residual risk or
residual return / tracking error ( = residual return / active risk).

That is, given my example:
Rf rate = 4%,
ERP/MRP = 6%
Expected market return = 4 + 6% = 10%
Portfolio beta = 1.5,
Portfolio return = 14%
Technically, the IR = residual return / residual risk = [14% - (4% + 6% * 1.5)] / residual risk
But can also be IR = residual return / residual risk = [14% - (4% + 6% * 1.5)] / tracking error
Alas, to your point, GARP has even previously employed the technically incorrect = active return / TE = (14% - 10%) / TE

To your point directly, the benchmark can be the market and, therefore, the benchmark return can be 10%. But we can speak of either an active return (14% - 10%) or a residual return (14% - 13%).

But alpha (the correct numerator in IR) is not active return (i.e., return above the benchmark). Rather, alpha is the return not due to common factor exposure; put another way, if your portfolio has beta (market exposure) of 1.5, then the portfolio should return 13.0% BEFORE (without) any skill!

So, you are quite right about the "benchmark" but this issue is whether you compare to the benchmark (active return) or whether you adjust for common (beta) factor exposure (residual return).

I hope that helps, David

 

[wrongsaidfred]

Hi David,

Thanks for your explanation. This expalins things very well. It is frustrating that a set definition does not exist. This may seem like a step backwards, but I guess my question now is what it the difference between residual risk and tracking error? I thought tracking error, in some sense, was measuring the residual risk of the portfolio over the benchmark.

Thanks,
Mike

 

[David Harper CFA FRM]

Hi Mike,

Well, we have had to switch the definition of tracking error also, depending on the assigned author (very frustrating: I think GARP should publish a set of definitions. I have even provided a sample for them to use). You will notice that in the 2011 videos I am using TE = active risk; TE as active risk is perfectly defensible definition. See http://en.wikipedia.org/wiki/Tracking_error and it is also Grinold's. TE as active risk is much easier to measure.

(I would stick with TE = active risk. You are absolutely correct to want TE as residual risk because that is the definition that makes the ratio consistent; i.e., residual in the numerator and denominator ... you could win an argument based on ratio consistency. Amenc also refers to TE, at one point, as residual risk, but Jorion calls it TEV and basically defines it as active risk)

Thanks, David

 

[wrongsaidfred]

Thank you!

Mike