Alpha

[ckyeh]

Dear David:

In bionic turtle’s tutorial 2010-8-a-Investment Page 6, you mentioned:
Tracking error is the residual risk

I I am confused.
Tracking error=σ(Rp-Rb) (see 2010-1[1].a-Foundations, page 57)

Here residual risk should be σ(residual risk)=σ(Alpha), right?

Why they are the same?

Thanks for your help!!!


CKyeh

 

[David Harper CFA FRM]

Hi ckyeh,

It is just the difference in the source material (I've long noted this discrepancy to GARP; actually, Jorion further confuses).

Amenc (foundations) actually allows for both definitions of tracking error including TE = σ(Rp-Rb).
But Grinold goes further, is more precise, due to his distinction between active and residual risk.

Both are correct in a key way: ratio consistency. Such that, collectively, you can (strictly) define:
TE = StdDev (active return) or StdDev (residual return = alpha) depending on how you want to define the "benchmark" such that:
IR = active return/StdDev (active return); i.e., Amenc, or
IR = residual return / StdDev (residual return) = alpha/StdDev(alpha) = alpha/TE; i.e., Grinold
... Grinold is arguably more correct but is only possible if you have the beta exposures.

David

 

[ckyeh]

Thanks!!!

And in 2010-8-a-Investment, page 8
you mentioned value added :
VA(P)=αp – λR*Wp^2 (Residual)

Compared to Portfolio Theory and Performance Analysis, page 101:
The amount of value added is Timing + Residual

So here we only consiered Residual, ignored Timing, right?

Any reason? And could you kindly give an example for the calculation of value added?

Thanks!!!

 

[David Harper CFA FRM]

Ckyeh,

Yes, that is exactly correct!
Grinold notes about this "We are ignoring benchmark timing, so active return equals residual return and active risk equals residual risk." (footnote 5, Chapter 5)

I replicated Grinold's Figure 5.6 (which illustrates this formula, and further finds the optimal residual risk by solving for the local maximum) in the THIRD SHEET of XLS 8.a.1 @
http://www.bionicturtle.com/how-to/spreadsheet/8.a.1_grinold_setup/

Snapshot of 3rd sheet of 8.a.1_Grinold_setup.xls:

http://learn.bionicturtle.com/images/forum/1020_grinold56.png

David