Pure Sector Allocation

There is something that is driving me crazy. I think of Pure Sector Allocation as the return attribution of the difference in the actual portfolio weights vs the Benchmark’s = Sum (Wp,j - Wb,j)(Rb,j - Rb(overall benchmark))

I am wondering why do we have to subtract the Rb (overall benchmark)??. Aren’t we supposed to capture the difference in weights by multiplying our “active weights” with the benchmark return, instead of the difference between the benchmark return and the overall benchmark?

Thanks!!

What you are describing is the interaction effect:

Pure Sector Allocation = (wP,i - wB,i )(rB,i - rB) Within-Sector Selection = (wB,i )(rP,i - rB,i) Interaction Effect = (wP,i - wB,i )(rP,i - rB,i)

Note their aggregate is the active return.

These formulas are far from trivial and are quite confusing.

No, krokodilizm, he is describing the Pure Sector Allocation.

OP - pure sector allocation measure how the managers select the weighting of the a particular sector. If a manager overweights a sector that outporforms the overall Benmark this will reflect positively for the Pure Sector allocation. If the manager underweights an underporforming sector this will also reflect positively.

Each sector contributes to the return of the overall benchmark…so we must back out the return of the benchmark to understand how that sector performed relative to all combined sectors at their respective weighting.

I don’t find this very intuitive either, joaquinaguirre. Here is (I think) an equivalent way to find pure sector effect:

Summation(w_pj * r_bj) - Summation(w_bj * r_bj)

= Summation(w_pj * r_bj) - R_b

The intuitive explanation is “assume the manager receive ‘passive’ sector returns, but at his ‘own’ sector weights w_pj” (the first term), and then subtract the benchmark return from this (second term). Build a portfolio that uses the manager’s weights and earns the passive return at each sector level." This shows excess return in the absence of stock selection.

Does anyone agree/disagree here? I’m able to show equivalency of this formula with Kaplan/CFA’s/krokodilizm’s in Excel, but not theoretically as I run into factoring summations and things get a bit hairy.

In level II, I think possibly even that last reading where we covered the law of fundamental active management I swear we learned it was (Wp-Wb)(Br)…but I’m taking LIII so I’ll worry about thus June 4th and go with way I see in this curriculumn lol

OP, If the exam question said choose the best answer… You best circle this post.

Intuitively I agree, and I used to think the same thing. But taking what is in the book as given I came up with this conclusion.

We are trying to find how much did he over/under perform the benchmark with his sector allocation. Not how much retrun he got from sector allocation.