why are the two similar factors have so different formula?

pure sector allocation=(wP -wB,j)(RB,j -RB) market allocation contribution = ( w p - w b) Rb,l why are the two similar factors have so different formula? one minus benchmark while the other not. Anyone could explain?

The second formula focuses on the weight difference only, while the first one considers both the weight difference and the sector’s performance.

Notice: sum(wP -wB,j)(RB)=0

thanks

why Rb=0?

RB is not 0, but sum(wP -wB,j)(RB)=0 since sum(wP)=sum(WB,j)=1.

But if sum(wP)=sum(WB,j)=1. the total value would be 0?

there are several differences that are confusing in this section. Wjp is used in pure sector allocation for global whereas Wjb is used in micro attribution. I never quite understood why there were differences so i just outright memorized the formulas. I think darkstar had an explanation at some point but i’ve forgotten. My advice is to memorize the formulas.

Ugh, this again? Thanks CFAI and Schweser for doing such a god-awful job of explaining this section…

There are two different models that are used for equity attribution.

  1. Brinson Fachler

This model comes from a paper entitled “Measuring Non-US Equity Portfolio Performance”, published in 1985.

The allocation term in this model is: (wPj - wBj) (RBj - RB)

  1. Brinson Hood Beebower

This model comes from a paper entitled “Determinants of Portfolio Performance”, published in 1986.

The allocation term in this model is: (wPj - wBj) (RBj)

Ultimately, it’s just two different approaches that will yield very different results at the sector/country level - but the same results at the total level. BF attribution appears in the first reading, BHB in the second. BF is considered the industry standard (likely because BHB results are nonsensical…). I can explain why BHB is nonsensical if anyone actually cares.

The other difference between the two readings is that the interaction term doesn’t appear in the second reading (BHB) because it’s collapsed into the selection term (which you can also do in BF if you don’t want to see an interaction term because it can be confusing to clients).

They don’t really explain either of these two differences which is a significant deficiency in the curriculum, if you ask me…

Wow, let me bookmark it first.:slight_smile:

good god you should write the curriculum darkstar !

Thanks! This just happens to be a particular topic that I know a lot about.

Let me know if anyone has any other questions on SS17.

I can explain why BHB is nonsensical if anyone actually cares.

Darkstar, pls explain. Thanks

OK, let’s assume the following:

Sector 1 Portfolio Weight: 50%

Sector 1 Benchmark Weight: 30%

Sector 1 Portfolio Return: 6.5%

Sector 1 Benchmark Return: 6.5%

Benchmark Return: 9.2%

BF Allocation = (50% - 30%) * (6.5% - 9.2%) = -.54%

BHB Allocation = (50% - 30%) * (6.5%) = 1.3%

Effectively, BF says that you benefit from overweighting a sector that outperforms the benchmark. On the other hand, BHB says that you benefit from overweighting a sector with a return above zero.

In this example, it’s clear that the manager allocated excess funds to a sector that dramatically underperfoms the overall benchmark…so it’s not reasonable to give the manager credit for doing so.

darkstar, but when we combine allocation, selection, and interaction to get the total active return for each asset class, we have to use BHB right? so I guess it’s still useful to some extent.

These two formulas are not both the ones used in the micro-atribution contribution. Only the Pure Sector Allocation is referred to in comparison with the market allocation contribution from global performance evaluation (second term in equation 6, pg 213).

No, you can use either BF or BHB to get the total active return.

I don’t have the books with me right now so I’ll double-check when I get home, but I think you’re getting confused because they refer to pure sector allocation in one reading, and market allocation in the other reading. These are really the same term.