Brinson Attribution Model Confusion in CFAI Text

CFA Level III
#1

In the beginning of the text in Reading 35, “the contribution to allocation in the ith sector is equal to the portfolio’s sector weight minus the benchmark’s sector weight, times the benchmark sector return.” Equation (3) Ai = (wi – Wi)Bi

However later on in the discussion of micro attribution, the text states: "We calculate the return attribution effects using the Brinson–Fachler approach at the segment level (i.e., small-cap value, large-cap value, and large-cap growth):

Allocation = (wi–Wi)(Bi–B)

Why are the equations different? Wouldn’t sector, market cap, or country allocation all fall under segment level?

Thanks

#2

Because the return B is the total return in the Benchmak with all asset allocations, you want to know the Allocation return to an specific allocation so the benchmark return for that particular allocation need to be substracted for the total return

#3

Thanks, but wouldn’t the same logic then apply to a sector allocation as with equation 3?

#4

In Sector Allocation (Ra - Rb)Wi the benchmank weight will sum to 100%, no need to adjust