investment manager level return - two different definitions investment, definition, different, category, manager

dcfox83

Page 90 Schweser Book 5:
R_IM = sum sum (w_i) (w_i,j)(R_i,j - R_B,i))
where
R_i,j = return for manager j’s portfolio in category i
R_B,j = return on the bench for asset category i
Then on Page 93 Schweser Book 5:
R_IM = sum sum (w_i)(w_i,j) (R_A,i,j - R_B,i,j)
where
R_A,i,j = return for manager j’s portfolio in category within category i
R_B,i,j = return for manager j’s benchmark in asset category i
The two definition R_B,j and R_B,i,j doesn’t match up. The first one implies subtracting the benchmark return in category i. The second definition implies subtracting the benchmark return in category i, manager j.
Which is the correct way to calculating the value of active management?

cfalevel2011

Have a look at the CFAI macro attribution, pg152 vol 6. It makes more sense really. The IM element can be worked out by using benchmark weights to sum up the actual returns from each manager, less the benchmark returns.
I.e. sum of [manager benchmark weight*asset category benchmark weight*(actual return - benchmark return)] try it with exhibit 3 and 5 in CFAI text, you’re only adding up 4 numbers at the end of the day, prob about as complicated as it will get!
In schweser they’ve just notated it differently, the definitions of the various elements are the same. I like remembering the principle rather than all the formulae.