I absolutely don’t get it… Please enlighten me on what the eff is going on… thanks 
(Both single and multiple attribute)
The main point here is that you cannot link multi-period attributions as you normally link multi-period returns… They are trying to show the math behind all this, which I highly doubt will show up on the exam… I don’t think they expect us to memorize these kinds of formulas… they just want us to understand the basic concepts … But to reproduce the math here: Single multi-period attribute return Rp - Rb = A1*(1+Rp2) + A2*(1+Rb1) where, Rp - portfolio return Rb - benchmark return A1 - attribute in year1 A2 - attribute in year2 Rp2 - portfolio return in year2 Rb1 - benchmark return in year1 … but who knows… they are trying to make the exams harder and harder by year… so they might throw in a couple of these…
So the reason you multiply the first years attribute return by the portfolio return is because it was the year in which the “Active” investment decision was made. And in the second year, the strategy didn’t change… thus you multiply it by the benchmark return instead of the portfolio return? Right? What i don’t get is why the years are flipped? Am i totally off base in my understanding of the logic behind what the equation is doing up until my confusion with the years?? — I understand the need for an equation like this for the reasons you’ve said about linking returns. However, I’m having trouble visualizing how/why this particular equation works to solve that problem 
- Rp - Rb = (1+Rp1) x(1+Rp2) - (1+Rb1) x(1+Rb2) is much easier ! 2. “Multi-period/multiple attributes” is most troublesome !
my bad… my formula was wrong… the formula is Rp - Rb = A1*(1+Rb2) + A2*(1+Rp1) where, Rp - portfolio return Rb - benchmark return A1 - attribute in year1 A2 - attribute in year2 Rb2 - benchmark return in year2 Rp1 - portfolio return in year1 - haven’t figured out the intuition yet… i’ll get back to you in a few mins…
let me give it a try… In year 1, due to your great selection skills, you earned an active return… In year 2, that active return accumulates with benchmark, if you assume that you did nothing in year 2… hence, A1*(1+Rb2)… Let’s now say that you did another selection bet, and earned an additional active return… that return is earned after you made your excellent decision in year1, so you have to accumulate that on top of what you earned in year1; hence A2*(1+Rp1)…
intuition for the first year is that the excess return generated by the manager in year 1 is now available to be compounded at the market rate in year 2. excess return generated in year 2… hmm, intuition is less clear here. You’ve got the excess return earned in year 2 and you are compounding it by your full portfolio return last year… I’m stumped on the logic, so I’ll have to think on it more, but it does work out.
there are 2 components to each return. Year 1 Manager = 5% Year 1 benchmark = 3% Year 2 Manager = 8% Year 2 Benchmark = 7% So one would think that total excess return = 2% + 1% = 3% or 1.02 * 1.01 = 3.02% It doesn’t - lets call the excess returns - attribute In reality, we made (1.05 * 1.08) -1 = 13.4% The benchmark made (1.03*1.07)-1 = 10.21% Excess Return = 3.19% So if we take attribute of year 1 * ( 1+ benchmark return yr 2) we get . 02 *1.07 = 2.14% If we take attribute of year 2 *( 1 + portfolio year 1 ), we get 01 * 1.05 = 1.05% Excess return = 3.19% The bottom line is this: the excess return of year 2 is compounded by the portfolios return in year 1 - this gives the contribution of the portfolio in year 1 to the 2 year portfolio excess return and the the excess return of year 1 is compounded by the benchmark in year 2 to give the contribution of the portfolio’s excess return in year 1 to the 2 year portfolio excess return.
How about “Multi-period/multiple attributes” ?
I wanted to write my “new finding” on Multi-period Performance Attribution, but I found it’s not new.
Check out AMC’s answer above: 1. Rp - Rb = (1+Rp1) x(1+Rp2) - (1+Rb1) x(1+Rb2) is much easier ! where, Rp1=Ra1+Rb1; Rp2=Ra2+Rb2. Schweser’s version: R(A2)=Ra1*(1+Rb2)+Ra2*(1+Rp1) In fact, R(A2) = Rp-Rb !!
ABAP (Advanced Business Application Programming, German for “general report creation processor”), pronounced as ‘ah-bop’, is a high-level programming language created by the German software company SAP. ---------- You may wonder why I post this - it’s ABAP(‘ah-bop’) a language created by SAP. Yes, it doesn’t make sense and it’s insane, just as the following formula(a1,b2,a2,p1). But it might be useful in the examples on Schweser Notes 5, Page 153. Who knows? - Rp-Rb = Ra1*(1+Rb2) + Ra2*(1+Rp1)