stock selection la Stock selection for z'th group of stocks 2 Allocation effect (group weight) 2a Allocation effect for z'th group of stocks 3 Interaction effect for z'th group of stocks 4 Relative vs. group (by asset) 5 Relative vs. total (by asset) 6 Absolute vs. group (by asset) 7 Absolute vs. total (by asset) 8 Relative vs. group by group (e.g., industry) 9 Relative vs. total by group (e.g., industry) 10 Absolute vs. group by group (e.g., industry) The total out-/underperformance of a stock or group of stocks, relative to a benchmark. The out-underperformance of a stock or a specific group, relative to a benchmark. A measure of total performance based on the relative weighting of one group vs. another. A measure of performance based on the relative weighting of one group vs. another. A cross term that captures the interaction of the active weights and stock selection. The active weight times the difference between the asset's return and the return on the z'th group as represented in the benchmark. The active weight times the difference between the asset's return and the total return on the benchmark. The managed weight times the difference between the asset's return and the total return on the benchmark. The managed weight times the difference between the asset's return and the total return on the benchmark. Same as 4 but use industry/country/sector in place of asset. Same as 5 but use industry/country/sectorin place of asset. Same as 6 but use industry/country/sector in place of asset. S(t) = 5>>-l)x[r^(t)-r^(t)] 1=1 Si(t)=wbi(t-l)x[rip(t)-rjt)\ i A(t) = ^A:(t) !=1 A,(t) = [wP(t-l) -u?(t-l)]x [rjt-rb(t)] It(t) = [wP(t - 1) - ufi(t - 1)] x [rjt) - rjt)] wKt-ljxiR^-rJt)] wn(t-l)x[Rn(t)-rb(t)] ^-l)x[K^)-VW] ^-l)x[K^)-r^)] Same as 4 but by group Same as 5 but by group Same as 6 but by group