The Brinson-Fachler Model

Beating a benchmark can happen two completely different ways: being in the right places, or picking the right names once there. A manager who overweighted Tech before a rally and simply held the sector's average stocks still beat the benchmark — that's a bet on where to be, not what to pick. A manager who held the benchmark's exact sector weights but consistently found the best stock in each one also beat the benchmark, for the opposite reason. The Brinson-Fachler model exists to tell those two managers apart, sector by sector.

Splitting active return into two effects

For each sector $i$, active return splits into:

$$\text{Allocation}_i = (w_{p,i} - w_{b,i})(r_{b,i} - r_b), \qquad \text{Selection}_i = w_{b,i}(r_{p,i} - r_{b,i}) .$$

In words: $w_{p,i}$ and $w_{b,i}$ are the portfolio's and benchmark's weight in sector $i$; $r_{p,i}$ and $r_{b,i}$ are the portfolio's and benchmark's return within that sector; $r_b$ is the benchmark's total return. Allocation asks: did the manager over- or underweight this sector relative to the benchmark, and did that sector go on to beat or lag the overall benchmark? Selection asks: within this sector specifically, did the manager's chosen stocks beat the sector's own benchmark return, weighted by how much the benchmark (not the portfolio) had in that sector, so a manager can't inflate their selection score just by overweighting a sector they're good at picking in. Summed across every sector, the two effects together reconstruct the total active return exactly.

Worked example — one sector, both effects

In the Technology sector, the benchmark holds a 20% weight and returns $12\%$; the overall benchmark returns $8\%$. The portfolio holds a 30% weight in Technology (a 10-point overweight) and its Technology stocks return $15\%$ (3 points ahead of the sector benchmark). Allocation: $(0.30 - 0.20)(12\% - 8\%) = 0.10 \times 4\% = 0.40\%$ — being overweight a sector that beat the overall benchmark added 40 basis points. Selection: $0.20 \times (15\% - 12\%) = 0.20 \times 3\% = 0.60\%$ — picking better stocks within Technology, weighted at the benchmark's 20% sector size, added another 60 basis points. This sector alone contributed $0.40\% + 0.60\% = 1.00\%$ of active return, split roughly 40/60 between being in the right place and picking the right names.

What this means in practice

Institutional performance reports break active return into these two effects sector by sector (often with a small interaction term for the part attributable to both effects acting together) precisely so an allocator can separate a top-down asset allocation decision from bottom-up stock-picking skill — a manager might be genuinely excellent at one and mediocre at the other, and blending both into a single "beat the benchmark by 2%" headline hides which one actually happened.