Brinson Performance Attribution

A backtest beats its benchmark by 3% over a quarter. Where did that 3% come from? It matters whether it came from being overweight a sector that happened to rally, or from picking the right individual names within sectors held at roughly benchmark weight — the first is a bet on sector calls, the second is stock selection skill, and they say very different things about whether the edge is repeatable. Brinson attribution is the standard framework for splitting a single relative-return number into these separately interpretable pieces.

Allocation and selection

Within each sector (or any grouping — country, factor bucket, market-cap band), Brinson attribution decomposes active return into two effects. Allocation effect asks: did the strategy hold more or less of this sector than the benchmark, and did that sector do better or worse than the overall benchmark?

$$\text{Allocation}_i = (w_i - b_i)(R_{b,i} - R_b)$$

where $w_i$ and $b_i$ are the strategy's and benchmark's weight in sector $i$, $R_{b,i}$ is the benchmark's return in that sector, and $R_b$ is the overall benchmark return. In plain English: reward or penalize the sector bet itself, independent of which stocks were picked within it.

Selection effect asks: within a sector, did the strategy's holdings beat the benchmark's holdings in that same sector?

$$\text{Selection}_i = b_i (R_i - R_{b,i})$$

where $R_i$ is the strategy's return within sector $i$. In plain English: reward or penalize stock-picking skill within the sector, holding the sector weight fixed at the benchmark's level.

Worked example: one sector, two effects

Technology is 30% of the benchmark, returning 20%; the overall benchmark returns 12%. The strategy holds technology at 40% (overweight by 10 points) and its technology holdings return 22%. Allocation effect: $(0.40 - 0.30)(20\% - 12\%) = 0.10 \times 0.08 = +0.8\%$ — being overweight a sector that beat the market average helped. Selection effect: $0.30 \times (22\% - 20\%) = 0.30 \times 0.02 = +0.6\%$ — picking better names within technology also helped. Total active contribution from technology: $0.8\% + 0.6\% = 1.4\%$, roughly split between a good sector call and good stock picking.

What this means in practice

The split matters for what a research team does next: consistently positive allocation effect with flat selection effect means the edge is in top-down sector calls, and the team should invest research time there, not in stock screens. The reverse pattern points to bottom-up skill worth scaling with more names and less sector timing. Brinson attribution is computed sector by sector and then summed, so a single quarter's total active return can hide sectors where allocation and selection pulled in opposite directions and cancelled out — always look at the sector-level table, not just the total.