Brinson Attribution

A portfolio beat its benchmark by 2% last quarter. The obvious next question, from a client or an allocator, is why, was it because the manager correctly overweighted the sector that ended up doing well, or because within each sector, the manager picked the specific stocks that outperformed their peers? These are genuinely different skills, one is a top-down call, the other is bottom-up stock selection, and a manager can be great at one and mediocre at the other. Brinson attribution is the standard method for splitting total outperformance into exactly these two pieces, plus a small interaction term.

Grading a sports team by lineup versus execution

A basketball coach's game plan can be evaluated two separate ways: did they choose to give more minutes to the positions that had a good night league-wide (a lineup decision), and, independent of that, did their specific players outperform their positional average given the minutes they got (an execution decision)? A coach who plays a genius lineup but whose players individually underperform can still lose; a coach with an ordinary lineup whose players individually overperform can still win. Brinson attribution asks the same two questions of a portfolio manager: did the sector weights add value (allocation), and did the stock picks within each sector add value (selection)?

The three terms

For each sector $i$, define the portfolio weight $w_i^P$ and benchmark weight $w_i^B$, and the portfolio return $r_i^P$ and benchmark return $r_i^B$ within that sector. Total active return decomposes as:

$\text{Allocation}_i = (w_i^P - w_i^B) \times r_i^B$

In words: being overweight or underweight a sector, multiplied by how that sector actually did in the benchmark, isolates the pure timing/weighting call, independent of stock-picking skill.

$\text{Selection}_i = w_i^B \times (r_i^P - r_i^B)$

In words: holding the benchmark's own sector weight fixed, did the manager's stocks within that sector beat the sector's benchmark return, isolating pure stock-picking skill.

$\text{Interaction}_i = (w_i^P - w_i^B) \times (r_i^P - r_i^B)$

In words: a cross term capturing the fact that being overweight a sector and picking good stocks in it compound together; many practitioners fold this into selection to keep the report to two clean numbers. Summed across all sectors, Allocation + Selection + Interaction equals total active return exactly.

Worked example

A portfolio holds two sectors. Tech: portfolio weight 40%, benchmark weight 25%, portfolio return 18%, benchmark (sector) return 15%. Energy: portfolio weight 60%, benchmark weight 75%, portfolio return 5%, benchmark (sector) return 8%.

Tech allocation: $(0.40 - 0.25) \times 0.15 = 0.15 \times 0.15 = 2.25\%$. Tech selection: $0.25 \times (0.18 - 0.15) = 0.25 \times 0.03 = 0.75\%$. Energy allocation: $(0.60 - 0.75) \times 0.08 = -0.15 \times 0.08 = -1.20\%$. Energy selection: $0.75 \times (0.05 - 0.08) = 0.75 \times (-0.03) = -2.25\%$.

Total allocation: $2.25 - 1.20 = 1.05\%$. Total selection: $0.75 - 2.25 = -1.50\%$. (Interaction terms omitted here for the simplified two-term version; a full three-term breakdown would additionally compute $(w^P-w^B)(r^P-r^B)$ per sector.) Net active return $\approx -0.45\%$: the manager's overweight to tech (a good call, tech beat the benchmark overall) was undermined by weak stock selection in both sectors, especially a poorly timed underweight to energy right as it modestly outperformed within its own return, combined with bad picks in energy specifically.

What this means in practice

• Separates a top-down call from a bottom-up call, which matters when a fund has separate sector-allocation and stock-picking decision-makers, or when an allocator is trying to judge which skill to pay for.
• Sensitive to how sectors/segments are defined. A coarser sector breakdown (10 GICS sectors) versus a finer one (sub-industries) can shift how much active return gets labeled "allocation" versus "selection."
• Extends to multiple periods by geometrically linking single-period Brinson results, which requires care (returns don't simply add across time) to keep the decomposition exact; see Time-Weighted vs Money-Weighted Returns for the underlying return-linking mechanics.

Practice

1. In the worked example, is the manager's active return driven more by sector calls or stock picks? What would you tell an allocator deciding whether to fund this manager's top-down process?
2. Explain why the allocation term uses the benchmark's sector return, $r_i^B$, rather than the portfolio's own sector return.
3. A single-sector portfolio (100% tech, benchmark also effectively 100% tech-relevant) shows zero allocation effect by construction. Why?