Pure Benchmarks · Explainer
Brinson Attribution Explained: Allocation, Selection and Interaction Effects
Short answer
Brinson attribution splits the difference between a portfolio’s return and its benchmark’s return into three parts. The allocation effect is what you gained or lost by weighting a group, such as stocks or a sector, differently from the benchmark. The selection effect is what you gained or lost by holding different securities inside that group. The interaction effect is the overlap of the two. Added together they equal the portfolio’s excess return over the benchmark exactly.
Brinson attribution is the method most asset managers, pension funds and performance teams use to explain why a portfolio beat or trailed its benchmark. It does not ask whether the return was good in absolute terms. It asks where the gap with the benchmark came from: from deciding how much to put in each part of the market, or from deciding what to buy inside each part. This page walks through the formulas with a two-group example you can check by hand, then covers the Brinson-Fachler variant and the limits of the method for individual investors.
The three Brinson effects for one group
| Effect | Formula (Brinson-Hood-Beebower) | What it measures |
|---|---|---|
| Allocation | (portfolio weight − benchmark weight) × benchmark group return | The result of overweighting or underweighting the group |
| Selection | benchmark weight × (portfolio group return − benchmark group return) | The result of picking different holdings inside the group |
| Interaction | (portfolio weight − benchmark weight) × (portfolio group return − benchmark group return) | The extra result from being overweight in a group where your picks also beat the benchmark, or the reverse |
| Total | Sum of the three across all groups | Portfolio return minus benchmark return |
Formulas follow Brinson, Hood and Beebower (Financial Analysts Journal, 1986) and Brinson and Fachler (Journal of Portfolio Management, 1985). Brinson-Fachler replaces the benchmark group return in the allocation term with the benchmark group return minus the total benchmark return.
A worked example
Take a benchmark that holds 60% stocks returning 10% and 40% bonds returning 2%, for a total of 6.8%. The portfolio holds 70% stocks returning 12% and 30% bonds returning 1%, for a total of 8.7%. The portfolio beat the benchmark by 1.9 percentage points. Brinson attribution explains where those 1.9 points came from, group by group.
Allocation effect
Allocation multiplies the weight difference by the benchmark’s return for that group. Stocks: (70% − 60%) × 10% = +1.0 point. Bonds: (30% − 40%) × 2% = −0.2 points. Total allocation effect: +0.8 points. Overweighting the group that did better added value, and underweighting bonds cost a little because bonds still returned something.
Selection effect
Selection multiplies the benchmark weight by the difference between the portfolio’s return and the benchmark’s return inside each group. Stocks: 60% × (12% − 10%) = +1.2 points. Bonds: 40% × (1% − 2%) = −0.4 points. Total selection effect: +0.8 points. The stock picks beat the stock benchmark, and the bond picks trailed the bond benchmark.
Interaction effect
Interaction multiplies the weight difference by the return difference. Stocks: 10% × 2% = +0.2 points. Bonds: −10% × −1% = +0.1 points. Total: +0.3 points. Adding the three gives 0.8 + 0.8 + 0.3 = 1.9 points, exactly the portfolio’s excess return. Many reports fold interaction into selection, which is why some tools show only two effects.
Brinson-Fachler: the allocation effect relative to the benchmark
Brinson-Hood-Beebower rewards overweighting any group with a positive return, even one that trailed the overall benchmark. Brinson-Fachler measures allocation against the total benchmark return instead: (portfolio weight − benchmark weight) × (benchmark group return − total benchmark return). In the example, stocks give 10% × (10% − 6.8%) = +0.32 points and bonds give −10% × (2% − 6.8%) = +0.48 points. The total allocation effect is still +0.8 points, but underweighting bonds now shows up as the larger contribution, because bonds lagged the benchmark as a whole. That per-group view is why most modern systems use Brinson-Fachler.
What Brinson attribution does not tell an individual investor
It needs a benchmark with group weights, and most personal portfolios have no natural one. It explains a period rather than a decision, so a sale in March and a purchase in June are blended into the same effects. And it compares you with an index, not with the portfolio you held before you made a change. If the question is whether your own buys and sells were worth making, decision-based attribution answers that directly. Pure Benchmarks, our own product, runs it through Decision Benchmark on linked accounts. It does not produce a Brinson decomposition.
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See Your Free Benchmark ReportFrequently asked questions
What is Brinson attribution?
A method that splits a portfolio’s return relative to a benchmark into an allocation effect, from weighting groups differently, a selection effect, from picking different holdings inside each group, and an interaction effect from the overlap of the two. The effects add up to the portfolio’s excess return.
What is the difference between Brinson-Fachler and Brinson-Hood-Beebower?
Only the allocation term differs. Brinson-Hood-Beebower multiplies the weight difference by the benchmark group’s return. Brinson-Fachler multiplies it by the benchmark group’s return minus the total benchmark return, so overweighting a group is rewarded only if that group beat the benchmark as a whole. Total allocation is the same under both; the split across groups changes.
What is the interaction effect in Brinson attribution?
The weight difference multiplied by the return difference for a group. It is positive when you overweighted a group where your holdings also beat the benchmark, or underweighted one where they trailed. Many reports add it to the selection effect.
Does asset allocation explain 90% of portfolio returns?
That is a common misreading of the 1986 Brinson, Hood and Beebower study of 91 large US pension plans. It found that investment policy explained about 93.6% of the variation in the plans’ quarterly returns over time, not 93.6% of the level of their returns.
Can Brinson attribution be used for bonds?
It can, but fixed income is usually attributed with models built around yield-curve, duration, spread and carry effects, because bond returns are driven by rates and credit more than by sector weights.
Is there an alternative to Brinson attribution for personal portfolios?
Decision-based attribution. It scores each buy and sell against the portfolio you held the moment before it, so it needs no benchmark weight file and tells you whether each change beat doing nothing.
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This page is an information baseline for comparison only. It is not investment advice and not a recommendation to buy, sell, replace, or transfer any specific asset, account, or firm. Past performance does not guarantee future results. All figures shown are illustrative.