Benchmark-Weighted Selection and Interaction in Brinson-Fachler Attribution
Summary
The document clarifies two formulas that can appear to measure security selection in performance attribution: benchmark weight multiplied by the portfolio-minus-benchmark return, and portfolio weight multiplied by that return. The distinction depends on whether the attribution separates the interaction between allocation and selection.
In the three-factor Brinson-Fachler approach, the benchmark-weighted return difference is the security selection component. The portfolio-weighted version combines selection with the interaction component, which captures the joint effect of portfolio positioning and relative returns. Some two-factor presentations combine interaction and selection into one component, so the latter formula can be appropriate under that convention. The example supplies sector weights and returns but no computed attribution totals; the key caveat is to identify the attribution convention before interpreting the component.
Key ideas
- Brinson-Fachler attribution can separate allocation, selection, and interaction effects.
- Benchmark weight times the portfolio-benchmark return difference gives the selection component in the three-factor method.
- Portfolio weight times that return difference combines selection and interaction.
- Two-factor attribution may intentionally report the combined measure as selection.
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Full text
# performance attribution - security selection= wB*(Rp-RB) or wP*(Rp-RB)? # performance attribution - security selection= wB*(Rp-RB) or wP*(Rp-RB)? Really confused. Finding various different ways of calculating security selection alpha. I believe it matters from whose perspective one is looking at. I am a portfolio manager and I want to know what my alpha from security selection was based on a benchmark. Example: Group | Portfolio Wgt| Portfolio Return| Benchmark Wgt| Benchmark Return Healthcare| 20% |3%| 50%| 1% Technology 80%| -2%| 50%| 0.50%| Is my Security Selection alpha from Technology = 80%*(-2-0.5) OR = 50%*(-2 - 0.5) - I apologize if this is really basic but I am having trouble getting my head around it. I feel like both are right. ## Answer by Tim Wilding (score 1, accepted) https://quant.stackexchange.com/a/38798 Brinson-Fachler attribution separates performance into three factors: a sector allocation, a security selection component and an interaction component. The interaction component measures the interaction between stock selection and sector allocation. Some people have trouble understanding the three-factor approach, so many people use a two-factor approach and combine the interaction component and the selection component into a single stock-selection component (see https://insight.factset.com/equity-attribution-and-the-delicate-art-of-interaction) $w_B(R_P - R_B)$ is the security selection component, and $w_p(R_P-R_B)$ is the combined security selection and interaction component.
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