The interaction effect captures the joint impact of having an active category weight and a portfolio return within that category that differs from the benchmark category return.
It appears in common three-part Brinson Attribution frameworks alongside Allocation Effect and Selection Effect.
Common formula
For category i:
Interaction_i = (wp,i - wb,i) × (Rp,i - Rb,i)
where:
wp,i - wb,iis the active category weight; andRp,i - Rb,iis the portfolio's within-category relative return.
The effect is a cross-product of allocation and selection differences.
Example
Assume a sector has:
- portfolio weight: 30%;
- benchmark weight: 20%;
- portfolio sector return: 10%; and
- benchmark sector return: 8%.
Then:
Interaction = (30% - 20%) × (10% - 8%) = 0.20%
The positive 20-basis-point effect reflects that the portfolio both overweighted the category and outperformed within it.
How the sign works
Interaction tends to be positive when active weight and within-category relative return have the same sign, such as:
- overweighting a category where selection outperforms; or
- underweighting a category where the portfolio's selected holdings underperform the category benchmark.
It tends to be negative when those two decisions work against each other.
Interaction is partly a convention
The interaction effect is not necessarily a standalone managerial decision. It exists because allocation and selection occur simultaneously and the arithmetic cross-product must be assigned somewhere.
Some attribution systems report interaction separately. Others combine it with selection or allocation.
That means interaction is partly a reporting convention, not necessarily a standalone source of manager skill.
Do not overinterpret it
A large positive interaction effect does not prove that a manager intentionally coordinated allocation and selection successfully.
It may simply reflect the mathematics of holding more of a category in which the portfolio happened to outperform.
For that reason, Performance Attribution should be interpreted in the context of the full investment process rather than treating every attribution component as an independent skill signal.
Sources
- CFA Institute, Portfolio Performance Evaluation, 2026
- CFA Institute, 2026 CIPM Level I Topic Outline
- CFA Institute Research Foundation, Performance Attribution
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