Decomposition✓ Mathematical
◆ The PatternBrinson decomposition — allocation, selection, interaction
Return attribution answers: "Where did excess return come from?" The Brinson-Fachler model splits active return into three effects:
Active Return = Allocation + Selection + Interaction
Allocation: over/underweighting sectors that outperform. Selection: picking better stocks within sectors. Interaction: the cross-term. Multi-period attribution chains single-period results.
// Return attribution — Brinson decomposition
Daily practice. Institutional managers report monthly attribution to explain why they beat (or missed) the benchmark.
Pattern bridge: Decomposing variance is explored in The Toolkit — ANOVA.