How does the Brinson performance attribution model decompose portfolio returns into allocation, selection, and interaction effects?

The Brinson-Hood-Beebower (BHB) attribution model decomposes the active return (portfolio return minus benchmark return) into three components that explain where the outperformance or underperformance came from.

The Three Components:

1. Allocation Effect — Did the manager add value by overweighting/underweighting sectors relative to the benchmark?
2. Selection Effect — Did the manager add value by picking better/worse securities within each sector?
3. Interaction Effect — The combined effect of simultaneously overweighting a sector AND picking better securities in it (or vice versa)

Formulas:

For each sector i:

• Allocation_i = (w_p,i - w_b,i) × (R_b,i - R_b)
• Selection_i = w_b,i × (R_p,i - R_b,i)
• Interaction_i = (w_p,i - w_b,i) × (R_p,i - R_b,i)

Where:

• w_p,i = portfolio weight in sector i
• w_b,i = benchmark weight in sector i
• R_p,i = portfolio return in sector i
• R_b,i = benchmark return in sector i
• R_b = total benchmark return

Total Active Return = Σ(Allocation_i) + Σ(Selection_i) + Σ(Interaction_i)

Worked Example — Clearwater Growth Fund vs. Russell 1000 Growth

Step 1 — Total Benchmark Return:

R_b = 0.30(10.5%) + 0.25(9.2%) + 0.20(6.0%) + 0.25(4.8%) = 3.15% + 2.30% + 1.20% + 1.20% = 7.85%

Step 2 — Total Portfolio Return:

R_p = 0.35(12.0%) + 0.20(8.0%) + 0.25(7.5%) + 0.20(5.0%) = 4.20% + 1.60% + 1.875% + 1.00% = 8.675%

Active Return = 8.675% - 7.85% = 0.825%

Step 3 — Allocation Effect by Sector:

The positive allocation effect (+0.125%) means the manager added value through sector weighting — primarily by overweighting Technology (a strong sector) and underweighting Financials (a weak sector).

Step 4 — Selection Effect by Sector:

Step 5 — Interaction Effect by Sector:

Verification:

0.125% + 0.500% + 0.200% = 0.825% (matches the active return)

BHB vs. Brinson-Fachler:

Some references combine the interaction effect into the selection effect (the Brinson-Fachler variant). The CFA exam typically uses the three-component BHB version but may present either. Read the question carefully to determine which decomposition is expected.

Exam Tip: Always construct the full table sector by sector. The most common errors are: (1) using portfolio weights instead of benchmark weights for the selection effect, and (2) forgetting to subtract the total benchmark return in the allocation formula. Verify that your three components sum to the total active return.

Practice performance attribution in our CFA Level III question bank.