How does the Brinson-Hood-Beebower performance attribution model separate allocation from selection effects?

The Brinson-Hood-Beebower (BHB) model is the most widely used framework for decomposing active portfolio returns into their sources. Let's break it down.

The Framework:

Total active return (portfolio return minus benchmark return) is decomposed into three components:

1. Allocation Effect — Did the manager overweight sectors that outperformed?
2. Selection Effect — Did the manager pick better stocks within each sector?
3. Interaction Effect — The combined effect of overweighting a sector AND picking good stocks within it

Formulas:

For each sector i:

• Allocation = (Wp_i - Wb_i) x (Rb_i - Rb_total)
• Selection = Wb_i x (Rp_i - Rb_i)
• Interaction = (Wp_i - Wb_i) x (Rp_i - Rb_i)

Where Wp = portfolio weight, Wb = benchmark weight, Rp = portfolio return, Rb = benchmark return.

Worked Example:

Silverleaf Capital manages a US equity fund benchmarked to the Silverleaf Broad Market Index.

Benchmark total return: 0.28(10%) + 0.22(9%) + 0.30(5%) + 0.20(3%) = 2.80% + 1.98% + 1.50% + 0.60% = 6.88%

Portfolio total return: 0.35(12%) + 0.25(8%) + 0.20(6%) + 0.20(4%) = 4.20% + 2.00% + 1.20% + 0.80% = 8.20%

Active return: 8.20% - 6.88% = +1.32%

Technology Sector Attribution:

• Allocation: (0.35 - 0.28) x (10% - 6.88%) = 0.07 x 3.12% = +0.218%
• Selection: 0.28 x (12% - 10%) = 0.28 x 2% = +0.560%
• Interaction: 0.07 x (12% - 10%) = 0.07 x 2% = +0.140%

The manager added value in Technology through both allocation (overweighting an outperforming sector) and selection (picking stocks that beat the sector benchmark).

Key Insight:

The interaction term is often controversial. Some practitioners fold it into either allocation or selection. The Brinson-Fachler variation assigns it to allocation, making the analysis simpler. The exam typically specifies which method to use.

Exam tip: CFA Level II often provides a table like the one above and asks you to calculate one or more attribution components. Practice the formulas until they're second nature, and remember that all three components should sum to the total active return.

Master performance attribution with our CFA Level II question bank on AcadiFi.