Interpret where a portfolio's returns came from using a given attribution method

CFA® Level III · Performance Measurement · Portfolio Performance Evaluation · L3.PF.1.e

The idea

In the Brinson–Fachler model, for each sector: allocation = (wp − wb) × (Rb,sector − Rb,total). Selection rewards holdings that beat their sector's index: selection = wb × (Rp,sector − Rb,sector). Interaction captures the joint effect of the weighting and the stock choice: interaction = (wp − wb) × (Rp,sector − Rb,sector). Suppose a portfolio holds 30% in a sector the benchmark weights at 20%; the sector index returns 8% against 5% for the whole benchmark, and the manager's holdings in it return 10%. Allocation is 0.10 × 3% = 0.30%, selection 0.20 × 2% = 0.40% and interaction 0.10 × 2% = 0.20%. Brinson–Hood–Beebower uses the sector's own benchmark return, not its excess over the total, so overweighting a sector with a positive but below-benchmark return wrongly looks helpful. Factor-based attribution instead splits return into exposure × factor return plus a residual.

Formulas

Allocation effect (Brinson–Fachler)

allocation = (wp − wb) × (Rb,sector − Rb,total)

wp: the portfolio's weight in the sector
wb: the benchmark's weight in the sector
Rb,sector: the benchmark's return in the sector
Rb,total: the whole benchmark's return

Measured against the benchmark's total return, so overweighting a sector that beat the benchmark adds value even if the sector fell. Summed over sectors, allocation, selection and interaction add up to the active return.

Selection effect

selection = wb × (Rp,sector − Rb,sector)

wb: the benchmark's weight in the sector
Rp,sector: the portfolio's return in the sector
Rb,sector: the benchmark's return in the sector

Weighted by the benchmark's weight, so it measures stock picking within the sector as if the sector were held at benchmark weight.

Interaction effect

interaction = (wp − wb) × (Rp,sector − Rb,sector)

wp: the portfolio's weight in the sector
wb: the benchmark's weight in the sector
Rp,sector: the portfolio's return in the sector
Rb,sector: the benchmark's return in the sector

The joint effect of overweighting a sector and outperforming within it. Some reports fold it into selection, so check which convention a report uses before comparing managers.

In the app: 2 practice questions on this outcome, a narrated walkthrough with diagrams, spaced review that brings it back before you forget it.

Take the free diagnostic →