Attribution methods - Brinson-fachler allocation selection a...

Learning Outcomes

After reading this article, you will be able to describe the Brinson-Fachler attribution approach and distinguish allocation, selection, and interaction effects in multi-sector portfolio analysis. You will calculate each effect, interpret their meaning, and apply them to performance attribution for CFA Level 3. You will understand the CFA exam’s requirements on attribution methods and avoid common calculation errors.

CFA Level 3 Syllabus

For CFA Level 3, you are required to understand and apply attribution methods, especially those for equity and multi-sector portfolios based on the Brinson-Fachler framework. In your revision, focus on:

• Understanding the purpose and context of portfolio performance attribution.
• Explaining the components of Brinson-Fachler attribution (allocation, selection, interaction).
• Calculating each effect for segmented portfolios.
• Interpreting the financial significance and exam relevance of each effect.
• Identifying practical uses and exam pitfalls in attribution analysis.

Test Your Knowledge

Attempt these questions before reading this article. If you find some difficult or cannot remember the answers, remember to look more closely at that area during your revision.

1. In the Brinson-Fachler attribution framework, which effect isolates the impact of choosing different sector weights than the benchmark?
2. If a sector’s portfolio weight exceeds the benchmark and its return lags the benchmark, which effect is likely negative?
3. Calculate the selection effect for a sector where the portfolio holds 20%, the benchmark 15%, the portfolio’s sector return is 12%, and the benchmark sector return is 8%.
4. Why is the interaction effect sometimes considered negligible or grouped with allocation or selection?

Introduction

Performance attribution helps portfolio managers and stakeholders understand the sources of outperformance or underperformance relative to a benchmark. The Brinson-Fachler method is the standard approach for decomposing value-added in a portfolio into allocation, selection, and interaction effects across multiple sectors or asset classes. This is a key skill for CFA Level 3 candidates and is frequently examined.

Key Term: performance attribution
The process of decomposing portfolio returns relative to a benchmark into distinct sources, such as allocation and selection effects.

Key Term: Brinson-Fachler method
A framework for multilevel portfolio attribution that breaks down excess returns into allocation, selection, and interaction contributions.

THE BRINSON-FACHLER ATTRIBUTION FRAMEWORK

Central to attribution is comparing the portfolio’s actual composition and results with those of its benchmark. In practice, attribution is typically performed for equity or multi-sector portfolios, with the benchmark representing the “neutral” policy or market weights.

The Three Effects

1. Allocation Effect: Measures the impact of over- or under-weighting sectors relative to the benchmark, holding all other returns constant.

2. Selection Effect: Assesses the outcome of choosing securities that outperform or underperform the sector benchmark, holding sector weights constant.

3. Interaction Effect: Captures the combined impact of both overweighting a sector and selecting securities that differ in performance from the sector benchmark.

Key Term: allocation effect
The portion of active return attributed to the portfolio’s sector weights being different from those of the benchmark, applied to benchmark sector returns.

Key Term: selection effect
The part of active return assigned to the difference between the portfolio’s sector returns and benchmark sector returns, weighted by the portfolio’s sector weights.

Key Term: interaction effect
The amount of value added (or lost) when the portfolio both deviates in sector weight and in performance versus benchmark within that sector.

Mathematical Formulation

The total value added by the portfolio over the benchmark can be decomposed as:

Total Active Return = Allocation Effect + Selection Effect + Interaction Effect

Where for each sector $i$:

• $w_{Pi}$ = Portfolio weight in sector $i$
• $w_{Bi}$ = Benchmark weight in sector $i$
• $r_{Pi}$ = Portfolio sector return
• $r_{Bi}$ = Benchmark sector return

The effects are calculated as:

• Allocation Effect: $(w_{Pi} - w_{Bi}) \cdot (r_{Bi} - r_{B})$
• Selection Effect: $w_{Pi} \cdot (r_{Pi} - r_{Bi})$
• Interaction Effect: $(w_{Pi} - w_{Bi}) \cdot (r_{Pi} - r_{Bi})$

where $r_{B}$ is the total benchmark return.

Step-by-Step Calculation

1. Calculate the return of each sector for both portfolio and benchmark.
2. Identify weights for each sector in both the portfolio and benchmark.
3. Compute the benchmark total return for reference.
4. Use the above formulas to determine each effect for each sector.
5. Sum effects across sectors for total attribution.

Worked Example 1.1

A portfolio consists of two sectors:

The total benchmark return is $r_B = 0.5 \times 4\% + 0.5 \times 8\% = 6\%$.

Calculate the allocation, selection, and interaction effects for each sector and in total.

Answer:
For Sector X:

• Allocation: (0.60 - 0.50) × (4% - 6%) = 0.10 × (−2%) = −0.2%
• Selection: 0.60 × (6% − 4%) = 0.60 × 2% = 1.2%
• Interaction: (0.60 − 0.50) × (6% − 4%) = 0.10 × 2% = 0.2% For Sector Y:
• Allocation: (0.40 − 0.50) × (8% − 6%) = (−0.10) × 2% = −0.2%
• Selection: 0.40 × (10% − 8%) = 0.40 × 2% = 0.8%
• Interaction: (0.40 − 0.50) × (10% − 8%) = (−0.10) × 2% = −0.2% Totals:
• Allocation: (−0.2%) + (−0.2%) = −0.4%
• Selection: 1.2% + 0.8% = 2.0%
• Interaction: 0.2% + (−0.2%) = 0.0%
• Total active return = (−0.4%) + 2.0% + 0.0% = 1.6%

Worked Example 1.2

An equity portfolio overweights the healthcare sector compared to the benchmark. This sector underperforms during the period. What is the expected sign of the allocation effect for healthcare?

Answer:
The allocation effect will be negative, as overweighting a sector that lags the benchmark reduces active return.

Exam Warning

If asked for the selection effect, always use portfolio weights—not benchmark weights. Mixing these will result in the wrong calculation and partial credit only.

Summary

The Brinson-Fachler attribution method splits portfolio active return into three effects: allocation (which captures value from sector over/underweights), selection (from security selection skill), and interaction (from weight and performance deviations in the same sector). Proper application is essential for clear attribution and CFA exam success.

Key Point Checklist

This article has covered the following key knowledge points:

• Define and explain the allocation, selection, and interaction effects using the Brinson-Fachler method.
• Perform step-by-step calculations of each effect for multi-sector portfolios.
• Recognize the impact of sector weights and returns in each attribution component.
• Avoid exam mistakes by using portfolio weights for selection, and interpreting interaction correctly.
• Interpret the real-world meaning of attribution results for portfolio performance.

Key Terms and Concepts

• performance attribution
• Brinson-Fachler method
• allocation effect
• selection effect
• interaction effect