Brinson-Fachler Attribution Model

Overview

The Brinson-Fachler attribution model is a widely used performance attribution methodology that decomposes the excess return of a portfolio relative to a benchmark into three main effects:

1. Allocation Effect: Measures the impact of allocating assets differently than the benchmark
2. Selection Effect: Measures the impact of selecting securities that perform differently than the benchmark within each category
3. Interaction Effect: Measures the combined impact of allocation and selection decisions.

The Brinson-Fachler model, developed by Gary P. Brinson and Nimrod Fachler in 1985, is an extension of the original Brinson-Hood-Beebower model. It is considered one of the most comprehensive and widely accepted frameworks for performance attribution in the investment industry. The model provides a clear separation between allocation decisions (asset allocation) and selection decisions (security selection), making it particularly useful for evaluating the performance of portfolio managers.

How It Works

The Brinson-Fachler model calculates these effects using the following formulas:

• Allocation Effect: (Portfolio Weight - Benchmark Weight) × (Benchmark Return - Total Benchmark Return)
• Selection Effect: Benchmark Weight × (Portfolio Return - Benchmark Return)
• Interaction Effect: (Portfolio Weight - Benchmark Weight) × (Portfolio Return - Benchmark Return)
• Total Effect: Allocation Effect + Selection Effect + Interaction Effect

The model also calculates risk attribution using covariance matrices and marginal risk contributions to understand the risk contribution of each component.

When to Use

Use the Brinson-Fachler attribution model when:

• You want to understand the sources of excess return in a traditional asset allocation framework
• You need to separate the impact of asset allocation decisions from security selection decisions
• You want to analyze performance at multiple levels (total portfolio, asset class, sector, etc.)

Hierarchical Attribution Model

Overview

The Hierarchical attribution model is an alternative performance attribution methodology based on the "Balanced Portfolio Attribution" approach by Stephen Campisi in this paper. It decomposes the excess return into:

1. Allocation Effect: Measures the impact of allocating assets differently than the benchmark
2. Selection (or Active) Effect: Measures the impact of active management decisions within each category

Stephen Campisi's "Balanced Portfolio Attribution" approach, published in the Journal of Performance Measurement, addresses some limitations of traditional attribution models by providing a more balanced framework that avoids the asymmetry issues present in other models. The hierarchical aspect of this model allows for a multi-level analysis of performance, starting from broad asset classes and drilling down to more specific categories, making it particularly useful for complex portfolio structures.

How It Works

The Hierarchical model calculates these effects using the following formulas:

• Allocation Effect: (Portfolio Weight - Benchmark Weight) × (Benchmark Return - Total Benchmark Return)
• Selection Effect: Portfolio Weight × (Portfolio Return - Benchmark Return)
• Total Effect: Allocation Effect + Selection Effect

Important: Contrary to the classical Brinson-Fachler model, the hierarchical model rescales the weights within a given asset class. See the original publication for a detailed of the advantages of doing so.

When to Use

Use the Hierarchical attribution model when:

• You want a simpler decomposition of excess return (two components instead of three)
• You're dealing with complex portfolios that include funds and indexes
• You need to account for unexplained components in the attribution analysis
• You prefer the balanced attribution approach described by Stephen Campisi

Differences between the Brinson-Fachler Model and the Hierarchical Model

The Brinson-Fachler model attributes 100\% of a security's active return to the category to which it is assigned by reference data (e.g., GICS Sector, Country of Domicile).

For a security like a US technology stock:

• Its contribution to the US Country category is 100% of its weight.
• Its contribution to the Technology Sector category is 100% of its weight.

The model is based on dollars invested in defined categories. If the stock provides a return, that return is attributed entirely to those fixed, reference categories.

The Hierarchical Model (Campisi) links a security's return directly to the underlying risk drivers revealed through time-series regression. This is essential for modern risk management.

For a security like Tesla:

• Risk Factor Data: Regression analysis might show Tesla's volatility is highly correlated with the broad market Technology Factor and much less correlated with the Automotive Factor.
• Therefore, Tesla contributes to the Technology Sector Attribution at a level corresponding to its high factor exposure.

The model attributes active return based on systematic risk exposure, meaning an instrument's contribution is scaled by its sensitivity (beta) to each risk driver. This provides a more accurate view of why the return occurred—was it because of the general technology trend, or company-specific news?