Brinson Model

The Brinson model, also known as the Brinson Fachler model is a model that is used to perform performance attribution. It is commonly used by investors to assess the performance of fund managers. In particular, both Bloomberg and Morningstar use this methodology for performance attribution. The model was developed by Gary Brinson in 1986, although the model is sometimes also referred to as the Brinson Hood Beebower attribution method.

On this page, we discuss Brinson attribution analysis, discuss the Brinson Fachler model formulas and conclude with a numerical example in Excel.

Brinson attribution model

The Brinson method works as follows. The approach consists of constructing a number of notional portfolios. In particular, we need to construct 4 portfolios. Two of these portfolios are easy to obtain.The first one is the benchmark return (Q1)

    $$ = \sum_j w_j^b \cdot r_j^b $$

where w is the weight of security j in the benchmark b, and r is the return of the security j in the benchmark. This portfolio uses benchmark sector weights and benchmark sector returns. The second portfolio is the fund itself. This portfolio uses portfolio sector returns and portfolio sector weights (Q4)

    $$ = \sum_j w_j^p \cdot r_j^p $$

Next, there’s the two portfolios that measure active stock selection and active asset selection. The active asset selection portfolio (Q2) uses benchmark sector returns and portfolio sector weights

    $$ = \sum_j w_j^p \cdot r_j^b $$

The stock selection portfolio (Q3) uses benchmark sector weights and portfolio sector returns

    $$ = \sum_j w_j^b \cdot r_j^p $$

We can then calculate the components of a fund’s performance as follows

    $$\textrm{Total Value-Added} = Q4 - Q1$$

    $$\textrm{Asset Allocation} = Q2 - Q1 $$

    $$\textrm{Stock Selection} = Q3 - Q1 $$

    $$\textrm{Interaction} = Q4 - Q3 - Q2 + Q1 $$

Brinson model example

Finally, let’s have a look at an example. The following spreadsheet implements the Brinson attribution model using some sample data.

Brinson model

The Brinson Fachler model Excel spreadsheet can be downloaded at the bottom of the page.


We discussed the Brinson Fachler attribution model. It is used extensively in the finance industry to analyze fund managers’ skill and whether or not they add value to the portfolio.