Performance Attribution for Equity Portfolios

Many portfolio managers measure performance with reference to a benchmark. The difference in return between a portfolio and its benchmark is the active return of the portfolio. Portfolio managers and their clients want to know what caused this active return. Performance attribution decomposes the active return. The two most common approaches are the Brinson-Hood-Beebower (hereafter referred to as the Brinson model) and a regression-based analysis. Portfolio managers use different variations of the two models to assess the performance of their portfolios. Managers of fixed income portfolios include yield-curve movements in the model Lord (1997) while equity managers who focus on the effect of currency movements use variations of the Brinson model to incorporate “local risk premium” Singer and Karnosky (1995). In contrast, in this paper we focus on attribution models for equity portfolios without considering any currency effect. The pa package provides tools for conducting both methods for equity portfolios. The Brinson model takes an ANOVA-type approach and decomposes the active return of any portfolio into asset allocation, stock selection, and interaction effects. The regression-based analysis utilizes estimated coefficients from a linear model to attribute active return to different factors. After describing the Brinson and regression approaches and demonstrating their use via the pa package, we show that the Brinson model is just a special case of the regression approach.