Geometric attribution and the interaction effect
Performance attribution aims to decompose the excess return of an investment portfolio versus its benchmark into the contributions of the active investment decisions. Practitioners divide the available attribution methods in two main categories; arithmetic and geometric methods.
The widely accepted method of Brinson and Fachler (1985) is an arithmetic attribution method, which measures the impact of allocation and selection decisions independently. Moreover, it presents an interaction effect, which represents the combined effect of the allocation and selection decisions. One of the earliest geometric attribution methods was developed by Burnie, Knowles and Teder (1998). In this method, the geometric excess return is explained by allocation and selection effects, without presence of an interaction effect. This phenomenon has led to the conviction among some practitioners that geometric attribution eliminates the interaction effect.
In this paper, we show that, despite this belief, an interaction effect does arise when a geometric method is directly derived from the arithmetic Brinson and Fachler method. We present a new geometric attribution variant suitable for performance analysts who prefer to measure the impact of allocation and selection decisions independently. In line with the Brinson and Fachler method, the new method presents an interaction effect as well.