Brinson-Style Attribution over Continuous Factors

Abstract

The authors develop a methodology to perform a Brinson-style attribution over a set of factors that may have continuous exposures to the assets. They show that for a set of factor returns, the Brinson-style allocation and selection effects are synonymous with the factor and specific contributions respectively. This puts an end to an open question of how to make sense of two different kind of attributions, namely, Brinson attribution over sectors and factor attribution over factors. The authors show that they are identical if the factor returns used in the attribution completely explain the underlying benchmark portfolio. Their method is simple, intuitive, and reduces to the standard Brinson attribution for the case of binary factors, such as industry, country, and currency factors.