How to calculate breadth: An evolution of the fundamental law of active portfolio management

Abstract

Grinold and Kahn's highly acclaimed fundamental law of active management has as a weak point the lack of a measurable definition of breadth. Buckle (2003) developed a more general model of active portfolio management that uses fewer assumptions than Grinold and Kahn, resulting in the generalised fundamental law of active management. This law unfortunately has quite a complex mathematical representation. By applying some of Grinold and Kahn's assumptions to this generalised law, however, one derives a semi-generalised law, which is identical in form to Grinold and Kahn's original law, but with a measurable definition of breadth. The simplicity of application of this semi-generalised law is illustrated in several worked examples.