Rethinking the Fundamental Law of Active Management
The fundamental law of active management provides a powerful framework for analyzing portfolio diversification and risk-adjusted returns. It states that the information ratio of an unconstrained optimal portfolio is given by the product of the information coefficient (a measure of skill) and the square root of breadth, where breadth is the number of “independent” bets. A basic limitation of previous formulations of the fundamental law is that it was not possible to determine portfolio breadth for realistic portfolios under a general covariance structure. In this paper, we present a new formulation of the fundamental law of active management. We derive a new measure of skill, denoted the Signal Quality, and obtain an exact closed-form expression for the square root of breadth, which we denote as the Diversification Coefficient. Our formulation is easily applied to real-world portfolios described by general covariance matrices. We conclude with a discussion of the transfer coefficient, which measures the drop in portfolio efficiency due to investment constraints.