The Limits of Expanding Breadth: The Trade-Offs between Diversification and Forecasting Ability

Abstract

One crucial element in portfolio construction is obtaining maximum benefit from diversification. The objective of holding multiple positions in a portfolio is to reduce the risks from unintended bets, and to diversify the risks from attractive positions, while still letting the expected returns flow through to the bottom line. This relationship is described and quantified by the Fundamental Law of Active Management. It relates an active investment strategy’s information ratio (ratio of expected active return to expected active risk) to manager skill and to portfolio breadth. This commentary explores the Law and its underlying assumptions, and examines how the implications of the Law can be used or misused. In order to understand the Law, we first discuss why the information ratio (IR) is the proper metric to use to evaluate unconstrained active strategies. Next we explore the Law, its assumptions, inputs, and implications. Most importantly, we examine the potential impact and limitations from expanding the number of positions in a portfolio on its IR. The objective of this article is to explore the trade-offs from expanding the number of positions in a portfolio (increasing the number of models, factors, and/or securities) on portfolios’ expected risks, expected returns and IRs.