Information Ratio = Selection × Breadth + Sizing

Abstract

Factor-based performance attribution is an established practice among quantitative and fundamental strategies alike. Although popular, this attribution technique is not of great help to investors interested in understanding the source of their idiosyncratic performance. Of special interest is the ability to separate stock selection skill and sizing skill. Methods aimed at measuring these skills are inspired by analogies to sports. In this article, the author presents an exact decomposition of the information ratio. The IR is the sum of a breadth-adjusted stock selection skill and a sizing skill. The definition of breadth relies on an intuitive measure of concentration—the Herfindahl Index—rather than on the “square root of <italic>n</italic>” measure. These quantities can be compared so that the portfolio manager can determine the percentage of their realized performance originating from each term. In addition, the decomposition empowers the manager to improve their risk-adjusted performance by choosing optimal position sizing, determined by the observed performance of their portfolio. Finally, the decomposition can be further extended to long–short analysis, and provides a natural explanation of an empirical phenomenon: The idiosyncratic performance of the long side of a strategy is often larger than that of the short side.