The Central Paradox of Active Management: Maximizing the Information Ratio Is Counterproductive

Abstract

The use of “information ratios” for benchmark relative (active) returns seems like a small step from the use of the Sharpe ratio for absolute returns. However, something very important got overlooked in that extension. While it possible (even likely) that all risky assets will outperform the risk-free rate over a sufficiently long horizon, it is impossible for all active managers to outperform sensible benchmarks, even though all active managers (and their investors) must believe they will outperform to rationally pursue active management. Obviously, a material portion of active investors must underperform benchmarks, even though none expects to do so. This failure to accept arithmetic reality is known as the “Central Paradox of Active Management.” This inherent “wrongness” is not reflected in the way in information ratio (IR) is calculated as a simple coefficient of variation, leaving conventional IR values upward biased as performance measure. In this article, the framing of the algebra shows that the degree of bias increases with IR in a nonlinear fashion, so the conventional view that portfolio managers should seek to maximize their information ratio is demonstrably counterproductive.