Information ratio
Quantitative Finance glossary · Numerical Methods & Optimization
Definition
Active return per unit of active risk: IR = (α)/(σ(R_p - R_b)), where the denominator is tracking error. The Sharpe-equivalent for benchmark-relative strategies. Grinold's Fundamental Law of Active Management decomposes IR = IC· √(BR) — information coefficient (forecast skill) times the square root of breadth (number of independent bets) — explaining why broad systematic strategies can match concentrated discretionary skill with lower per-bet IC.
Information ratio in plain English
Imagine two students who both beat the class average on a test — but one did it by getting lucky on a couple of questions, while the other beat it steadily on almost every question. The information ratio measures that second kind of skill: how much extra return a manager earns above their benchmark (a yardstick like 'the whole stock market') divided by how bumpy and unreliable that extra return is. A higher ratio means the outperformance is consistent, not a fluke. There's even a neat rule of thumb (Grinold's Fundamental Law) that says your skill-per-bet times the square root of how many independent bets you make sets this ratio — which is why a strategy that makes thousands of tiny, so-so bets can rival a genius who makes just a few big ones.
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