Information Ratio¶

One-line definition¶

Active return per unit of active risk — the benchmark-relative analogue of the Sharpe ratio, and the standard single-number measure of a manager's skill.

Formula¶

Ex-ante (from a covariance matrix, given active weights):

IR = active_return / tracking_error

using tracking_error as the denominator.

Ex-post (realized, from a matched portfolio/benchmark return series):

IR = mean(active_returns) / std(active_returns) * sqrt(periods_per_year)

active_returns_t = portfolio_return_t - benchmark_return_t

Why PMs care¶

Absolute return says nothing about how much risk was taken to earn it; information ratio does the same job Sharpe does for total risk, but against a benchmark instead of cash — which is the right comparison for almost any institutional mandate. It's the headline number in manager selection and in the Fundamental Law of Active Management, where it's the quantity IC and breadth are trying to explain (see Fundamental Law).

Worked example¶

Portfolio returns 3%, 5%, 2%; benchmark returns 1%, 2%, 1% over three periods. Active returns: 2%, 3%, 1% — mean 2%, sample std 1%. IR = 0.02 / 0.01 = 2.0 (unannualized, matching src/pm/active.py::information_ratio at periods_per_year=1).

Common mistakes¶

comparing information ratios computed over different sampling frequencies without annualizing both consistently
treating a high IR over a short, lucky window as durable skill — IR estimated from a handful of observations is itself very noisy
confusing the ex-ante IR (built from a risk model's covariance matrix, forward-looking) with the ex-post IR (realized from actual returns, backward-looking) — they answer different questions and won't generally match

Limitations¶

The realized version assumes active returns are independent and identically distributed across periods; serial correlation or a fat-tailed active-return distribution both bias the ratio.

Free resources¶

Information ratio — Wikipedia — definition, the Sharpe-ratio comparison, and common criticisms
CFA Institute, Analysis of Active Portfolio Management (already linked in resources/active_management.md) — the IR/IC/breadth/transfer-coefficient/Fundamental-Law treatment this repo's Phase 3 follows