Information Ratio Calculator (active return ÷ tracking error, annualized)

Understanding the information ratio calculator — concept and principle

This calculator measures how much extra return a portfolio earned over its benchmark per unit of extra risk: the information ratio (IR). From matching lists of portfolio and benchmark returns it gives the annualized IR, active return per year, tracking error per year, the share of periods beating the benchmark and the per-period IR. Use it to evaluate fund managers and active strategies.

How it is calculated

• Active return each period = portfolio return − benchmark return.
• Mean active return = average of the active returns.
• Tracking error = sample standard deviation of the active returns.
• IR per period = mean active return ÷ tracking error.
• Annualized: active return × periods per year; tracking error × √(periods per year); IR × √(periods per year).

The principle

An active manager takes risk relative to the benchmark to try to beat it. The information ratio asks whether the extra return was worth that risk: it divides the average outperformance by how much it fluctuated. A manager who beats the index by a little every period has a high IR; one who beats it on average but with wild swings has a low IR. Annualizing uses the square-root-of-time rule because, for independent periods, standard deviations grow with the square root of the number of periods.

Worked example

Default inputs: 12 monthly returns for the portfolio and benchmark (made-up example data).

1. Active returns: 0.3, 0.3, 0.2, 0.4, 0.6, 0.1, 0.2, 0.1, 0.4, 0.4, 0.4, 0.3 (%); mean ≈ 0.308%.
2. Tracking error per month ≈ 0.144%; IR per period ≈ 2.136.
3. Active return per year ≈ 0.308 × 12 = 3.7%; tracking error per year ≈ 0.144 × √12 = 0.5%.
4. Annualized IR ≈ 2.136 × √12 ≈ 7.4.
5. The portfolio beat the benchmark in 100% of periods.

How to read the result

An IR of about 0.5 sustained over years is often called good and 1.0 exceptional. The example's 7.4 is unrealistically high because the made-up data beat the benchmark every month by a steady amount; real managers rarely do that. Short samples are noisy, so use at least 36 monthly returns where possible.

Common mistakes

• Using returns for different periods in the two lists.
• Choosing a benchmark that does not match the strategy.
• Drawing conclusions from a short sample.
• Confusing the information ratio with the Sharpe ratio, which uses the risk-free rate instead of a benchmark.

Frequently asked questions

What is a good information ratio?

Around 0.5 over several years is often considered good and 1.0 exceptional.

What is tracking error?

The standard deviation of the difference between portfolio and benchmark returns.

How is IR different from the Sharpe ratio?

The Sharpe ratio measures excess return over the risk-free rate per unit of total volatility; IR measures excess return over a benchmark per unit of tracking error.

Sources: Information ratio = mean active return ÷ tracking error, annualized with the square-root-of-time rule (standard performance-measurement formulas; e.g. R. C. Grinold and R. N. Kahn, Active Portfolio Management, 2nd ed., McGraw-Hill, 2000)