Information Ratio and Tracking Error Calculator
Measure active return relative to a benchmark and the consistency of that active return. Use summary statistics or paste matched portfolio and benchmark return series.
Active-performance results
| Measure | Per period | Annualized |
|---|
Information ratio formula
The information ratio divides average active return by tracking error:
Information ratio = average(portfolio return − benchmark return) ÷ tracking error
Tracking error = standard deviation of portfolio return − benchmark return
When periodic data are used, the calculator annualizes active return by multiplying by periods per year and annualizes tracking error by the square root of periods. Therefore:
Annualized information ratio = periodic information ratio × √periods per year
Verified examples
| Inputs | Periodic result | Annualized result |
|---|---|---|
| Monthly averages: portfolio 1.2%, benchmark 0.8%, tracking error 2.5% | Active return 0.4%; ratio 0.160000 | Active return 4.8%; tracking error 8.6603%; ratio 0.554256 |
| Monthly series: portfolio 2, −1, 3, 0.5%; benchmark 1, −0.5, 2, 0%; sample convention | Mean active return 0.5%; tracking error 0.707107%; ratio 0.707107 | Active return 6%; tracking error 2.449490%; ratio 2.449490 |
| Monthly averages: portfolio 0.3%, benchmark 0.7%, tracking error 1.6% | Active return −0.4%; ratio −0.250000 | Active return −4.8%; tracking error 5.5426%; ratio −0.866025 |
How to use return series
- Use total returns for the portfolio and benchmark, including distributions under the same convention.
- Align every observation to the same dates and interval; do not mix daily portfolio returns with monthly benchmark returns.
- Paste matching lists. The calculator subtracts benchmark from portfolio for each period, then calculates the mean and standard deviation of those active returns.
- Choose sample or population standard deviation and disclose that convention when comparing results.
How to interpret the result
A positive information ratio means average portfolio return exceeded the benchmark during the selected observations. A negative ratio means it lagged. A larger positive value indicates more active return per unit of tracking error, but there is no universal “good” cutoff and past performance does not predict future results.
Compare ratios only when portfolios use the same benchmark, return frequency, date range, fee treatment, annualization and tracking-error convention.
Information ratio versus Sharpe and Treynor
Information ratio uses benchmark-relative return and tracking error. Sharpe ratio uses return above a risk-free rate and total volatility. Treynor ratio uses return above a risk-free rate and beta. They answer different questions and should not be substituted without changing the inputs and interpretation.
Limits and assumptions
- Summary returns may range from −100% through 1,000% per period; tracking error must be greater than zero and no more than 1,000%.
- Series mode accepts 2–1,000 matched observations. Each return may range from −100% through 1,000% with up to six decimal places.
- Scientific notation and decimal commas are not supported. Commas separate observations; use a decimal point inside a number.
- Tracking error of zero makes the information ratio undefined and is rejected.
- Annualized average active return is arithmetic, not compounded. Square-root annualization assumes comparable periods and stable, sufficiently independent active returns.
- The tool does not download market data, correct missing dates, account automatically for fees or taxes, or choose an appropriate benchmark.
- Results are educational historical estimates, not investment advice or a forecast.
A low tracking error is not automatically better: it can indicate close benchmark replication, while a high value indicates larger active deviations. Interpret it together with active return and the strategy’s mandate.
Frequently asked questions
Is tracking error a percentage?
Yes. It is the standard deviation of active returns and uses the same return unit and period. The information ratio itself has no unit.
Why do sample and population tracking error differ?
Sample standard deviation divides squared deviations by n−1; population standard deviation divides by n. The sample value is larger for the same finite list unless every active return is identical.
Can the information ratio be negative?
Yes. With positive tracking error, a negative ratio means the portfolio’s average return was below the benchmark.
Related calculators
- Sharpe Ratio Calculator — compare return with total and downside volatility.
- Treynor Ratio Calculator — compare excess return with beta and CAPM.
- Portfolio Variance Calculator — calculate volatility from weights and correlations.
- Portfolio Beta Calculator — calculate weighted market sensitivity.