The information ratio calculator above takes a portfolio return series and a matching benchmark return series, subtracts one from the other period by period to give the active return, and divides the mean of that active return by its standard deviation. The result is the information ratio: active return per unit of tracking error. It is the standard measure of whether a manager's deviations from a benchmark have been worth the deviation.
Arb Digital builds free tools that state plainly what a number is and what it is not. Every return on this page is one you type in. The page publishes no market data, names no fund, index or manager, and recommends nothing. It computes a published statistic from your own series and tells you where that statistic stops being informative.
What This Information Ratio Calculator Does
Active return is the portfolio's return minus the benchmark's return in the same period. A manager who holds exactly the benchmark has an active return of zero every period. A manager who deviates — by overweighting sectors, holding cash, or picking securities the index does not hold in the same proportions — produces a series of non-zero active returns, some positive and some negative.
The information ratio asks two things about that series at once. Was the average positive, and how noisy was it? A manager who beat the benchmark by 0.3 per cent a month with almost no variation has produced something quite different from one who averaged the same 0.3 per cent while swinging between plus four and minus four. The first is a repeatable process; the second is indistinguishable from luck over any realistic sample.
The calculator reports the ratio per period and annualised, along with the two components separately, because the components are what you actually diagnose from. It also reports the portfolio's own volatility and the benchmark's volatility next to the tracking error, which shows at a glance how much of the portfolio's movement is shared with the benchmark and how much is genuinely its own.
How to Use It
- Enter matched pairs. Each portfolio figure needs the benchmark's return for the same period in the same position. The calculator uses only as many periods as both series have.
- Use one periodicity. Monthly against monthly, quarterly against quarterly. Mixing intervals corrupts both the mean and the standard deviation.
- Set the periods per year for the annualisation. Twelve for monthly, four for quarterly, roughly 252 for daily.
- Choose the tracking error definition deliberately. The standard deviation about the mean is the usual academic form; the root mean square about zero is common in index-tracking mandates because it charges a persistent shortfall as well as its variability.
- Read the number of paired periods. An information ratio computed over eight observations is a description of eight observations, not evidence of skill.
The Formula: How the Information Ratio Is Calculated
For each period, active return at = Rp,t − Rb,t. The mean active return is ā = Σat ÷ n. Tracking error is the standard deviation of that active series, TE = √(Σ(at − ā)² ÷ (n − 1)) on the sample divisor. The information ratio is IR = ā ÷ TE. Annualising multiplies the mean by the number of periods per year and the tracking error by the square root of that number, so the ratio itself is multiplied by the square root.
Work the defaults. The twelve monthly active returns are 0.4, 0.4, 0.7, −0.4, 0.5, 0.7, 0.3, −0.4, 0.7, −0.5, 0.3 and 0.7. They sum to 3.4, so the mean active return is 3.4 ÷ 12 = 0.283333 per cent a month. The squared deviations from that mean sum to 2.316667, so the sample variance is 2.316667 ÷ 11 = 0.210606 and the tracking error is √0.210606 = 0.4589 per cent a month.
The monthly information ratio is 0.283333 ÷ 0.458918 = 0.6174. Annualised, the mean active return becomes 3.4 per cent, the tracking error becomes 0.458918 × √12 = 1.5897 per cent, and the ratio becomes 3.4 ÷ 1.5897 = 2.1387 — which is also 0.6174 × √12, as it must be.
That square-root scaling is worth pausing on. The annualised ratio is always larger than the per-period one, by a factor that depends on how often you measure. The same portfolio measured monthly and quarterly produces different annualised information ratios, so a figure quoted without its periodicity is not comparable to anything.
The Boundary With the Sharpe Ratio
This is the distinction that matters most, and it is a single substitution in the numerator. The Sharpe ratio calculator subtracts the risk-free rate from the portfolio's return and divides by the portfolio's total standard deviation. The information ratio subtracts the benchmark's return and divides by the standard deviation of that difference. Sharpe asks whether holding a risky portfolio beat holding nothing risky. The information ratio asks whether holding this portfolio beat holding the index it is measured against.
The consequences run deeper than the definition suggests. A portfolio can have an excellent Sharpe ratio and a terrible information ratio, which happens whenever the benchmark itself performed well and the manager's deviations from it did not. It can equally have a poor Sharpe ratio and a strong information ratio: in a year when the whole asset class fell, a manager who lost less than the index has a negative Sharpe ratio and a positive information ratio, and both are correct descriptions of different things.
The denominators differ too, and by more than most summaries admit. Tracking error is the volatility of the difference, so it strips out everything the portfolio and benchmark share. An index fund can have 15 per cent annual volatility and a tracking error of 0.2 per cent. Total volatility and tracking error are not comparable magnitudes, and dividing by one rather than the other produces numbers on entirely different scales — which is why an information ratio above one is considered strong while a Sharpe ratio above one is considered strong for quite different reasons.
Four Measures, Four Denominators
Together with three tools in the same family, this page completes a set in which each measure owns exactly one job:
- Sharpe divides excess return over the risk-free rate by total volatility. Total risk, absolute benchmark. The Sharpe ratio calculator covers it.
- Sortino divides the same numerator by downside deviation only. Asymmetric risk against a minimum acceptable return, which the Sortino ratio calculator computes from a series.
- Treynor divides the same numerator by beta. Systematic risk only, on the assumption that idiosyncratic risk has been diversified away — the Treynor ratio calculator.
- Jensen's alpha subtracts the CAPM-required return rather than dividing at all. It is a return in percentage points, not a ratio, and the Jensen's alpha calculator produces it.
- The information ratio divides active return over a benchmark by tracking error. Relative risk against a stated index.
The practical rule follows from what each denominator ignores. If the portfolio is someone's whole holding, Sharpe is the honest test, because total risk is what they bear. If it is one sleeve of a diversified whole, Treynor or Jensen's alpha fit better. If it is managed against a stated index with a mandate to beat it, the information ratio is the only one of the four that asks the question the mandate actually poses.
Tracking Error Is Not a Risk Budget
Tracking error is frequently used as a constraint — a mandate might cap it at three per cent a year. That use is reasonable, but it invites a misreading. A low tracking error does not mean a low-risk portfolio; it means a portfolio that closely resembles its benchmark. If the benchmark is concentrated in a handful of names, a fund tracking it tightly inherits that concentration and reports a small tracking error while carrying substantial absolute risk. The FINRA guidance on asset allocation and diversification makes the point about concentration from the investor's side.
The reverse misreading is just as common. A high tracking error is not evidence of skill or of recklessness on its own; it is only evidence of difference. Whether that difference was worth having is precisely what dividing by it answers, and the answer requires the numerator too. The standard deviation calculator and the variance calculator handle the underlying dispersion arithmetic if you want to compute either quantity separately.
What Breaks the Information Ratio
Three things reliably break it. The first is a wrong benchmark. If the index does not represent the portfolio's investable universe, the active return is measuring a style difference rather than a decision, and the ratio flatters or punishes the manager for something they never chose. This is the most common defect in practice and no amount of statistical care corrects it.
The second is a short sample. Tracking error is estimated from the same small set of observations as the mean, and both estimates are noisy. Over twelve months, an information ratio well above one is entirely achievable by chance. The standard error of an information ratio is roughly one over the square root of the number of years, so distinguishing a genuine ratio of 0.5 from zero takes many years of data. The MIT OpenCourseWare lectures on portfolio theory develop the underlying mean and variance arithmetic these estimates rest on.
The third is a negative mean active return. When the numerator is negative, dividing by tracking error inverts the ranking: of two underperforming managers, the one with the larger tracking error shows the less negative ratio, which reads as better and is not. The same defect afflicts the Sharpe and Treynor ratios and is well documented in performance-measurement practice. When active return is negative, compare the raw shortfalls instead. The CFA Institute's professional learning resources cover performance measurement for practitioners in far more depth.
Arb Digital builds free tools like this one because useful pages earn attention. If you want tools, calculators or content built for your own audience, we can help.
Browse All Free Tools Talk to Arb DigitalCommon Mistakes to Avoid
- Comparing an information ratio with a Sharpe ratio — they use different numerators and denominators on different scales, and the comparison is meaningless.
- Quoting a ratio without its periodicity — annualisation multiplies by the square root of the periods per year, so monthly and quarterly measurement give different annual figures for the same portfolio.
- Using a benchmark the portfolio was never managed against — the active return then measures a style mismatch rather than any decision the manager made.
- Reading a high ratio over a short window as skill — both the mean and the tracking error are noisy estimates, and short samples produce impressive ratios by chance.
- Ranking underperformers by the ratio — with a negative numerator, more tracking error makes the ratio look better, which reverses the ordering you want.
Related Free Tools From Arb Digital
The neighbouring risk-adjusted measures each answer a different question: the Sharpe ratio calculator uses the risk-free rate and total volatility, the Sortino ratio calculator uses downside deviation, the Treynor ratio calculator uses beta, and the Jensen's alpha calculator subtracts a CAPM-required return instead of dividing.
For the inputs themselves, the standard deviation calculator and variance calculator handle dispersion, the annualized return calculator converts a period result to an annual basis, and the stock return calculator builds a return figure from prices and income. Everything else is on the free tools hub.
Frequently Asked Questions
It is the mean active return of a portfolio against its benchmark, divided by the standard deviation of that active return, which is called tracking error. It measures how much excess return a manager produced for each unit of deviation from the index they were measured against.
The Sharpe ratio subtracts the risk-free rate and divides by the portfolio's total volatility. The information ratio subtracts the benchmark's return and divides by the volatility of that difference. Sharpe asks whether taking risk paid; the information ratio asks whether deviating from the index paid.
It is the standard deviation of the difference between the portfolio's returns and the benchmark's returns. It measures how much the portfolio moves independently of its index, and it strips out everything the two share, so it is usually far smaller than the portfolio's own volatility.
Because the mean active return scales with the number of periods per year while the tracking error scales with the square root of that number. The ratio therefore scales with the square root too, which is why a quoted figure is meaningless without stating the measurement frequency.
This page does not offer thresholds, because a ratio is only interpretable against the benchmark, mandate and sample length that produced it. What is worth checking is the number of periods behind it: short samples produce impressive ratios by chance, and the estimate becomes reliable only over many years.
The ratio is undefined, because you would be dividing by zero. Zero tracking error means the portfolio matched the benchmark in every period, so there were no active decisions to evaluate. The calculator says so in words rather than printing a number.
No. Every return in both series is a figure you type in. The page publishes no market data, names no fund, index or manager, and takes no view on whether any portfolio or strategy is worth holding.
This tool is provided for educational and estimating use only. It is not investment advice and does not recommend any fund, manager, index or strategy. Past performance does not indicate future results, and anyone making an investment decision should take advice from a qualified financial adviser.
