Information Ratio Calculator

Measure active return against tracking error to see whether outperformance was consistent or occasional.

The information ratio asks whether a portfolio beat its benchmark reliably rather than merely by how much. Its numerator is the average active return — the portfolio less the benchmark, period by period — and its denominator is the tracking error, which is how much that margin varied around its own average; this information ratio calculator reports both halves alongside the ratio they produce.

Formula: information ratio = active return / tracking error

Your figures

Returns by period

One row per period, oldest first, with both returns as a percentage of the value at the start of that period. Enter losses as negative figures. Every row must be the same length of period, and the count below has to match it.

Portfolio return 1

Benchmark return 1

Portfolio return 2

Benchmark return 2

Portfolio return 3

Benchmark return 3

Portfolio return 4

Benchmark return 4

Portfolio return 5

Benchmark return 5

Portfolio return 6

Benchmark return 6

Periods in a year

The cadence of the returns above. It is used only to annualise the ratio.

Custom periods in a year

Only used when the frequency is set to Custom.

Results

Annualised information ratio

1.46

0.423 per period, multiplied by the square root of 12

Information ratio per periodMean active return divided by the tracking error, both measured over a single period. The figure above is this one annualised, and the two must never be quoted side by side without saying which is which.: 0.423
Mean active return per periodThe arithmetic mean of portfolio less benchmark, period by period. This is the numerator.: +0.200%
Tracking error per periodThe sample standard deviation of those active returns, n − 1. This is the denominator, and it is what turns a margin into a measure of consistency.: 0.473%
Annualised active returnThe mean multiplied by 12, because a mean grows with time.: +2.400%
Annualised tracking errorThe tracking error multiplied by the square root of 12, because dispersion grows with the square root of time. The ratio inherits that square root and nothing else.: 1.640%
Periods ahead of the benchmarkHow often the portfolio finished the period in front. A high count with a low ratio means the wins were small and the losses were not.: 4 of 6
Periods countedBlank rows are not counted. Everything above is estimated from this many paired observations, and a short record moves a long way on one more of them.: 6
Periods in a yearUsed for nothing but the annualisation above.: 12
Period 1 — +2.400% against +1.900%: +0.500%
Period 2 — -1.900% against -1.500%: -0.400%
Period 3 — +3.500% against +2.600%: +0.900%
Period 4 — +0.900% against +1.100%: -0.200%
Period 5 — -2.100% against -2.400%: +0.300%
Period 6 — +1.300% against +1.200%: +0.100%

What this means

Across the 6 periods entered the portfolio finished ahead of its benchmark in 4 of them, and the active returns — one column less the other, period by period — averaged +0.200%. The sample standard deviation of those same active returns is the tracking error of 0.473%, and dividing one by the other gives 0.423 per period, or 1.46 once multiplied by the square root of 12. Where alpha asks whether a portfolio beat its benchmark, this asks whether it did so reliably: two records can add the same margin over a year, one by adding a little in most periods and the other by trailing throughout and being rescued by a single one, and the denominator here is the only thing that separates them.

Annualising multiplies the mean by the periods in a year and the tracking error by the square root of it, so the ratio moves by that square root — the same monthly record reads about 3.46 times better annualised than it does per period. The two figures are both above, labelled, for exactly that reason.
That scaling assumes each period is independent of the one before. A persistent tilt produces active returns that move together, whose true annual tracking error is larger than the square root rule suggests, so the annualised figure flatters a record that drifts and is trustworthy on one that does not.
Tracking error here is the sample standard deviation of the active returns. Some factsheets publish a mean absolute deviation under the same name, and the two do not agree.
The numerator is the plain arithmetic mean of the active returns rather than a compounded figure, because the denominator measures the dispersion of exactly those numbers. Mixing a geometric numerator with an arithmetic denominator would put two different quantities either side of the divide.
A record that beat its benchmark by the same margin in every period has a tracking error of zero and no ratio at all, however good the margin. That is refused rather than reported, because an index fund with a fixed fee is not a portfolio of infinite skill.
Every dispersion figure here — the variance, the covariance, the standard deviations and the tracking error — divides by n − 1 rather than by n, because the mean subtracted from each observation was itself estimated from the same handful of returns. Across twelve observations that lifts a variance or a covariance by 12 ÷ 11, about 9.1%, and a standard deviation or a tracking error by the square root of that, about 4.4% — enough either way to move the second decimal place. It is also the convention published performance statistics are quoted on.
Both columns must describe the same periods in the same order. A period filled in on one side and left blank on the other is refused rather than dropped, because shortening one column would pair every later return with the wrong period's benchmark — an error that changes the answer without changing anything visible.
Nothing here is fetched. The returns, the benchmark, the rate and the beta are all as entered, so the same arithmetic works on a backtest, a factsheet and a live account. The risk-free rate a field opens with is a round illustration, not a current market rate.
This describes a record that has already happened. It summarises the figures entered and says nothing about the ones that follow them, and no particular level of it carries a meaning beyond the arithmetic that produced it.

The link reopens this calculator with the same numbers. Nothing you enter is sent to a server.

Continue with these figures

About the Information Ratio calculation

The distinction is the reason to compute it. Two records can add the same two points over a year: one by adding a sixth of a point in most months, the other by trailing all year and being rescued by a single quarter. Measured only by how far they finished ahead, the two records are indistinguishable. The first has a small tracking error and a high ratio, the second a large tracking error and a low one, and this is the only statistic in the group that separates them.

The calculator takes a paired table of returns — portfolio and benchmark for each period, oldest first, at least three periods — plus how many of those periods make a year. It reports the ratio per period and annualised, along with the mean active return, the tracking error, how many periods finished ahead, and every period's active return so the working is visible rather than assumed. Because those components are shown in full, the page can be used as a tracking error calculator or an active return calculator on its own.

Information Ratio formula

activeᵢ        = portfolioᵢ − benchmarkᵢ

mean active    = Σ activeᵢ ÷ n
tracking error = √( Σ (activeᵢ − mean active)² ÷ (n − 1) )

IR             = mean active ÷ tracking error

annualised active return  = mean active × k
annualised tracking error = tracking error × √k
annualised IR             = IR × √k

activeᵢ: The active return in period i: what the portfolio returned less what the benchmark returned over the same period.
mean active: The plain arithmetic mean of those active returns, in percentage points per period.
tracking error: The sample standard deviation of the active returns, n − 1. It is how much the margin moved about, not how large the margin was.
k: How many of your periods make a year — 12 for monthly, 52 for weekly, 4 for quarterly, or your own trading-day count for daily returns.
IR: Mean active return per unit of tracking error. Unitless, because both halves are in percentage points per period.

The denominator of the information ratio formula measures the dispersion of the active returns themselves, not of the portfolio's own returns. That is what makes this a measure of benchmark-relative return rather than a variant of the Sharpe ratio: a fund that swung violently but swung exactly with its index has a large standard deviation and a tiny tracking error, and this ratio would call it consistent because relative to the thing it is measured against, it was.

The numerator is a plain arithmetic mean rather than a compounded figure, and that is deliberate. The denominator measures the spread of exactly those per-period active returns, so putting a geometric numerator over it would place two different quantities either side of the divide. The annualised active return reported alongside is the mean multiplied by the periods in a year, which is also not a compound figure and will not match a chain-linked calculation over the same record.

Annualising scales the mean by k and the dispersion by √k, because a mean grows with time while a standard deviation grows with the square root of it, so the ratio itself moves by √k alone. The same twelve monthly returns therefore read about 3.46 times better annualised than per period, which is why the two figures must never be quoted side by side without saying which is which. The assumption underneath is that each period is an independent draw, and it fails in the flattering direction: a persistent tilt produces active returns that move together, whose true annual tracking error is larger than the square root rule allows, so the annualised figure overstates a record that drifts and can be trusted on one that does not.

A tracking error of zero has no ratio at all, however good the margin, and is refused rather than reported. A portfolio that beat its benchmark by exactly the same amount in every period — which an index fund charging a fixed annual fee very nearly does — has perfect consistency and no dispersion to divide by. Reporting that as an infinite information ratio would turn a tracking fund into a record of unbounded skill.

Information Ratio: a worked example

Six monthly returns for a portfolio and its benchmark: +2.4% against +1.9%, −1.9% against −1.5%, +3.5% against +2.6%, +0.9% against +1.1%, −2.1% against −2.4% and +1.3% against +1.2%.

Active returns+0.5, −0.4, +0.9, −0.2, +0.3, +0.1 percentage points
Mean active return1.2 ÷ 6 = +0.20% per month
Squared deviations from that mean0.3² + 0.6² + 0.7² + 0.4² + 0.1² + 0.1² = 1.12
Tracking error√(1.12 ÷ 5) = √0.224 = 0.473% per month
Information ratio per period0.20 ÷ 0.473 = 0.423
Annualised information ratio0.423 × √12 = 1.46
Annualised active return and tracking error0.20 × 12 = 2.40%, and 0.473 × √12 = 1.64%

An annualised information ratio of 1.46, from a portfolio that finished ahead in four of the six months and added 0.20 points a month on average. The figure looks strong and rests on six observations: multiplying the per-period ratio by the square root of the number of periods gives a t-statistic of about 1.04, which is a long way from distinguishing this record from an evenly matched coin.

How to use the Information Ratio calculator

Enter one row per period, oldest first, with the portfolio return and the benchmark return for that same period. Both columns must use the same period length and the same return basis.
Set the periods-in-a-year box to match the rows above it. It touches nothing but the annualisation, and entering the wrong count scales the headline figure by the square root of the ratio between the two counts — quarterly data annualised as monthly reads 73% too high.
Use the per-period ratio when comparing against anything quoted per period, and the annualised one against annualised figures. Mixing them overstates or understates by a factor of √k, which for monthly data is nearly three and a half.
Read the per-period active returns listed underneath the summary. In a short record one unusual period frequently drives both the mean and the tracking error, and that is visible in the column and invisible in the ratio.
Compare the periods-ahead count with the ratio. A high count beside a low ratio means the wins were small and the losses were not, which is a different record from one that won half the time by a consistent margin.

Limitations of the Information Ratio calculator

Every calculation makes assumptions. These are the ones that matter here.

The sampling error is larger than most readers expect. The standard error of an annualised information ratio is roughly one over the square root of the number of years, so telling a genuine ratio of 0.5 from zero at conventional confidence takes something like fifteen years of data.
The statistic is only as meaningful as the benchmark. Measured against a series the portfolio was never trying to track, the active returns are mostly the difference between two unrelated things, and both the numerator and the tracking error inflate together.
Annualising assumes each period is independent of the one before. Persistent tilts, momentum in the active return and slow-moving positioning all break that assumption in the direction that flatters the record.
Tracking error is defined here as the sample standard deviation of the active returns. Some factsheets publish a mean absolute deviation under the same name and others divide by n rather than n − 1, so a figure computed elsewhere will not always match.
Whether the portfolio column is gross or net of fees changes everything and the calculator cannot tell which you entered. A fee charged evenly shifts the mean active return down without touching the tracking error, moving the ratio directly.
In a short record a single unusual period drives both halves of the ratio, and it moves them in opposite directions — one large win raises the mean and raises the dispersion, so the effect on the ratio is not intuitive and can go either way.
A record with a constant active return has a tracking error of zero and no ratio at all, so it is refused. That is not a defect but the arithmetic declining to divide by nothing.

Frequently asked questions about Information Ratio

What is a good information ratio?

This page reports the figure rather than grading it, and any level quoted from a short record should be read against its own sampling error first. What can be said plainly is that the ratio is a description of a completed record: it summarises how large the average margin was relative to how much it varied, and says nothing about whether either will continue.

What exactly is tracking error?

The standard deviation of the active returns — how much the margin over the benchmark moved around its own average, period by period. It is not the size of the margin and not the portfolio's own volatility. A fund that trailed its index by close to 0.1% in every single month has a persistently negative mean active return and a tracking error near zero, because the shortfall itself barely varied.

Why is the annualised ratio so much larger than the per-period one?

Because the mean scales with the number of periods in a year while the dispersion scales with the square root of it, so the ratio picks up that square root and nothing else. For monthly data the multiplier is √12, about 3.46. Both figures appear on the results panel, labelled, precisely so that they are not confused for one another.

How many periods do I need before the ratio means anything?

More than most records contain. Multiplying the per-period ratio by the square root of the number of observations gives a t-statistic, and reaching a conventional threshold of about 2 with a modest ratio takes many years of monthly data. Three periods is the arithmetic minimum the calculator will accept, not a sample size that supports a conclusion.

How does this differ from the Sharpe ratio?

The Sharpe ratio measures return above the risk-free rate against the portfolio's own total volatility, so it evaluates an account in isolation. The information ratio measures return above a benchmark against the volatility of that margin, so it evaluates a portfolio relative to the thing it was meant to track. A fund can score well on one and poorly on the other without any contradiction.

Can the information ratio be negative?

Yes, whenever the mean active return is negative — the portfolio trailed its benchmark on average across the periods entered. The tracking error is a standard deviation and is never negative, so the sign of the ratio is entirely the sign of the numerator, and a large negative ratio means the shortfall was consistent rather than merely large.

Does the benchmark have to be an index?

No. The second column is whatever series you are measuring against, and the arithmetic treats a fund, a sector, a competitor or your own previous strategy identically. What matters is that the comparison is one you would defend, since the ratio measures the relationship to that series and to nothing else.

Last reviewed 29 August 2026. See our methodology and editorial policy.

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