Sharpe and Sortino ratio calculator
A Sharpe ratio is an estimate with error bars, and the bars are usually wider than the differences people argue about. Paste your own return series for both annualisations, both Sortino denominators, and the 95% interval most calculators never show.
Worked example — Annualised Sharpe, 3-year illustrative series: 1.00. 95% interval -0.15 to 2.16, which contains zero on 36 months at a 4% risk-free rate
Paste a return series
One period per line. The confidence interval, both annualisations, and both Sortino denominators update as you type.
3-year illustrative series: The page default: 36 months of the illustrative series, where a Sharpe near 1.0 has a 95% interval that still contains zero.
36 values read. The series on load is an illustrative one, not a real fund, index, or strategy. Replace it with your own.
Advanced options 2
The 95% interval contains zero. On 36 months of data this Sharpe has not been separated from no skill at all.
The probability below is 95.1% and the interval above still contains zero. Both are right. The interval asks the two-sided question, is this Sharpe different from zero in either direction, and the probability asks the one-sided one, is it above zero. A borderline record passes the second and fails the first, and which one you should care about depends on whether you had a view before you saw the data.
The whisker is the 95% interval and the dot is the point estimate. The dashed line at zero is "no skill": while the whisker crosses it, the data cannot rule out that this Sharpe is actually zero or negative.
What is a good Sharpe ratio?
The common thresholds are a Sharpe under 0.5 is poor, around 1.0 is good, and above 2.0 is very good. Those labels describe the point estimate and say nothing about the sample behind it. On this page's own 3-year illustrative series the Sharpe comes out to 1.00, comfortably "good" by that convention. Its 95% confidence interval runs from -0.15 to 2.16, which comfortably contains zero. A number that could just as easily be a loss as a 1.0 is not "good", it is unresolved. The thresholds only mean something once the interval around them is narrow enough to matter.
How many months of data do I need to trust a Sharpe ratio?
Enough that the minimum track record length clears your actual sample size. On this page's 3-year default, a Sharpe near 1.0 needs about 3.0 years of data to be called positive at 95% confidence, which is almost exactly the 3 years shown. A higher Sharpe needs less time to prove itself and a lower one needs more, because the formula divides a roughly fixed quantity by the Sharpe squared. Load the 10-year preset above the calculator to see the identical point estimate with the interval visibly narrower.
Naive vs autocorrelation-adjusted annualisation, by frequency
Multiplying by the square root of the number of periods in a year is correct only when returns are independent from one period to the next. The table below reinterprets this page's own illustrative series at each frequency and prints both the familiar √f factor and the Lo (2002) autocorrelation-adjusted one, computed by the same function the calculator runs.
| Frequency | √f factor | Lo-adjusted factor | Gap |
|---|---|---|---|
| Daily | 15.8745 | 14.0705 | -11.4% |
| Weekly | 7.2111 | 6.3813 | -11.5% |
| Monthly | 3.4641 | 3.0448 | -12.1% |
| Quarterly | 2.0000 | 1.7280 | -13.6% |
The gap widens as the frequency coarsens, because a coarser period aggregates more of the return series' own positive autocorrelation into each observation. Positive autocorrelation smooths a series and makes any ratio built on its standard deviation look better than the strategy is; that is exactly what the Lo correction is for.
The two annualisations, and the two Sortino denominators
Two annualisations are printed side by side in the calculator above: the square root of the number of periods per year, which assumes independent returns, and the Lo (2002) correction, which adjusts for the sample's own autocorrelation. Two Sortino denominators are printed side by side too: dividing the sum of squared shortfalls by every period in the sample (Sortino and Price), or by only the losing ones. The second is always the larger deviation and the smaller ratio, by exactly the square root of the ratio of losing periods to all periods. A Sortino quoted anywhere else is not comparable to yours until you know which denominator produced it, and almost no source says.
What JMM thinks: under five years, the number is decoration
Run three years of monthly data through the standard error formula and a Sharpe of 1.0 comes with a 95% interval that comfortably contains zero. That is the default on this page, and it is not an unusual case chosen to make a point: it is what a three-year track record is worth. A fund reporting 1.2 and a fund reporting 0.8 over the same short window have not been distinguished from each other, or from luck. If you are choosing between managers, strategy variants, or your own backtests on a Sharpe difference of less than about half a point, you are reading noise and should decide on something else: cost, capacity, drawdown behaviour, or whether the thing makes sense. The interval assumes returns are independent and roughly normal, which makes it if anything too narrow for a fat-tailed series, and nothing here corrects for the strategies you tried and discarded before pasting this one. To see the shape of the losses rather than their typical size, use the drawdown calculator.
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Max drawdown calculatorCalculatorStandard deviation treats a gain and a loss alike. This measures the loss that actually happened, and how long it lasted.Open nextOther questions
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