Tools · Is this ratio any good?
A Sharpe ratio is an estimate, not a grade.
Every page that answers “what is a good Sharpe ratio” gives you a table: 1 to 2 adequate, 2 to 3 very good. None of them asks how long the record is. That is the only question that matters, because a ratio measured over three years carries an error wide enough to swallow the distinctions those tables draw. Enter what you have and see the range of true ratios it is actually consistent with.
Interpreter
This page is showing a worked example. The figures below are for an annualised Sharpe ratio of 1.20 observed over 3 years of monthly returns, at 95% confidence, with no return smoothing assumed. Enable JavaScript to enter your own; the table, chart and method on this page do not need it.
The interval is exact for Sharpe and the information ratio. For the other two it is a floor, not an estimate — see below.
The first-order autocorrelation assumed. Nothing is inferred from an asset-class name, because a table of typical ratios by asset class would be a number nobody has measured.
The honest reading
An annualised Sharpe ratio of 1.20 measured over 3 years of monthly returns is consistent with a true ratio between 0.03 and 2.37 at 95% confidence. The interval excludes zero, so the record is evidence of a positive ratio — but it spans everything up to 2.37, so it does not establish where in that range the truth sits.
- Interval
- 0.03 to 2.37
- true ratios consistent with it, at 95%
- Standard error
- 0.59
- of the ratio itself
- Probability from luck
- 0.022
- one‑sided, if the true ratio were zero
The band is the confidence interval; the horizontal line is the ratio as reported. Over one year it runs −0.82 to 3.22. It first clears zero at about 3.0 years — and even then only just, at 0.03 to 2.37, a range that still contains 0.4. At twenty years it is 0.75 to 1.65. The band narrows with the square root of the record, which is why it never narrows quickly.
Reference
What each reported ratio is consistent with.
Read across from the ratio you were shown to the length of the record behind it. The cell is the range of true annualised ratios that record cannot rule out, at 95% confidence, on monthly observations.
| Observed ratio | 1 year | 2 years | 3 years | 5 years | 10 years | 20 years |
|---|---|---|---|---|---|---|
| 0.25 | −1.71 to 2.21 | −1.14 to 1.64 | −0.88 to 1.38 | −0.63 to 1.13 | −0.37 to 0.87 | −0.19 to 0.69 |
| 0.50 | −1.47 to 2.47 | −0.89 to 1.89 | −0.64 to 1.64 | −0.38 to 1.38 | −0.12 to 1.12 | 0.06 to 0.94 |
| 0.75 | −1.23 to 2.73 | −0.65 to 2.15 | −0.39 to 1.89 | −0.14 to 1.64 | 0.12 to 1.38 | 0.31 to 1.19 |
| 1.00 | −1.00 to 3.00 | −0.41 to 2.41 | −0.15 to 2.15 | 0.11 to 1.89 | 0.37 to 1.63 | 0.55 to 1.45 |
| 1.25 | −0.77 to 3.27 | −0.18 to 2.68 | 0.08 to 2.42 | 0.35 to 2.15 | 0.61 to 1.89 | 0.80 to 1.70 |
| 1.50 | −0.55 to 3.55 | 0.05 to 2.95 | 0.32 to 2.68 | 0.58 to 2.42 | 0.85 to 2.15 | 1.04 to 1.96 |
| 2.00 | −0.12 to 4.12 | 0.50 to 3.50 | 0.78 to 3.22 | 1.05 to 2.95 | 1.33 to 2.67 | 1.53 to 2.47 |
| 2.50 | 0.30 to 4.70 | 0.94 to 4.06 | 1.23 to 3.77 | 1.52 to 3.48 | 1.80 to 3.20 | 2.01 to 2.99 |
Highlighted cells are the combinations whose interval excludes zero — the only ones where the record alone distinguishes the result from no skill at all. Every other cell is consistent with a true ratio of zero.
Method
How the interval is calculated.
A Sharpe ratio is a sample statistic, so it has a sampling distribution, and the width of that distribution is a function of how many observations went into it.
The standard error
SE = √((1 + SR² ÷ 2q) ÷ years)
From Lo (2002). q is the number of observations a year, so monthly data gives q = 12. The error falls with the square root of the record length, which is why four times the record is needed to halve it. A ratio of 1.20 over 3 years of monthly data has a standard error of 0.59.
The interval
interval = SR ± z × SE
Two-sided, with z = 1.6449 at 90%, 1.9600 at 95% and 2.5758 at 99%. The probability shown alongside is one-sided: the chance of observing a ratio at least this strong if the true ratio were zero, computed from a normal approximation accurate to about 1.5 × 10⁻⁷.
The smoothing adjustment
η(q) = q ÷ √(q + 2Σ(q − k)ρᵏ)
Annualising a ratio by √q assumes each period is independent of the last. Where returns are autocorrelated — anything appraisal-priced, or priced monthly against a market that moves daily — that assumption inflates the ratio. Lo’s factor η(q) replaces √q. At ρ = 0.30 on monthly data it reduces a reported 1.20 to 0.91, a change of −24.5%. At ρ = 0 it reduces to √q exactly, so the adjustment does nothing when nothing needs adjusting.
Why there is no grading table here
A grading table asserts that some fixed value is “good” without reference to how much evidence stands behind it, what the holdings are, or what the alternative was. The same reported 1.5 is strong evidence over twenty years of daily-priced listed holdings and almost no evidence over two years of monthly appraisals. A single scale cannot carry both, and publishing one implies a precision the arithmetic does not support.
Reference
What smoothing does to a reported ratio.
The factor each assumption substitutes for √12 or √4, and what it does to a reported ratio of 1.20.
| Return smoothing | Monthly factor | 1.20 becomes | Quarterly factor | 1.20 becomes |
|---|---|---|---|---|
| Daily-liquid listed holdingsassumed first-order autocorrelation 0.00 | 1.000 | 1.20 | 1.000 | 1.20 |
| Some smoothing or monthly pricingassumed first-order autocorrelation 0.15 | 0.871 | 1.05 | 0.895 | 1.07 |
| Illiquid or appraisal-priced holdingsassumed first-order autocorrelation 0.30 | 0.755 | 0.91 | 0.802 | 0.96 |
This is the correction that is almost never applied in practice, and it runs one way: positive autocorrelation always flatters the ratio. Where a manager prices monthly against holdings that trade daily, a reported figure should be read as an upper bound.
Limits
What this does and does not settle.
- The interval is exact only for Sharpe and the information ratio. The information ratio is a Sharpe ratio computed on the active return, so the same arithmetic applies to it unchanged. The other two are different.
- For Sortino, treat the interval as a floor. Its denominator uses only the observations below the threshold, so fewer observations carry it than carry a Sharpe ratio over the same period. No simple closed form is standard, and the true interval is wider than the one shown, never narrower.
- For Calmar, no interval is shown, because none is meaningful. Its denominator is a single worst observed event rather than a distribution. Lengthen the record and the maximum drawdown almost always gets worse, so the ratio falls for a reason that has nothing to do with the manager. It is the least comparable of the four across records of different lengths.
- Independent returns, and normality. The interval assumes returns are independent and identically distributed. The smoothing control relaxes the first assumption to an AR(1) process; nothing here relaxes the second. Fat tails and strong skew both need more evidence than this calculates, not less.
- One ratio, chosen in advance. Selecting the best record from a group and then testing it is a different question with a much higher bar, and this does not answer it.
- A wide interval is not an accusation. It says the record alone cannot settle the question, which is an argument for examining process, risk architecture and the reasoning behind positions — not for treating a short record as either proof or disproof.
This calculator is provided for general information only and is directed to wholesale and professional investors. It is not personal advice: it does not take into account the objectives, financial situation or needs of any person, and it is not an offer, invitation or recommendation to acquire any financial product. Investing involves risk, including the possible loss of capital. Past performance is not a reliable indicator of future performance.
Definitions
Terms on this page.
Each links to the glossary entry, which states the convention the term assumes as well as what it means.
- Sharpe ratio — excess return per unit of volatility, annualised.
- Sortino ratio — the same idea with only downside variation below the line.
- Calmar ratio — annualised return divided by the worst drawdown.
- Information ratio — active return per unit of tracking error.
- Confidence interval — the range of true values the evidence is consistent with.
- Standard error — how much the estimate would vary from sample to sample.
- Autocorrelation — correlation of a series with its own previous values.
Questions
Common questions.
What is a good Sharpe ratio?
There is no threshold that makes a ratio good, because the figure on its own is an estimate with a margin of error, and the margin is usually wider than the differences people are trying to draw. An annualised Sharpe ratio of 1.20 measured over 3 years of monthly returns is consistent with a true ratio anywhere from 0.03 to 2.37. It only just excludes zero, and it comfortably contains 0.4 — so a manager reporting 1.20 over three years and a manager reporting 0.4 cannot be separated by their records. The same 1.20 over twenty years is consistent with 0.75 to 1.65, which is genuine evidence. The length of the record, and how the holdings are priced, decide what the number is worth.
What does a Sharpe ratio of 1.5 mean?
It means the record returned 1.5 times its own annualised volatility above the risk-free rate, over whatever period was measured. Whether that is distinguishable from 0.5 depends entirely on the length of the record: over one year of monthly data it is not, over ten years it is. The reference table above gives the interval for 1.5 at each record length.
Why do other sites publish Sharpe ratio grading tables?
Because a table is easier to write than an interval, and it answers the question the searcher asked in the form they asked it. The tables in circulation do not cite a source, do not agree with each other, and do not mention sample length, which is the variable that dominates the answer. A ratio graded “very good” on a two-year record is frequently indistinguishable from one graded “adequate”.
What is a good maximum drawdown?
The comparison is only meaningful between records of the same length, because a longer record contains more opportunities to have had a bad one. A worst drawdown is a single observed event, not an average, so it carries no useful confidence interval and should be read as a fact about what has happened rather than an estimate of what could. The same applies to the Calmar ratio built on it.
Why does the smoothing setting lower my ratio?
Because annualising by the square root of time assumes each period is independent of the last, and positive autocorrelation breaks that assumption in one direction only. Where holdings are priced monthly or by appraisal, reported returns are smoother than the underlying exposure, volatility is understated and the ratio is overstated. The adjustment removes that effect rather than adding a penalty.
Is anything I enter sent to KyperX Capital?
No. Every figure is calculated in your browser. Nothing is transmitted, recorded or stored, and this website receives none of it.
- Track record significanceHow many years a track record needs before a Sharpe ratio can be separated from luck, and how strong the evidence is at the length you have.
- Risk ratiosPaste a series of monthly returns. Get cumulative and annualised return, volatility, Sharpe, Sortino, Calmar and maximum drawdown.
- GlossaryEvery term these tools use, defined.