Audited 27 Jul 2026·Last updated 28 Oct 2026·7 citations·Tier 1·0 uses

Sharpe Ratio Calculator

Find the Sharpe ratio from return, risk-free rate and volatility on an annual, monthly or daily basis, with the excess return and a √N annualised ratio.

Sharpe Ratio Calculator

Portfolio return (%)Portfolio or strategy return for the chosen time basis.

Risk-free rate (%)Risk-free reference rate on the same time basis as the portfolio return (for example a Treasury bill rate).

Portfolio volatility / standard deviation (%)Standard deviation of portfolio returns on the same time basis as the portfolio return.

Time basis

Sharpe ratio

0.4432

Excess return divided by volatility for the time basis you chose; a pure number with no unit.

Annualized Sharpe ratio

0.4432

Excess return

8.20

Excess return (decimal)

0.082

Portfolio return (decimal)

0.124

Risk-free rate (decimal)

0.042

Volatility (decimal)

0.185

Background.

One fund returned 12.4% last year with a volatility of 18.5%. Another returned 8% with a volatility of 6%. With Treasury bills paying 4.2%, which manager did the better job? On raw return the first, comfortably. Per unit of risk the second: it earned 3.8 percentage points over cash for 6 points of volatility, a ratio of about 0.63, while the first earned 8.2 points for 18.5, about 0.44.

That ratio is the Sharpe ratio, introduced by William Sharpe in 1966 under the name reward-to-variability and revisited by him in a 1994 article on how it should be used. Take the portfolio's return, subtract what a risk-free asset paid over the same period, and divide by the standard deviation of the portfolio's returns. The result says how much reward above cash each unit of volatility bought.

The comparison is fairer than it first looks. In principle an investor could borrow at the risk-free rate and hold the second fund at about 3.08 times its size, which brings its volatility up to 18.5%, the same as the first fund's, and lifts its expected excess return to roughly 11.72%, a total near 15.92%. Matched for risk, the lower-returning fund comes out ahead, and that is the sense in which a higher Sharpe ratio means a better trade-off.

Enter the three figures on one time basis, annual, monthly or daily, and you get the ratio for that period together with an annualised version, scaled by the square root of the number of periods in a year. The excess return is shown as well, since a negative one tells you more than any ratio.

The Sharpe ratio is a summary of past or assumed numbers, not a forecast. It treats a sudden gain as just as much "risk" as a sudden loss, and it can look excellent right up to the month a strategy that sells insurance against crashes pays out.

What is sharpe ratio calculator?

The Sharpe ratio measures risk-adjusted return: the average return a portfolio earned above a risk-free benchmark, divided by the standard deviation of its returns. Both numerator and denominator are percentages over the same period, so the units cancel and the result is a pure number. A ratio of 0.5 means the portfolio earned half a percentage point of excess return for every percentage point of volatility it carried. Zero means it did no better than the risk-free asset, and a negative ratio means it did worse. Because return and volatility grow at different rates as the measurement period lengthens, a ratio computed on monthly or daily figures is much smaller than an annual one for the same investment, which is why ratios are normally quoted annualised. Sharpe distinguished an ex ante version, built from expected returns and expected risk, from an ex post version computed from realised history. The arithmetic is identical; only the second can be checked against what actually happened.

How to use this calculator.

Choose the time basis first: annual, monthly or daily. All three numbers you enter must describe the same period length.
Enter the portfolio return for that period as a percentage. Use the average period return (the arithmetic mean of monthly returns, for example) rather than a compound annual growth rate, and include fees if you want a net-of-fee ratio.
Enter the risk-free rate for the same period and currency, typically a short-term Treasury bill rate. An annual 4.2% becomes about 0.35% for a monthly basis.
Enter the volatility, the standard deviation of the portfolio's returns for that period; it must be greater than zero. From a column of monthly returns, a spreadsheet's STDEV.S function gives the sample standard deviation. Many fund factsheets quote a three-year annualised figure, which belongs with annual inputs.
Read the Sharpe ratio for your chosen period and the annualised figure beside it. When comparing funds or strategies, compare annualised ratios computed over the same dates.

The formula.

S = (Rp − Rf) ⁄ σ

S · Sharpe ratio for the chosen periodRp · average portfolio return for the periodRf · risk-free rate for the same periodσ · standard deviation of portfolio returns

S = (Rp − Rf) ÷ σ, where Rp is the portfolio's average return over the period, Rf the risk-free rate for the same period and σ the standard deviation of the portfolio's returns. The percentages you enter are converted to decimals first (12.4% becomes 0.124), which changes nothing in the ratio but explains the decimal outputs. Rp − Rf is the excess return, the reward for taking risk at all; dividing by σ scales that reward by how bumpy the ride was. Volatility of zero is refused because the ratio is undefined: no real portfolio's returns are perfectly constant.

The annualised ratio is S × √N, with N = 1 for annual inputs, 12 for monthly and 252 for daily, the usual count of trading days in a year. The square root comes from how the two parts of the ratio grow with time. If each period's return is independent of the last and drawn from the same distribution, the expected excess return over N periods is N times the one-period figure, but the standard deviation grows only by √N. Their ratio therefore grows by N ÷ √N = √N. A monthly Sharpe ratio is multiplied by about 3.4641, a daily one by about 15.8745.

That scaling is an assumption, and it fails when returns are serially correlated. Funds holding illiquid assets that are valued infrequently report smooth month-to-month returns, which understates σ and inflates both the monthly ratio and its annualised version; Andrew Lo's 2002 paper on the statistics of Sharpe ratios showed how large the distortion can be.

Two input choices move the result more than people expect. The first is the return measure: a compound growth rate sits below the arithmetic average by roughly half the variance, about 1.71 percentage points at 18.5% volatility, which would cut the example's ratio from 0.4432 to about 0.3507. The second is the risk-free rate, which shifts every ratio in a comparison by different amounts depending on each portfolio's volatility.

A worked example.

Example

A portfolio returned an average of 12.4% a year, Treasury bills paid 4.2%, and the standard deviation of the portfolio's annual returns was 18.5%. The time basis is annual. In decimals the inputs are 0.124, 0.042 and 0.185. The excess return is 0.124 − 0.042 = 0.082, or 8.2%. Dividing by volatility gives 0.082 ÷ 0.185 = 0.4432. Because the inputs are already annual, N = 1 and the annualised Sharpe ratio is the same 0.4432. The same portfolio described monthly gives the same answer, which is a useful check on the annualisation. Monthly average return is 12.4 ÷ 12 = 1.0333%, the monthly risk-free rate 0.35%, and monthly volatility 18.5 ÷ √12 = 5.3405%. The monthly ratio is (1.0333 − 0.35) ÷ 5.3405 = 0.12795, and 0.12795 × √12 = 0.4432 again. Another way to read 0.4432: it is the excess return measured in standard deviations. If annual returns were normally distributed, the portfolio would trail Treasury bills in about one year in three (the probability of a value more than 0.4432 standard deviations below the mean is about 33%). A ratio of 0.4432 rewards patience; it does not promise a good year.

portfolio Return Percent12.4

volatility Percent18.5

risk Free Rate Percent4.2

time Basisannual

Frequently asked questions.

What Sharpe ratio counts as good?

There is no official threshold. Rules of thumb that call 1 good and 2 excellent circulate widely, but they come from no standard and ignore the asset class, the period and the data. The meaningful comparison is with alternatives measured the same way: other funds in the same category over the same dates, or a low-cost index fund. In the opening example, 0.63 beats 0.44, and that comparison says more than either number alone.

Should I enter the compound annual growth rate or the average annual return?

Sharpe's definition uses the average excess return, so the arithmetic mean of period returns is the consistent choice. A compound growth rate is lower by roughly half the variance of returns. At 18.5% volatility that gap is about 1.71 percentage points, and entering a CAGR of about 10.69% instead of 12.4% would show a ratio near 0.3507 rather than 0.4432 for the same portfolio.

Which risk-free rate should I use, and how do I convert it to monthly or daily?

Use a short-term government bill in the portfolio's currency, matched to the period you are measuring; for US dollar portfolios the 3-month Treasury bill is the usual choice. Divide an annual rate by 12 for a monthly basis or by 252 for daily: 4.2% a year is 0.35% a month. Compounding gives 0.3434% instead, a difference too small to matter for most comparisons.

Why is the annualised figure the monthly ratio times the square root of 12?

Over twelve independent months, expected excess return adds up twelve times, while volatility grows only by the square root of twelve, about 3.4641, because random ups and downs partly cancel. The ratio therefore grows by √12. That holds only if one month's return tells you nothing about the next; smoothed or trending returns break it, usually in the direction of flattering the result.

Why does a Sharpe ratio from daily data look so small?

Because a day is a short period. A strategy averaging 0.05% a day above cash with a daily standard deviation of 1% has a daily ratio of just 0.05. Multiplied by √252, about 15.8745, it becomes an annualised 0.7937. Always compare annualised ratios, and treat an annualised figure from only a few months of daily data with suspicion, since short samples produce noisy estimates.

How should I compare two negative Sharpe ratios?

Carefully, because the ratio misbehaves below zero. With an excess return of −2%, a fund with 10% volatility scores −0.2 while a fund with 20% volatility scores −0.1, so the riskier loser looks better. When excess returns are negative, compare the excess returns and the drawdowns directly; the ratio stops being a fair ranking.

Does borrowing to leverage a portfolio change its Sharpe ratio?

In theory, no. Doubling a position with money borrowed at the risk-free rate doubles both the excess return and the volatility, so the ratio is unchanged: 16.4% over 37% is still 0.4432. In practice borrowing costs more than the Treasury bill rate, which pulls the leveraged ratio down, and margin calls can force sales at the worst moment, a risk standard deviation does not capture.

Why can a very high Sharpe ratio be a warning sign?

Some strategies earn small, steady gains most of the time and lose heavily on rare occasions, selling options against market crashes being the classic case. Until the loss arrives, their volatility looks low and the ratio looks superb. Illiquid holdings priced by appraisal produce the same effect through smoothed returns. Check the maximum drawdown and the length of the record before trusting a ratio well above that of comparable funds.

How does the Sharpe ratio differ from the Sortino, Treynor and information ratios?

All four divide a return by a risk measure. Sortino uses only downside deviation, so upside volatility is not penalised. Treynor divides excess return by beta, the market risk that cannot be diversified away, which suits a fund held inside a larger portfolio. The information ratio divides return above a benchmark index by tracking error, judging an active manager against the index rather than against cash.

Do fees and taxes affect the Sharpe ratio?

Only through the return you enter. A fund's gross return before management fees produces a higher ratio than its net return, and an investor in a taxable account experiences something different again. Fees lower the excess return without lowering volatility, so a 1% annual fee on the example portfolio would cut its ratio from 0.4432 to about 0.3892. Compare gross with gross and net with net.

References& sources.

How this page was produced

Published by: Quanta Calculator
Overseen by: Daniel, Quanta Calculator Researcher
Primary sources: 7 cited below
Method: S = (Rp − Rf) ⁄ σ
Published: 8 June 2026
Last verified: 27 July 2026

Built with AI assistance and verified by automated tests against the cited sources — every worked example on this page is computed by the same code that runs the calculator. How we build and check calculators.

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