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Sharpe Ratio Calculator

Measure return per unit of risk: the Sharpe ratio from an average return and standard deviation or from a list of period returns, annualised, with the Sortino ratio for downside risk.

Calculate from

Annualised with √12.

% a year

Treasury bill yield; 0 is common for trading.

% / month

Mean return per month.

% / month

Of the monthly returns.

Annualised Sharpe

1.01

0.292 per month × √12

Sharpe per month

0.292

before annualising

Excess return

1.167%

per month, after 0.333% risk-free

Annualised return

18.00%

1.50% × 12, simple

Annualised volatility

13.86%

4.00% × √12

Over a year the average return is multiplied by 12 but the standard deviation only by √12, so the ratio scales by √12. This assumes each month's return is independent of the last. Compare Sharpe ratios only when both are annualised the same way.

Show the math
  1. Risk-free rate per period = annual rate ÷ periods per year4.0000% ÷ 12 = 0.3333%
  2. Sharpe per period = (average return − risk-free) ÷ standard deviation(1.5000% − 0.3333%) ÷ 4.0000% = 0.2917
  3. Annualised Sharpe = Sharpe per period × √(periods per year)0.2917 × √12 (3.4641) = 1.0104
  4. Annualised return (simple) = average × periods1.5000% × 12 = 18.0000%
  5. Annualised volatility = standard deviation × √(periods)4.0000% × 3.4641 = 13.8564%
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Quick answer

Sharpe ratio = (average return − risk-free rate) ÷ standard deviation, annualised by multiplying by √(periods per year). A strategy averaging 1.5% a month with a 4% standard deviation and a 4% annual risk-free rate has a monthly Sharpe of (1.5 − 0.333) ÷ 4 = 0.292, or 0.292 × √12 = 1.01 annualised.

What is the Sharpe Ratio Calculator?

The Sharpe ratio measures how much return a strategy or portfolio earns above the risk-free rate for each unit of volatility it takes. Two accounts that both made 18% a year are not equally good if one got there with twice the swings; the Sharpe ratio tells them apart.

Sharpe (per period) = (Average return − Risk-free rate per period) ÷ Standard deviation
Annualised Sharpe = Sharpe per period × √(Periods per year)

A strategy averaging 1.5% a month with a 4% monthly standard deviation, against a 4% annual risk-free rate (4 ÷ 12 = 0.333% a month), has a monthly Sharpe of (1.5 − 0.333) ÷ 4 = 0.292. Annualised: 0.292 × √12 = 1.01.

Why annualise with the square root

Over a year, average returns add up: twelve months of 1.5% is 18% (simple, without compounding). Volatility does not add up the same way. If each month is independent of the last, the variance adds up, so the standard deviation grows with the square root of the number of periods: 4% × √12 = 13.86% a year. The annual Sharpe is therefore 12 × excess ÷ (√12 × σ) = √12 × the monthly Sharpe. Use √252 for daily trading-day returns, √365 for crypto that trades every day, √52 for weekly and √4 for quarterly. A Sharpe ratio quoted without saying how it was annualised cannot be compared with another.

Sortino ratio

The Sortino ratio replaces the standard deviation with the downside deviation: only returns below a target count as risk, so a strategy is not penalised for large gains. It is calculated from a list of returns as √(Σ min(0, return − target)² ÷ n). The target defaults to the risk-free rate per period; zero is also common.

As rough guides, an annualised Sharpe below 0 means the strategy did worse than cash, around 0.5 is typical of a broad stock index over the long run, above 1 is good and above 2 is rare outside short or backfitted samples.

How to use this calculator

  1. Calculate from — Average and std dev if you already have the summary figures (from a broker report, Myfxbook or a spreadsheet); List of returns to paste the returns themselves.
  2. Return period — the length of each return: daily, weekly, monthly, quarterly or yearly. It sets the annualisation factor.
  3. Risk-free rate — the annual yield on short government bills. Traders often use 0, which gives a slightly higher ratio.
  4. Average and std dev: enter the mean return and the standard deviation per period, in %. List of returns: paste one return per period in %, separated by commas, spaces or new lines.
  5. More options (list) — the Sortino target: the risk-free rate, zero or a custom return per period.

The result shows the annualised Sharpe ratio, the ratio per period, the annualised return and volatility and, for a list, the Sortino ratio, downside deviation, compounded return and best and worst period. Show the math lists each step with your numbers.

Worked example

Monthly figures. Average 1.5% a month, standard deviation 4%, risk-free rate 4% a year.

(1.5% − 4% ÷ 12) ÷ 4% = 0.292 per month → 0.292 × √12 = 1.01

Annualised return 1.5% × 12 = 18% (simple), annualised volatility 4% × √12 = 13.86%.

Daily returns. An average of 0.08% a day with a 1% daily standard deviation and no risk-free rate: 0.08 per day × √252 = 1.27 annualised.

From a list. Four monthly returns of 2%, −1%, 3% and 0%, risk-free rate 0. The average is 1%; the squared differences from it are 1, 4, 4 and 1, so the sample standard deviation is √(10 ÷ 3) = 1.826%. Sharpe = 1 ÷ 1.826 = 0.548 per month, or 1.90 annualised. Only −1% is below the 0% target, so the downside deviation is √(1 ÷ 4) = 0.5% and the Sortino ratio is 1 ÷ 0.5 = 2 per month, or 6.93 annualised.

The calculator's sample list (12 monthly returns from −2.2% to +3.4%) averages 0.79% with a 1.91% standard deviation. With a 4% risk-free rate that is a Sharpe of 0.83 and a Sortino of 1.41, annualised; the twelve months compound to +9.71%.

When to use it

  • Comparing strategies or funds with different returns and volatility on one scale.
  • Reviewing a trading account — monthly returns from a broker statement give a quick risk-adjusted score.
  • Checking a backtest — an unusually high Sharpe ratio is often a sign of overfitting or too short a sample.
  • Copy trading and signal providers — compare their reported returns with the swings it took to get them.
  • Strategies with uneven returns — use the Sortino ratio when large gains inflate the standard deviation.

Common mistakes

  • Annualising with the wrong factor. Daily returns from forex or stocks use √252; using 12 for daily data understates the ratio by a factor of about 4.6.
  • Comparing ratios from different periods. A daily Sharpe of 0.08 and a monthly Sharpe of 0.29 cannot be compared until both are annualised.
  • Trusting a short sample. Twelve monthly returns give a rough estimate; the true ratio could easily be half or double.
  • Ignoring fat tails. Strategies that sell options or use a martingale show a high Sharpe until the rare large loss arrives; the standard deviation does not see a loss that has not happened yet.
  • Mixing deposits with returns. Use percentage returns on the account, not changes in the balance that include deposits and withdrawals.

Frequently asked questions

How do you calculate the Sharpe ratio?

Subtract the risk-free rate from the average return and divide by the standard deviation of the returns, all for the same period. Then multiply by the square root of the number of periods per year to annualise. With 1.5% a month, a 4% monthly standard deviation and a 4% annual risk-free rate: (1.5 − 0.333) ÷ 4 = 0.292, × √12 = 1.01.

How do you annualise a Sharpe ratio?

Multiply the per-period Sharpe ratio by the square root of the number of periods in a year: √252 (15.87) for daily trading-day returns, √52 (7.21) for weekly, √12 (3.46) for monthly. The average return scales with the number of periods and the standard deviation with its square root, so the ratio scales with the square root.

What is a good Sharpe ratio?

Above 1 annualised is generally considered good and above 2 very good, but it depends on the sample and the strategy. A broad stock index has averaged roughly 0.4 to 0.6 over long periods. Very high ratios from a short track record or a backtest should be treated with suspicion.

What risk-free rate should I use?

The yield on short-term government bills in your account's currency, as an annual percentage, for example a 3-month US Treasury bill for a USD account. Many traders use 0 for simplicity, which gives a slightly higher Sharpe ratio. The calculator divides the annual rate by the number of periods per year.

What is the difference between the Sharpe and Sortino ratio?

The Sharpe ratio divides excess return by the standard deviation of all returns, so large gains count as risk too. The Sortino ratio divides by the downside deviation, which counts only returns below a target. A strategy with occasional large gains has a Sortino ratio well above its Sharpe ratio.

Should I use the sample or population standard deviation?

The sample standard deviation, which divides by n − 1, is the usual choice because your returns are a sample of what the strategy could produce. This calculator uses it for the Sharpe ratio. The downside deviation for the Sortino ratio divides by n, the common convention.

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