Sharpe Ratio Calculator: From Returns, with Sortino

Sharpe ratio formula

A Sharpe ratio calculator works out (average return − risk-free rate) ÷ standard deviation of returns, with all three measured over the same period. To annualise the result, multiply by the square root of the number of periods in a year: √12 for monthly returns, √52 for weekly, √252 for daily. Above 1 is generally good. Below 0 means the strategy earned less than cash.

The ratio tells you how much extra return each unit of volatility bought. Two strategies with the same average return rank differently if one of them got there with much larger swings. Sharpe index, Sharpe measure and Sharpe ratio are the same number. William F. Sharpe, who it is named after, called it the reward-to-variability ratio.

How to calculate the Sharpe ratio from 12 monthly returns

Take twelve monthly returns and a 4% annual risk-free rate. These are the defaults in the "From a list of returns" mode above, so you can follow each step on screen.

1. Mean monthly return: 11.2 ÷ 12 = 0.9333%.
2. Sample standard deviation: 38.0267 ÷ (12 − 1) = 3.4570, and √3.4570 = 1.8593%. The divisor is n − 1 because twelve months are only a sample of what the strategy does.
3. Monthly risk-free rate: (1 + 0.04)^(1/12) − 1 = 0.3274%. Dividing by 12 instead gives 0.3333%. The difference is small and moves the final answer from 1.13 to 1.12.
4. Excess return: 0.933333 − 0.327374 = 0.605959% per month.
5. Monthly Sharpe: 0.605959 ÷ 1.859293 = 0.3259.
6. Annualised Sharpe: 0.3259 × √12 = 0.3259 × 3.4641 = 1.13.

The calculator also reports the annualised return (0.9333 × 12 = 11.20%), the annualised volatility (1.8593 × √12 = 6.44%), and a standard error of about ±1.03 for this estimate. That last figure matters more than it looks. The mistakes section below explains why.

What is a good Sharpe ratio?

These are the bands the calculator uses for an annualised Sharpe ratio. Treat them as rules of thumb. Nobody standardised them, and they only mean much on long samples.

Annualising the Sharpe ratio with √12, √52 or √252

Mean return grows in line with the number of periods, while standard deviation grows with the square root, so the ratio scales by √(periods per year). The rule assumes each period's return is independent of the one before it.

So a daily Sharpe of 0.08 is 0.08 × 15.8745 = 1.27 a year, and a weekly Sharpe of 0.2 is 1.44.

Sharpe vs Sortino

Sharpe divides by total standard deviation, so a large gain counts as risk just as much as a large loss does. The Sortino ratio divides by downside deviation instead: the root-mean-square of only the returns below a target, taken over all observations. The calculator lets you set that target at 0% or at the risk-free rate.

For the 12-month example, downside deviation against 0% is 0.8416% a month, which gives an annualised Sortino of 3.84 next to a Sharpe of 1.13. Against the risk-free rate it is 2.06. Now flip each month around the mean (2 × 0.9333 − return). Mean and standard deviation are unchanged, so the Sharpe ratio is still 1.13, but the worst month improves from −2.2% to −1.53% and the Sortino climbs to 5.45. Sharpe gives the same answer for both return streams. Sortino tells them apart.

Common mistakes

• Mixing periods. Subtract a 4% annual rate from a 0.9333% monthly return and the example's annualised Sharpe comes out at −5.71 instead of 1.13. Convert the rate to the same period first. The calculator does this for you.
• Scaling by 12 instead of √12. Multiplying the monthly Sharpe of 0.3259 by 12 gives 3.91, which looks spectacular and is wrong.
• Small samples. With 12 observations the standard error is about ±1.03, so the true annualised Sharpe could plausibly sit anywhere from 0.10 to 2.16. At the same Sharpe, getting the error down to ±0.5 takes about 51 months, and ±0.25 about 202 months. The calculator prints this figure under the result.
• Non-normal returns. Strategies that sell options, or pick up pennies in front of a steamroller, show high Sharpe ratios right up until the rare large loss arrives. Sharpe sees the mean and the standard deviation and nothing about the shape of the tail.
• Smoothed or autocorrelated returns. Monthly marks on illiquid assets understate volatility, and the √n rule overstates the annual figure when returns trend from one period to the next.
• Using prices instead of returns. The inputs are percentage returns per period. Account balances and price series have to be turned into returns first.

How to use this calculator

1. Average & std dev mode: choose annual or monthly figures, enter your average return and standard deviation for that period, and the annual risk-free rate. In monthly mode the rate is de-compounded to a monthly figure and the result is annualised with √12.
2. From a list of returns mode: paste percentage returns, one per line or separated by commas, say whether they are daily, weekly, monthly or yearly, and enter the annual risk-free rate. The calculator shows how many values it parsed and lists any it ignored.
3. Read the annualised Sharpe ratio and its band, then the mean, sample standard deviation, per-period risk-free rate, per-period Sharpe, annualised return and volatility, Sortino ratio and standard error.

If you log trades in the trading journal, its CSV export lists the P&L of every trade. Total it by month, divide by the account balance at the start of the month, and you have returns to paste here. Sharpe treats upside and downside swings alike, so pair it with the drawdown recovery calculator to see what your worst losing stretch costs to recover. For options strategies, the Black-Scholes calculator shows the volatility the market is pricing in.

The calculator is arithmetic on the numbers you enter. It does not recommend any strategy or investment.