The Sharpe ratio is your average return above the risk-free rate, divided by the standard deviation of those returns. It tells you how much return you earned for each unit of swing in your results. William Sharpe introduced it in 1966 to compare mutual funds. For a trader, it answers one question: is this account growing steadily, or is the same profit coming from wild up and down days?
The Sharpe ratio formula
Sharpe ratio = (average return − risk-free rate) ÷ standard deviation of returns
- Average return: the mean of your returns over one period, such as a day or a month.
- Risk-free rate: what you could have earned with no risk, usually a short-term Treasury bill rate, converted to the same period.
- Standard deviation: how far your returns typically land from their average. This is the "risk" in the ratio.
The result is for one period. To compare it with the annual figures funds publish, annualise it by multiplying by the square root of the number of periods in a year: √252 for daily returns (about 15.9) and √12 for monthly returns.
A worked example with 10 trading days
Ten days of account returns, as a percentage of the balance at the start of each day:
| Day | Return |
|---|---|
| 1 | +0.8% |
| 2 | −0.4% |
| 3 | +1.2% |
| 4 | +0.3% |
| 5 | −0.9% |
| 6 | +0.6% |
| 7 | 0.0% |
| 8 | +1.1% |
| 9 | −0.5% |
| 10 | +0.7% |
- Average daily return: 2.9% ÷ 10 = 0.29%
- Standard deviation of the ten returns (sample): 0.72%
- Risk-free rate: assume 4% a year, which is 4% ÷ 252 = 0.016% a day
- Daily Sharpe: (0.29 − 0.016) ÷ 0.72 = 0.38
- Annualised: 0.38 × √252 = 6.1
A 6.1 is far above the 1 to 2 that counts as good for a fund. It is also built on ten days, which is far too few to trust.
Same profit, different Sharpe
Now give a second trader the same ten-day total, +2.9%, but bigger swings: +2.4%, −1.8%, +3.0%, −0.6%, −2.7%, +1.9%, −1.2%, +2.8%, −1.6%, +0.7%. The average is still 0.29% a day. The standard deviation is 2.13%, three times larger.
Annualised Sharpe = (0.29 − 0.016) ÷ 2.13 × √252 = 2.0
Both traders finished level. The second one had to sit through days of −2.7% and −1.8% to get there, and a string of those days in a row is what breaks a prop firm's daily loss limit.
What is a good Sharpe ratio?
The rules of thumb you will see quoted for funds:
- Below 0: you did worse than the risk-free rate.
- 0 to 1: positive but modest. A long-only stock fund held for decades usually sits here.
- 1 to 2: good for a fund.
- Above 2: very good for a fund, and rare to keep up over many years.
Day trader vs fund
Day traders often see annualised Sharpe ratios of 3, 4 or higher. Three reasons, none of them a sign of skill on their own:
- Short history. A few months of results never include the bad year that a fund's 20-year record does.
- Flat overnight. A day trader carries no overnight gap risk, so daily returns swing less than a fund that holds positions for weeks.
- Small account, big return. Returns of 50% to 100% a year are possible on a small futures account. A billion-dollar fund cannot do that, whatever its Sharpe.
So compare your Sharpe with your own earlier periods, or with another strategy of yours measured the same way, rather than with a fund. A Sharpe that falls from 3 to 1 over two quarters says more than any single reading.
How many days before the Sharpe ratio means anything
A Sharpe ratio is an estimate, and it has an error bar. Andrew Lo worked out its size in The Statistics of Sharpe Ratios (Financial Analysts Journal, 2002). Applied to daily returns, for a measured annual Sharpe of 2.0:
| Trading days | 95% range for the true Sharpe |
|---|---|
| 20 (a month) | −5.0 to 9.0 |
| 60 (a quarter) | −2.0 to 6.0 |
| 252 (a year) | 0.0 to 4.0 |
| 756 (three years) | 0.9 to 3.1 |
After a quarter of trading, a Sharpe of 2.0 cannot rule out a strategy that loses money. It takes about a year before the range stops including zero. This assumes each day is independent of the last; Lo also shows that streaky returns make the ratio look better than it is. The same logic applies to your win rate, covered in how many trades before you can trust a statistic.
Where the Sharpe ratio misleads traders
- It punishes big winning days. Standard deviation counts a +5% day as risk, the same as a −5% day. If your strategy lives on a few large winners, the Sortino ratio, which counts only downside swings, is the fairer read.
- It hides how deep the losses went. Two accounts with the same Sharpe can have very different worst drawdowns. The Calmar ratio and max drawdown cover that.
- It assumes well-behaved returns. Selling options or averaging down can produce a smooth curve and a high Sharpe right up to the day it does not. Sharpe himself discussed what the ratio can and cannot show in The Sharpe Ratio (Journal of Portfolio Management, 1994).
- Trade-level returns are not daily returns. If you take ten trades on one day and two the next, a Sharpe built from individual trades cannot be annualised with √252. Measure it on daily account returns, and use expectancy and profit factor for per-trade quality.
Your own Sharpe ratio, without the spreadsheet
Import your broker's CSV and ExpectancyIQ's Performance report shows your annualised Sharpe, Sortino and Calmar ratios next to profit factor and expectancy, for any date range or strategy tag. The report is part of the free trial. It uses the formula above with the sample standard deviation, a daily return of each trading day's P&L divided by the balance going into that day, and a risk-free rate of 0. On the ten days above that gives an annualised Sharpe of 6.4 rather than 6.1. The trading dashboard shows how the rest of the numbers fit together.
The glossary has short definitions of every other metric in the report.