# Sharpe Ratio

> The Sharpe ratio measures return per unit of volatility. Learn the formula, how to annualize it from daily P&L, what counts as good, and where it misleads.

Canonical: https://www.journalx.io/glossary/sharpe-ratio

The **Sharpe ratio** is the return a strategy earns above a risk-free rate for each unit of volatility it carries. Two traders can both finish the year up 20%, and one of them can have gotten there on a calm, steady climb while the other rode a roller coaster. Raw return can't tell them apart. The Sharpe ratio can, and that is why it has become one of the most quoted risk-adjusted performance measures in finance.

William F. Sharpe introduced it in 1966 as the "reward-to-variability ratio" and published a revised version in 1994 in [The Journal of Portfolio Management](https://web.stanford.edu/~wfsharpe/art/sr/sr.htm). He went on to share the [1990 Nobel Memorial Prize in Economic Sciences](https://www.nobelprize.org/prizes/economic-sciences/1990/summary/) for his work on asset pricing. Fund managers use the ratio to compare portfolios. For an active trader, it answers a simpler question: is the ride worth what it pays?

## How the Sharpe Ratio Works

> Sharpe ratio = (Average return − Risk-free rate) ÷ Standard deviation of returns

The top line is your **excess return**, what you earned beyond what cash in Treasury bills would have paid for doing nothing. The bottom line is the **standard deviation** of your returns, a measure of how much they swing around their average. Divide one by the other and you get return per unit of volatility.

Here is how two traders compare when the risk-free rate is 4%:

|                          | Trader A | Trader B |
| ------------------------ | -------- | -------- |
| Annual return            | 30%      | 18%      |
| Excess return (minus 4%) | 26%      | 14%      |
| Annual volatility        | 25%      | 10%      |
| **Sharpe ratio**         | **1.04** | **1.40** |

Trader A made more money. Trader B earned about a third more return for every unit of volatility. If both kept trading the same way, B's account would spend far less time in deep [drawdowns](/glossary/drawdown), and that is usually the account that survives long enough to compound.

![Two equity curves that both finish the year up 20%, a smooth one with 8% volatility and a Sharpe ratio of 2.5, and a jagged one with 27% volatility and a Sharpe ratio of 0.8](https://assets.journalx.io/marketing/glossary/sharpe-ratio/sharpe-ratio-equity-curves.avif)

The chart shows the same idea on an [equity curve](/glossary/equity-curve). Both years end at +20%. The smooth one has a Sharpe ratio of 2.5. The jagged one, with an 18% drop along the way, has a Sharpe ratio of 0.8. Same finish line, a much rougher trip.

## How to Calculate the Sharpe Ratio From Daily P\&L

Most traders compute it from daily account returns:

1. **Turn each day into a percentage return.** Divide the day's P\&L by the account equity at the start of that day. Leave deposits and withdrawals out.
2. **Include the days you didn't trade** as 0% returns. Skipping them is the most common way traders inflate the number (more on that below).
3. **Average the daily returns** and subtract the daily risk-free rate, which is the annual rate divided by 252. Many traders use zero here, which is fine as long as you are consistent.
4. **Find the standard deviation** of the same daily returns.
5. **Divide, then annualize** by multiplying by the square root of 252, roughly 15.9.

Say your account averaged 0.08% a day with a daily standard deviation of 0.9%. The daily Sharpe ratio is 0.08 ÷ 0.9 = 0.089, and the annualized figure is 0.089 × 15.9 = **1.41**. Subtract a 4% annual risk-free rate (0.016% a day) first and it comes out at 1.13.

For monthly returns, annualize with the square root of 12. For weekly returns, use the square root of 52. Square-root scaling assumes each period's return is independent of the last. When it isn't, the annualized figure can be badly off: Andrew Lo [showed in 2002](https://rpc.cfainstitute.org/research/financial-analysts-journal/2002/the-statistics-of-sharpe-ratios) that serial correlation in monthly returns can overstate a hedge fund's annual Sharpe ratio by as much as 65%.

## What Is a Good Sharpe Ratio?

A common rule of thumb for an annualized Sharpe ratio:

| Sharpe ratio | Usual reading                           |
| ------------ | --------------------------------------- |
| Below 0      | Earned less than cash                   |
| 0 to 1       | Positive, but modest for the volatility |
| 1 to 2       | Good                                    |
| 2 to 3       | Very good                               |
| Above 3      | Exceptional, and worth questioning      |

Treat these bands as conventions, not laws. A Sharpe ratio depends on the period you measure, how often you sample returns, and the risk-free rate you assume, so only compare ratios computed the same way. A reading above 3 on a short track record is more often a small sample or a hidden tail risk than a sign of genius.

## How Much Data Does a Sharpe Ratio Need?

Far more than most traders expect. If daily returns are independent, the standard error of an annualized Sharpe ratio is roughly 1 divided by the square root of the number of years of data, using the formula in [Lo's paper](https://rpc.cfainstitute.org/research/financial-analysts-journal/2002/the-statistics-of-sharpe-ratios). One year of daily data gives a standard error of about 1.0. A Sharpe ratio is a noisy estimate until the record gets long.

![The 95% range of measured Sharpe ratios for a strategy whose true Sharpe ratio is 1.5, narrowing from minus 2.4 to 5.4 after three months to 0.6 to 2.4 after five years, and only clearing zero after about two years](https://assets.journalx.io/marketing/glossary/sharpe-ratio/sharpe-ratio-track-record.avif)

Here is the range a strategy with a true Sharpe ratio of 1.5 can produce, 95% of the time, depending on how long you measure it:

| Daily track record | Measured Sharpe ratio could land anywhere from |
| ------------------ | ---------------------------------------------- |
| 3 months           | −2.4 to 5.4                                    |
| 6 months           | −1.3 to 4.3                                    |
| 1 year             | −0.5 to 3.5                                    |
| 2 years            | 0.1 to 2.9                                     |
| 5 years            | 0.6 to 2.4                                     |

A good strategy can show a negative Sharpe ratio for a whole year. A mediocre one can show a 4 over a hot quarter. Before you scrap a strategy or size it up, ask whether the record is long enough to tell the difference.

Three months of results can't separate a strategy with a real edge from one with none, and the Sharpe ratio is no exception. Judge a short record by whether you followed your process, and let the ratio settle before it drives big decisions.

## Position Size Doesn't Change Your Sharpe Ratio

Double every position and you double your excess return and your volatility at the same time. The ratio stays where it was, apart from financing costs and the worse fills that come with larger size. The Sharpe ratio measures the quality of the edge per unit of variability. [Position sizing](/glossary/position-sizing) and [risk per trade](/glossary/risk-per-trade) decide how much of that variability you live with.

That is a useful split. If your Sharpe ratio is low, trading bigger won't fix it, it only makes the swings larger. If your Sharpe ratio is solid but the drawdowns are more than you can stomach, the fix is smaller size, not a new strategy.

## Where the Sharpe Ratio Misleads

- **It treats upside as risk.** A big winning day raises your standard deviation and lowers your Sharpe ratio. Strategies built on occasional large winners, like trend following, look worse than they feel. The [Sortino ratio](/glossary/sortino-ratio) exists to fix this by counting only downside volatility.
- **It assumes volatility captures risk.** Strategies that win small and often but take rare, large losses, such as selling options or averaging down, can show a high Sharpe ratio right up until the loss arrives. Read it next to your maximum drawdown and your worst single day.
- **It is a time-series measure.** Calculating a Sharpe ratio per trade and annualizing it with the square root of 252 mixes units. For trade-level quality, look at [expectancy](/glossary/expectancy) in [R-multiples](/glossary/r-multiple) next to how widely those R-multiples spread.

## Key Takeaways

- The Sharpe ratio is excess return divided by the standard deviation of returns: return per unit of volatility.
- Annualize a daily Sharpe ratio by multiplying by the square root of 252, about 15.9.
- Above 1 is generally good and above 2 very good, but only over a long enough record.
- One year of daily data still leaves an error band of about ±2 around the measured figure.
- Position size doesn't change the ratio. It changes the drawdowns you sit through.

## Common Mistakes

**Leaving out days with no trades.** If you trade two days a week and only count those days, your Sharpe ratio comes out about 1.6 times too high. Your capital was committed on every trading day whether you traded or not, so count them all.

**Using dollar P\&L without the account size.** A $500 day on a $10,000 account and on a $50,000 account are different returns. Divide by start-of-day equity, and keep deposits and withdrawals out of the series.

**Comparing ratios built differently.** Daily versus monthly returns, a zero versus a 4% risk-free rate, last year versus the last five: each changes the number. Only compare like with like.

**Trusting a hot quarter.** A Sharpe ratio above 3 after a few months is almost always a small sample. Wait for more data before you size up.

**Ignoring the left tail.** A smooth record with a high Sharpe ratio can hide a strategy that hasn't met its bad day yet. Check the worst day and the deepest drawdown before you trust the ratio.

## How JournalX Tracks Your Sharpe Ratio Inputs

A Sharpe ratio is only as good as the daily record behind it. JournalX builds that record from your trades, synced from your broker or imported by CSV, and rolls them up into daily P\&L, an equity curve, and drawdown, with the calendar showing quiet days alongside active ones.

From there you can filter by account, setup, or session to see where the biggest swings in your daily P\&L come from, and read it next to your expectancy, [profit factor](/glossary/profit-factor), and win rate. The question shifts from "am I making money?" to "am I being paid enough for the swings I take?"