| Input | What it is | Where it commonly goes wrong |
|---|---|---|
| Portfolio return | The mean return of the strategy or portfolio over the period, at a fixed observation frequency. | Mixing frequencies. A daily mean with a monthly standard deviation produces a number that means nothing. |
| Risk-free rate | The return available on short-term government debt over the same period — what the money would have earned sitting in cash. | Setting it to zero. Harmless when rates are near zero, materially flattering when they are not. |
| Standard deviation | The volatility of the excess return: the return minus the cash rate, measured period by period. | Using the volatility of the raw return instead. Sharpe’s 1994 revision is explicit that the denominator belongs to the excess return. |
How to calculate a Sharpe ratio
Pick one observation frequency and keep it
Daily, weekly or monthly returns — it does not matter which, but every step below has to use the same one. Most errors in a hand-calculated Sharpe ratio are frequency errors.
Build the excess return series
For each period, subtract the risk-free rate for that period from the portfolio return for that period. This gives you a new series: what the strategy earned over and above holding cash.
Take the mean of that series
The average excess return per period. This is the numerator.
Take the standard deviation of the same series
The volatility of the excess returns, not of the raw returns. This is the denominator, and getting it from the wrong series is the most common mistake in the whole calculation.
Divide, then annualize once
Mean divided by standard deviation gives the per-period Sharpe ratio. Multiply by the square root of the number of periods in a year — about 252 for daily, 12 for monthly — to state it annually. Annualize once, at the end, and never twice.
What does the Sharpe ratio actually measure?
It measures return per unit of volatility, above what cash would have paid. The intuition is that earning 12% while swinging violently is a different achievement from earning 12% in a straight line, and the ratio puts a number on that difference.
William Sharpe introduced it in 1966, under the name reward-to-variability ratio, and revised the definition in 1994 to make explicit that both the numerator and the denominator refer to the excess return over a benchmark. The 1994 version is the one in use today, and the 1966 name is a better description of what the number does.
One consequence is worth internalizing early: the Sharpe ratio treats volatility as the definition of risk. That is a modeling choice, not a fact about markets, and most of what the ratio cannot see follows from it.
What is the Sharpe ratio formula?
Sharpe ratio = (Rp − Rf) ÷ σ, where Rp is the portfolio return, Rf is the risk-free rate over the same period, and σ is the standard deviation of the excess return Rp − Rf.
A worked example, using monthly data. A strategy averages 1.0% a month. Cash pays 0.3% a month. The excess return averages 0.7% a month, and its standard deviation is 2.5% a month. The monthly Sharpe ratio is 0.7 ÷ 2.5 = 0.28. Annualized, that is 0.28 × √12 ≈ 0.97.
Notice how much moved in the last step. The same strategy reports 0.28 or 0.97 depending only on whether the figure was annualized, and a great deal of published performance data does not say which convention it used.
How do you annualize a Sharpe ratio?
Multiply the per-period ratio by the square root of the number of periods in a year: √252 for daily returns, √52 for weekly, √12 for monthly. The square root appears because mean return scales with time while standard deviation scales with the square root of time.
That rule carries an assumption that is easy to miss and often false: it requires returns to be independent from one period to the next. Andrew Lo set this out in "The Statistics of Sharpe Ratios" in 2002 — when returns are serially correlated, as they are for trend-following, illiquid holdings and anything with smoothed pricing, the square-root rule can overstate the annualized figure substantially.
- Positive serial correlation — momentum, or stale prices in an illiquid asset — inflates the annualized Sharpe ratio relative to the truth.
- Negative serial correlation — mean reversion — deflates it.
- Because the rule is applied mechanically almost everywhere, two annualized figures from different strategies may not be comparable even when both were computed correctly.
What can a Sharpe ratio not see?
Four things, and each of them has ended a real fund.
- The shape of the losses. Standard deviation counts a gain and a loss of the same size identically, so a strategy that occasionally jumps upward is penalized exactly like one that occasionally collapses.
- Fat tails. The ratio summarizes a return distribution with its mean and standard deviation, which is only sufficient if the distribution is well behaved. Strategies that collect small premiums and rarely lose a great deal — selling options, carry, most short-volatility exposure — post excellent Sharpe ratios for years and then post one month that undoes them.
- The path. Two strategies with the same Sharpe ratio can have very different drawdown profiles, and drawdown is what a person actually has to sit through.
- How the number was found. This is the largest blind spot and the least discussed. A Sharpe ratio calculated on a live track record is a measurement; the same figure taken from a backtest is the winner of a search, and the arithmetic is identical either way.
The last one is the reason the deflated Sharpe ratio exists: it asks how high this figure would have to be before it is surprising, given how many variants were tried to find it. If you only take one thing from this page into a backtest, take that distinction.
Backtested and hypothetical results are not indicative of future performance. Nothing here is investment advice.
Which other measures cover the Sharpe ratio’s blind spots?
Each of the blind spots above has a measure built to address it, and none of them is a replacement — they are companions, best read next to the Sharpe ratio rather than instead of it.
- For the upside penalty: the Sortino ratio, which counts only the volatility below a target, so a strategy with violent gains and gentle losses is no longer punished for the gains.
- For the path: the Calmar ratio, or better, the drawdown profile directly. Both speak to what holding the strategy would actually have felt like, which variance does not.
- For the search: the deflated Sharpe ratio, which is a different kind of object altogether — not a performance measure but a probability that the result is more than the best draw from a pile of noisy attempts.
Only the last one addresses the largest blind spot. A Sortino or Calmar ratio computed on the best of fifty thousand backtested variants is exactly as selected as the Sharpe ratio would have been, and looks just as good.
Common questions
What is a good Sharpe ratio?
For a live, multi-year track record, convention treats above 1 as good and above 2 as strong. For a backtest those bands do not transfer, because they assume the figure was measured rather than selected from many attempts. The judgement question has its own page, which is where the reasoning lives.
What is the Sharpe ratio formula in Excel?
Build a column of excess returns — portfolio return minus the periodic risk-free rate — then divide AVERAGE of that column by STDEV.S of the same column. Multiply by SQRT(252) for daily data or SQRT(12) for monthly. The frequent error is running STDEV.S over the raw return column instead of the excess return column.
Can a Sharpe ratio be negative?
Yes. A negative Sharpe ratio means the strategy returned less than cash over the period. The magnitude is not very informative once it goes below zero, because dividing a negative number by volatility makes a more volatile losing strategy look better than a steady one.
What risk-free rate should I use?
The short-term government rate for the currency and period you are measuring — three-month Treasury bills for US strategies is the usual choice. Use the rate that applied during each period rather than today’s rate, and if you set it to zero, say so, because that decision flatters every result in a high-rate environment.
Is the Sharpe ratio still useful?
Yes, as one summary statistic among several. It is compact, comparable across strategies when computed consistently, and universally understood. The failure mode is not using it — it is reading it alone, without the drawdown profile, the trade count, and how many variants were tried before this one was chosen.