What the Sharpe ratio measures
Two portfolios returned 12% last year. One did it with 8% volatility, the other with 24%. They are not the same result, and the Sharpe ratio is the standard way of saying so in one number: subtract the risk-free rate from the return, divide by the standard deviation, and you have excess return per unit of risk.
The subtraction matters as much as the division. Return above the risk-free rate is the only part that required taking risk at all; a Treasury bill delivers the rest with no volatility. So the numerator is the compensation you actually earned for bearing uncertainty, and the denominator is how much uncertainty you bore to earn it. The ratio is dimensionless, which is what makes it comparable across strategies, asset classes and currencies.
William Sharpe introduced the measure in 1966 as a "reward-to-variability" ratio and revised the definition in 1994 to use the differential return between the fund and a benchmark, which is the form in use today. The revision matters for a subtle reason: the standard deviation should be that of the excess return series, not of the raw returns. When the risk-free rate is roughly constant over the window — which it usually is not, but often nearly is — the two are close enough that most published figures use the standard deviation of raw returns, as this calculator does.
The critical restriction is in the denominator. Standard deviation counts all volatility, including the idiosyncratic part that a diversified investor never bears. That makes Sharpe the right measure for a complete portfolio and the wrong one for a single holding inside a diversified account, where CAPM's beta is the relevant risk measure instead.
Why the annualisation uses a square root
Almost every Sharpe ratio you see quoted is annualised, and the annualisation is where most of the errors live.
Returns add over time; volatility does not. If monthly returns are independent, the variance of a twelve-month return is twelve times the variance of a one-month return, so the standard deviation is √12 ≈ 3.4641 times the monthly figure. The mean, meanwhile, is simply 12 times the monthly mean. So the ratio scales by 12 ÷ √12 = √12 — which is why the annualisation factor is the square root of the number of periods in a year, and why a monthly Sharpe of 0.25 becomes an annual 0.866.
Three consequences follow directly. First, you must know the data frequency before you can interpret a Sharpe ratio: a strategy with a daily Sharpe of 0.10 has an annualised ratio of 0.10 × √252 = 1.587, and quoting the raw daily figure makes it look thirty times worse than the monthly-quoted equivalent. Second, the higher the sampling frequency the larger the multiplier, so a manager reporting daily and a manager reporting quarterly are not on the same footing unless both annualise. Third, and most important, the square-root rule assumes returns are serially uncorrelated.
That last assumption is not innocent. Return series that are smoothed — illiquid holdings marked infrequently, private assets, some credit strategies — show positive serial correlation, which suppresses measured period-by-period volatility and inflates the annualised Sharpe ratio. A suspiciously high Sharpe ratio on an illiquid strategy is usually a statement about the valuation process, not about the returns.
Note also the convention this calculator follows: the annualised mean return is the arithmetic mean times the number of periods, not the geometric compounded figure. Arithmetic annualisation is what keeps the numerator and denominator consistent with the square-root rule. The compounded return you actually experienced is lower whenever volatility is non-zero, which is a real effect and a separate calculation — see the CAGR calculator.
Worked example: a fund with monthly returns
A fund's monthly returns over five years have an arithmetic mean of 0.85% and a sample standard deviation of 3.60%. Treasury bills yielded 4.30% a year over the same window.
- Convert the risk-free rate to a monthly rate. (1 + 0.0430)1/12 − 1 = 0.351459% per month. Compounding down rather than dividing by twelve keeps the annual figure exact.
- Excess return per month. 0.850000% − 0.351459% = 0.498541%.
- Sharpe ratio per month. 0.498541 ÷ 3.600 = 0.138484.
- Annualise. √12 = 3.4641016, so 0.138484 × 3.4641016 = 0.479721.
Read the components back to check the story. The annualised volatility is 3.60 × 3.4641016 = 12.4708%, and the annualised excess return is 0.498541 × 12 = 5.9825%. Dividing those two annualised figures gives 5.9825 ÷ 12.4708 = 0.4797, the same answer — which is the useful cross-check that your annualisation is internally consistent.
Now change one assumption. Suppose you had used a 0% risk-free rate, as several free screeners do. The excess return becomes the full 0.85% a month, the monthly Sharpe is 0.85 ÷ 3.60 = 0.236111, and the annualised figure is 0.8179 — seventy percent higher than the correct one, from an assumption nobody stated. This is the single largest source of disagreement between two published Sharpe ratios for the same fund, and it is why the sensitivity table below varies the risk-free rate rather than anything else.
What counts as a good Sharpe ratio
Rules of thumb circulate widely and deserve to be treated as rough. Broadly, an annualised ratio below 0.5 means the excess return is small relative to the volatility taken to earn it; around 1.0 is respectable for a diversified equity portfolio over a long window; above 2.0 is exceptional and usually indicates either a short sample, an illiquid mark, or leverage applied to a low-volatility strategy. Above 3.0, check the arithmetic before believing the number.
Three cautions do more work than any threshold.
Compare like windows. The Sharpe ratio is a sample statistic and it moves a great deal with the period chosen. Two funds quoted over different windows tell you mostly about the windows. Always benchmark against a passive alternative measured over exactly the same dates.
Negative ratios cannot be ranked. When the excess return is negative, dividing by a larger standard deviation produces a number closer to zero — so of two funds with the same shortfall, the more volatile one scores higher. This is not a subtlety you can ignore; it makes the Sharpe ratio meaningless for ranking in a losing period, and it is why comparisons during drawdowns should use a different measure.
Standard deviation is symmetric and returns are not. The ratio penalises upside surprises exactly as heavily as downside ones, and it says nothing about skewness or fat tails. A strategy that sells insurance — collecting steady small premiums and occasionally paying a large claim — posts an excellent Sharpe ratio right up until the claim arrives. If downside risk is what concerns you, the Sortino ratio replaces the denominator with downside deviation, and maximum drawdown captures the path in a way no ratio of moments can.
Annualisation factors and what a periodic ratio becomes
| Data frequency | Periods per year | Factor √m | Periodic 0.10 becomes | Periodic 0.25 becomes |
|---|---|---|---|---|
| Daily | 252 | 15.8745 | 1.5875 | 3.9686 |
| Weekly | 52 | 7.2111 | 0.7211 | 1.8028 |
| Monthly | 12 | 3.4641 | 0.3464 | 0.8660 |
| Quarterly | 4 | 2.0000 | 0.2000 | 0.5000 |
| Annual | 1 | 1.0000 | 0.1000 | 0.2500 |
A per-period Sharpe ratio of 0.25 is unremarkable at annual frequency and implausible at daily frequency. Always establish the frequency before comparing two quoted ratios.
Mistakes that produce a wrong Sharpe ratio
- Mixing frequencies. A monthly mean with an annual standard deviation, or the reverse, is the most common error and it is wrong by a factor of roughly √12 in one direction or the other.
- Assuming a zero risk-free rate. When bills yield 4%, ignoring them inflates the ratio substantially — in the worked example above, by about seventy percent.
- Dividing the annual risk-free rate by the number of periods instead of compounding it down. The difference is small at low rates but it is free to get right: use (1 + Rf)^(1/m) − 1.
- Using the population standard deviation on a sample. Divide by n − 1, not n. The difference matters for short series.
- Comparing ratios measured over different windows. The Sharpe ratio is a sample statistic and moves substantially with the period; two funds on different windows are not comparable.
- Ranking negative Sharpe ratios by size. With a negative numerator, more volatility produces a higher ratio, so the ordering inverts.
- Trusting a very high ratio on an illiquid strategy. Smoothed valuations suppress measured volatility and inflate the annualised figure, sometimes dramatically.
- Applying it to a single stock inside a diversified portfolio. Total volatility is the wrong denominator when you are only exposed to the systematic part.
Sharpe, Sortino, Treynor and information ratio
All four divide a return by a risk measure and differ only in what goes where. Sharpe divides excess return over the risk-free rate by total standard deviation. Sortino keeps the same numerator and replaces the denominator with downside deviation, so upside volatility no longer counts against you. Treynor divides the same excess return by beta instead of standard deviation, which is the right choice for one holding inside a diversified portfolio rather than for the portfolio itself. The information ratio changes the numerator: active return against a benchmark, divided by tracking error, which is the measure to use when the question is whether a manager added value over the index they are paid to beat.
Using the ratio well
The Sharpe ratio is a comparison instrument, and comparisons need a control. Compute it for the portfolio you hold and for a plausible passive alternative over precisely the same dates, and read the difference rather than the level. That single discipline strips out most of the ways the number can mislead, because the market environment applies to both.
Two of the inputs are calculations in their own right. The standard deviation calculator gives the denominator from a return series, and the variance calculator the quantity it is the square root of. Once you have the ratio, remember it is silent about the path: two portfolios with identical Sharpe ratios can have very different worst drawdowns, and it is the drawdown that determines whether an investor actually stays invested.
Finally, the ratio measures gross-of-fee returns unless the series you feed it is already net. Fees reduce the numerator without touching the denominator, so they reduce the Sharpe ratio proportionally more than they reduce return — the expense ratio impact calculator shows what that costs over a full holding period. And if you are comparing across accounts with different tax treatment, run the returns after tax first, since the risk-free rate you subtract should be measured on the same basis.