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FinanceSharpe Ratio
By Sitraka Forler · Lecturer, Durham Business SchoolUpdated 13 September 2026 About this site
Risk-adjusted return: excess return divided by volatility.
The Sharpe ratio measures how much excess return (above the risk-free rate) a strategy earns per unit of standard deviation. A Sharpe > 1 is generally considered good; > 2 is excellent.
Two paths, same destination: the Sharpe ratio
EUR 100 invested for 252 trading days. Both portfolios finish at EUR 112.00; only the ride differs.
excess = return 12.00% - rf 2.00% = 10.00% · Sharpe: smooth 10.00% / 6.09% = 1.64 · wild 10.00% / 22.09% = 0.45
The intuition
The Sharpe ratio is the price you were paid for the risk you took: excess return per unit of volatility. Sharpe = (return - rf) / σ, where rf is the risk-free rate and σ the annualised standard deviation of returns. Return alone cannot rank strategies, and the chart above shows why: both portfolios turn €100 into €112.00 over the same 252 trading days, but the blue path does it with about 6% annualised volatility and the rose path with about 22%. Same reward, wildly different risk. At a 2% risk-free rate the smooth ride scores a Sharpe of about 1.64 and the wild one about 0.45.
Two conventions do the work. Excess return is measured over cash, because rf is what you would have earned by taking no risk at all; drag the rf slider up and both Sharpes fall together as that hurdle rises. Volatility is annualised from daily data by multiplying by √252, the number of trading days in a year, and return by multiplying the daily mean by 252 (or, as in the chart, by taking the year's realised return directly). Both scalings assume each day is independent of the last; when returns trend or cluster, √252 understates the true annual volatility and flatters the Sharpe.
Read it as an exchange rate that leverage cannot change. Borrowing at rf to double a position doubles both the excess return and the volatility, so the ratio is untouched, which is why a Sharpe of 1.20 on an 8% strategy really is better than 0.72 on a 20% one: lever the first up to the same volatility and it earns more. The limits are the ones inherited from standard deviation: it counts upside swings as risk, it says nothing about the shape of the tail, and a strategy that quietly sells insurance can post a superb Sharpe for years before one bad month erases it.
Example
sharpe = (ann_return − risk_free) / ann_volatility
From annual figures to a Sharpe ratio, then the scaling trap and the comparison trap
- Start with a strategy that returned 12% over the year with annualised volatility of 15%, while the risk-free rate was 2%. Excess return = 0.12 - 0.02 = 0.10.
- Sharpe = excess return / volatility = 0.10 / 0.15 = 0.6667, so about 0.67: each unit of volatility bought two thirds of a unit of excess return.
- Now start from daily data instead: mean daily return 0.05% and daily standard deviation 1.2%. Annualised return ≈ 0.0005 × 252 = 0.126, or 12.6%.
- Annualised volatility = 0.012 × √252 = 0.012 × 15.8745 = 0.19049, or 19.05%. Return scales with time but volatility only with its square root, which is why the ratio depends on the horizon you quote it on.
- Sharpe at rf = 2%: (0.126 - 0.02) / 0.1905 = 0.106 / 0.1905 = 0.556, about 0.56. A slightly higher return than in step 1, but the extra volatility drags the ratio down.
- The comparison trap: strategy A returns 8% with 5% volatility, Sharpe = (0.08 - 0.02) / 0.05 = 0.06 / 0.05 = 1.20; strategy B returns 20% with 25% volatility, Sharpe = (0.20 - 0.02) / 0.25 = 0.18 / 0.25 = 0.72.
- Check what the higher Sharpe is worth in cash: lever A five times, up to B's 25% volatility, and it earns 0.02 + 5 × 0.06 = 0.32, or 32%, against B's 20%, while its Sharpe stays (0.32 - 0.02) / 0.25 = 1.20.
A is the better strategy despite less than half the raw return: Sharpe ranks reward per unit of risk, and because leverage cannot change it, the higher ratio is a real edge rather than an accounting trick. Always state the horizon and the risk-free rate next to the number.
Common pitfalls
- Annualising with √252 when returns are autocorrelated. The square-root rule assumes independent days; trending or volatility-clustered returns make the true annual volatility larger, so a Sharpe built from daily data overstates risk-adjusted performance. Check it against the standard deviation of actual monthly or yearly returns.
- Comparing Sharpes computed on different horizons or risk-free rates. A daily, a monthly and an annual Sharpe of the same strategy are three different numbers, and so is the same strategy measured against 0% and 5% cash. Line up the conventions before ranking anything.
- Treating a high Sharpe as proof of skill. Strategies with negatively skewed payoffs, such as selling options or carry trades, collect small steady gains and post Sharpes above 2 for years, then give it all back in one drawdown that standard deviation never warned about. Read skew, kurtosis and maximum drawdown alongside it.
- Dividing raw return by volatility and calling it a Sharpe. Without subtracting rf the ratio is no longer leverage-invariant and flatters cash-heavy portfolios; the excess return over cash is what makes the comparison fair, and rf should match the currency and horizon of the returns.
Frequently asked questions
What is a good Sharpe ratio?
A Sharpe above 1 is generally considered good, above 2 very good, and above 3 rare enough to double-check. Context matters: a broad equity index has averaged roughly 0.3 to 0.5 over long periods, so 1 is already unusual for a long-only fund, while a diversified market-neutral book targets 1 to 2. Short windows and backtests inflate the number through luck and overfitting, so a live track record of 1.5 is worth more than a simulated 3.
What is the difference between the Sharpe ratio and the Sortino ratio?
The Sortino ratio divides excess return by downside deviation only, the standard deviation of returns below a target such as zero or rf, whereas Sharpe divides by total volatility. Sortino therefore does not punish upside swings and rewards positively skewed strategies: a portfolio with the same total volatility but fewer bad days scores higher on Sortino than a symmetric one. Sharpe remains the default because it needs fewer choices and is easier to compare across managers.
Why do you multiply by the square root of 252 to annualise volatility?
Because variances add across independent periods while standard deviations do not. If daily returns are independent with variance σ², the variance over 252 trading days is 252σ², so the annual standard deviation is σ√252 ≈ 15.87σ; the mean, by contrast, scales by 252. The rule breaks when returns are autocorrelated: momentum makes true annual volatility higher than √252 suggests, mean reversion makes it lower, so check the scaled figure against actual monthly or yearly data.
Can the Sharpe ratio be negative, and what does it mean?
Yes: a negative Sharpe means the strategy earned less than the risk-free rate, so its risk went unrewarded. Ranking negative Sharpes is treacherous: because the denominator is volatility, a fund that lost 2% with 20% volatility (Sharpe -0.20 at rf 2%) looks better than one that lost 2% with 5% volatility (Sharpe -0.80), although the calmer fund took less risk for the same loss. When both are negative, compare excess returns and drawdowns instead.
Test yourself
Further reading
Where to go deeper. Free means a full, legal copy is online.
Sharpe's own 1994 restatement: ex-ante vs ex-post, and where the ratio misleads.
Chapter 14 on the deflated Sharpe: why a high backtest ratio can be luck.