The formula
Sharpe = (annualised return − risk-free rate) ÷ annualised volatility
annualised return = mean per period × periods
annualised volatility = standard deviation per period × √periods
The square root on the volatility side is the part worth noticing. Returns scale linearly with time and volatility scales with its square root, which is why the ratio improves as you measure over longer periods — the same strategy has a higher annual Sharpe than monthly Sharpe, without anything having changed.
A 1.8% monthly return with a 4.2% monthly standard deviation annualises to 21.6% return and 14.5% volatility. Against a 4% cash rate that is a Sharpe of 1.21.
The risk-free rate is not optional
Most calculators quietly set it to zero. That was almost harmless when cash paid nothing and is badly wrong now.
A strategy returning 6% with 5% volatility has a Sharpe of 1.2 when cash pays nothing and 0.4 when cash pays 4%. Same strategy, same year, and the second number is the honest one: you are being paid 2% over the alternative for taking real risk.
This is also why Sharpe ratios from different decades cannot be compared without checking what cash paid at the time.
What the number means
| Sharpe | Reading |
|---|---|
| Below 0 | Worse than cash |
| 0 to 1 | Below the usual threshold |
| 1 to 2 | Good |
| 2 to 3 | Very good — check the sample |
| Above 3 | Implausible for a long live record |
The last row is the useful one. A Sharpe above 3 sustained over years is exceptionally rare in live trading. In a backtest it usually means overfitting; in a short live sample it usually means a period that happened to suit the strategy. Treat it as a prompt to check the sample length, not as a result.
The flaw Sortino exists to fix
Sharpe uses standard deviation, which treats upside and downside variance identically. A month that returns +12% raises the volatility figure exactly as much as one that returns −12%, and therefore lowers the Sharpe.
That is backwards for anyone who actually holds the strategy. Nobody has ever complained about upside variance.
It also creates a specific blind spot: strategies with many small gains and rare large losses — selling options, carry trades, mean reversion into a trend — show a flattering Sharpe precisely because their returns are smooth right up until they are not. Sortino divides by downside deviation only and is the fairer measure for those shapes.