Sharpe ratio

The Sharpe ratio, introduced by economist William Sharpe in 1966, asks how much return a strategy produced for the ups and downs it put you through.

• Sharpe ratio = (return − cash rate) ÷ standard deviation of returns

The cash rate is what you could have earned with almost no risk, such as a short-term government bill rate. Subtracting it isolates the extra return earned for taking risk. The standard deviation measures how much returns varied from period to period.

Example

Illustrative annual figures:

• Strategy A returns 8%, the cash rate is 3%, and returns have a standard deviation of 10%. Sharpe ratio: (8 − 3) ÷ 10 = 0.5.
• Strategy B returns 14%, with the same cash rate and a standard deviation of 30%. Sharpe ratio: (14 − 3) ÷ 30 ≈ 0.37.

B made more money, but A produced more return per unit of variability. Using leverage, a trader could in principle scale A up to a similar return, though with its own risks.

Limitations

• Volatility is not the same as risk of loss. Standard deviation treats a sharp rise the same as a sharp fall. Strategies that collect small, steady gains and occasionally suffer a large loss can show a high Sharpe ratio right up until the loss arrives.
• Short records mislead. A ratio from a few months of data is unreliable, and it depends on whether returns are measured daily, weekly or monthly.
• Comparisons need the same basis. Ratios are usually annualised; check how before comparing two figures.

For individual traders, drawdown and risk of ruin are often more intuitive measures of pain than the Sharpe ratio. Our guide to drawdown and recovery explains why.