Sharpe Ratio

The Sharpe ratio is the most widely used measure of risk adjusted performance. Developed by economist William F. Sharpe in 1966, it divides a strategy's excess return over a risk free rate by the volatility of its returns. A higher Sharpe ratio means more return for each unit of risk taken. It lets you compare a calm strategy earning 8% with a wild one earning 20% on equal terms, and it is the first number most professional allocators look at.

The formula#

Sharpe ratio = (Portfolio return - Risk free rate) / Standard deviation of returns

• Portfolio return: usually annualised.
• Risk free rate: typically the yield on short term government bills. See Treasury Bills, Notes and Bonds.
• Standard deviation: the annualised volatility of returns. See Variance and Standard Deviation.

Annualising the Sharpe ratio#

When working with daily returns, compute the mean and standard deviation of daily excess returns, divide, then multiply by the square root of 252 (trading days). With a mean daily excess return of 0.04% and daily volatility of 1%, the daily Sharpe is 0.04, and the annualised Sharpe is 0.04 times about 15.87, or roughly 0.63. Use monthly data with the square root of 12. Try the numbers in the Sharpe and Sortino Calculator.

What is a good Sharpe ratio?#

Broad stock market indices have historically delivered long run Sharpe ratios roughly in the 0.3 to 0.5 range, depending on the period. Context matters: high frequency strategies can sustain much higher ratios with limited capacity. See Alpha Capacity and Crowding.

Limitations#

Statistical uncertainty#

The Sharpe ratio is an estimate with error. Roughly, the standard error of an annualised Sharpe ratio is about the square root of (1 divided by the number of years) for modest ratios. With 4 years of data, that is about 0.5, so a measured Sharpe of 1.0 could plausibly reflect a true value anywhere from near 0 to 2. Long track records matter. See Sampling and Standard Error and Statistical Significance in Trading.

Common mistakes#

1. Annualising incorrectly, for example multiplying the daily ratio by 252 instead of its square root.
2. Ignoring costs in backtest Sharpe ratios.
3. Comparing Sharpe ratios from different periods or frequencies.
4. Trusting very high backtest ratios. See Overfitting and Curve Fitting.
5. Using it alone without drawdown and tail measures. See Maximum Drawdown.

Frequently asked questions#

What does the Sharpe ratio measure?#

Excess return over the risk free rate per unit of volatility, showing how much return a strategy earns for the risk it takes.

What is a good Sharpe ratio for a trading strategy?#

Above 1.0 sustained in live trading is very good; backtest figures above 2.0 deserve scepticism.

How do I annualise a Sharpe ratio from daily returns?#

Divide the mean daily excess return by the daily standard deviation, then multiply by the square root of 252.

Next, learn a version that only penalises downside risk in Sortino Ratio.