Definition
The Sharpe ratio measures a portfolio's average return above the risk-free rate per unit of total volatility. It was introduced by William Sharpe to compare risk-adjusted performance across strategies.
How it works
Subtract the risk-free return from the portfolio return, then divide by the standard deviation of the portfolio's returns. All inputs must use the same unit: if returns are daily, the risk-free rate must also be converted to a daily rate and the standard deviation must be daily too.
A daily or monthly ratio is annualized by multiplying by √252 or √12 respectively, which assumes returns are independent from period to period. A higher ratio means more excess return per unit of volatility; it does not say how deep losses could be.
Formula / convention
Sharpe = (R(p) − R(f)) ÷ σ(p), with R(p), R(f) and σ(p) in the same period unit; Annualized Sharpe ≈ periodic Sharpe × √(periods per year)
Illustrative example
Illustrative: a fictional portfolio earned 9% in a year when the risk-free rate was 3%, with annual volatility of 12%, so Sharpe = (9% − 3%) ÷ 12% = 0.50. In daily terms the excess return is about 6% ÷ 252 ≈ 0.0238% and the volatility is about 12% ÷ √252 ≈ 0.756%, a daily ratio of 0.0315; multiplying by √252 gives about 0.50 again.
What to watch for
Mixing units, such as subtracting an annual 3% risk-free rate from average daily returns, gives meaningless results. The ratio treats upside and downside volatility alike and can look flattering for strategies with rare large losses, smoothed or illiquid returns, or heavy parameter searching, while short histories give noisy estimates.