Sharpe Ratio
Calculate the Sharpe ratio: S = (Rp - Rf) / sigma.
Measure risk-adjusted investment returns developed by William Sharpe.
The Formula
The Sharpe ratio measures the risk-adjusted return of an investment or portfolio. It was developed by Nobel laureate William F. Sharpe in 1966 and has become one of the most widely used metrics in finance. The ratio tells you how much excess return you receive for each unit of risk (volatility) you take on.
The numerator (Rp − Rf) represents the excess return — the portfolio's return minus the risk-free rate. The risk-free rate is typically the yield on government bonds, such as U.S. Treasury bills, which are considered virtually risk-free. By subtracting this rate, the formula isolates the return that is attributable to taking on investment risk rather than simply earning the safe rate.
The denominator σp is the standard deviation of the portfolio's returns, which measures volatility or total risk. A higher standard deviation means the returns fluctuate more widely, indicating greater uncertainty. By dividing excess return by volatility, the Sharpe ratio normalizes performance across investments with different risk levels, making it possible to compare a conservative bond fund with an aggressive stock portfolio on equal footing.
A Sharpe ratio above 1.0 is generally considered good. A ratio above 2.0 is very good, and above 3.0 is excellent. A negative Sharpe ratio means the investment returned less than the risk-free rate, which indicates the investor would have been better off holding safe government bonds. Most diversified equity portfolios have historical Sharpe ratios between 0.4 and 0.8 over long periods.
The ratio has limitations. It assumes returns are normally distributed, which is not always the case — investments can have fat tails or be skewed. It also treats upside and downside volatility equally, even though investors typically only dislike downside risk. The Sortino ratio addresses this limitation by using only downside deviation in the denominator. Despite these caveats, the Sharpe ratio remains the standard benchmark for evaluating risk-adjusted performance across the investment industry.
Variables
| Symbol | Meaning |
|---|---|
| S | Sharpe ratio (dimensionless) |
| Rp | Portfolio return — annualized return of the investment (%) |
| Rf | Risk-free rate — return on a risk-free asset like Treasury bills (%) |
| σp | Standard deviation of portfolio returns — measures volatility (%) |
Example 1
A mutual fund returned 12% annually with a standard deviation of 15%. The risk-free rate is 3%. What is its Sharpe ratio?
Excess return = 12% − 3% = 9%
S = 9% / 15% = 0.60
Sharpe ratio = 0.60 (reasonable risk-adjusted return)
Example 2
Fund A returned 18% with σ = 25%. Fund B returned 10% with σ = 8%. Risk-free rate is 4%. Which fund performed better on a risk-adjusted basis?
Fund A: S = (18% − 4%) / 25% = 14% / 25% = 0.56
Fund B: S = (10% − 4%) / 8% = 6% / 8% = 0.75
Fund B has the higher Sharpe ratio (0.75 vs 0.56), meaning it delivered more return per unit of risk
When to Use It
The Sharpe ratio is used by investors, fund managers, and financial analysts to evaluate and compare investment performance.
- Comparing the risk-adjusted performance of different mutual funds or ETFs
- Evaluating whether a portfolio manager is generating returns through skill or simply taking on more risk
- Optimizing portfolio allocation to maximize risk-adjusted returns
- Benchmarking hedge fund performance against industry standards
- Deciding between two investments with different return and risk profiles
- Academic finance research and portfolio theory applications