MathLiveSharpe ratio
The Sharpe ratio gives the expected excess return of an investment over a benchmark, divided by the volatility of that excess return. It is used to compare how much reward an investment earns for each unit of risk taken.
S_a = \frac{E[R_a - R_b]}{\sigma_a} = \frac{E[R_a - R_b]}{\sqrt{\mathrm{var}[R_a - R_b]}}What the symbols mean
| Sharpe ratio of investment a (dimensionless) | |
| return of investment a | |
| return of the benchmark or risk-free asset | |
| expected value of the excess return of a over b | |
| standard deviation of the excess return, i.e. its volatility | |
| variance of the excess return |
About this formula
- FieldEconomics and finance
- TopicPortfolio performance measurement
- LevelUniversity
- Also calledSharpe index, reward-to-variability ratio, Sharpe measure, excess return per unit of risk, risk premium to volatility ratio
- SourceWikidata Q1501898
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