The Sharpe ratio is a measure of risk-adjusted return in finance. It was developed by economist William F. Sharpe in 1966 as a way to compare the performance of an investment, such as a security or portfolio, to a risk-free asset, after adjusting for its risk. The ratio is widely used to evaluate the performance of portfolio or mutual fund managers.
The Sharpe ratio is calculated by taking the difference between the returns of the investment and the risk-free return, and dividing it by the standard deviation of the investment returns. The numerator represents the excess returns over a period of time, while the denominator measures the volatility and risk of the investment. A higher Sharpe ratio indicates better risk-adjusted returns, with the ideal scenario being high returns and low volatility.
The formula for the Sharpe ratio is:
$$ Sharpe\ Ratio = \frac{Rx - Rf}{StdDev\ Rx} $$
Where:
- $$Rx$$ is the return of the investment
- $$Rf$$ is the risk-free rate of return
- $$StdDev\ Rx$$ is the standard deviation of the investment returns.
