Risk-Adjusted Return
Investors care about both expected returns and risk. All else being equal, given the choice between two investments with the same level of risk, investors will prefer the investment with a higher expected return. In a similar way, all else being equal, given the choice between two investments with the same expected return, investors will prefer the investment with a lower level of risk. This leads naturally to the idea of a risk-adjusted return.
We would like some measure, such as
[Risk-Adjusted Return] = f(Return) / g(Risk)
where f(...) and g(…) are functions to be determined. Our risk-adjusted return increases when f(Return) increases, or when g(Risk) decrease. On of the most popular measure of risk-adjusted returns is the Sharpe ratio. For the Sharpe ratio, f(Return) is the average excess return, and g(Risk) is the standard deviation of the excess returns.
While the Sharpe ratio is a popular choice, arguments can be made for other measure. For example, if we are comparing two investments with very different skewness, we might make g(Risk) a function of both standard deviation and skewness.