Expected return

The expected return (or expected gain) on a financial investment is the expected value of its return (of the profit on the investment). It is a measure of the center of the distribution of the random variable that is the return. It is calculated by using the following formula:

${\displaystyle E[R]=\sum _{i=1}^{n}R_{i}P_{i}}$

where

${\displaystyle R_{i}}$ is the return in scenario ${\displaystyle i}$;

${\displaystyle P_{i}}$ is the probability for the return ${\displaystyle R_{i}}$ in scenario ${\displaystyle i}$; and

${\displaystyle n}$ is the number of scenarios.

The expected rate of return is the expected return per currency unit (e.g., dollar) invested. It is computed as the expected return divided by the amount invested. The required rate of return is what an investor would require to be compensated for the risk borne by holding the asset; "expected return" is often used in this sense, as opposed to the more formal, mathematical, sense above.