What is Expected Return?

Legal Definition
The expected return (or expected gain) refers to the value of a random variable one could expect if the process of finding the random variable could be repeated an infinite number of times. Formally, it gives the measure of the center of the distribution of the variable.

It is calculated by using the following formula:

Although this is what one expects the return to be, this only refers to the long-term average. In the short term, each instance of the event can be very different. As denoted by the above formula, simply take the probability of each possible return outcome and multiply it by the return outcome itself. For example, if one knew a given investment had a 50% chance of earning a return of 10, a 25% chance of earning 20 and a 25% chance of earning –10, the expected return would be equal to 7.5:

Although this is what one expects the return to be, there is no guarantee that it will be the actual return.
-- Wikipedia
Legal Definition
The method of predicting the likelihood, on average, of a gain from investing in a particular asset. Varying factors, representing market conditions and perceived asset worth, varies the predicted return.