The expected return (or expected gain) is the expected value of a random variable usually representing a gain, i.e. the weighted-average outcome in gambling, probability theory, economics or finance.
It is calculated by using the following formula:
- E(R) = Sum: probability (in scenario i) × the return (in scenario i) .
How do you calculate the average of a probability distribution? 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 you knew a given investment had a 50% chance of earning a 10 return, a 25% chance of earning 20 and a 25% chance of earning -10, the expected return would be equal to 7.5:
- E(R) = 0.5 × 10 + 0.25 × 20 + 0.25 × (-10) = 7.5 .
Although this is what you expect the return to be, there is no guarantee that it will be the actual return.
Read more about Expected Return: Discrete Scenarios, Continuous Scenarios, Alternate Definition
Famous quotes containing the words expected and/or return:
“What strikes me as odd now is how much my father managed to get across to me without those heart-to-hearts which I’ve read about fathers and sons having in the study or in the rowboat or in the car.... Somehow I understood completely how he expected me to behave, in small matters as well as large, even though I can’t remember being given any lectures about it beyond the occasional, undramatic “You might as well be a mensch.””
—Calvin Trillin (20th century)
“At twelve, the disintegration of afternoon
Began, the return to phantomerei, if not
To phantoms. Till then, it had been the other way:
One imagined the violet trees but the trees stood green,
At twelve, as green as ever they would be.
The sky was blue beyond the vaultiest phrase.”
—Wallace Stevens (1879–1955)