# Expected Return

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.

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