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.

Read more about Expected ReturnDiscrete Scenarios, Continuous Scenarios, Alternate Definition

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