Expectation

Expected value or expectation is simply the average of all possible outcomes.

Example The price of a stock is $100. And, there are equal chances that after one year it could be $90, $110, $120 or remains the same.
(a) What is the expected value of the stock?
(b) What is the expected return from the stock?
Solution
(a) As expected value is the average of all possible outcomes. Hence,

(b) As, we have calculated the expected value. So, we can find the expected return as in example 6,

The prices $90, $110, $120 and the same price will generate return of -10%, 10%, 20% and 0% respectively. So, the expected return can also be calculated as average of percentages, i.e.

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