Expected Value and Expected Return

Statistics → Variable → Average → Expected Value

Expectation (Expected Value)
Expected value (or expectation) is simply the average of all possible outcomes.

Example 1. 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,

$\textrm{Expected Value}=\frac{90+110+120+100}{4} \\ = 105$

Expected Return
The expected return can be calculated using the formula

$\textrm{Expected Return}=\frac{\textrm{Expected Value}-\textrm{Initial Value}}{\textrm{Initial Value}}\times 100\%$

Solution (b)

$\textrm{Expected Return}=\frac{\textrm{Expected Value}-\textrm{Initial Value}}{\textrm{Initial Value}}\times 100\% \\ = \frac{105-100}{100}\times 100\% \\ = 5\%$