Next year, we will be in a boom, bust, or normal state with 25%, 25% and 50% probabilities respectively. Apple will return 15%, -22% and 7% in each state (again respectively). a) What is the expected return for Apple next year?
b) What is the standard deviation of returns for Apple next year?

Explanation:

a. Expected return:

This will be a weighted average of the returns in different states.

= (25% * 15%) + (25% * -22%) + (50% * 7%)

= 1.75%

b. Standard deviation:

= √ Variance

= √(25% * (15% - 1.75%)²) + (25% * (-22% - 1.75%)²) + (50% * (7% - 1.75%)²)

= √0.01986875

= 14.10%

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