You recently purchased a stock that is expected to earn 10 percent in a booming economy, 4 percent in a normal economy, and lose 4 percent in a recessionary economy. There is a 15 percent probability of a boom, a 70 percent chance of a normal economy, and a 15 percent chance of a recession. What is your expected rate of return on this stock? a. 1.85 percent b. 3.70 percent c. 10.00 percent d. 4.67 percent e. 3.33 percent

Question

Business

Allie Caldwell

15 November, 07:33

You recently purchased a stock that is expected to earn 10 percent in a booming economy, 4 percent in a normal economy, and lose 4 percent in a recessionary economy. There is a 15 percent probability of a boom, a 70 percent chance of a normal economy, and a 15 percent chance of a recession. What is your expected rate of return on this stock? a. 1.85 percent b. 3.70 percent c. 10.00 percent d. 4.67 percent e. 3.33 percent

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Answers (1)

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Jayleen Black · Answer 1

b. 3.70 percent

Explanation:

Expected rate of return of a stock, given probabilities, is calculated by summing up the product of probability of each state occurring by the expected return of the stock should that happen.

Expected rate of return = SUM (probability * return)

Boom; (probability * return) = (0.15 * 0.10) = 0.015 or 1.5%

Normal; (probability * return) = (0.70 * 0.04) = 0.028 or 2.8%

Recession; (probability * return) = (0.15 * - 0.04) = - 0.006 or - 0.6%

Next, sum up the expected return for each state of the economy to find the expected rate of return on this stock;

= 1.5% + 2.8% - 0.6%

= 3.7%

Therefore, the correct answer is choice B.