Question

A stock ABC can be in one of the four economic states in 2020. The return for each state is shown below. The probability of each state is the same = 25%:

• Good state of the economy will cause the stock to return 35%
• Normal state of the economy will cause the stock to return 15%
• A bad state of the economy will cause the stock to be flat, return 0%
• In case of a severe crash in the economy, the stock will lose 20%

What is the stock’s average return and standard deviation?

Answer 1

Probability of Good State = 0.25
Probability of Normal State = 0.25
Probability of Bad State = 0.25
Probability of Severe Crash = 0.25

Expected Return in Good State = 0.35
Expected Return in Normal State = 0.15
Expected Return in Bad State = 0.00
Expected Return in Severe Crash = -0.20

Average Return = 0.25 * 0.35 + 0.25 * 0.15 + 0.25 * 0.00 + 0.25 * (-0.20)
Average Return = 0.075 or 7.50%

Variance = 0.25 * (0.35 - 0.075)^2 + 0.25 * (0.15 - 0.075)^2 + 0.25 * (0.00 - 0.075)^2 + 0.25 * (-0.20 - 0.075)^2
Variance = 0.040625

Standard Deviation = (0.040625)^(1/2)
Standard Deviation = 0.2016 or 20.16%