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ABC Corporation stock is expected to return 25 percent in a boom, 12 percent in a...

ABC Corporation stock is expected to return 25 percent in a boom, 12 percent in a normal economy, and -13 percent in a recession. The probabilities of a boom, normal economy and a recession are 7 percent, 90 percent and 3 percent, respectively. What is the standard deviation of the returns on this stock?

2.15 percent

19.54 percent

5.53 percent

6.23 percent

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Answer #1

Answer is 5.53%

Probability of Boom = 0.07
Return during Boom = 0.25
Probability of Normal = 0.90
Return during Normal = 0.12
Probability of Recession = 0.03
Return during Recession = -0.13

Expected Return = 0.07 * 0.25 + 0.90 * 0.12 + 0.03 * (-0.13)
Expected Return = 0.1216 or 12.16%

Variance = 0.07 * (0.25 - 0.1216)^2 + 0.90 * (0.12 - 0.1216)^2 + 0.03 * (-0.13 - 0.1216)^2
Variance = 0.00305544

Standard Deviation = (0.00305544)^(1/2)
Standard Deviation = 0.0553 or 5.53%

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