You have observed the following annual returns for Motherboard Inc.: 25%, 15%, -20%, 30%, and -15%.What are the variance and standard deviation of the returns?
A)Variance = 0.00425; standard deviation = 0.06519
B)Variance = 0.06519; standard deviation = 0.00425
C)Variance = 0.05325; standard deviation = 0.23076
D)Variance = 0.23076; standard deviation = 0.05325

Question

Quizplus · Accepted Answer

First, calculate the mean of the returns: (25% + 15% - 20% + 30% - 15%) / 5 = 7%. Then, calculate each year's deviation from the mean, square those deviations, and average them to find the variance: ((25-7)^2 + (15-7)^2 + (-20-7)^2 + (30-7)^2 + (-15-7)^2) / 5 = 0.05325. The standard deviation is the square root of the variance: sqrt(0.05325) = 0.23076.

You Have Observed the Following Annual Returns for Motherboard Inc