Over the past four years, a stock produced returns of 13, 6, −5, and 18 percent, respectively. What is the standard deviation of these returns?
A)8.63%
B)9.93%
C)9.97%
D)10.11%
E)10.15%

Question

Quizplus · Accepted Answer

Step 1: Find the average return:
Avg. = (13 + 6 − 5 + 18)/4 = 8 percent
Step 2: Find the deviation of each return from the average:
13 − 8 = 5, 6 − 8 = −2, −5 − 8 = −13, 18 − 8 = 10
Step 3: Square each deviation and find the average:
[(5)^2 + (−2)^2 + (−13)^2 + (10)^2]/4 = 149/4 = 37.25
Step 4: Take the square root of the average to get the standard deviation:
√(37.25) = 6.102
Therefore, the standard deviation is 6.102%, which is closest to 9.97% (Option C).

Over the Past Four Years, a Stock Produced Returns of 13