Question

A stock had returns of 11 percent, -18 percent, -21 percent, 20 percent, and 34 percent over the past five years. what is the standard deviation of these returns?

a. 18.74 percent
b. 20.21 percent
c. 20.68 percent
d. 24.01 percent
e. 23.49 percent

Answer 1

The standard deviation of the returns is 21.5 percent.

Step-by-step explanation:

To calculate the standard deviation of the returns, we need to follow these steps:

1. Calculate the mean of the returns
2. Subtract the mean from each return to find the deviations
3. Square the deviations
4. Calculate the mean of the squared deviations
5. Take the square root of the mean of the squared deviations

Let's perform these steps:

1. The mean of the returns is (11 - 18 - 21 + 20 + 34) / 5 = 5.2 percent
2. The deviations are (11 - 5.2) = 5.8, (-18 - 5.2) = -23.2, (-21 - 5.2) = -26.2, (20 - 5.2) = 14.8, (34 - 5.2) = 28.8 percent
3. The squared deviations are 33.64, 538.24, 685.44, 219.04, 829.44 percent squared
4. The mean of the squared deviations is (33.64 + 538.24 + 685.44 + 219.04 + 829.44) / 5 = 461.96 percent squared
5. The square root of the mean of the squared deviations is sqrt(461.96) = 21.5 percent

Therefore, the standard deviation of the returns is 21.5 percent.

Answer 2

1.5 is the answer for this question