Question

A stock had returns of 6 percent, -8 percent, 2 percent, and 14 percent over the past 4 years. What is the standard deviation of this stock for the past four years?

Answer 1

The standard deviation of the stock returns of 6%, -8%, 2%, and 14% over the past four years is approximately 7.92%.

Step-by-step explanation:

To calculate the standard deviation of the given stock returns over the past four years, we need to follow several steps. First, we find the mean (average) return of the stock. Then we calculate the variance by finding the squared differences between each return and the mean, averaging those squared differences, and finally we take the square root of the variance to get the standard deviation.

The returns over the past four years were 6%, -8%, 2%, and 14%. To compute the mean:

• (6 - 8 + 2 + 14) / 4 = 3.5%

Next, we compute the squared differences from the mean:

• (6 - 3.5)^2 = 6.25
• (-8 - 3.5)^2 = 132.25
• (2 - 3.5)^2 = 2.25
• (14 - 3.5)^2 = 110.25

The variance is the average of these squared differences:

• (6.25 + 132.25 + 2.25 + 110.25) / 4 = 62.75

Finally, the standard deviation is the square root of the variance:

• sqrt(62.75) ≈ 7.92%

Therefore, the standard deviation of the stock for the past four years is approximately 7.92%.