Question

Over the past six years, a stock had annual returns of 14 percent, -3 percent, 8 percent, 21 percent, -16 percent, and 4 percent, respectively. What is the standard deviation of these returns?

11.27 percent
13.05 percent
13.59 percent
15.08 percent
14.40 percent

Answer 1

The standard deviation of the stock's annual returns is calculated by finding the mean return, computing the squared differences from the mean for each year, then finding the variance and taking its square root.

Step-by-step explanation:

To find the standard deviation of the stock's annual returns, we need to follow a step-by-step process. The returns over the past six years are 14%, -3%, 8%, 21%, -16%, and 4%.

1. First, calculate the mean (average) return: (14 - 3 + 8 + 21 - 16 + 4) / 6 = 28 / 6 = 4.67%.
2. Next, find the squared differences from the mean for each year's return, and then sum up these squared differences.
3. The variance is calculated by dividing the sum of squared differences by the number of data points minus one (n-1).
4. Finally, take the square root of the variance to get the standard deviation.

After performing these calculations, you would find the standard deviation of these returns. The correct answer must match one of the options provided, ensuring the calculated value is rounded to two decimal places.