Question

Suppose a stock has generated the following annual returns: 11.4%,

-7.9% and 5.4%. What was the standard deviation of its returns?
Answer in percent, rounded to two decimal places (e.g., 4.32% =
4.32)

Answer 1

The standard deviation of the stock's returns is 9.88%, calculated by averaging the squared differences between each year's return and the mean, then taking the square root of that average.

Step-by-step explanation:

To calculate the standard deviation of the stock's returns, we first find the mean (average) return. Adding the returns (11.4%, -7.9%, 5.4%) and dividing by the number of years (3) gives us a mean of (11.4 - 7.9 + 5.4) / 3 = 3.0%. Next, we calculate the squared differences from the mean for each year: (11.4 - 3.0)², (-7.9 - 3.0)², and (5.4 - 3.0)². These are 70.56, 118.81, and 5.76 respectively.

We then average these squared differences by adding them together and dividing by the number of observations minus one (which is 2 for three observations): (70.56 + 118.81+ 5.76) / 2 = 97.565. Taking the square root of this average gives us the standard deviation: √97.565 = 9.877. Therefore, the standard deviation of the stock's returns is 9.88%, rounded to two decimal places.

Answer 2

To calculate the standard deviation of the stock's annual returns, use the formula: Standard Deviation = SQRT(SUM((X - Mean)^2) / (n - 1)). Calculate the mean of the returns, calculate the squared differences from the mean, sum the squared differences, divide by (n - 1), and take the square root of the result.

Step-by-step explanation:

To calculate the standard deviation of the stock's annual returns, we can use the formula:

Standard Deviation = SQRT(SUM((X - Mean)^2) / (n - 1))

Where X represents each individual return, Mean is the average return, and n is the number of returns.

Using the given returns: 11.4%, -7.9%, and 5.4%, we can calculate the standard deviation as follows:

1. Calculate the mean: (11.4 + -7.9 + 5.4) / 3 = 2.97%
2. Calculate the squared differences from the mean: (11.4 - 2.97)^2, (-7.9 - 2.97)^2, (5.4 - 2.97)^2
3. Sum the squared differences: (139.24 + 128.41 + 2.89) = 270.54
4. Divide the sum by (n - 1): 270.54 / 2 = 135.27
5. Take the square root of the result: SQRT(135.27) = 11.63%

Therefore, the standard deviation of the stock's returns is approximately 11.63%.