Question

Calculate the standard deviation for a common stock with annual returns of 20%,25%,-10%,10%, and -20%.

Answer 1

To calculate the standard deviation for a common stock with annual returns of 20%, 25%, -10%, 10%, and -20%, sum up the returns, calculate the mean, find the deviations from the mean, square each deviation, calculate the mean of the squared deviations, and finally take the square root of the mean of the squared deviations.

Step-by-step explanation:

To calculate the standard deviation for a common stock with annual returns of 20%, 25%, -10%, 10%, and -20%, follow these steps:

1. Calculate the mean of the returns by summing them up and dividing by the total number of returns: (20 + 25 - 10 + 10 - 20) / 5 = 5%.
2. Calculate the deviation of each return by subtracting the mean from each return: 20% - 5%, 25% - 5%, -10% - 5%, 10% - 5%, and -20% - 5%.
3. Square each deviation: (20% - 5%)^2, (25% - 5%)^2, (-10% - 5%)^2, (10% - 5%)^2, and (-20% - 5%)^2.
4. Calculate the mean of the squared deviations by summing them up and dividing by the total number of returns: (175 + 400 + 225 + 25 + 525) / 5 = 270.
5. Take the square root of the mean of the squared deviations to find the standard deviation: √(270) ≈ 16.43%.