Question

A stock had returns of 18.28 percent, -5.40 percent, 20.63 percent, and 8.77 percent for the past four years. What is the variance of the returns?

Answer 1

The variance of the stock returns given by the student is calculated to be 104.78215% squared, following the procedure of finding the mean, calculating the deviations, squaring the deviations, and averaging them.

Step-by-step explanation:

The student is asking how to calculate the variance of stock returns based on the returns from the past four years. To compute the variance, follow these steps:

1. Calculate the mean (average) of the returns.
2. Subtract the mean from each of the individual returns to find the deviation of each return from the mean.
3. Square each of these deviations.
4. Compute the average of these squared deviations; this is the variance of the returns.

Here is how to apply these steps:

1. The mean is (18.28 + (-5.40) + 20.63 + 8.77) / 4 = 10.57%.
2. The deviations are 18.28 - 10.57 = 7.71%, -5.40 - 10.57 = -15.97%, 20.63 - 10.57 = 10.06%, and 8.77 - 10.57 = -1.80%.
3. Square the deviations to get 59.4841, 255.2009, 101.2036, and 3.24 respectively.
4. The variance is (59.4841 + 255.2009 + 101.2036 + 3.24) / 4 = 104.78215% squared.

The variance of the stock returns is 104.78215% squared.