Question

The last four years of returns for a stock are as shown​ here:

Year 1-4%
Year 2-28%
Year 3-12%
Year 4-4%
a. What is the average annual​ return?
b. What is the variance of the​ stock's returns?
c. What is the standard deviation of the​ stock's returns?
Note​: Notice that the average return and standard deviation must be entered in percentage format. The variance must be entered in decimal format.

Answer 1

The average annual return is 12%. The variance of the stock's returns is 62. The standard deviation of the stock's returns is approximately 7.87%.

Step-by-step explanation:

To find the average annual return, you need to add up all the returns and divide by the number of years. In this case, the returns are 4%, 28%, 12%, and 4%. Adding them up gives you 48%. Dividing by 4 (the number of years) gives you an average of 12%.

To find the variance of the stock's returns, you first need to find the average return (which we already calculated as 12%). Then, for each return, subtract the average return, square the result, and add them all up. In this case, the calculations are: (4% - 12%)^2 + (28% - 12%)^2 + (12% - 12%)^2 + (4% - 12%)^2. Adding these up gives you 248. Dividing by 4 (the number of returns) gives you a variance of 62.

To find the standard deviation, you take the square root of the variance. So the standard deviation of the stock's returns is the square root of 62, which is approximately 7.87%.