Question

You invest in a stock for 4 years and achieve the following rates of return. The arithmetic average return over the 4 year period is 12.01%. What is the variance of returns?

year 1- 13.76%
year 2- 8.48%
year 3- 23.19%
year 4- 2.62%

Answer 1

To calculate the variance of returns, find the average return for each year and subtract the average return over the 4-year period from each year's return. Square these differences and find their average. The variance of returns is 28.76%.

Step-by-step explanation:

To calculate the variance of returns, we need to find the average return for each year and then subtract the average return over the 4-year period from each individual year's return. We square each of these differences and then find the average of these squared differences. Here are the calculations:

1. Year 1: (13.76% - 12.01%)^2 = 3.09%
2. Year 2: (8.48% - 12.01%)^2 = 11.79%
3. Year 3: (23.19% - 12.01%)^2 = 26.65%
4. Year 4: (2.62% - 12.01%)^2 = 71.52%

To find the variance, we take the average of these squared differences:

(3.09% + 11.79% + 26.65% + 71.52%) / 4 = 28.76%