For the past three years, Acme has generated the following sample returns on equity (ROE): 4%, 10%, and 1%. What is the sample variance of the ROE over the last three years?
Why is the correct answer 21.0(%^2) and not 21.0% ?
What is the significance of having the % to the power of two?
Percent (or %) means “divided by 100”.
The variance is 0.0021, or (21 ÷ 100) ÷ 100 or 21 ÷ 1002, or 21%2. It’s not 21%, which is 0.21, which is not 0.0021.
Note that the sample standard deviation is 4.5826%, so the sample variance is (4.5826%)2 = 4.58262%2 = 21%2.
Note than in practice, nobody really writes %2. (Well, I do, and a student of mine several years ago did, but nobody else really does.) The true point is that whatever the variance is, it most certainly isn’t 21%.
Perfect explanation, thank you! Once you made me step back and use numeracy, the variance must be smaller than the S.D.
Also, excellent information in your last paragraph. Thanks again!
My pleasure.