In Question 1-1, I intentionally omitted the initial investment amount. John's initially invested $100 at the beginning of first year. Then, his investment became $50 after losing 50% in the first year. And, based on that $50 his return in the second year was 100% and he ended up having $100 total at the end the second year.

0---------------------1---------------------2

$100 $50 $100

-50% 100%

I am sure everybody now can see that John just got his $100 back after that two-year period. So, intuitively we would say John's return, either the two-year, or the average one-year (annual) return, should be zero.

But, things wouldn't be that obvious when you were just given the return for each year, instead of the whole picture, i.e., seeing John had just got his $100 back.

And, I saw some of you had thought about that when giving your answer by using the Geometric Average Return (GAR), instead of the Arithmetic Average Return (AAR), and came up with the zero average return.

But, my question for you here is the following (Question 1-2):

(1) Why in this case it can come up with an incorrect (and even counter-intuitive) answer when one is using AAR, instead of GAR, as the "average"?

(2) Which average would you be using, AAR or GAR, when you are calculating your average grade in a class?

(3) If the "averages" that you are using for case (1) and case (2) above are different, then what is the factor that determines which average you should be using?

(Question1-1) is already answered, ONLY answer (Question1-2), which has 3 parts