AM/GM Index

This question got me confused… Geometric Mean gives me D Arithmetic mean gives me C Which should be the choice on the Exam day?? ************ An investor observes the following information about a three-stock market unweighted index: Stock***Shares outstanding***Price on Day 1***Price on Day 2 W***200,000***$20***$18 X***40,000***$40***$50 Y***10,000***$80***$85 Which of the following is closest to the calculated percentage change in the index? a. 0.8% b. 6.3% c. 7.1% d. 9.3% - Dinesh S

I am pretty sure we use geometric mean. as GM is a better indicator of past performance. AM is better for forward looking performance. But, How do you calculate the change in an unweighted index. I am completely blanked out.


from what i recall, i thought gm’s were used for returns, hm’s used when it’s a unit in relation to another i.e dollars per share… and am’s for all else… unless stated otherwise?

why would you have to calculate gm in this question i don’t get it

I thought exactly the same and used GM here… but the CORRECT answer is C and it corresponds to AM. They say that since the geometric mean of returns is always less than the arithmetic mean as geometric mean is downward biased. (So I though, GM is good and provides a much better conservative figure), it seems not the case when we are doing index calculations :frowning: - Dinesh S

For an unweighted index calculation is always Sigma (d2/d1 - 1) ---------------------- # of items in this case ((18/20 - 1) + (50/40-1) + (85/80 - 1) ) / 3 = 7.08% Choice C

My bad…I went back and checked the book, it does not say which one should be used, but mentions that in practice AM is used. But Value line & FT uses GM. I like the way cielito put it…if not otherwise mentioned in the exam, use AM. BTW Dinesh, how did you get D with GM?:slight_smile: shouldn’t GM be 6.12%. I think you took the sq root of multiple of the three returns instead of the cube root since n=3. (been there done that)

wonderful delhirocks, thanks… I really did take the square root instead of the cube root and was wondering if “GM returns are always lower or equal to AM returns” was a rumour that I just picked up from somewhere… -Dinesh S