Price weighted indices

CFA Level I Equities
#1

Question from Schweser:

What is the price-weighted index of the following three stocks?

As of December 31, 2001 Company Stock Price__Shares Outstanding A $50 10,000 B $35 20,000 C $110 30,000

a) 65

b) 75

c) 80

Why is the answer a? I thought price weighting meant that the index value of each security would be Price(X)/Price(Total) so we would get

(50/195)*50 = 12.82

(35/195)*35 = 6.28

(110/195)*110 = 62.05

Total index value = 12.82+6.28+62.05 = 81.15 making c the closest answer. Can anyone please explain?

#2

I’m really stuck on this, any help would be appreciated!

#3

Think of price weighting as buying one share of each stock. Thus, the average would be:

(50 + 35 + 110) / 3 = 195 / 3 = 65.

If the constituent stocks undergo stock splits, undergo reverse stock splits, or receive stock dividends, the divisor (here, 3) will be adjusted so that the split, reverse split, or dividend does not change the index value.

If one of the constituent stocks is replaced with another stock, the divisor will be adjusted so that the substitution does not change the index value.