Equity stock indices

CFA Level I Equities
#1

Question from Schweser:

A stock index consists of two stocks:

Company A has 50 shares outstanding valued at $2 each

Company B has 10 shares outstanding valued at $10 each

The price-weighted index is 6, and the value-weighted index is 100.

If the price of company A’s stock increases to $4 per share and company B’s stock splits 2-for-1 and is priced at $5, the value of the price-weighted and value-weighted index are:

a) Price-weighted: 7; Value-weighted:150

b) Price-weighted: 7; Value-weighted:125

c) Price-weighted: 4.5; Value-weighted:150

The answer is a) but what I don’t understand is why the divisor on the price-weighted index doesn’t change after the stock split. The schweser answer says that “a price-weighted index is not affected by a [stock] split” which is completely contradictory to the CFAI text. Can someone please explain?

#2

The index value doesn’t change, but the divisor has to. Our pre-split divisor was 2. So, (2+10)/2 =6. Stock A increased in price, so now you have (4+10)/2=7. To account for the split, we need to satisfy the equation (4+5)/X = 7, because in the absence of the split, our index would be at 7. So the new divisor for the price weighted index is 9/7=1.2857… That is a really terrible way of showing the difference between a price weighted and value weighted index.

#3

Not sure I completely understand your explanation. S2000Magician! Can you shed some more light on this please?