Question

Suppose there are only 3 stocks in an index with the following information:

Stock	Shares Outstanding	Beginning Share Price	Ending Share Price
A	4,000	$22	$15
B	1,000	$47	$60
C	3,000	$32	$37

a) Calculate the value-weighted return on the index.

b) Calculate the price-weighted return on the index.

c) Suppose Company B announces a 4:1 stock split prior to the end of the year, what is the new price-weighted return without adjustment of the index divisor? (1 mark)

d) What would be the new index divisor after the stock split?

Answer 1

	a	b	c	d	e
Stock	Shares Outstanding	Beginning Share Price	Ending Share Price	Market Capitalization at the beginning =a*b	Market Capitalization at the end =a*c
A	4,000	$               22	$               15	$           88,000	$           60,000
B	1,000	$               47	$               60	$           47,000	$           60,000
C	3,000	$               32	$               37	$           96,000	$         111,000
			Total	$         231,000	$         231,000
		Change in Market Value =		Nil
	Ans a.	Value weighted return=		0%

		a	b	c
	Stock	Shares Outstanding	Beginning Share Price	Ending Share Price
	A	4,000	$               22	$               15
	B	1,000	$               47	$               60
	C	3,000	$               32	$               37
		Total	$             101	$             112
		Average Price	$          33.67	$         37.33
		Increase in average Price=		$           3.67
Ans .b		Price Weighted return=3.67/33.67=			10.89%

		a	b	c
	Stock	Shares Outstanding at the beginning	Beginning Share Price	Ending Share Price
	A	4,000	$               22	$               15
	B	1,000	$               47	$               15	After split of 4:1 share price becomes =60/4 =15
	C	3,000	$               32	$               37
		Total	$             101	$               67
		Average Price	$          33.67	$         22.33
		Decrease in average Price=		$       (11.33)
Ans c		Return of Price weighted Index=			-33.66%

Stock	Shares Outstanding at the beginning	Beginning Share Price	Ending Share Price
A	4,000	$               22	$                  15
B	1,000	$               47	$                  15	After split of 4:1 share price becomes =60/4 =15
C	3,000	$               32	$                  37
	Total	$             101	$                  67
	Average	$         33.67
Ans d.	New Index Divisor=67/33.67=1.99