Question

Consider the three stocks in the following table.

Stock	Initial Price	Final Price	Shares Outstanding (millions)
A	$80	$100	100
B	$50	$30	300
C	$120	$125	100

1. Calculate the rate of return on an equally weighted index of the three stocks.

2. Calculate the rate of return on a price-weighted index of the three stocks.

3. Calculate the rate of return on a market-weighted index of the three stocks.

Answer 1

Please see the table below:

Stock	Initial Price	Final Price	Shares Outstanding (millions)	Return	Market value initially	Market value finally
	IP	FP		FP / IP - 1	N x IP	N x FP
A	$80	$100	100	25.00%	$8,000	$10,000
B	$50	$30	300	-40.00%	$15,000	$9,000
C	$120	$125	100	4.17%	$12,000	$12,500
Average	$83.33	$85		-3.61%
Total					$35,000	$31,500

Part (1)

The return on an equally weighted index of the three stocks = average of the return of the individual stocks =  - 3.61%

Part (2)

Price weighted index initially = average of initial price = $ 83.33

Price weighted index finally = average of final price = $ 85

Hence, return of price weighted index = 85 / 83.33 - 1 = 2.00%

Part (3)

The rate of return on a market-weighted index of the three stocks = Market value finally / market value initially - 1 = 31,500 / 35,000 - 1 = -10.00%