Question

Please show all your work and reasonings!

1). Consider the following information for three stocks Price per share 12/31/2003 $65.75 Price per shareDividends per Total shares outstanding 150 60 125 Stock 3/31/2004 $48.25 $28.125 $150.25 share $0.00 $1.25 $2.00 $24.125 $112.00 a) Calculate the value-weighted, equal-weighted, and price weighted index weights of stocks A, B and C at 12/31/2003 b) Calculate the holding period return on stocks A, B, and C in the first quarter of 2004 c) Calculate the value-weighted, equal-weighted, and price-weighted index returns on a portfolio of stocks A, B, and C in the first quarter of 2004?

Answer 1

1 a) Value Weighted: In Value weighted, a weight is assigned to each company based on the company's value. Investors value a company based on its market capitalization, which is the price of its stock times the number of shares outstanding.

Stock	Price Per Share	Shares Outstanding	Market Capitalization	Weights
A	65.75	150	65.75*150 = 9862.5	(9862.5/25310)* 100= 38.97%
B	24.125	60	24.125*60 = 1447.5	(1447.5/25310)* 100= 5.72%
C	112	125	112*125= 14000	(14000/25310)* 100= 55.31%

Equal Weighted: In equal weighted, weights of all companies are equally, regardless of size. Here, there are three companies in the stock universe, and therefore each gets a one- third weight in the index.   

Price Weighted: In Price Weighted, the weight of a component is calculated by dividing the price of a security by the sum of prices of all index components.

Stock	Price Per Share	Weights
A	65.75	((65.75)/(65.75+24.125+112))*100 = 32.57%
B	24.125	((24.125)/(65.75+24.125+112))*100 = 11.95%
C	112	((112)/(65.75+24.125+112))*100 = 55.48%

1b) Holding Period Return is the change in value of an investment, asset or portfolio over a particular period.

• HPR = (End Value - Initial Value) / Initial Value

• Stock	Price Per Share(in $) 12/31/2003	Price per Share(in $) 3/31/2004	Holding Period Return
  A	65.75	48.25	((48.25-65.75)/65.75)* 100= -26.62%
  B	24.125	28.125	((28.125-24.125)/24.125)* 100= 16.58%
  C	112	150.25	((150.25-112)/112)* 100= 34.15%

1c) Value Weighted index return:

• Total Market Capitalisation 0n 12/31/2003 is $(65.75*150 + 24.125*60 +112*125) = $25310
• Total Market Capitalisation 0n 03/31/2004 is $(48.25*150 + 28.125*60 +150.25*125) = $27706.25

Value Weighted Index return = ((Total Market Cap on 03/31/2004- Total Market Cap on 12/31/2003)/Total Market Cap on 12/31/2003)*100 = ((27706.25-25310)/25310)*100 = 9.467%

Equal Weighted index return: The return of an equal weighted index over a given period is calculated as a simple average of the returns of the index stocks

=( -26.62%+16.58%+34.15%)/3 = 8.03%

Price Weighted index return:

• The price weighted index as of 12/31/2003 is (65.75+ 24.125+112)/3 = 201.875
• The price weighted index as of 03/31/2004 is $(48.25 + 28.125 +150.25) = 226.625

The price weighted return =( (226.625/201.875)-1)*100 = 12.26%