Question

You are given the following information regarding prices for a sample of stocks.

			PRICE
Stock	Number of Shares		T		T + 1
A	2,700,000		$64		$78
B	14,000,000		26		41
C	26,000,000		22		28

1. Construct an equal-weighted index by assuming $1,000 is invested in each stock. What is the percentage change in wealth for this portfolio? Do not round intermediate calculations. Round your answer to two decimal places.

     %

2. Compute the percentage of price change for each of the stocks. Do not round intermediate calculations. Round your answers to two decimal places.

   Stock A:   %

   Stock B:   %

   Stock C:   %

   Compute the arithmetic mean of these percentage changes. Do not round intermediate calculations. Round your answer to two decimal places.

     %

3. Compute the geometric mean of the percentage changes in Part b. Do not round intermediate calculations. Round your answer to two decimal places.

     %

Answer 1

Answers:

a)

Stock	Price	Amount Invested	No. of Shares	Value of T+1
T	T+1
A	$64	$78	$1,000	15.625	$1,218.75
B	$26	$41	$1,000	38.461	$1,576.92
C	$22	$28	$1,000	45.45	$1,272.72
	Total	$3,000	Total	4,068.40

No. of Shares calculation:

Amount Invested(A) = $1000/$64 = 15.625

Amount Invested(B) = $1000/$26 = 38.461

Amount Invested(C) = $1000/$22 = 45.45

Change of Wealth = 4,068.40 – 3,000/3,000 = 0.356 = 35.6%

Hence, percentage change of wealth is 35.6%

b)

Stock	Price	Change %
T	T+1
A	$64	$78	21.875
B	$26	$41	57.69
C	$22	$28	27.27

For Stock A = $78 -$64/$64 = 21.875%

For Stock B = $41 -$26/$26 = 57.69%

For Stock C = $28 -$22/$22 = 27.27%

Arithmetic Mean = Sum of % Changes in all Stocks/No. of Stocks

                            = 21.875% +57.69% +27.27%/ 3 = 35.61%

                           

c)

Stock	Price	Change %
T	T+1
A	$64	$78	21.875
B	$26	$41	57.69
C	$22	$28	27.27

Geometric Mean = [(1+Ra)*(1+Rb)*(1+Rc)] ^(1/No. of Stock) – 1

                            = (1+21.875%) * (1+57.69%) * (1+27.27%) ^ (1/3) – 1

                             = 2.4459^ (1/3) – 1

                            = 0.347347 = 34.73%