Question

The market consists of the following stocks. Their prices and number of shares are as follows:

    Stock Price Number of Shares Outstanding

      A $10 100,000

      B 20 10,000

      C 30 200,000

      D 40 50,000

a. What is the aggregate market value if a S&P 500 type of measure of the market (value-weighted average) is used?

b. The price of Stock C doubles to $60. What is the percentage increase in the market if a S&P 500 type of measure of the market (value-weighted average) is used?

c. Repeat question (b) but use a Value Line type of measure of the market (i.e., a geometric average) to determine the percentage increase.

d. Suppose the price of stock B doubled instead of stock C. How would the market have fared using the aggregate measures employed in (b) and (c)? Why are your answers different?

Answer 1

a)

total shares = 360000

total index = 10*100000 + 20*10000 + 30*200000 + 40*50000 = 9200000

avg = 9200000 / 360000 = 25.56

b)

if Stock C = 60,

then index = 10*100000 + 20*10000 + 60*200000 + 40*50000 = 15200000

avg = 15200000 / 360000 = 42.22

% increase = (42.22 - 25.56) / 25.56 = 65.18%

due to higher weight for C, index is increased by 65.22%

c)

current price = (10*20*30*40)^(1/4) = $22.13

After C increases = (10*20*60*40)^(1/4) = $26.32

% change = (26.32 - 22.13) / 22.13 = 18.93%

d)

if Stock B = 40,

then index = 10*100000 + 40*10000 + 30*200000 + 40*50000 = 9400000

avg = 9400000 / 360000 = 26.11

% increase = (26.11 - 25.56) / 25.56 = 2.16%

due to lower weight for C, index is marginally increased by 2.16%

Value line

After B increases = (10*40*30*40)^(1/4) = $26.32

% change = (26.32 - 22.13) / 22.13 = 18.93%

As this does not depend on stocks outstanding, answer wont change from part c