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The market consists of the following stocks. Their prices and number of shares a

ID: 2754869 • Letter: T

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. 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 is used?

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

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

Explanation / Answer

Answer:a The S&P 500 uses a value-weighted average. The value of the market is

Average prices: $9,200,000/360,000 = $25.56

The price of Stock C doubles to $60.

Average prices: $15,200,000/360,000 = 42.22

Percentage increase: $14.56/$25.56 = 65.18%

Answer:(b) Value Line uses a geometric average. The average prices are

($10 x 20 x 30 x 40) .25 = $22.13

($10 x 20 x 60 x 40) .25 = $26.32

Percentage increase: $4.19/$22.13 = 18.9%

Answer:(c) The new prices and percentage changes:

Value-weighted average:

Average price: $9,400,000/360,000 = $26.11

Percentage increase: $.55/$25.56 = 2.15%

Geometric average: ($10 x 40 x 30 x 40) .25 = $26.32

Percentage increase: $4.19/$22.13 = 18.9%

The value-weighted average places emphasis on the number of shares outstanding while the geometric average is unaffected by the number of shares.

A $10 x 100,000 = 1,000,000 B 20 x 10,000 = 200,000 C 30 x 200,000 = 6,000,000 D 40 x 50,000 = 2,000,000 Total 9200000