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 9200000Related Questions
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