The following three defense stocks are to be combined into a stock index in Janu

Question

The following three defense stocks are to be combined into a stock index in January 2013 (perhaps a portfolio manager believes these stocks are an appropriate benchmark for his or her performance). Assume the index is scaled by a factor of 10 million; that is, if the total value of all firms in the market is $5 billion, the index would be quoted as 500.

Calculate the initial value of the index if a value-weighting scheme is used. (Round your answer to 2 decimal places.)

What is the rate of return on this index for the year ending December 31, 2013? For the year ending December 31, 2014? (Negative values should be indicated by a minus sign. Do not round intermediate calculations. Enter your answers as a percent rounded to 2 decimal places. Omit the "%" sign in your response.)

The following three defense stocks are to be combined into a stock index in January 2013 (perhaps a portfolio manager believes these stocks are an appropriate benchmark for his or her performance). Assume the index is scaled by a factor of 10 million; that is, if the total value of all firms in the market is $5 billion, the index would be quoted as 500.

Explanation / Answer

a. Value of Index at the beginning:

Douglas McDonnell = 340,000,000 x $103 = $35,020,000,000
Dynamics General = 450,000,000 x $45 = $20,250,000,000
International Rockwell = 410,000,000 x $74 = $30,340,000,000

Value of Index = ($35,020,000,000 + $20,250,000,000 + $30,340,000,000) / $10,000,000 = 8,561

b. Value of Index at the beginning of 2014:

Douglas McDonnell = 340,000,000 x $106 = $36,040,000,000
Dynamics General = 450,000,000 x $39 = $17,550,000,000
International Rockwell = 410,000,000 x $63 = $25,830,000,000

Value of Index = ($36,040,000,000 + $17,550,000,000 + $25,830,000,000) / $10,000,000 = 7,942

Return in 2013 = (7,942 – 8,561)/8,561 = -7.23%

Value of Index at the beginning of 2015:

Douglas McDonnell = 340,000,000 x $118 = $40,120,000,000
Dynamics General = 450,000,000 x $53 = $23,850,000,000
International Rockwell = 410,000,000 x $79 = $32,390,000,000

Value of Index = ($40,120,000,000 + $23,850,000,000 + $32,390,000,000) / $10,000,000 = 9,636

Return in 2014 = (9,636 – 7,942)/7,942 = 21.33%

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