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.

a. Calculate the initial value of the index if a value-weighting scheme is used.

b. What is the rate of return on this index for the year ending December 31, 2013? For the year ending December 31, 2014?

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.

Price Shares (in millions) 1/1/13 1/1/14 1/1/15 Douglas 180 $60 $64 $77 Dynamics 325 68 64 78 International 370 97 86 100

a. Calculate the initial value of the index if a value-weighting scheme is used.

b. What is the rate of return on this index for the year ending December 31, 2013? For the year ending December 31, 2014?

Explanation / Answer

A. 1/1/13: Index value = (60 + 68 + 97) / 3 = 75

B. 1/1/14: Index value = (64 + 64 + 86) / 3 =71.33

2013 return = (75 – 71.33) / 75 = 4.89%

1/1/15: Index value (77 +78 +100) / 3 = 84

2014 return = (84 – 71.33) / 84 = 15.08%

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