Question

1. The following three defense stocks are to be combined into a stock index in January 2016 (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 (millions)		1/1/16			1/1/17			1/1/18
   Douglas McDonnell	350		$	65		$	69		$	81
   Dynamics General	450			25			19			33
   International Rockwell	210			54			43			57

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

   Index Value:

   b. What is the rate of return on this index for the year ending December 31, 2016? For the year ending December 31, 2017? (A negative value should be indicated by a minus sign. Do not round intermediate calculations. Enter your answers as a percent rounded to 2 decimal places.)

   2016 Return: %

   2017 Return: %

Answer 1

a). Index Value(2016) = [$\sum_{i=1}^{n}$(Price_i * Shares_i)] / Scales Factor

= [(65 * 350) + (25 * 450) + (54 * 210)] / 10

= [22,750 + 11,250 + 11,340] / 10 = 45,340 / 10 = 4,534.00

b). Index Value(2017) = [$\sum_{i=1}^{n}$(Price_i * Shares_i)] / Scales Factor

= [(69 * 350) + (19 * 450) + (43 * 210)] / 10

= [24,150 + 8,550 + 9,030] / 10 = 41,730 / 10 = 4,173.00

Return(2016) = [Index Value(2017) - Index Value(2016)] / Index Value(2016)

= [4,173 - 4,534] / 4,534 = -361 / 4,534 = -0.0796, or -7.96%

Index Value(2018) = [$\sum_{i=1}^{n}$(Price_i * Shares_i)] / Scales Factor

= [(81 * 350) + (33 * 450) + (57 * 210)] / 10

= [28,350 + 14,850 + 11,970] / 10 = 55,170 / 10 = 5,517.00

Return(2017) = [Index Value(2018) - Index Value(2017)] / Index Value(2017)

= [5,517 - 4,173] / 5,517 = 1,344 / 4,534 = 0.2964, or 29.64%