Question

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	360		$	65		$	69		$	83
Dynamics General	450			52			46			60
International Rockwell	170			81			70			86

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

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.)

Answer 1

(a) Value of stock = Number of shares * Price of share

Value on 1/1/16

Value of Douglas McDonnell = 360*65 = $23400m

Value of Dynamics General = 450*52 = $23400m

Value of International Rockwell = 170*81 = $13770

Total Value = 23400 + 23400 + 13770 = $60570m

Value of index = Total Value / 10m = 60570/10 = $6057

(b) Value on 1/1/17

Value of Douglas McDonnell = 360*69 = $24840m

Value of Dynamics General = 450*46 = $20700m

Value of International Rockwell = 170*70 = $11900m

Total Value = 24840 + 20700 + 11900 = $57440m

Value of index = Total Value / 10m = 57440/10 = $5744

Rate of return = (5744 - 6057)/6057 *100% = -5.16%

Value on 1/1/18

Value of Douglas McDonnell = 360*83 = $29880m

Value of Dynamics General = 450*60 = $27000m

Value of International Rockwell = 170*86 = $14620m

Total Value = 29880 + 27000 + 14620 = $71500m

Value of index = Total Value / 10m = 71500/10 = $7150

Rate of return = (7150 - 6057)/6057 *100% = 18.04%