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	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.)

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

Part a.

The initial value of the index, at 01/1/16, is computed as follows:

Value of DM = 350,000,000 * $65 = $22,750,000,000

Value of DG = 450,000,000 * $25 = $11,250,000,000

Value of IR = 210,000,000 * $54 = $11,340,000,000

The sum of these values is $45,340,000,000

Now, we must scale the index, by dividing that amount by 10,000,000. The final value of the index is 4,534 (45,340,000,000 / 10,000,000 = 4534).

The value of the index, at 01/1/17, is computed as follows:

Value of DM = 350,000,000 * $69 = $24,150,000,000

Value of DG = 450,000,000 * $19 = $8,550,000,000

Value of IR = 210,000,000 * $43 = $9,030,000,000

The sum of these values is $41,730,000,000

Now, we must scale the index, by dividing that amount by 10,000,000. The final value of the index is 4,173.

The value of the index, at 01/1/18, is computed as follows:

Value of DM = 350,000,000 * $81 = $28,350,000,000

Value of DG = 450,000,000 * $33 = $14,850,000,000

Value of IR = 210,000,000 * $57 = $11,970,000,000

The sum of these values is $55,170,000,000

Now, we must scale the index, by dividing that amount by 10,000,000. The final value of the index is 5517.

(b)     2016 2017 2018

Value of index 4534 4173 5517

Therefore, the rate of return (ROR) for the year ending

December 31, 2016 ROR = 4173/4534 - 1 = -.096 or -7.96%

December 31, 2017 ROR = 5517/4173 - 1 = .3221 or 32.21%