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	425		$	72		$	75		$	92
Dynamics General	530			50			43			57
International Rockwell	310			79			68			85

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

Solution to part a.

Calculation of initial value of the Index on 1/1/2016:

To find the initial value of index we calculate the total market value of all the three firms on 1/1/2016 and then divide it by 10 million ( scaling the factor by 10 million) as given in question.

Market value = Number of shares x share price

	Shares (millions)	Price on 1/1/2016	Market value
Douglas McDonnell	425	$ 72	$ 30,600
Dynamics General	530	$ 50	$ 26,500
International Rockwell	310	$ 79	$ 24,490
Total			$ 81,590

Value of Index on 1/1/2016 = Total value of firms on 1/1/2016 / 10 million

= $ 81,590 million / 10 million

Value of Index on 1/1/2016 = $ 8,159

Solution to part b.

To calculate the rate of return on index for 2016 and 2017 we first calculate the index values on 1/1/2017 and 1/1/2018. Then we calculate the return based on percentage change in index values.

Index value on 1/1/2017 & 1/1/2018

	Shares (millions) [a]	Price on 1/1/2017 [b]	Market value on 1/1/2017 [c] = [a] x [b]	Price on 1/1/2018 [d]	Market value on 1/1/2018 [e] = [a] x [d]
Douglas McDonnell	425	$ 75	$ 31,875	$ 92	$ 39,100
Dynamics General	530	$ 43	$ 22,790	$ 57	$ 30,210
International Rockwell	310	$ 68	$ 21,080	$ 85	$ 26,350
Total			$ 75,745		$ 95,660

So Index value on 1/1/2017 = $ 75,745 million / 10 million = 7,574.5

We calculate the rate of return for the year ended December 2016 by :

[ (Index value on 1/1/2017 - Index value on 1/1/2016 ) / Index value on 1/1/2016 ] x 100

[ (7,574.5 - 8,159 ) / 8,159 ] x 100

= - 7.16%

Index value on 1/1/2018 = $ 95,660 million / 10 million = 9,566

We calculate the rate of return for the year ended December 2017 by :

[ (Index value on 1/1/2018 - Index value on 1/1/2017 ) / Index value on 1/1/2017 ] x 100

[ (9,566 - 7,574.5 ) / 7,574.5] x100

= 26.29 %

So, rate of return for Year ended December 2016 = - 7.16% & rate of return for Year ended December 2017 = 26.29%