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 215 $ 64 $ 68 $ 82 Dynamics General 455 72 64 78 International Rockwell 250 101 90 106 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)
	Douglas McDonnell			Dynamics General
Shares (millions)	215			455
Price
01-01-2016	64			72
01-01-2017	68			64
01-01-2018	82			78
Index scale factor =		10 million
Initial value of index = (No. of shares * Price of share)+(no. of shares * price of shares) / 10 million
(as on 1/1/2016)
	{ (215 millions * 64) + (455 millions* 72) } / 10 million
	4652
So, Initial value of index is $4652.
Part (b)
Opening value of index on 1/1/2016 = 4652
Opening Value of index on 1/1/2017 = { (215 million * 68) + (455 million * 64) } / 10 million
	4374
So, Closing value of index on year ending 31/12/2016   =   4374
Rate of return = (Closing value of index - opening value of index)/Opening value of index * 100
	(4374 - 4652)/4652 * 100
	-5.97592	or 5.98%
Opening value of index on 1/1/2017 =			4374
Opening value of index on 1/1/2018 = { (215 million *82) + (455 million * 78) } / 10 million
	5312
So, closing value of index on year ending 31/12/2017 = 5312
Rate of return = (Closing value of index - opening value of index)/Opening value of index * 100
	(5312 - 4374)/4374 * 100
	21.4449	or 21.44%
So, Rate of return on this index for year ending Dec. 31, 2016 is -5.98% and rate of return for year ending Dec 31, 2017 is 21.44%