Question

The following three defense stocks are to be combined into a stock index in January 2019 (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)		1/1/19			1/1/20			1/1/21
Douglas McDonnell	355		$	86		$	91		$	103
Dynamics General	455			55			52			66
International Rockwell	270			84			73			87

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, 2019? For the year ending December 31, 2020? (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.)

2019 return		%
2020 return		%

Answer 1

a.Initial value of the index if a value-weighting scheme is used

1/1/2019 Index value=((355*86)+(455*55)+(270*84))/10=

7823.50

Index value= 7823.50

b.Rate of return on this index for the year ending December 31, 2019

1/1/2020 Index value=

(355*91)+(455*52)+(270*(73)/10=

7567.50

so, ROR   on this index for the year ending December 31, 2019=

(7567.50-7823.50)/7823.50=

-3.27%

Rate of return on 1/1/2019 index for the year ending December 31, 2020

1/1/21 Index value= (355*103)+(455*66)+(270*87)/10=

9008.5

so, ROR on initial index for the year ending December 31, 2020=

(9008.50-7823.50)/7823.50=

15.15%