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).

		Price
	Shares (millions)		1/1/16			1/1/17			1/1/18
Douglas McDonnell	540		$	62		$	66		$	81
Dynamics General	455			49			43			57
International Rockwell	290			78			67			81

a. Calculate the initial value of the index if a price-weighting scheme is used.

Index value:

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.)

	2016 return % 2017 return %

Answer 1

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

Initial value of the index = [$62 + $49 + $78] / 3

= $189 / 3

= $63.00

“Index Value = $63.00”

(b)- The rate of return on this index for the year ending December 31, 2016 & December 31, 2017?

Rate of return on this index for the year ending December 31, 2016

Average Index Value on 01/01/2016 = $63

Average Index Value on 01/01/2017 = $58.67 [($66 + $43 + $67) / 3]

Therefore, the Rate of Return = [(Average Index Value on 01/01/2017 - Average Index Value on 01/01/2016) / Average Index Value on 01/01/2016] x 100

= [($58.67 / $63.00) / $63.00] x 100

= [-$4.33 / $63.00] x 100

= -6.88% (Negative)

Rate of return on this index for the year ending December 31, 2017

Average Index Value on 01/01/2017 = $58.67

Average Index Value on 01/01/2018 = $73 [($81 + $57 + $81) /32]

Therefore, the Rate of Return = [(Average Index Value on 01/01/2018 - Average Index Value on 01/01/2017) / Average Index Value on 01/01/2017] x 100

= [($73 - $58.67) / $58.67] x 100

= [$14.33 / $58.67] x 100

= 24.43%

Therefore,

2016 Return = -6.88% (Negative)

2017 Return = 24.43%