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	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 price-weighting scheme is used.

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

(a) Calculation of initial value of index using price-weighting scheme

Initial value of index on 1/1/16 = ($65+$25+$54)/3

= $48

(b) Calculation of rate of return for December 31, 2016

Index on 1/1/17 = ($69+$19+$43)/3

= $43.67

Return for December 31, 2016 = ( Index value on 1/1/17 - Index value on 1/1/16) / Index value on 1/1/16

= ($43.67 - $48) / 48

= -9.03%

Calculation of rate of return for December 31, 2017

Index on 1/1/18 = ($81+$33+$57)/3

= $57

Return for December 31, 2017 = ( Index value on 1/1/18 - Index value on 1/1/17) / Index value on 1/1/17

= ($57 - $43.67) / 43.67

= 30.53%