Question

In addition to price-weighted and value-weighted indexes, an equally weighted index is one in which the index value is computed from the average rate of return of the stocks comprising the index. Equally weighted indexes are frequently used by financial researchers to measure portfolio performance.

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	420		$	63		$	67		$	84
Dynamics General	450			53			47			61
International Rockwell	250			82			71			87

a. Compute the rate of return on an equally weighted index of the three defense stocks for the year ending December 31, 2016. (A negative value should be indicated by a minus sign. Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places.)

index return

b. If the index value is set to 100 on January 1, 2016, what will the index value be on January 1, 2017? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

index value

c. What is the rate of return on the index for 2017? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places.)

index return

Answer 1

a) Rate of return for year ending Dec 31, '16:

Douglas McDonnell = (67-63)/63 = 6.35%

Dynamics General = (47-53)/53 = -11.32%

International Rockwell = (71-82)/82 = -13.41%

Average rate of return = (6.35-11.32-13.41)/3 = -6.13%

b) If initial value of index =100

Index will fall by 6.13%

New index value = 100*(1-0.0613) = 93.87

c)

Douglas McDonnell = (84-67)/67 = 26.56%

Dynamics General = (61-47)/47 = 29.79%

International Rockwell = (87-71)/71 = 22.54%

Average rate of return = (26.56+29.79+22.54)/3 = 26.30%