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	205		$	103		$	109		$	123
Dynamics General	450			48			44			58
International Rockwell	290			77			66			80

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.)

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.)

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.)

Answer 1

a.

Rate of return of an equally weighted index is simply the average rate of return on individual stocks. As shown above it is equal to -3.95% for the year 2016

b.

Index values can be calculated either using unitary method i.e. if 76 (average price in 2016) is 100, then 73 is (100/76 * 73) = 96.05. A more elegant method is to increase the previous year's index value by the average return. i.e. index value in 2017 is equal to 100 * (1-3.95%) = 96.05

c.

The rate of return on index in 2017 is the same as average return in 2017 which is 19.18%