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 190 $ 105 $ 111 $ 124 Dynamics General 450 68 64 78 International Rockwell 330 97 86 102 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): Douglas McDonnell return = (111-105)/105 = 5.71%

Dynamics General return = (64-68)/68 = -5.88%

International Rockwell return = (86-97)/97 = -11.34%

Thus 2016 Index return = (5.71% - 5.88% - 11.34%)/3

= -3.84%

(b): Value = 100*(1-3.84%)

= 96.16

(c): Douglas McDonnell return = (124-111)/111 = 11.71%

Dynamics General return = (78-64)/64 = 21.88%

International Rockwell return = (102-86)/86 = 18.60%

Thus index return = (11.71%+21.88%+18.60%)/3 = 17.40%

[Index value = 96.16*(1+17.40%) = 112.89]