Answer:
The full question is "The following three defense stocks are to be combined into a stock index in January 2013 (perhaps a portfolio manager believes these stocks are an appropriate benchmark for his or her performance): Price Shares (millions) 1/1/13 1/1/14 1/1/15 Douglas McDonnell 355 $ 86 $ 91 $ 103 Dynamics General 455 55 52 66 International Rockwell 270 84 73 87 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, 2013? For the year ending December 31, 2014?"
a. Initial value for Index = Sum of prices / Number of stocks
Initial value for Index = ($86+$55+$84)/3
Initial value for Index = $225/3
Initial value for Index = $75
b. For the year ending December 31, 2013
Index value at the end of 2013 = ($91+$52+$73)/3
Index value at the end of 2013 = $216/3
Index value at the end of 2013 = 72
Rate of Return = (Ending price - Beginning price) / Beginning price
Rate of Return = (72-75)/75
Rate of Return = -3/75
Rate of Return = -0.04
Rate of Return = -4%
For the year ending December 31, 2014
Index value at the end of 2014 = ($103+$66+$87)/3
Index value at the end of 2014 = $256/3
Index value at the end of 2014 = $85.33
Rate of Return = (Ending price - Beginning price) / Beginning price
Rate of Return = (85.33-72)/72
Rate of Return = 13.33/72
Rate of Return = 0.1851
Rate of Return = 18.51%