The following three defense stocks are to be combined into a stock index in Janu
ID: 2733065 • Letter: T
Question
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):
What is the rate of return on this index for the year ending December 31, 2013? For the year ending December 31, 2014? (Negative values should be indicated by a minus sign. Do not round intermediate calculations. Enter your answers as a percent rounded to 2 decimal places. Omit the "%" sign in your response.)
Price Shares(millions) 1/1/13 1/1/14 1/1/15 Douglas McDonnell 420 $ 63 $ 67 $ 84 Dynamics General 450 53 47 61 International Rockwell 250 82 71 87
Explanation / Answer
A price-weighted index is simply the sum of the members' stock prices divided by the number of members.
So Initial Value of index containing three stock is the average price of stock at the beginning of year 2013.
Initial Value of index = ($63 + $53 + $82) / 3
= $198 / 3
= $66
So initial value of Index is 66.
Again index value at end of year 2013 is calculated below:
Index value at end of 2013 = ($67 + $47 + $71) / 3
= $185 / 3
= $61.67
So, index value at end of year 2013 is 61.67.
Return on index for the year ending December 31, 2013 is calculated below:
Return = ($61.67 - $66) / $66
= -6.57%
Return on index for the year ending December 31, 2013 is -6.57%.
Similarly,
Index value at end of year 2014 is calculated below:
Index value at end of 2013 = ($84 + $61 + $87) / 3
= $212 / 3
= $70.67
So, index value at end of year 2014 is 70.67.
Return on index for the year ending December 31, 2014 is calculated below:
Return = ($70.67 - $61.67) / $61.67
= 14.59%
Return on index for the year ending December 31, 2014 is 14.59%.
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