In addition to price-weighted and value-weighted indexes, an equally weighted in
ID: 2613042 • Letter: I
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.
a. Using the following information, compute the rate of return on an equally weighted index of the three defense stocks for the year ending December 31, 2013. (Information: Douglas McDonnell: shares (millions) 340, Price 1/1/13 $103, 1/1/14 $106, 1/1/15 $118. Dynamics General: shares (millions) 450, Price 1/1/13 $45, 1/1/14 $39, 1/1/15 $53. International Rockwell: shares (millions) 410, Price 1/1/13 $74, 1/1/14 $63, 1/1/15 $79.
b. If the index value is set to 100 on January 1, 2013, what will the index value be on January 1, 2014? What is the rate of return on the index for 2014?
Explanation / Answer
a. Rate of return on an equally weighted index of the three defense stocks for the year ending December 31, 2013. Douglas Dynamic International Total Rate of return/share' (106-103)/103 (39-45)/45 (63-74)/74 ie. 0.0291 -0.13333 -0.135135 No.of shares in MN 340 450 410 1200 Product 9.894 -59.9985 -55.40535 -105.51 Weighted rate of return= -105.51/1200 -0.08793 ie. -0.09% b. If the Index value is set to 100 on Jan.1,2013, Index value on Jan.1,2014, will be decreased by 0.09 ie. 100-0.09= 99.91 c.Rate of return on the index for 2014 Douglas Dynamic International Total Rate of return/share' (118-106)/106 (53-39)/39 (79-63)/63 ie. 0.1132 0.3589 0.2539 No.of shares in MN 340 450 410 1200 Product 38.488 161.505 104.099 304.092 Weighted rate of return= 304.092/1200 0.25341 ie. 25.34% Index for 2014 99.91 Rate of return as above 25.34% Rate of return on this index= 99.91*20.46% = 25.317194 ie. 25.32%
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