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Question:

An analyst gathered the following information regarding an equity market index. The index was created on January 1, 2009 at which time its value was set to 1,000. It consists of the following 3 securities:
Given that dividends are paid at the end of the year and that the price return on the index for 2009 was 8.25%, the value of the price return index at the end of 2010 is closest to:

A 1,108.
Explaination

Price return on security A = (31 − 35) / 35 = –11.43%
Price return on security B = (45 − 48) / 48 = –6.25%
Price return on security C = (32 − 27) / 27 = 18.52%
Price return on the index for 2010:
= (–0.1143 x 0.25) + (–0.0625 x 0.35) + (0.1852 x 0.4) = 2.36%
Therefore, value of the price return index at the end of 2010:
= 1,000 x 1.0825 x 1.0236 = 1,108.047