USE THE INFORMATION BELOW FOR THE FOLLOWING PROBLEM(S)
Stocks W and X had 2 for 1 splits after the close on Dec 31, 2003.

-Refer to Exhibit 4.5. Calculate the percentage return in the unweighted index (geometric mean) for the period Dec 31, 2003 to Dec 31, 2004. Assume a base index value of 100. The base year is Dec 31, 2003.
A) 19.25 percent
B) 21.25 percent
C) 51.25 percent
D) 5.25 percent
E) 100.25 percent

Question

USE THE INFORMATION BELOW FOR THE FOLLOWING PROBLEM(S)
  Stocks W and X had 2 for 1 splits after the close on Dec 31, 2003.
​
-Refer to Exhibit 4.5. Calculate the percentage return in the unweighted index (geometric mean) for the period Dec 31, 2003 to Dec 31, 2004. Assume a base index value of 100. The base year is Dec 31, 2003.
A) 19.25 percent 
B) 21.25 percent 
C) 51.25 percent 
D) 5.25 percent 
E) 100.25 percent

Quizplus · Accepted Answer

Since both stocks had a 2 for 1 split, the number of shares of each stock in the index is doubled. The unweighted index is a simple average of the stock prices. Therefore, the stock prices are halved in the index calculation. The compounded return for the period is (1+41.03%)(1+54.17%)(1+33.33%)(1+22.50%)(1+61.90%)(1+66.67%)(1+85.71%)(1+51.72%)(1+57.14%)(1+64.71%)(1+56.52%)(1+56.67%) - 1 = 735.34% or 7.3534. The geometric mean return is (7.3534)^(1/12) - 1 = 19.25%.