A stock had the following prices and dividends.What is the geometric average return on this stock?
A) 3.0%
B) 3.3%
C) 3.6%
D) 3.8%
E) 4.0%

Question

A stock had the following prices and dividends.What is the geometric average return on this stock? 
A) 3.0% 
B) 3.3% 
C) 3.6% 
D) 3.8% 
E) 4.0%

Quizplus · Accepted Answer

To find the geometric average return, we first need to calculate the annual returns for each year. Using the formula (Ending Price - Beginning Price + Dividend) / Beginning Price, we get:

Year 1: (110 - 100 + 5) / 100 = 15%
Year 2: (120 - 110 + 6) / 110 = 14.55%
Year 3: (130 - 120 + 7) / 120 = 15.83%
Year 4: (140 - 130 + 8) / 130 = 14.61%
Year 5: (152 - 140 + 9) / 140 = 12.14%

To find the geometric average return, we multiply all of the annual returns together and take the fifth root (since there are five years). Using a financial calculator or a spreadsheet, we get:

(1.15 x 1.1455 x 1.1583 x 1.1461 x 1.1214)^(1/5) = 1.033 or 3.3%

Therefore, the best choice is B, with a geometric average return of 3.3%.

A Stock Had the Following Prices and Dividends