A stock had returns of 14.21 percent (1 year ago), -32.69 percent (2 years ago), X (3 years ago), and 22.82 percent (4 years ago) in each of the past 4 years. Over the past 4 years, the arithmetic average annual return for the stock was 8.25 percent. What was the geometric average annual return for the stock over the past 4 years? Answer as a rate in decimal format so that 12.34% would be entered as .1234 and 0.98% would be entered as .0098.
The geometric average annual return is computed as shown below:
Return of 3rd year is computed as follows:
(14.21 - 32.69 + X + 22.82) / 4 = 8.25
4.34 + X = 33
X = 28.66%
So, the geometric return will be as follows:
= [ (1 + 0.1421) x (1 - 0.3269) x (1 + 0.2866) x (1 + 0.2282) ] 1 / 4 - 1
= [ (1.1421 x 0.6731 x 1.2866 x 1.2282) ] 0.25 - 1
= 0.0498% Approximately
Feel free to ask in case of any query relating to this question
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