Question

Suppose you observe that Sleppough Inc.'s annual returns for the last five years were, from oldest...

Suppose you observe that Sleppough Inc.'s annual returns for the last five years were, from oldest to most recent, -7.32%, 5.44%, -3.01%, -0.24%, and 2.65%. What is Sleppough's geometric mean of returns for the five year period? Submit your answer as a percentage and round to two decimal places (ex. 0.00%)

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Answer #1

The returns are: -7.32%, 5.44%, -3.01%, -0.24%, and 2.65%
Number of observations is 5

Now,
(1-7.32%)=0.9268
(1+5.44%)=1.0544
(1-3.01%)=0.9699
(1-0.24%)=0.9976
(1+2.65%)=1.0265

Geometric mean=(0.9268*1.0544*0.9699*0.9976*1.0265)^(1/5) -1

Here, 1/5 refers to the 1/(Number of total observations)
=(0.970585449)^(1/5) -1
=0.994046625 -1
=-0.005953375 or -0.60% (Rounded to 2 decimal places)

Answer: Hence, the geometric mean of returns for the 5 year period is  -0.60%

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