Calculate the geometric mean return for the following data set: (Negative value should be indicated by a minus sign. Round your intermediate calculations to at least 4 decimal places and final answer to 2 decimal places.)

Question

−15% 16% −17% 14.7% 15.1%

Answer 1

To calculate the geometric mean return, we need to first convert the percentage returns to decimal form.

-15% = -0.15
16% = 0.16
-17% = -0.17
14.7% = 0.147
15.1% = 0.151

Next, we multiply all the decimal returns together and take the nth root, where n is the number of returns.

Geometric mean return = (1 + -0.15) * (1 + 0.16) * (1 + -0.17) * (1 + 0.147) * (1 + 0.151)^(1/5) - 1

= (0.85) * (1.16) * (0.83) * (1.147) * (1.151)^(1/5) - 1

= 0.805859 - 1

= -0.19

Rounded to 2 decimal places, the geometric mean return for the data set is -0.19 or -19%.