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.)
−7% 8% −9% 6.7% 7.1%
To calculate the geometric mean return, we need to multiply all the returns together and then take the Nth root, where N is the number of returns.
(-0.07) * 0.08 * (-0.09) * 0.067 * 0.071 = -0.000058902
Now we need to take the 5th root of the product.
(-0.000058902)^(1/5) = -0.1171
The geometric mean return of the data set is -0.1171, or -11.71%.
To calculate the geometric mean return, we need to multiply all the returns together and then take the nth root, where n is the number of returns in the dataset.
Step 1: Convert the percentages to decimal form.
-7% = -0.07
8% = 0.08
-9% = -0.09
6.7% = 0.067
7.1% = 0.071
Step 2: Multiply all the returns together.
-0.07 * 0.08 * -0.09 * 0.067 * 0.071 = -0.0000222856
Step 3: Take the fifth root of the product.
(-0.0000222856)^(1/5) = -0.1703
Step 4: Convert the result back to a percentage.
-0.1703 * 100 = -17.03
Therefore, the geometric mean return for the given data set is -17.03%.