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.
So, we have:
(-7%)(8%)(-9%)(6.7%)(7.1%)
Using a calculator or spreadsheet, we can calculate this to be -2.71461%.
Rounding this to 2 decimal places, the geometric mean return is -2.71%.
To calculate the geometric mean return, follow these steps:
Step 1: Convert the percentage values to decimal values.
-7% = -0.07
8% = 0.08
-9% = -0.09
6.7% = 0.067
7.1% = 0.071
Step 2: Calculate the product of the decimal values.
(-0.07) * (0.08) * (-0.09) * (0.067) * (0.071) ≈ -0.0000302672
Step 3: Raise the product to the power of 1 divided by the number of values (5 in this case).
(-0.0000302672)^(1/5) ≈ -0.3802
Step 4: Convert the result back to a percentage.
-0.3802 * 100 = -38.02
The geometric mean return for the given data set is approximately -38.02%.