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.)
−15% 16% −17% 14.7% 15.1%
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%.
To calculate the geometric mean return, we need to follow these steps:
Step 1: Convert the percentages to decimal form.
-15% = -0.15
16% = 0.16
-17% = -0.17
14.7% = 0.147
15.1% = 0.151
Step 2: Calculate the product of all the decimal returns.
-0.15 * 0.16 * -0.17 * 0.147 * 0.151 = -0.0001823786
Step 3: Take the absolute value of the product.
|-0.0001823786| = 0.0001823786
Step 4: Raise the absolute value to the power of 1/n, where n is the number of returns.
(0.0001823786)^(1/5) ≈ 0.0717
Step 5: Subtract 1 from the result to get the geometric mean return.
0.0717 - 1 ≈ -0.9283
Therefore, the geometric mean return for the given data set is approximately -0.93, or -93.00%