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.)
−5% 6% −7% 4.7% 5.1%
To calculate the geometric mean return, we need to multiply all the individual returns together and then take the nth root, where n is the number of returns.
Return 1: -5% = -0.05
Return 2: 6% = 0.06
Return 3: -7% = -0.07
Return 4: 4.7% = 0.047
Return 5: 5.1% = 0.051
Multiply all the returns together: (-0.05)(0.06)(-0.07)(0.047)(0.051) ≈ -0.000029358
Now, we need to take the 5th root of this product:
(-0.000029358)^(1/5) ≈ -0.0390
The geometric mean return for this data set is approximately -3.90%.
To calculate the geometric mean return, follow these steps:
Step 1: Convert the percentages to decimals:
-5% = -0.05
6% = 0.06
-7% = -0.07
4.7% = 0.047
5.1% = 0.051
Step 2: Calculate the product of the decimal returns:
(-0.05) * (0.06) * (-0.07) * (0.047) * (0.051) = -0.000009679
Step 3: Take the absolute value of the product:
| -0.000009679 | = 0.000009679
Step 4: Take the nth root of the absolute value, where n is the total number of returns:
nth root(0.000009679, 5) = 0.01813
Step 5: Subtract 1 from the result:
0.01813 - 1 = -0.98187
Step 6: Multiply by 100 to convert to a percentage:
-0.98187 * 100 = -98.19
The geometric mean return for the given data set is -98.19%.