Answer:
The geometric average return for the period 2.60%.
Explanation:
Note: The data in this question are merged together. They are therefore sorted before answering the question. See the attached pdf file for the complete question with the sorted data.
Also note: See the attached excel file for the calculation of the return for each year.
In the attached excel file, return is calculated using the following formula:
Return = (Current year price - Previous year price) / Previous year price
The formula for calculating the geometric average return is given as follows:
Geometric average return = [(1 + R1)(1 + R2)(1 + R3)...(1 + Rn)]^(1/n) – 1 ……….. (1)
Where;
Ri = Return over the years I, where i = 1, 2, 3, …. n
n = number of years = 3
R1 = 2012 return = 0.10
R2 = 2013 return = -0.0727272727272727
R3 = 0.0588235294117647
Substituting the values into equation (1), we have:
Geometric average return = ((1 + 0.10)(1 - 0.0727272727272727)(1 + 0.0588235294117647))^(1/3) – 1
Geometric average return = (1.10 * 0.927272727272727 * 1.0588235294117647)^(1/3) – 1
Geometric average return = 1.07999999999999^0.333333333333333 - 1
Geometric average return = 1.02598556800602 - 1
Geometric average return = 0.02598556800602 = 0.0260, or 2.60%
Therefore, the geometric average return for the period 2.60%.
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