Answer:
Arithmetic mean = 3.67%
Geometric mean = 3.02%
Explanation:
The following sorted data are given in the question:
Year Beginning-of-Year Price Dividend Paid at Year-End
2015 $130 $5
2016 144 5
2017 120 5
2018 125 5
Therefore, we have:
Arithmetic average return = Sum of returns/ number of years ………....….. (1)
Geometric average return = n * ((1+r1)*(1+r2)*(1+r3)…(1+rn)^(1/n) - 1 .……….. (2)
Where;
n = years 1, 2, 3….
r1, r2, r3… are the returns for year 1, 2, 3….
Return for each year = ((Current year Beginning-of-Year Price – Previous year Beginning-of-Year Price) + dividend) / Previous year Beginning-of-Year Price .................... (3)
Using equation (3), we have:
2016 Return = ((144 - 130) + 5) /130 = 0.146153846153846
2017 Return = ((120 - 144) + 5) /159 = -0.119496855345912
2018 Return = ((125 - 120) + 5) /120 = 0.0833333333333333
Using equation (1), we have:
Arithmetic mean = (2016 Return + 2017 Return + 2018 Return) / 3 = (0.1461538461538460 - 0.1194968553459120 + 0.0833333333333333) / 3 = 0.0367, or 3.67%.
Using equation (2), we have:
Geometric mean = ((1 + 2016 Return) * (1 + 2017 Return) * (1 + 2018 Return))^(1/3) - 1 = ((1 + 0.146153846153846) * (1 - 0.119496855345912) * (1 + 0.0833333333333333))^(1/3) - 1 = 0.0302, or 3.02%
