Answer:
Arithmetic average return = 7.23%
Geometric average return=6.44%
Explanation:
Calculation for the Arithmetic average return
First step is to calculate the return for each year
Using this formula
Return=(Current year price amount-Previous price amount + Current year dividend)/ Previous year price amount ×100
Let plug in the formula
Year 1 Return= ($71.60-$64.73 + $.68) / $64.73
Year 1 Return=$7.55/$64.73
Year 1 Return= 11.66%
Year 2 Return= ($77.40-$71.60 + $.73) / $71.60
Year 2 Return=$6.53=$71.60
Year 2 Return = 9.12%
Year 3 Return= ($63.67-$77.40 +$ .79) / $77.40 Year 3 Return=$-12.94/$77.40
Year 3 Return=-16.72%
Year 4 Return= ($73.91-$63.67 +$ .88) / $63.67
Year 4 Return=$11.12/$63.67
Year 4 Return = 17.47%
Year 5 Return= ($83.75-$73.91 + $.95) / $73.91 Year 5 Return=$10.79/$73.91
Year 5 Return= 14.60%
The second step is to calculate the arithmetic average return
Using the formula
Arithmetic average return = (Addition of the each year return percentage /Numbers of years)
Let plug in the formula
Arithmetic average return (.1166 + .0912-.1672 + .1747 + .1460) / 5
Arithmetic average return =0.3613/5
Arithmetic average return = .0723 ×100
Arithmetic average return = 7.23%
Calculation for the geometric average return
Using this formula
Geometric average return=(1+Each year return percentage)^1/Numbers of years-1)
Let plug in the formula
Geometric average return== [(1 + .1166)×(1 + .0912)×(1-.1672)×(1 + .1747)×(1 + .1460)]^1/5-1
Geometric average return=[(1.1166)×(1.0912)(0.8328)×(1.1747)×(1.146)]^1/5-1
Geometric average return=(1.366011)^1/5-1
Geometric average return=1.0644
Geometric average return=1.0644-1
Geometric average return=0.0644
Geometric average return=0.0644 ×100
Geometric average return=6.44%
Therefore the Arithmetic average return is 7.23% while Geometric average return is 6.44%.
