Question

A stock has had the following year-end prices and dividends:Year Price Dividend1 $ 64.73 â 2 71.60 $ .68 3 77.40 .73 4 63.67 .79 5 73.91 .88 6 83.75 .95 What are the arithmetic and geometric returns for the stock? (Do not round intermediate calculations and enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.)Arithmetic average return %Geometric average return %

Answer 1

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%.