Question

A stock has had the following year-end prices and dividends: Year Price Dividend $64.10 1 $1.10 2 74.05 3 67.61 1.25 76.25 1.45 5 82.70 1.60 6 93.15 175 What are the arithmetic and geometric returns for the stock? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.) Arithmetic average return Geometric average return %

Answer 1

Year 2:

Rate of Return, r1 = (Closing Price + Dividend - Opening Price) / Opening Price
Rate of Return, r1 = ($74.05 + $1.10 - $64.10) / $64.10
Rate of Return, r1 = 0.1724

Year 3:

Rate of Return, r2 = (Closing Price + Dividend - Opening Price) / Opening Price
Rate of Return, r2 = ($67.61 + $1.25 - $74.05) / $74.05
Rate of Return, r2 = -0.0701

Year 4:

Rate of Return, r3 = (Closing Price + Dividend - Opening Price) / Opening Price
Rate of Return, r3 = ($76.25 + $1.45 - $67.61) / $67.61
Rate of Return, r3 = 0.1492

Year 5:

Rate of Return, r4 = (Closing Price + Dividend - Opening Price) / Opening Price
Rate of Return, r4 = ($82.70 + $1.60 - $76.25) / $76.25
Rate of Return, r4 = 0.1056

Year 6:

Rate of Return, r5 = (Closing Price + Dividend - Opening Price) / Opening Price
Rate of Return, r5 = ($93.15 + $1.75 - $82.70) / $82.70
Rate of Return, r5 = 0.1475

Arithmetic Average Return = [r1 + r2 + r3 + r4 + r5] / 5
Arithmetic Average Return = [0.1724 + (-0.0701) + 0.1492 + 0.1056 + 0.1475] / 5
Arithmetic Average Return = 0.5046 / 5
Arithmetic Average Return = 0.1009 or 10.09%

Geometric Average Return = [(1 + r1) * (1 + r2) * (1 + r3) * (1 + r4) * (1 + r5)]^(1/5) - 1
Geometric Average Return = [(1 + 0.1724) * (1 - 0.0701) * (1 + 0.1492) * (1 + 0.1056) * (1 + 0.1475)]^(1/5) - 1
Geometric Average Return = 1.589492^(1/5) - 1
Geometric Average Return = 1.0971 - 1
Geometric Average Return = 0.0971 or 9.71%