Question

A stock has had the following year-end prices and dividends: Year Price Dividend 0 $ 14.25 — 1 16.43 $ 0.15 2 17.43 0.22 3 15.93 0.27 4 18.27 0.28 5 21.38 0.32 What are the arithmetic and geometric returns for the stock?

Answer 1

Year 1:

Rate of Return = (Closing Price + Dividends - Opening Price) / Opening Price
Rate of Return = ($16.43 + $0.15 - $14.25) / $14.25
Rate of Return = 0.1635

Year 2:

Rate of Return = (Closing Price + Dividends - Opening Price) / Opening Price
Rate of Return = ($17.43 + $0.22 - $16.43) / $16.43
Rate of Return = 0.0743

Year 3:

Rate of Return = (Closing Price + Dividends - Opening Price) / Opening Price
Rate of Return = ($15.93 + $0.27 - $17.43) / $17.43
Rate of Return = -0.0706

Year 4:

Rate of Return = (Closing Price + Dividends - Opening Price) / Opening Price
Rate of Return = ($18.27 + $0.28 - $15.93) / $15.93
Rate of Return = 0.1645

Year 5:

Rate of Return = (Closing Price + Dividends - Opening Price) / Opening Price
Rate of Return = ($21.38 + $0.32 - $18.27) / $18.27
Rate of Return = 0.1877

Arithmetic Return = [r1 + r2 + r3 + r4 + r5] / 5
Arithmetic Return = [0.1635 + 0.0743 + (-0.0706) + 0.1645 + 0.1877] / 5
Arithmetic Return = 0.5194 / 5
Arithmetic Return = 0.1039 or 10.39%

Geometric Return = [(1+r1) * (1+r2) * (1+r3) * (1+r4) * (1+r5)]^(1/5) - 1
Geometric Return = [(1+0.1635) * (1+0.0743) * (1-0.0706) * (1+0.1645) * (1+0.1877)]^(1/5) - 1
Geometric Return = 1.606723^(1/5) - 1
Geometric Return = 1.0995 - 1
Geometric Return = 0.0995 or 9.95%