Question

A stock has had the following year-end prices and dividends:

Year		Price			Dividend
0		$	14.75			—
1			16.93		$	.15
2			17.93			.24
3			16.43			.28
4			18.77			.29
5			21.88			.34

What are the arithmetic and geometric returns for the stock? (Do not round intermediate calculations. Enter your answers as a percent rounded to 2 decimal places. Omit the "%" sign in your response.)

Arithmetic returns	%
Geometric returns	%

Answer 1

Year 0 - Year 1:

Rate of Return, r1 = (Closing Price + Dividend - Opening Price) / Opening Price
Rate of Return, r1 = ($16.93 + $0.15 - $14.75) / $14.75
Rate of Return, r1 = 0.1580

Year 1 - Year 2:

Rate of Return, r2 = (Closing Price + Dividend - Opening Price) / Opening Price
Rate of Return, r2 = ($17.93 + $0.24 - $16.93) / $16.93
Rate of Return, r2 = 0.0732

Year 2 - Year 3:

Rate of Return, r3 = (Closing Price + Dividend - Opening Price) / Opening Price
Rate of Return, r3 = ($16.43 + $0.28 - $17.93) / $17.93
Rate of Return, r3 = -0.0680

Year 3 - Year 4:

Rate of Return, r4 = (Closing Price + Dividend - Opening Price) / Opening Price
Rate of Return, r4 = ($18.77 + $0.29 - $16.43) / $16.43
Rate of Return, r4 = 0.1601

Year 4 - Year 5:

Rate of Return, r5 = (Closing Price + Dividend - Opening Price) / Opening Price
Rate of Return, r5 = ($21.88 + $0.34 - $18.77) / $18.77
Rate of Return, r5 = 0.1838

Arithmetic Return = [r1 + r2 + r3 + r4 + r5] / 5
Arithmetic Return = [0.1580 + 0.0732 + (-0.0680) + 0.1601 + 0.1838] / 5
Arithmetic Return = 0.5071 / 5
Arithmetic Return = 0.1014 or 10.14%

Geometric Return = [(1+r1) * (1+r2) * (1+r3) * (1+r4) * (1+r5)]^(1/5) - 1
Geometric Return = [(1+0.1580) * (1+0.0732) * (1-0.0680) * (1+0.1601) * (1+0.1838)]^(1/5) - 1
Geometric Return = 1.5906656^(1/5) - 1
Geometric Return = 1.0973 - 1
Geometric Return = 0.0973 or 9.73%