Question

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

Year	Price			Dividend
1	$	64.23			—
2		71.10		$	.58
3		76.90			.63
4		63.17			.69
5		72.91			.78
6		78.75			.85
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

Year 2:

Return, r1 = (Closing Price + Dividend - Opening Price) / Opening Price
Return, r1 = ($71.10 + $0.58 - $64.23) / $64.23
Return, r1 = 0.1160

Year 3:

Return, r2 = (Closing Price + Dividend - Opening Price) / Opening Price
Return, r2 = ($76.90 + $0.63 - $71.10) / $71.10
Return, r2 = 0.0904

Year 4:

Return, r3 = (Closing Price + Dividend - Opening Price) / Opening Price
Return, r3 = ($63.17 + $0.69 - $76.90) / $76.90
Return, r3 = -0.1696

Year 5:

Return, r4 = (Closing Price + Dividend - Opening Price) / Opening Price
Return, r4 = ($72.91 + $0.78 - $63.17) / $63.17
Return, r4 = 0.1665

Year 6:

Return, r5 = (Closing Price + Dividend - Opening Price) / Opening Price
Return, r5 = ($78.75 + $0.85 - $72.91) / $72.91
Return, r5 = 0.0918

Arithmetic Return, r = (r1 + r2 + r3 + r4 + r5) / 5
Arithmetic Return, r = (0.1160 + 0.0904 + (-0.1696) + 0.1665 + 0.0918) / 5
Arithmetic Return, r = 0.0590 = 5.90%

Geometric Return, r = [(1+r1)*(1+r2)*(1+r3)*(1+r4)*(1+r5)]^(1/5) - 1
Geometric Return, r = [(1+0.1160)*(1+0.0904)*(1-0.1696)*(1+0.1665)*(1+0.0918)]^(1/5) - 1
Geometric Return, r = [1.28696]^(1/5) - 1
Geometric Return, r = 1.0518 - 1
Geometric Return, r = 0.0518 = 5.18%