A stock has had the following year-end prices and dividends: |
Year | Price | Dividend | |||||
1 | $ | 63.40 | - | ||||
2 | 70.20 | $ | .85 | ||||
3 | 79.18 | .95 | |||||
4 | 75.32 | 1.03 | |||||
5 | 84.18 | 1.11 | |||||
6 | 98.62 | 1.20 | |||||
What are the arithmetic and geometric average 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.) |
Return = [P1 - P0 + D] / P0
R1 = [$70.20 - $63.40 + $0.85] / $63.40 = 12.07%
R2 = [$79.18 - $70.20 + $0.95] / $70.20 = 14.15%
R3 = [$75.32 - $79.18 + $1.03] / $79.18 = -3.57%
R4 = [$84.18 - $75.32 + $1.11] / $75.32 = 13.24%
R5 = [$98.62 - $84.18 + $1.20] / $84.18 = 18.58%
A.M. = [Ri] / n = [12.07% + 14.15% - 3.57% + 13.24% + 18.58%] / 5 = 54.45% / 5 = 10.89%
G.M. = [(1 + R1) x (1 + R2) x ----- x (1 + RN)]^{1/N}
= [1.1207 x 1.1415 x 0.9643 x 1.1324 x 1.1858]^{1/5} = [1.6562]^{0.2} - 1 = 1.1062 - 1 = 0.1062, or 10.62%
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