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A stock had returns of 15 percent, 14 percent, 18 percent, 5 percent, 16 percent, and...

A stock had returns of 15 percent, 14 percent, 18 percent, 5 percent, 16 percent, and 2 percent over the last six years. What is the arithmetic return for the stock? What is the geometric return for the stock?

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Answer #1

Return during Year 1, r1 = 0.15
Return during Year 2, r2 = 0.14
Return during Year 3, r3 = 0.18
Return during Year 4, r4 = 0.05
Return during Year 5, r5 = 0.16
Return during Year 6, r6 = 0.02

Arithmetic Return = [r1 + r2 + r3 + r4 + r5 + r6] / 6
Arithmetic Return = [0.15 + 0.14 + 0.18 + 0.05 + 0.16 + 0.02] / 6
Arithmetic Return = 0.70 / 6
Arithmetic Return = 0.1167 or 11.67%

Geometric Return = [(1+r1) * (1+r2) * (1+r3) * (1+r4) * (1+r5) * (1+r6)]^(1/6) - 1
Geometric Return = [(1+0.15) * (1+0.14) * (1+0.18) * (1+0.05) * (1+0.16) * (1+0.02)]^(1/6) - 1
Geometric Return = 1.9219061^(1/6) - 1
Geometric Return = 1.1150 - 1
Geometric Return = 0.1150 or 11.50%

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