Question

A stock had returns of 19 percent, 14 percent, 12 percent, -4 percent, 17 percent, and 7 percent over the last six years. What is the arithmetic return for the stock? What is the geometric return for the stock?

Answer 1

Arithmetic Return = Sum of all returns

It ignore compunding effect.

Hence,

Arithmetic Return = 19% + 14% + 12% + (-4%) + 17% + 7%

Arithmetic Return = 65%

Now, number of observations = 6

Hence, Average Arithmetic Return = Arithmetic Return / Number of observations

Average Arithmetic Return = 65% / 6 = 10.833%

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Geometric Return:

Geometric Return = (1 + Period 1 return) * (1 + Period 2 return) *  (1 + Period 3 return) * (1 + Period 4 return) *  (1 + Period 5 return) * (1 + Period 6 return) - 1

Putting values:

Geometric Return = (1 + 19%) * (1 + 14% ) * (1 + 12% ) * (1 + (-4%) ) * (1 + 17%) * (1 + 7%) - 1

Geometric Return = (1.19 * 1.14 * 1.12 * 0.96 * 1.17 * 1.07) - 1

Geometric Return = 1.826 - 1  

Geometric Return = 82.60%