Question

La Maudite Corporation’s annual returns for the past five years were: 11.5%, 18%, -12%, -16.5%, and 28%. What are the arithmetic and geometric average annual returns for La Maudite over the five-year period?

Answer #1

Arithmetic Mean is the average of the returns and is calculated by adding all the returns and dividing it by the number of periods.

Arithmetic annual returns = (11.5% + 18% -12% -16.5% + 28% ) / 5

Arithmetic annual returns = **5.80%**

Geometric mean is the average mean which has been compounded over
the period.

GM = [ (1 + R1) * (1 + R2) * (1 + R3) * (1 + R4) * (1 + R5) ]
^{1/5} -1

GM = [ ( 1+ 0.115) * ( 1 + 0.18) * (1 -0.12) * (1-0.165) *
(1+0.28) ] ^{1/5} - 1

GM = [ ( 1.115 * 1.18 * 0.88 * 0.835 * 1.28 )]^{1/5} -
1

GM = [ 1.237474 ] ^{1/5} - 1

GM = 1.043535 - 1

GM = 0.043535

GM = 4.3535%

**Geometric mean is 4.35%**

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