Question

what is the difference between arithmetic and geometric averages?

Answer 1

Arithmetic average is simple average of all observation or returns. Return of each period is independent of previous period hence adding each return and dividing the result with total observation would give arithmetic average.

Arithmetic average = Sum of the return / total number of returns or observations

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In geometric average the subsequent periods are dependent on result of previous periods because geometric average gives compounding impact to the return based on per period.

Geometric average is obtained by adding 1 to each return and multiplying each result then, taking period’s (1/n) root of that product and then subtracting result by 1.

Geometric average = ((1+rate period 1) x (1+rate period 2) x …… x (1+Rate period n))^(1/n) -1