Lesson 3 of 10 · All lessons in this module

Lesson 3 of 10 · 13 min

Arithmetic and geometric mean returns

The arithmetic mean is the typical single-period return; the geometric mean is the steady rate that would have produced the same ending wealth.

In short

Arithmetic mean: add the period returns and divide by the number of periods.
Geometric mean: multiply the $(1+R_t)$ , take the T-th root, subtract 1. It is the compound rate of growth.
Geometric ≤ arithmetic; they are equal only if every return is the same. The gap widens as returns become more dispersed.
The arithmetic mean overstates past wealth growth when returns vary. Use the geometric mean to describe multi-period performance.
Use the arithmetic mean for the average return over a single future period.

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