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Lesson 5 of 9 · 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+Rt)(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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Arithmetic and geometric mean returns · Returns of Financial Assets and Instruments