Lesson 5 of 10 · All lessons in this module
- Financial assets, yields and expected versus actual returns
- What an interest rate is made of
- Required return, risk premia and excess returns
- Holding period return
- Arithmetic and geometric mean returns
- Annualised and continuously compounded returnsVideo lesson
- Gross, net, after-tax, real and leveraged returnsVideo lesson
- Taxing price and income returns
- Leverage through call options
- Integrated cases: from total return to what the investor keeps
This lesson is part of the 2027 curriculum. You are following the 2026 curriculum, where it is not taught in this form. Switch if you are sitting the exam under the 2027 curriculum.
Lesson 5 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 , 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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