AlibomicsMoney and Economics
CONCEPT LESSON

Geometric average return

The constant periodic return that produces the same compounded growth as the actual returns.

Why it matters

Growth depends on multiplication across periods. Gains and losses of equal percentages do not cancel when they apply to different balances.

A worked example

£100 grows by 20% to £120, then falls by 20% to £96. The two-period geometric average is √0.96 − 1 ≈ −2.02%.

Illustrative example · simplified assumptions

A common mistake

Adding periodic returns to predict the final balance.

Where the idea needs care

The arithmetic average here is 0%, despite the loss. This example assumes no cash added or withdrawn.

Apply the idea

Explain this concept using a different example from your spending, work, business or a policy debate. State what stays fixed and what could change the result.

CHECK YOUR UNDERSTANDING
£100 gains 20% then loses 20%. What remains?

Read the answer and explanation

£96. The arithmetic average here is 0%, despite the loss. This example assumes no cash added or withdrawn.

See the supporting infographicGeometric average return: The constant periodic return that produces the same compounded growth as the actual returns.

The written explanation above is the main lesson. This image offers another way to remember it.

Sources and further study

Examples and explanations by Alibomics. Numeric illustrations are not current market quotations.