Arithmetic vs Geometric Mean

Most performance headlines report the arithmetic mean — the simple average of yearly returns. But your account balance grows at the geometric mean, the compound annual growth rate. The difference between them is volatility drag: rough returns erode compounding, so the average return always flatters the real outcome.

Why Volatility Costs You

Returns of +50% and −50% average to 0%, but $1,000 becomes $750. Losses compound against a shrinking base while gains compound from a smaller one. The geometric mean captures this: with 50% and −50%, the CAGR is −13.4% despite a 0% arithmetic average. Smooth, consistent returns beat volatile ones at equal averages.

Using the Numbers

For projections and goal planning, always use the geometric mean. For comparing managers or funds over the same period, arithmetic mean plus volatility tells you the full story. A high arithmetic mean with high volatility is the classic illusion — the geometric mean reveals what you'll actually keep.