Compare arithmetic average return against the geometric (CAGR) return that actually matters.
The arithmetic mean of investment returns overstates actual performance whenever returns vary year to year. If a portfolio gains 50% then loses 50%, the arithmetic average is 0% — but you actually lost 25% of your money. The geometric mean (CAGR) accounts for compounding and represents the true annual growth rate. The difference between the two is called volatility drag and equals roughly half the variance of returns.
Arithmetic mean return
Arithmetic mean = (r₁ + r₂ + … + rₙ) / n
Geometric mean return (CAGR)
Geometric mean = [(1+r₁)(1+r₂)…(1+rₙ)]^(1/n) − 1
CAGR from start/end value
CAGR = (End Value / Start Value)^(1/n) − 1
This follows from the AM-GM inequality in mathematics. Any time there is variation in returns, the geometric mean will be strictly less than the arithmetic mean. The greater the volatility, the larger the gap. Only when every year has the exact same return are they equal.
Always use the geometric mean (CAGR) for forecasting what your money will actually grow to. The arithmetic mean is useful for estimating expected return in a single future period, but for multi-year projections the geometric mean is the correct tool.
Volatility drag is the return lost due to the asymmetry of gains and losses. A 50% loss requires a 100% gain to break even. The larger the swings in returns, the more this effect erodes wealth. Diversification and lower-volatility strategies reduce drag.
A −100% return means the entire investment was wiped out, making the geometric mean undefined (you'd be taking the nth root of zero). This calculator rejects returns at or below −100% because no meaningful multi-year average exists.