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Geometric return

The constant per-period return that would produce your actual ending balance, which is the only average that matches reality.

Compounding against a flat returnTwo account balances over fifteen years at the same yearly rate: one curve bends upwards as gains are left in, the other rises in a straight line.ACCOUNT VALUE$10k$20k$30k$40k051015YEARSCOMPOUNDED 10% a yearSIMPLE: 10% of the original sumboth start at $10,000 and run 15 years$41,772DIFFERENCE$16,772$25,000
Compounding against a flat return. Two accounts start at $10,000 and earn 10% a year for fifteen years. Leaving the gains in means each year earns on a larger balance, so the curve bends away from the straight line and ends $16,772 higher.

Multiply the return factors, take the nth root, subtract one. For the sequence 1.20, 0.85, 1.25, 0.90: product 1.1475, fourth root 1.0350, so 3.50% per quarter.

It is always less than or equal to the arithmetic-return, with equality only when every period is identical. A useful approximation is geometric ≈ arithmetic minus variance / 2, which makes the penalty explicit: a strategy averaging 12% with 30% volatility gives up roughly 4.5 points to variance and compounds nearer 7.5%.

This is why volatility is not merely discomfort - it is a direct deduction from compounded wealth, and why halving position size can raise long-run growth even when it lowers average return. It is also the number every honest track record should quote.

Related: arithmetic-return, variance-drain, annualised-return, compounding

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