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Compound annual growth rate

The constant annual rate that would take a starting value to an ending value over a period; the standard way to express multi-year performance.

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.

The formula is (ending / beginning) ^ (1 / years) - 1. Growing $50,000 to $86,000 over seven years gives (86,000 / 50,000) ^ (1/7) - 1 = 8.05% a year.

CAGR smooths away the path entirely, which is its use and its danger. Two strategies with identical 8% CAGR can have maximum drawdowns of 12% and 55%. Always publish CAGR beside max-drawdown and a volatility figure.

Note also that CAGR is not the arithmetic average of annual returns. A +50% year followed by a -50% year averages 0% but compounds to -13.4%, a CAGR of -6.9%. The gap between arithmetic and compound return widens with volatility, which is the arithmetic reason volatility drag matters.

Related: total-return, max-drawdown, time-weighted-return, volatility-drag, sharpe-ratio

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