CAGR

CAGR formula and worked example

CAGR answers a specific question: what constant annual growth rate connects a starting value to an ending value? With a positive starting value and a holding period longer than zero, the formula is CAGR = (ending value / starting value)^(1 / years) - 1. Multiply by 100 to express the result as a percentage.

For an investment that grows from $10,000 to $15,000 in five years, the calculation is (15,000 / 10,000)^(1/5) - 1, or about 8.45% a year. This is an annualized summary of those endpoints. It does not mean the investment earned 8.45% in each calendar year. Enter your own endpoints in the CAGR calculator.

CAGR versus an arithmetic average

A 20% gain followed by a 20% loss takes $100 to $120 and then to $96. The arithmetic average of those two returns is zero, but the investment lost 4% overall. Its two-year CAGR is approximately -2.02%. Multiplying the period growth factors captures the changing base; averaging the percentages does not.

FINRA's guide to calculating investment returns explains why annualizing a return differs from dividing the total percentage gain by the number of years. FINRA also emphasizes including investment income and costs when evaluating performance.

When account balances give the wrong answer

The simple endpoint formula assumes there are no external deposits or withdrawals during the interval. If you add $5,000 to a $10,000 account and it ends at $15,000, the balance rose 50%, but that alone establishes no investment gain. Cash flows need separate treatment, such as a money-weighted return using their dates and amounts, or time-weighted subperiod returns.

Use a consistent definition of value. A share-price CAGR excludes cash dividends that were paid out. A total-return series with dividends reinvested answers a different question. State whether the numbers include fees, taxes and inflation, and compare like with like.

What CAGR leaves out

CAGR hides the path between the endpoints. Two investments can share the same CAGR even if one suffered a severe drawdown. It also depends on the chosen dates and is not a forecast of future returns. Negative starting values do not support the usual investment interpretation. A complete loss has a -100% endpoint return; it provides no remaining capital from which to compound a recovery.