CAGR: Calculate Annualized Growth without Hiding the Path

Write the endpoint equation

For positive beginning value B, positive ending value E and elapsed time T in years, CAGR is (E ÷ B) raised to the power 1/T, minus one. The equation comes from solving E = B × (1 + g) to the power T for a constant annual growth rate g. The time basis must be stated, especially when the interval is not an exact number of years.

PerformanceAnalytics documents annualizing a chained return series. A properly constructed return series can account for information that simple raw account endpoints omit. Do not substitute ending account balance for cumulative performance when external cash flows occurred.

Verify a three-year example

Assume 10,000 grows to 13,310 over exactly three years without deposits or withdrawals, after the costs included in the measurement. The value ratio is 1.331. Its cube root is 1.10, so CAGR is 10% per year. Checking forward, 10,000 × 1.10 × 1.10 × 1.10 returns 13,310.

That same endpoint can result from a volatile sequence. Returns of +50%, −20% and approximately +10.91667% also multiply to 1.331. CAGR remains 10%, despite the very different experience. It does not show the losing year, the interim peak or the maximum drawdown.

Understand short-sample annualization

If a hypothetical account gains 5% over exactly one quarter of a year, annualizing the factor gives 1.05 to the fourth power minus one, or 21.550625%. This number describes repeating the quarter's growth factor four times. It is not evidence that the next three quarters will resemble the first.

State actual elapsed time and the observation dates beside the annualized figure. For example, calling a 70-day sample “three months” changes the exponent. Different day-count conventions can produce small differences, so use a documented convention rather than selecting the one that produces the most attractive output.

Recognize invalid interpretations

If 10,000 becomes 15,000 solely because 5,000 was deposited, the raw ratio suggests 50% growth even though trading may have earned nothing. Use time-weighted subperiod returns or an appropriate money-weighted measure when answering a cash-flow-sensitive question. Those methods solve different questions and should not be relabeled as the same endpoint CAGR.

Zero or negative beginning value and non-positive duration make the ordinary formula invalid. A zero ending value represents total loss under the simple model, while a negative ending value requires liability-aware analysis rather than a routine percentage. Always report costs, currency, sample duration and relevant path statistics alongside CAGR. In copied-account comparisons, synchronize the time interval and cash-flow treatment before attributing a difference to trading execution.