Key takeaways
Growth rates compound, so their average is a geometric mean, not an arithmetic one. The compound annual growth rate is the single rate that would have produced the same end result.
- Never average percentage growth rates arithmetically.
- CAGR = (end ÷ start)^(1 ÷ years) − 1.
- A loss followed by the same percentage gain leaves you below where you started.
The trap
An investment gains 50 % one year and loses 50 % the next. The "average" is 0 %, but $100 became $150 and then $75: a 25 % loss.
The honest average
Compound annual growth rate: (end ÷ start)^(1 ÷ years) − 1. Here (75 ÷ 100)^(1 ÷ 2) − 1 = −13.4 % per year, which is what actually happened on average.
A longer example
Revenue grows from $2.0 M to $3.2 M over four years: (3.2 ÷ 2.0)^(0.25) − 1 = 12.5 % per year, regardless of how uneven the individual years were.
Related questions
- What is CAGR?
- How do I calculate average growth over 5 years?
