Quick answer: Returns of 10%, −5%, 20%, 8% and 12% average 9% arithmetically, but the investment actually grew at 8.69% a year (CAGR), turning 10,000 into 15,168.38.
How it's calculated
Arithmetic average = sum of returns ÷ number of years. Geometric average (compound annual growth rate, CAGR) = (product of (1 + return))^(1/n) − 1: the steady yearly rate that gives the same end result.
The geometric average is never above the arithmetic one, and the gap grows with volatility. After +100% and −50% the arithmetic average is 25%, but you are back where you started: the geometric average is 0%.
Use the geometric average for what an investment actually earned per year; the arithmetic average is an estimate of a typical single year. With only a start and end value, use the ROI calculator.
Worked examples
- 10, −5, 20, 8, 12: arithmetic 9%, geometric 8.69%
- +100, −50: arithmetic 25%, geometric 0%
Frequently asked questions
Which average do funds report?
Performance tables usually show average annual total returns, which are geometric (compound) averages over 1, 5 and 10 years.
What does the standard deviation show?
How much yearly returns swing around the arithmetic average. A higher figure means a bumpier ride and a bigger gap between the two averages.
How do I enter a loss?
With a minus sign: −5 or -5. Returns must be above −100%.
Why is the geometric average lower than the arithmetic one?
Losses hurt more than equal gains help. A 50% gain followed by a 50% loss averages 0% arithmetically, but turns 100 into 75, which is −13.4% a year.
Which average should I use for my own investment?
The geometric average (CAGR), because it shows the steady rate that gives what you actually ended up with.
Should I include deposits and withdrawals?
This tool assumes the same money stayed invested throughout. If you added or took out money, use the IRR calculator, which handles cash flows.