Average Return: Arithmetic vs Geometric Mean Explained

Published October 11, 2026

Free tool: Average Return Calculator→

If an investment returned 12%, −5%, 15% and so on over ten years, what was its "average" return? There are two very different answers, and the more common one is the misleading one. This guide explains the arithmetic and geometric averages, why they differ, and how volatility eats into returns, using the free Average Return Calculator.

The classic trap: +50% then −50%

Suppose $100 rises 50% one year and falls 50% the next:

• Year 1: $100 → $150
• Year 2: $150 → $75

The arithmetic average of the two returns is (50% − 50%) ÷ 2 = 0%, suggesting you broke even. In reality, you lost a quarter of your money. The geometric average, which compounds the returns, gives the true answer: about −13.4% a year, since 0.866 × 0.866 ≈ 0.75.

The two averages

• Arithmetic mean: add up the yearly returns and divide by the number of years. It describes a typical single year, but overstates growth over several years.
• Geometric mean: (final value ÷ starting value)^(1 ÷ years) − 1. It's the constant yearly return that would produce the same ending value. This is also the compound annual growth rate (CAGR).

The geometric mean is always lower than or equal to the arithmetic mean; the gap grows with volatility, how much the returns jump around.

Worked example: ten years of returns

$10,000 invested for ten years with these yearly returns:

12%, −5%, 15%, 8%, −3%, 20%, 10%, −8%, 18%, 5%

The arithmetic average suggests 7.2% a year, but the money actually grew at 6.79% a year: the volatility, with three down years, cost about 0.4 percentage points a year. Over ten years, that's the difference between $20,000 and $19,287.

Why volatility costs you

A loss needs a bigger gain to recover: after a 20% fall, you need a 25% rise to get back to where you started; after a 50% fall, you need 100%. That's why steady returns compound better than bumpy ones with the same arithmetic average. A useful rule of thumb: the geometric mean is roughly the arithmetic mean minus half the variance (the standard deviation squared).

Which average should you use?

• For your actual growth over time, or comparing investments: the geometric mean (CAGR).
• For a typical year, or as an input to some statistical forecasts: the arithmetic mean.

When a fund advertises an "average annual return", check which one it means. Most reputable reports of multi-year performance use the annualized (geometric) figure.

How to use the Average Return Calculator

1. Open the Average Return Calculator.
2. Enter your initial investment.
3. Add each year's return in percent with Add Annual Return, in order; remove any with its delete button. The calculator starts with the ten-year example above.
4. Read the results: the arithmetic mean, the geometric mean (CAGR), the final value and the standard deviation, with charts and a year-by-year table of the portfolio value, gain or loss and cumulative return.

For a quick CAGR from just a start and end value, use the CAGR Calculator.

Frequently asked questions

What's the difference between arithmetic and geometric mean returns?

The arithmetic mean is the simple average of yearly returns; the geometric mean compounds them to give the true average growth rate. For investments held over several years, the geometric mean is the accurate one.

Why is the geometric mean lower?

Because losses hurt more than equal gains help: a 50% loss followed by a 50% gain leaves you 25% down. The more returns swing, the bigger the gap between the two averages.

Is CAGR the same as the geometric mean return?

Yes. Both describe the constant yearly rate that turns the starting value into the ending value.