The difference in one table
| Metric | Formula idea | What it answers |
|---|---|---|
| CAGR | Geometric endpoint growth | What constant compound rate links start and end? |
| Arithmetic average return | Sum of yearly returns ÷ number of years | What is the simple average of the observed annual returns? |
CAGR formula
CAGR = (Ending Value ÷ Starting Value)^(1 ÷ Years) − 1
CAGR compounds. It does not average the percentages reported in each individual year.
Average annual return formula
If yearly returns are r1, r2, and r3, a simple arithmetic average is:
Average Return = (r1 + r2 + r3) ÷ 3
This is easy to calculate, but it does not reproduce the ending value when the yearly returns vary because investment growth compounds multiplicatively.
Worked example: +50% followed by −50%
Suppose $100 grows by 50% in year one and then falls by 50% in year two.
- After year one: $100 × 1.50 = $150.
- After year two: $150 × 0.50 = $75.
- Arithmetic average return: (50% + −50%) ÷ 2 = 0%.
- CAGR from $100 to $75 over two years: about −13.40%.
The arithmetic average is 0%, yet the value actually declined from $100 to $75. CAGR captures that compounded endpoint loss.
Why volatility creates a gap
When annual returns differ, gains and losses apply to a changing base. A 50% loss requires a 100% gain just to get back to the starting value. Arithmetic averaging treats the percentages as additive observations; compounded growth treats them as multiplicative factors.
The more volatile the annual returns are, the more likely the arithmetic average and compounded growth rate are to diverge.
When the two can match
If every annual return is identical, the arithmetic average and CAGR are the same. For example, if a value grows exactly 10% in each of three years, both measures are 10%.
Which metric should you report?
- Use CAGR when you want one compounded annual rate connecting a beginning value to an ending value.
- Use arithmetic average return when you specifically need the mean of a set of yearly observations and understand that it is not a compounded growth rate.
- Show both when discussing a volatile return history, because the difference itself can be informative.
Terminology warning
“Average annual return” is sometimes used loosely. A page, report, or platform may mean arithmetic average, geometric average, or annualized return. Check the formula or methodology before comparing figures from different sources.