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CAGR vs average annual return

By the CAGR Calculator team · Published

Quick answer

The average annual return adds up each year’s return and divides by the number of years (an arithmetic mean). CAGR is the constant rate that actually links the start and end values (a geometric mean). When returns vary, the average is always higher: gaining 50% then losing 50% averages 0%, but the CAGR is −13.40% — you really lost money.

Average annual return
Sum of yearly returns ÷ number of years
CAGR
(End ÷ Start)^(1 ÷ Years) − 1
+50% then −50%
Average 0% · CAGR −13.40%
Rule of thumb
CAGR ≈ average − (volatility² ÷ 2)
Use for real growth
CAGR

A five-year example

$10,000 is invested and earns these returns:

YearReturnValue at year end
1+20%$12,000
2−10%$10,800
3+30%$14,040
4−25%$10,530
5+15%$12,110
  • Average annual return: (20 − 10 + 30 − 25 + 15) ÷ 5 = 6.00%
  • CAGR: (12,110 ÷ 10,000)^(1/5) − 1 = 3.90%

If the investment had really grown 6% every year, it would be worth $13,382 — about $1,270 more than it is. The average describes a portfolio that never existed. CAGR describes yours: 10,000 × 1.0395 = 12,110.

Why the average is always too high

Returns compound by multiplication, not addition. A 25% loss takes $14,040 down to $10,530, and the next year’s 15% gain is earned on that smaller base. The arithmetic mean treats each percentage as if it applied to the same starting amount, so it gives losses too little weight. Mathematically, the geometric mean can never exceed the arithmetic mean (the AM–GM inequality), and the gap widens as returns become more volatile.

The volatility drag shortcut

CAGR ≈ Average return − (Standard deviation² ÷ 2)

In the example, the yearly returns have a standard deviation of about 20.3%. So CAGR ≈ 6.00% − (0.203² ÷ 2) ≈ 3.93% — very close to the exact 3.90%. This “volatility drag” is why two funds with the same average return can leave you with very different amounts: the steadier one compounds to more.

Same average, different outcomes

Two-year pathAverageCAGR$10,000 becomes
0%, 0%0%0.00%$10,000
+40%, −40%0%−8.35%$8,400
+50%, −50%0%−13.40%$7,500

Which number to use

  • To measure what happened to your money: CAGR. It is the figure fund fact sheets label “annualised return”.
  • To compare investments over different periods: CAGR, ideally over the same dates.
  • To estimate next year’s expected return in a statistical model: the arithmetic average has a role there — but not as a growth rate.
  • When money was added along the way: neither — use XIRR.

Paste a series of yearly values into the Yearly data tab of the CAGR calculator to see both numbers, plus best and worst years and volatility, side by side. For stocks, thestock CAGR calculator explains how dividends change the picture.

Sources and further reading

Educational information only — not investment advice. Past performance does not guarantee future results.

Related questions

Why is CAGR lower than the average annual return?

Because losses hurt more than equal gains help: after a 50% fall you need a 100% gain to break even. The arithmetic average ignores this; CAGR, the geometric mean, includes it. The more returns vary, the bigger the gap.

Can CAGR ever be higher than the average return?

No. The geometric mean is always less than or equal to the arithmetic mean. They are equal only when every year’s return is exactly the same.

Which should I use to compare mutual funds?

CAGR (often labelled “annualised return”). It reflects what actually happened to money left in the fund. The average annual return is useful only as an input to statistical models, not as a measure of growth.

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