CAGR vs Average Return: Why the Two Disagree

An investment that gains 50% and then loses half of what is left has an average return of zero. The money is down a quarter.

That gap between the average return and what actually happened is the difference between the arithmetic mean and the compound annual growth rate (CAGR). From 2000 to 2009 US shares averaged plus 1.12% a year. Over the same ten years $10,000 in them fell to $9,037.

The average return is the mean of the yearly returns. CAGR is the single rate that reproduces the whole run.

Take the two-year example. A dollar grows to $1.50, then halves to $0.75. The two yearly returns are plus 50% and minus 50%, so the arithmetic mean is 0%.

No year delivers the average. Both years happen, one after the other. What is left is 75 cents.

CAGR asks a different question: what single rate, applied twice, turns $1 into $0.75? The answer is minus 13.40% a year. It is the rate that reproduces the actual outcome.

Chart 1 sets the two measures against each other on US shares. Throughout this guide that means SPY (the S&P 500 exchange-traded fund, or ETF) with dividends reinvested, measured by calendar year. The arithmetic average sits above the CAGR in every window.

Because a loss takes back more than the same percentage gain puts on.

A 50% loss needs a 100% gain to recover. A 20% loss needs 25%. The gain is earned on the smaller sum left behind, so the percentages are not symmetric. Unless every return is the same, a run of returns averaging zero ends below where it started.

Chart 2 plots each calendar year from 1994 to 2025 against that window's compound rate of 10.71%. The years scatter widely around it. That scatter is the whole reason the two measures differ.

The arithmetic average is greater than or equal to the CAGR for any set of returns. The two are equal only when every year is the same.

A steady series has almost no gap. A violent one has a wide gap.

When the returns are spread out. A decade can then show a positive average while the money falls.

From 2000 to 2009 the arithmetic average return on US shares was plus 1.12% a year. On that figure alone the decade looks flat but positive.

Chart 3 follows $10,000 through those ten years. It ends at $9,037, a fall of 9.6%. The CAGR is minus 1.01% a year. Compounding at the arithmetic average instead would have shown $11,176.

Source: YX Insights price data

The table gives three windows. Over the 32 years from 1994 the gap is 1.57 percentage points a year. Over the twenty years from 2006 it is 1.52. Over the 2000s it is 2.13, because the returns were spread widely, from minus 36.81% in 2008 to plus 26.37% in 2009.

The effect is just as large over a long window. From 1994 to 2025, $10,000 in US shares became $259,050. Compounding at that window's arithmetic average of 12.27% would have claimed $406,403, overstating the result by about $147,000.

2008 and 2009 make the mechanism visible on their own. The market fell 36.81%, then rose 26.37%. The average of those two years is minus 5.22%. The CAGR is minus 10.64%. At that rate $10,000 becomes $7,985.

CAGR, for the question of what an investment delivered.

A past result is a move from one sum to another. CAGR is the rate that describes it, so any performance figure, a fund's record, a backtest, a track record, belongs in compound terms. CAGR assumes no money went in or out along the way.

The arithmetic average has its uses. It is the right input when estimating a single future period. It does not answer the question of what an investment delivered.

Our guide to reading a backtest covers the other places a performance figure can mislead.

The check on any figure described as an average annual return is to compound it over the same number of years and compare the result with the actual ending value. Over a calm stretch the two are close. Over a volatile one they are not. The average can only flatter.

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The average annual return adds the yearly returns and divides by the number of years. CAGR is the single annual rate that would turn the starting value into the ending value. Gain 50% then lose 50% and the average is 0%, while the CAGR is minus 13.40% and $100 has become $75.

It is never higher. It is lower whenever the yearly returns differ. The two are equal only when every year's return is identical. The gap widens the more the yearly returns are spread out.

Because the gain is calculated on the smaller amount left after the loss. $100 falling 50% leaves $50. That $50 must double to get back to $100. The same asymmetry applies at every size, which is why a series averaging zero ends below where it started unless every return is the same.

CAGR. It is the rate that reproduces the actual outcome, so it answers what the investment did. The arithmetic average answers what the yearly returns average to, which is a different question. Over a volatile period the arithmetic average is the more flattering of the two.

DISCLAIMER: This article is strictly educational. Any information or analysis in this note is not an offer to sell or the solicitation of an offer to buy any securities. Nothing in this note is intended to be investment advice and nor should it be relied upon to make investment decisions. Any opinions, analyses, or probabilities expressed in this note are those of the author as of the note's date of publication and are subject to change without notice.