Skip to content
Compounding · Average vs. Geometric

The average return that never happened

A portfolio earns a different number every year, and those returns compound in sequence — a single bad year shrinks the base every later gain must rebuild from. The arithmetic average of those yearly returns flatters that journey, because it ignores how losses and gains interact; the geometric CAGR is the one honest rate that turns your starting dollar into the balance you actually ended with.

$292,664Actual ending balance
$10,000 compounded at a 10.1% CAGR
+$130,700Money the average return wrongly implies
the average-return projection overstates the truth by 1.2% a year
Over 35 years the arithmetic-average projection grows to $423,364 — but the same returns, taken in the order they actually arrived, compound to only $292,664.
The honest figure is the CAGR of 10.1%, which lands the portfolio within a dollar of its true ending value, while the quoted 11.3% average overstates it.
Portfolio value over time
Actual · returns compounded in sequenceAverage-return projection · the illusionCAGR · the honest constant rate
Compounding the 11.3% arithmetic average would imply $423,364, but the sequence actually delivered $292,664 — the average overstates your real outcome by $130,700, a 1.2%-per-year illusion the CAGR strips away.
Initial investment$10,000
Start year1990
S&P 500 allocation90% S&P · 10% bond

Slide the start year back to a decade that opened with a crash, and watch the ember line — the average-return projection — float above the real gold trajectory. That gap is not a rounding error; it is money a brochure can quote as your "average annual return" even though no investor ever held it. Volatility is the tax, and the arithmetic mean is blind to it.

The CAGR line sits exactly on top of where actual compounding lands, because that is what CAGR is defined to do: the single constant rate that reconciles your beginning and ending balance. When someone advertises a fund by its average yearly return, ask for the CAGR instead — the spread between them is precisely the part of the story the average erases.

Model assumptions, all adjustable above: returns are the historical annual series for a blended S&P 500 / U.S. Treasury portfolio, applied with no contributions, fees, taxes, or rebalancing drag; the average projection compounds the simple arithmetic mean of the realized yearly returns. A teaching instrument, not financial advice.