The average return is the one number your money never earns
Hold US stocks from 1928 to 2025 and the average annual return is 11.86%. Compound the actual years and you get 10.02%. Nobody was cheated, and the missing 1.84 points a year were never yours to begin with.
Take a year that gains 10% and a year that loses 10%. The average return is zero. A pound put through both is worth 99p, because (1 + p)(1 − p) = 1 − p², and the p² never comes back. Nothing went wrong; no fee was charged. The average simply is not the thing that happened to the money.
That gap has a size. Over 1928–2025 the arithmetic mean of US equity returns is 11.86% and the compound rate is 10.02% — a drag of 1.84 points a year, against half the variance of 1.86. The agreement is not a coincidence: a small return contributes r to the mean but only about r − r²/2 to compounding, and averaging that r²/2 term is half the variance. Across equity shares from 0% to 100% the measured drag lands between 0.93 and 0.99 times half the variance.
So the first correction is mechanical, and a smoother 8% genuinely beats a wilder 8%. But it is the smallest of the four.
Your money experiences an order, not a set
Compounding does not care about order. Multiply a pot by thirty growth factors in any sequence and the answer is the same product, measurably the same, to sixteen decimal places. This is why a savings calculator can honestly ask only for an average.
Start withdrawing and the symmetry breaks, because a subtraction interleaved with multiplications does not commute with them. Retire in 1929 with a million, draw 4% in the first year and raise it with prices, hold 60/40, and the pot is empty by 1950. Run the identical thirty years in reverse order and it ends at $3.48 million. Same returns, same average, same everything except which years arrived first.
No summary statistic distinguishes those two retirements. They differ only in a quantity the average deliberately discards.
The average weight is not where the risk is
A 60/40 portfolio sounds like a compromise: most of the money in shares, a serious minority in bonds. Split the risk instead of the money and the equity sleeve carries about 90% of the portfolio's variance while holding 60% of the capital. The split is exact: portfolio volatility is homogeneous of degree one in the weights, so Euler's theorem divides it among the holdings with nothing left over.
This is why the phrase "balanced fund" can be true of the money and false of the experience, and why risk-parity strategies exist at all: they are the answer to noticing that 60/40 by capital is roughly 90/10 by risk.
And the average itself is barely known
The three corrections above all assume you at least know the average. You mostly do not.
Over the same 98 years, small US companies beat large ones by 5.92% a year, and did so in 49 of those 98 years. A coin flip that pays 5.92% on average is still a coin flip, and its standard deviation of 27.48% is the reason. To pull an average that size two standard errors clear of zero you need roughly 87 years of data. The record holds 98, so the size premium clears the bar by a whisker.
The term premium does not clear it at all. Lending long rather than short paid 1.41% a year with a standard deviation of 7.63%, a t-statistic of 1.82, and a required sample of about 118 years. There is not enough history. Not "we should gather more" — there is not enough history, and there will not be for another twenty years.
That figure is itself optimistic, because it assumes each year is an independent draw. Credit spreads and term premia persist for years at a time, and persistence shrinks the effective sample further.
What survives
None of this says premia are fake or that investing is hopeless. It says something narrower and more useful: the confidence usually attached to a long-run average is borrowed from the size of the number rather than earned from the size of the sample.
The four corrections are separable, and only one of them is a matter of behaviour. Volatility drag is arithmetic and cannot be avoided, only reduced by holding less volatile things. Sequence risk is arithmetic too, but it only bites while money is being withdrawn, which is exactly when most people have stopped paying attention to it. The risk-versus-capital split is a modelling choice you can make deliberately. The uncertainty around the average is a fact about the world, and the honest response is to hold the estimate loosely rather than to switch strategy after a bad decade.
An average is a summary of years that already happened, computed after the fact, in an order that has been thrown away. It is a good way to describe a century. It has never been a description of anyone's money.