At a 5% real return, a portfolio's annual investment gain first exceeds its annual contribution in year 16. Cumulative gains overtake cumulative contributions in year 27.
Both numbers come from arithmetic, not from history. Neither one changes if you double the amount saved.
That second sentence is the whole argument. The crossover is a fact about the shape of the curve. It says nothing about the height.
The model, stated in full
Here's every assumption. A saver contributes a fixed real amount once a year, at the end of the year. The portfolio earns a constant real return, r, in every single year. Nothing is withdrawn. There are no fees, no taxes and no gaps in contributions. The horizon runs 40 years.
That's a spreadsheet, not a forecast. Real portfolios don't earn the same return twice running. Real savers change jobs, stop contributing and take money out. The model earns its keep by isolating one question: when does the compounding term start to dominate the contribution term? Adding realistic noise makes the answer fuzzier without changing its structure.
The balance after t years is B(t) = C x [(1+r)^t - 1] / r, where C is the annual contribution. Cumulative contributions are simply C x t. Everything below falls out of those two expressions.
Two crossovers, not one
"Returns take over" can mean two different things. They happen about a decade apart.
The first is a flow crossover. It's the year in which the investment return earned during that year first exceeds the contribution paid in during that year. At a 5% real return, that's year 16.
The second is a stock crossover. It's the year in which total returns ever earned first exceed the total amount ever contributed. At the same 5% real return, that's year 27.
The eleven-year gap matters. For more than a decade after the portfolio starts out-earning the saver annually, contributed money is still the larger share of the balance. A statement showing a big gain in one year doesn't mean the pot is mostly market gains.
Run the same model to 40 years and the balance is 120.8 times one year's contribution. Of that, 40 is contributed and 80.8 is return, so returns are 66.9% of the end value. Cut the return assumption to 3% and returns fall to 47.0% of the balance after four decades. Raise it to 6.6% and they reach 77.8%. The end state is return-dominated in every case. The path to it isn't.
Why the contribution amount cancels out
The return earned in year t is r x B(t-1). Substituting the balance formula gives C x [(1+r)^(t-1) - 1]. Set that above C and the contribution term cancels on both sides of the inequality.
What's left is (1+r)^(t-1) > 2. The condition is a doubling. Annual returns exceed annual contributions in the first year after a single pound invested at the start would have doubled.
At 5% a year, doubling takes 14.2 years. Fifteen full years clears the bar, so the crossover lands in year 16. A saver putting away 100 pounds a year and one putting away 100,000 pounds a year reach it on the same date. Every figure on the chart simply scales by the same multiple.
The cumulative crossover behaves the same way. It requires [(1+r)^t - 1] / r > 2t, which again contains no C.
How far the return assumption moves it
The return does move both dates, and it moves them sharply.
- 3% real: flow crossover in year 25, cumulative crossover in year 44.
- 4% real: year 19 and year 33.
- 5% real: year 16 and year 27.
- 6.6% real: year 12 and year 21.
- 8% real: year 11 and year 18.
Halving the assumed return from 6% to 3% pushes the flow crossover from year 13 to year 25. The relationship isn't linear, because the underlying condition is a doubling time.
Where the return assumptions come from
The 6.6% figure isn't invented. It's the annualised real return on US equities from 1900 to 2025 in the Dimson-Marsh-Staunton database, published in the UBS Global Investment Returns Yearbook 2026. Over the same 126 years, US bonds returned 1.6% a year in real terms and Treasury bills returned 0.5%. US inflation averaged 2.9%.
US equities are the flattering case. The 2025 edition of the same yearbook reports that across the 21 markets with continuous histories, the average annualised real bond return from 1900 to 2024 was 0.9%. Any portfolio holding a meaningful weight in bonds sits below the equity line.
Costs pull it down further. A percentage point of annual charges is a percentage point off r, and the list above prices that in years. The long-run compounding of exactly that gap is set out in the comparison of 0.2% and 1% fund fees over 30 years, which is the same arithmetic viewed from the cost side.
What people actually contribute
Vanguard's How America Saves 2025 covers nearly five million defined contribution participants. In 2024 the average employee deferral rate was 7.7% of pay and the median was 6.8%. Adding employer contributions, the average total rate was 12.0% and the median 11.5%.
Those averages hide a steep age gradient. Participants under 25 deferred an average of 5.5% of pay. The 55-to-64 group deferred 9.3%, and the over-65s 10.1%. Saving rates rise with age. That is the opposite of the pattern the crossover arithmetic rewards.
Balances follow the same shape. Median account balances ran from $1,948 for participants under 25 to $16,255 at ages 25-34, $39,958 at 35-44 and $95,642 at 55-64.
Employer money matters to the sum being modelled. Some 96% of Vanguard plans provided an employer contribution, which is why the average total rate of 12.0% sits so far above the 7.7% employees choose themselves. In the model, an employer match simply raises C. It doesn't shift either crossover by a single year.
Coverage outside employer plans is thinner. The Federal Reserve's 2022 Survey of Consumer Finances found that 54.3% of US families held any retirement account. Among those that did, the median value was $86,900 and the mean was $334,000. The distance between those two figures is the usual reminder that averages describe very few people.
UK figures tell a similar story from a different angle. The ONS reports that 82% of UK workers were members of a workplace pension in 2024. Median employer contributions in the private sector were 6% of qualifying earnings for men and 5% for women, against 27% and 26% in the public sector.
The case against the crossover framing
The strongest objection isn't that the arithmetic is wrong. It's that mainstream life-cycle economics argues that back-loading contributions can be entirely rational. Earnings rise with age, and smoothing consumption across a working life means spending more of a thin early income.
There's real evidence behind that. Scholz, Seshadri and Khitatrakun built a life-cycle model with uncertain lifetimes, uninsurable earnings and medical expenses, then solved it household by household against Health and Retirement Study data. They found that over 80% of households had accumulated more wealth than their optimal targets. Fewer than 20% fell short, and those deficits were generally small.
The earnings premise holds up too. Guvenen, Karahan, Ozkan and Song, using a 10% panel of US Social Security records, found that average earnings rise 60% from age 25 to age 55 for the median lifetime-earnings group, and 4.8-fold at the 95th percentile. For the top 1% the multiple is 27.8-fold. If income is going to rise like that, deferring saving is a defensible choice rather than a mistake.
Three things weaken the objection anyway.
First, the crossover date is invariant to the contribution level. Saving more never moves it. So "returns take over in year 16" can't be evidence that saving less early is harmless. Year 16 applies identically to someone saving 3% of pay and someone saving 15%.
Second, the arithmetic weights early money heavily. Over 40 years at a 5% real return, the first ten years of contributions are a quarter of the money but 45% of the final balance. At 6.6% they are 51% of it.
Third, delay costs more than the framing suggests. Contributing for 30 years instead of 40 at the same rate leaves 55% of the balance. Matching the 40-year outcome from a decade-late start takes 1.82 times the annual contribution, every year, for 30 years.
The Scholz result also has limits the authors are careful about. It rests on 1992 wealth data from a cohort with far more defined benefit pension coverage than workers have now. Exclude half of housing equity from the resources counted and the share meeting targets falls from over 80% to 57.9%. Whether it carries over to a defined-contribution cohort is open, not settled.
The contribution effect, and what it hides
Contributions dominating early has a second-order consequence. Vanguard states it plainly: because of ongoing contributions, account balances "will appear to be less negatively impacted during falling markets". The report calls this the contribution effect and notes it "may mask the psychological impact of falling stock prices".
In 2024, among participants holding a balance at both ends of the year, the median balance rose 23% and 93% saw an increase. Payroll deductions did part of that work. A saver in year three watching a rising balance is largely watching their own contributions.
It cuts both ways. Early on, a bear market barely dents the balance, which makes it easy to overestimate one's tolerance for loss. Later, once returns dominate, the same market move lands with full weight. The distance between what a fund returns and what its investors actually capture is documented in the evidence on what bad market timing costs.
What would change the conclusion
Several things could. They're worth naming precisely.
Returns don't arrive in a constant stream. The 2025 yearbook records that US equities bottomed in July 1932 and didn't recover in real terms until February 1945, fifteen and a half years later. After the 1973-74 crash they were underwater for over a decade. In a sequence like that, a crossover computed from a smooth average means very little. Order of returns drives outcomes, which is the point made by the sequence-risk evidence on identical average returns producing opposite results.
Contributions aren't level either. The same Social Security panel shows that workers below the 20th percentile of lifetime earnings see their earnings decline from age 25 to 55. For them a model with flat or rising real contributions is wrong in the direction that matters most.
Growing contributions push the crossover later, not earlier. Assume real contributions rise 2% a year and the flow crossover moves from year 16 to year 18, and the cumulative crossover from year 27 to year 29. The thing being overtaken keeps rising, so it takes longer to overtake.
Fees, taxes and cash drag all reduce r. Start from a 5% gross assumption, subtract a point of total cost, and the flow crossover slides from year 16 to year 19 while the cumulative one slides from year 27 to year 33.
Withdrawals break the model outright. So does an interruption that forces contributions to stop, which is one reason reserve sizing turns out to be a question about income volatility rather than a fixed multiple of spending.
Finally, real against nominal. Everything here uses real returns and real contributions. Run the same arithmetic on nominal figures and the crossover arrives several years earlier, because inflation inflates the return term while the contribution term is held flat. That's a measurement artefact rather than a gain.
What the arithmetic supports
Two claims survive all of that.
The crossover is real, and it's late. Under conventional assumptions, most of a portfolio's balance is contributed money for roughly the first quarter of a century.
And the crossover date carries no information about how much to save. It's a function of the assumed return alone. The height of the curve, which is the part that determines whether the eventual balance is adequate, is set entirely by contributions.