Sequence-of-returns risk — same average, different depletion year

Order only matters when money is moving

Start with the case where sequence risk does not exist, because it defines the boundary. A lump sum left untouched compounds by multiplication, and multiplication does not care about order: −20% then +20% ends in exactly the same place as +20% then −20%. Shuffle thirty years of returns any way you like and an untouched portfolio lands on the same terminal value to the penny. For a pure buy-and-hold accumulator with no cash flows, "sequence risk" is a misnomer — what that investor faces is uncertainty about the realized compound rate, not about its ordering.

Withdrawals break the symmetry. Every withdrawal is a sale at that year's prices, and a sale during a drawdown converts a temporary price decline into a permanent reduction in the number of shares you still own. Those shares are gone when the recovery arrives, so the recovery compounds on a smaller base. Contributions create the mirror image (early losses are cheap purchases), which is why the same crash that injures a retiree can quietly subsidize a saver. Sequence-of-returns risk is therefore a property of portfolios with flows — and a retirement portfolio under steady withdrawals is the strongest case of it.

A two-year example you can check by hand

Take $1,000,000, withdraw $50,000 at the start of each year, and apply two returns: −20% and +20%, in both orders.

Path	Year 1	Year 2	End balance
Down first	(1,000,000 − 50,000) × 0.80 = 760,000	(760,000 − 50,000) × 1.20	$852,000
Up first	(1,000,000 − 50,000) × 1.20 = 1,140,000	(1,140,000 − 50,000) × 0.80	$872,000
No withdrawals (either order)	1,000,000 × 0.80 × 1.20	—	$960,000

Same two returns, same 0% arithmetic average, same −2.0%-a-year compound average — and a $20,000 gap after two years, produced by ordering alone. Two years and two returns keep the arithmetic checkable; stretch the horizon to a thirty-year retirement and let the bad years cluster at the start, and the gap stops being a rounding story and becomes the difference between a plan that holds and one that runs dry.

The worked example: 1969–1998, forward and reversed

To make the ordering effect concrete on real data, take the thirty annual real returns of the S&P 500 (total return, dividends reinvested, deflated by December-over-December CPI-U) for 1969 through 1998 — Damodaran's NYU Stern series and BLS inflation, both asOf 2026-01, the same dataset our calculators run on. Build two paths from the identical thirty numbers:

• Path A — calendar order. 1969 first: the sequence opens −13.6%, −1.9%, +10.6%, +14.9%, then the 1973–74 crash lands in years 5 and 6 at −21.2% and −34.0% in real terms.
• Path B — the same thirty returns, reversed. 1998 first: the sequence opens +26.3%, +30.9%, +18.8%, +33.9%, and the 1974 crash does not arrive until year 25. This is a counterfactual permutation, not any actual retiree's history — it exists to isolate ordering while holding everything else fixed.

Because both paths use the same thirty returns, every order-blind statistic is identical: the arithmetic average is +8.4% real per year on both, the compound (geometric) average is +7.0% real per year on both, and a $1,000,000 portfolio with no withdrawals ends both paths at the same $7,619,855 in real terms. Any calculator that consumes only an average return rates these two retirements as the same retirement.

Now add the flows: withdraw a constant $50,000 in real terms (a 5% initial rate) at the start of each year, no taxes, no fees — deliberately stripped down so ordering is the only variable in play. Figures below are the engine's exact outputs in inflation-adjusted dollars.

End of year	Path A — 1969 first	Path B — same returns, reversed
1	$820,829	$1,200,030
5	$622,051	$2,166,892
10	$280,285	$3,166,397
15	$80,358	$5,069,656
16	$31,016	$5,916,230
17	depleted — cannot fund the withdrawal	$6,805,505
20	—	$7,128,301
25	—	$5,850,471
30	—	$4,734,317 remaining

Path A funds 16 years. Path B funds all 30 and ends with $4.7 million. The gap in depletion years is at least fourteen — "at least" because Path B is still compounding when the window closes. The same experiment at a $40,000 withdrawal (a 4% initial rate) narrows but does not close the gap: Path A fails in year 27 after funding 26 years, while Path B again survives all 30 with about $5.3 million left. Lowering the withdrawal rate buys years; it does not repeal the ordering effect.

It is worth pausing on what did not change between the two rows of that experiment: not the average return, not the compound return, not the volatility, not the terminal value of an untouched portfolio. A single summary statistic — "the market averaged 8.4% real over those thirty years" — is true of both paths and useless for distinguishing them. Depletion is decided by the interaction of the return path with the withdrawal schedule, and that interaction is exactly what point-estimate retirement calculators average away.

Why the damage concentrates early

The mechanics are visible in the table's first rows. Path A's retiree sells into weak prices from year one: by the end of year 10 the portfolio holds $280,285, so the recovery years that follow — 1975 arrives at +28.2% real — are compounding a base one-eleventh the size of Path B's $3.17 million at the same mile-marker. The −34.0% year of 1974 costs Path A's retiree about a third of a portfolio that still has 24 years of withdrawals ahead of it; the same −34.0%, arriving in Path B's year 25, subtracts from a portfolio that has grown to $8.9 million and has five withdrawals left. Identical return, wildly different consequence — the cost of a bad year is proportional to how much future spending still depends on the money.

This is why the years immediately around the retirement date are the fragile window. Before it, the portfolio is near its lifetime peak and the full withdrawal schedule still lies ahead; a deep drawdown then does damage that later strong years arithmetically struggle to undo, because the withdrawals keep harvesting shares all the way down. The published record points the same direction: William Bengen's 1994 study — the origin of the 4% figure — found that on a 50/50 stock/Treasury portfolio, historical worst cases clustered around retirements that walked straight into poor early sequences, and the Trinity study (Cooley, Hubbard & Walz, 1998) reported success rates across 1926–1995 start dates rather than one outcome, precisely because start-date luck dominates.

From one path to a distribution

A worked example proves the mechanism; it is not a projection. Honest projection means running every start date the data allows and reporting the spread. That is what our How long will my money last calculator does: it replays a drawdown from all 98 historical start years since 1928 in the order the returns actually arrived, grosses federal tax up out of every withdrawal, drags an explicit fee, scales spending by each sequence's own CPI path, and reports the depletion age as a p10 / median / p90 band against SSA life-table longevity.

On its default inputs (age 65, $1,000,000, $48,000 after-tax spending, 60/40 allocation, traditional account, single filer, 50 bps fee, data asOf 2026-01), the replay currently shows a median depletion age of 97 — but a p10 of just under 84, a p90 that outlives the 119-year edge of the life table, and a worst start year (1937) that runs dry at age 80. Roughly 90% of sequences reach SSA life expectancy; about 14% never deplete at all. That spread of thirty-five-plus years between the unlucky and lucky tails, on identical inputs, is sequence risk measured — a single-number answer would have to throw the spread away.

Runs to reproduce this guide, every input in the URL:

• The worked example's inputs across all 98 start years — $1M, $50,000 real spending, 100% stocks, no tax (Roth), no fee. The 1969 start sits in the band's unlucky tail; the band shows where every other start year landed.
• The 4% version of the same run — watch the whole band shift later rather than a single number improve.
• The default replay with tax and fees on — the p10/median/p90 figures quoted above, with the gross→tax→fee→spendable waterfall printed per year 1.

What moves the band

The research literature studies several levers, and the calculator lets you watch each one move the band rather than take any claim on faith. The initial withdrawal rate is the heaviest: the worked example's 16-vs-30 gap at 5% became 26-vs-30 at 4%, and Bengen's and the Trinity study's core finding is how sharply historical success rates fall as the initial rate climbs. Spending flexibility — guardrail and floor-and-ceiling rules that cut withdrawals after bad years — attacks sequence risk directly by selling fewer shares at depressed prices; our safe withdrawal rate page runs fixed, Guyton-Klinger, and VPW rules side by side with the income variability each implies. Allocation changes the shape of the return path itself, trading depth of drawdowns against long-run growth. And taxes and fees act as a withdrawal you did not choose: a 1% fee behaves like raising your own withdrawal rate by a point, which is why the calculator refuses to model them implicitly. None of this is a prescription — which trade-off fits a given household depends on facts no backtest can see. The estimates only show what each lever did across history.

Sources and limitations

• Return and inflation series: Aswath Damodaran, Historical Returns on Stocks, Bonds and Bills: 1928–Current (NYU Stern), S&P 500 total return and 3-month T-bill, asOf 2026-01; BLS CPI-U, December 12-month change, asOf 2026-01.
• William P. Bengen, "Determining Withdrawal Rates Using Historical Data," Journal of Financial Planning 7(4), October 1994, pp. 171–180.
• Philip L. Cooley, Carl M. Hubbard & Daniel T. Walz, "Retirement Savings: Choosing a Withdrawal Rate That Is Sustainable," AAII Journal, February 1998 (the "Trinity study").
• Longevity references in the linked calculator: SSA period life table, 2023.

Limitations to keep in view: the worked example is deliberately simplified — annual granularity, constant real spending, no taxes or fees, one country's equity market — and its reversed path is a constructed counterfactual, not a historical possibility anyone could have chosen. Historical start years overlap, so 98 sequences are not 98 independent draws, and no backtest window binds the future. Every figure here is an illustrative estimate; the full method, data contracts, and test suite are documented on the methodology page, and outputs are always presented as ranges because a distribution is the only honest shape for a projection.