The Sequence.
When markets meet withdrawals.
For years, Maria put money away for this part of life. Now she has retired. Her paycheck has stopped; her savings help pay for the days ahead. Markets can rise or fall. Maria cannot know which years will arrive first. In this study, the investment gains, losses, and withdrawals stay the same. Only the order of the market years changes.
Maria is fictional. Illustrative, not a forecast. Not a recommendation, safe-withdrawal rule, or personal result.See the calculation ↓
MARIA / THE START
Savings have
a new job.
They help pay for life today, while the money still invested faces tomorrow’s markets. For this study, Maria starts with $1 million and takes out $50,000 at the end of every year.
Still invested. Still exposed to gains and losses.
Money for bills, meals, and everyday life. The amount stays the same throughout this example.
While money comes out for life, markets keep moving too. A gain can add to Maria’s savings; a loss can reduce them. Let’s see why the order matters.
MARIA / THE SEQUENCE
One difficult year.
Ten arrival points.
In this hypothetical example, one year’s investments fall 25%. In the other nine, they gain 8%. Maria takes out $50,000 at every year-end. Move the difficult year: the returns and withdrawals stay the same; only their order changes.
Hypothetical returns: one −25% year; nine +8% years. Withdrawal at each year-end. No taxes, inflation, fees, other income, contributions, spending adjustments, asset allocation, or actual market history.
The loss arrives in Year 1.
End-of-year savings · after the $50,000 withdrawal
Move one difficult year. See what changes.
Years 1–4: −10% each.
Years 5–10: +8% each.
The loss comes first. Later +8% years act on savings already reduced by the loss and withdrawals.
Read every year in this illustration
| Year | Return | Start of year | Investment gain / loss | Withdrawal | End of year |
|---|---|---|---|---|---|
| 1 | −25% | $1,000,000 | −$250,000 | $50,000 | $700,000 |
| 2 | +8% | $700,000 | +$56,000 | $50,000 | $706,000 |
| 3 | +8% | $706,000 | +$56,480 | $50,000 | $712,480 |
| 4 | +8% | $712,480 | +$56,998 | $50,000 | $719,478 |
| 5 | +8% | $719,478 | +$57,558 | $50,000 | $727,037 |
| 6 | +8% | $727,037 | +$58,163 | $50,000 | $735,200 |
| 7 | +8% | $735,200 | +$58,816 | $50,000 | $744,016 |
| 8 | +8% | $744,016 | +$59,521 | $50,000 | $753,537 |
| 9 | +8% | $753,537 | +$60,283 | $50,000 | $763,820 |
| 10 | +8% | $763,820 | +$61,106 | $50,000 | $774,925 |
MARIA / THE ORDER
Why the order
changes the path.
Follow the version where the loss comes first. Year 1 ends with $700,000. That is exactly where Year 2 begins. Its 8% gain works on $700,000—not the $1 million Maria started with.
Walk-through: the first two years when the loss arrives in Year 1
Year 1 / −25% loss
Year 2 / +8% gain
Blue column: savings left at year-end. Gold cap: $50,000 withdrawn. Both columns use the same $0–$1.5 million scale as the experiment.
If the loss comes later, positive years and withdrawals have already changed the balance before it arrives. The returns are the same. The withdrawals are the same. But the money exposed to each return is not.
Without withdrawals, all ten positions finish at the same $1,499,253. With withdrawals, the order changes the ending. These results belong to these assumptions; they do not establish a universally “best” or “worst” retirement year.
MARIA / THE DURATION
A difficult stretch
is a different question.
Now imagine four −10% years, followed by six +8% years. The same $50,000 leaves at each year-end. This changes the returns themselves as well as the length of difficulty.
Markets can improve
while savings still shrink.
The investments gained value. But the withdrawal exceeded the gain, so the savings balance still fell.
MARIA / THE QUESTIONS
Examine more
than one path.
Maria cannot choose which years arrive. She can see why a retirement plan needs to be examined across different sequences—and why a positive return alone does not answer the spending question.
If a loss arrives early?
How much remains invested for the years and withdrawals still ahead?
If difficulty lasts?
Could savings and other income continue to support the planned spending?
If markets gain value?
How does the gain compare with the money coming out for life?
This study reorders one set of hypothetical returns, then examines a separate difficult-stretch pattern. Studio examines a wider retirement structure: fixed stress tests examine defined adverse sequences; modeled analysis examines other possible sequences alongside household facts and assumptions. Neither predicts your future nor chooses your spending.
THE SEQUENCE / EVERY ASSUMPTION
Small experiment.
Open arithmetic.
The calculation
Begin with $1,000,000. For each year: ending savings = starting savings × (1 + annual return) − $50,000. The return is applied before the fixed year-end withdrawal. That ending becomes the next year’s starting savings. Calculations use full precision; displayed dollars are rounded only afterward.
What stays fixed—and what changes
Every slider position includes exactly one −25% year, nine +8% years, and ten $50,000 withdrawals. Only the return order changes. The separate stretch starts with four −10% years, then six +8% years. It changes the return set and duration; it is not another ordering of the original ten returns.
What the example leaves out
No taxes, inflation, fees, other income, contributions, spending adjustments, account rules, asset allocation, or historical market data are included. There are no probabilities or Datumae engine outputs. Ten years is an illustration window, not a complete retirement horizon. These assumptions are chosen for teaching, not as expected returns or a withdrawal recommendation.
Why this is sequence risk
With no additions or withdrawals, rearranging the same percentage returns does not change their compounded product. Once money comes out along the way, order can change how much remains for later returns. This study shows that arithmetic; it does not establish a response to market events or a safe spending amount.
| End of year | −25% in Year 1 | −25% in Year 5 | −25% in Year 10 | Four −10% years, then six +8% |
|---|---|---|---|---|
| 1 | $700,000 | $1,030,000 | $1,030,000 | $850,000 |
| 2 | $706,000 | $1,062,400 | $1,062,400 | $715,000 |
| 3 | $712,480 | $1,097,392 | $1,097,392 | $593,500 |
| 4 | $719,478 | $1,135,183 | $1,135,183 | $484,150 |
| 5 | $727,037 | $801,388 | $1,175,998 | $472,882 |
| 6 | $735,200 | $815,499 | $1,220,078 | $460,713 |
| 7 | $744,016 | $830,738 | $1,267,684 | $447,570 |
| 8 | $753,537 | $847,197 | $1,319,099 | $433,375 |
| 9 | $763,820 | $864,973 | $1,374,627 | $418,045 |
| 10 | $774,925 | $884,171 | $980,970 | $401,489 |
Educational background: Schwab Center for Financial Research, “What Is Sequence-of-Returns Risk?”; Clare and colleagues, “Measuring sequence of returns risk”. These explain the general concept. The figures on this page are this study’s own hypothetical arithmetic, not those sources’ examples.
Maria is fictional. General education, not personalized financial, investment, tax, or retirement advice. Illustrative, not a forecast. Not a recommendation, safe-withdrawal rule, historical replay, or personal result.
Your life is more
than ten market years.
Studio helps you bring your own structure into view—then examine how spending, timing, and market conditions can act upon it.
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