Sequence of Returns Risk Calculator
The portfolio, the flows, and the two decades
Your result will appear here
Fill in the fields on the left and this updates as you type.
Know what this estimate is based on
- Jurisdiction
- General mathematical model
- Scope and limitations
- Long-range scenario, not a guarantee. Small changes in returns, inflation, fees, taxes, and withdrawal timing can materially change the result.
- Source links checked
- Jul 30, 2026
Built and regression-tested by Smart Tools Lab. It has not been individually reviewed by a licensed financial, tax, or legal professional.
How to use
- 01
Enter the portfolio value at the start. Both runs begin from the same balance, because the point of the page is that nothing differs between them except the order of the returns.
- 02
Enter the annual withdrawal for the retiree and the annual contribution for the saver. Both are in today's dollars and both are indexed, and the page runs the same two sequences past each of them.
- 03
Enter the number of years to run.
- 04
Set how many bad years there are back to back, the return in each bad year, and the return in each of the remaining good ones. The second run is that list REVERSED, so the two hold the same numbers and cannot differ in their average or their compound rate.
- 05
Open Advanced options for the inflation the withdrawal and the contribution rise with. Then read the two ending balances, the control run with no withdrawals at all, the level benchmark on the chart, and the year-by-year table where the two balances separate.
Formula
Build one array of returns: the bad years first, then the good ones. The second sequence is that array REVERSED, which guarantees an identical multiset — identical arithmetic mean, identical compound rate, identical in every way except order. The mean is the sum of the returns ÷ the number of years; the compound rate is the product of (1 + each return), taken to the power 1 ÷ n, minus 1. Ten years at −1% and twenty at 11% give a mean of 7.00% and a compound rate of 6.85%, a drag of 0.15 points. The retiree's run takes the withdrawal first and grows what is left: balance = (balance − withdrawal × (1 + inflation)^t) × (1 + that year's return). The saver's run adds the contribution first and grows the whole thing. The control run does neither, so its ending balance is simply the starting balance × the product of all the returns — the same number in both orders, which is the proof that the order alone did the damage.
Example
$1,000,000, thirty years, ten bad years at −1% and twenty good ones at 11%, a $45,000 withdrawal rising 3% a year, and a $24,000 contribution for the saver running alongside. Year one, bad first: $1,000,000 − $45,000 = $955,000, down 1% to $945,450. Year one, bad last: the same $955,000 up 11% to $1,060,050 — $114,600 apart after a single year. By year ten the bad-first retiree holds $414,851 against $1,905,665, and the withdrawal has risen to $58,715 whether the portfolio can afford it or not. The good years then arrive too late: the money runs out in year 20, while the reversed sequence finishes at $2,874,551. Both runs averaged 7.00% and compounded at 6.85%. Left untouched, both finish at exactly $7,291,410. And the same two sequences past the saver hand the bad decade to the person who wanted it: $12,196,146 for bad-first against $9,647,068 for bad-last.
Definitions
- Sequence of returns risk
- The risk that the order in which returns arrive changes the outcome, even when the average and the compound rate do not. It is inert on a portfolio nobody touches and it bites hardest on one being drawn down.
- Compound annual return
- The single rate that would have produced the same ending balance: the product of (1 + each year's return), to the power 1 ÷ n, minus 1. It is always at or below the arithmetic average, and it is the one to plan on.
- Variance drag
- The gap between the arithmetic average and the compound return, caused by percentage gains applying to smaller balances than the losses did. Here 7.00% averages down to 6.85% — 0.15 points a year, before order is considered at all.
Good to know
Why the order can matter at all
The intuition most people carry is that markets average out. Over a long enough horizon you get the long-run return, and the order in which the good and bad years arrive is noise. That intuition is exactly right for a portfolio nobody touches, and this page proves it on your own numbers: run any sequence of returns and its reverse on an untouched balance and the two finish at precisely the same figure — $7,291,410 from $1,000,000 on the default returns. Multiplication does not care what order you do it in. The moment money moves in or out, the symmetry breaks, and it breaks because a withdrawal is not a percentage, it is a sale. When a retiree takes $45,000 out of a portfolio that has fallen, they sell more shares to raise it than they would have at a higher price, and those shares are permanently gone; they are not there to participate in the recovery. Across the ten bad years in the default run the retiree sells $515,875 of spending out of a falling portfolio — 52% of everything they started with. When the good years finally arrive there is much less left to compound, and the arithmetic never catches up. The retiree who met the identical bad decade at the END sold the same dollars out of a portfolio that had already grown, so each sale cost a much smaller fraction of it. That is the entire mechanism. Two runs, one list of returns and its reverse, the same 7.00% average and the same 6.85% compound rate: one retiree is out of money in year 20 and the other finishes with $2,874,551. Nothing about the market was different. Only when the money left.
The mirror: a saver should want the crash
The same arithmetic with the sign flipped produces one of the most useful facts in personal finance, and this page runs it alongside so the two can be read together. Give the identical two sequences to somebody still contributing $24,000 a year, and bad years FIRST leaves them with $12,196,146 while bad years last leaves $9,647,068. The lost decade is worth $2,549,078 to them. Every contribution made while the market is down buys shares at prices the good-first saver never sees, and all of them are still there when the recovery comes. A twenty-five-year-old with thirty-five years of contributions ahead should genuinely hope for a bad decade early; the only thing that ruins them is stopping. A sixty-five-year-old cannot survive the same decade. This is why sequence risk is not a market phenomenon at all — it is a phenomenon of the direction your money is flowing, and the risk arrives on the day the flow reverses. It also explains why the danger is concentrated rather than spread. The years immediately around retirement are the ones where the portfolio is at its largest relative to your remaining contributions and the horizon over which a fall can be waited out is at its shortest. A bad market at 45 is a buying opportunity; the same market at 65 is the thing that decides the rest of your life; the same market at 85, oddly, matters much less again, because most of the withdrawals have already happened out of a portfolio that survived. That concentration is what makes the risk manageable. You cannot defend a whole retirement against a bad sequence, but you can defend the decade in which it would do permanent damage — which is what a spending rule, a cash and bond buffer, or a more conservative allocation at the start and a rising equity share afterwards are all trying to do.
Averages lie, in two separate ways
This page reports both an arithmetic average and a compound rate for the same list of returns, and the gap between them is worth understanding on its own. Ten years at −1% and twenty at 11% average 7.00% a year, and multiply out to 6.85%. That 0.15-point gap is variance drag, and it exists before order is considered at all: a portfolio that falls 10% and then rises 10% has averaged zero and lost 1%, because the gain applies to a smaller balance than the loss did. The bumpier the path, the wider the gap, which is why a volatile portfolio with a high average return can compound more slowly than a steadier one with a lower average. Any projection quoting an arithmetic mean is therefore already flattering itself before a single withdrawal is modelled. The second lie is subtler and is what the chart's third line is for. That line runs the same money at a flat 7.00% every year and finishes at $1,370,820 — comfortably ahead of the bad-first run and far behind the good-first one. It is a benchmark, not a scenario. Its usefulness is entirely as a measuring stick for the other two, and its danger is that it looks like a plan: nobody in the history of markets has been handed the average thirty times in a row. Almost every retirement projection on the internet, including several on this site, is a version of that line. They are not wrong so much as incomplete — they answer the question 'what happens if the future is smooth?', which is the one question you can be certain the future will not answer. This page exists to put a number on the difference. The honest use of a single-rate projection is as the midpoint of a range whose width you have measured somewhere else, and the width is not small: on identical returns, identical average and identical compound rate, the two orders here differ by the entire portfolio.
What actually defends against it
None of the defences is a better forecast, and that is the point — the whole problem is that the sequence is unknowable in advance. The first and most powerful is flexible spending. A rule that skips the inflation raise after a down year, or cuts spending by ten percent when the balance falls through a line, recovers most of the gap this page measures, because it directly reduces the forced selling in the years when selling is most destructive. The studies that produce conservative safe withdrawal rates assume a retiree who takes the same real cheque in January regardless of a 40% drawdown; almost nobody would, and the difference between the assumption and the behaviour is worth more than any allocation decision. The second is a buffer: holding some years of spending in cash and bonds so that a down year can be funded without selling equities at all. That is a strategy in its own right, with its own page and its own honest accounting of what the buffer costs when no fall arrives. The third is simply starting at a lower rate — this run withdraws 4.50% of the portfolio in its first year, and each half-point below that buys room for the sequence you actually get. A fourth, less commonly discussed, is a rising equity glidepath: entering retirement more conservatively than you intend to end it and drifting back toward equities as the dangerous decade passes, which is the opposite of the conventional advice to de-risk with age and follows directly from where the risk is concentrated. What none of them requires is predicting the market. Finally, remember what this page's own scope note says: two blocks of identical returns is a deliberately crude sequence, chosen so that nothing except the order can possibly explain the difference. Real markets are messier, and messier is usually worse for the retiree, because a crude sequence at least arrives in a predictable shape.
Frequently asked questions
What is sequence of returns risk?
It is the risk that the ORDER of your returns ruins you even when their average is fine. Ten years at −1% followed by twenty at 11% averages 7% a year and compounds at 6.85%. So does the same list backwards. But a retiree drawing $45,000 a year from $1,000,000 who meets the bad decade first is out of money in year 20, while the one who meets it last finishes with $2,874,551. Same returns, same average, same compound rate, entirely different lives.
How can identical returns end so far apart?
Because withdrawals turn percentages into shares. Take the withdrawals away and run both sequences on an untouched $1,000,000 and they finish at exactly the same $7,291,410 — multiplication does not care what order you do it in, so a portfolio nobody touches is completely immune. Put the withdrawals back and the bad-first retiree has to sell $515,875 of spending out of a falling portfolio across the first decade, 52% of everything they started with. Those shares are gone. When the good years finally arrive there is much less left to compound.
Why is the average 7.00% but the compound return 6.85%?
That gap is variance drag and it exists before order is considered at all. A portfolio that falls 10% and then rises 10% has averaged 0% and lost 1%, because the gain applies to a smaller balance than the loss did. The bumpier the path, the wider the gap. It is also why an arithmetic mean flatters any projection: the chart's third line runs the same money at a flat 7.00% every year and finishes at $1,370,820, ahead of the bad-first run and far behind the good-first one — a benchmark, never a scenario, since nobody has ever been handed the average thirty times in a row.
Does this hurt someone who is still saving?
It helps them, and by almost the same amount. Run the identical two sequences past a saver putting in $24,000 a year and bad years FIRST leaves $12,196,146 while bad years last leaves $9,647,068 — the lost decade is worth $2,549,078 to them. Every contribution made during the fall buys shares the good-first saver never gets, and all of them are there for the recovery. A twenty-five-year-old should want the bad decade. A sixty-five-year-old cannot survive it. It is the same arithmetic with the sign flipped, and it is why the risk arrives on the day you stop contributing and start withdrawing.
When does the risk matter most?
In roughly the first decade of retirement, which is also the decade before Social Security has fully started for many people, so the two problems overlap exactly. After that the portfolio has either survived and grown past the danger, or it has not. It is not a thought experiment: a US retiree who stopped work in 1966 met a sixteen-year stretch in which stocks went nowhere in real terms, and one who stopped in 2000 met a decade in which the S&P 500 returned about nothing across two crashes. Both cohorts got respectable long-run averages afterwards. That is precisely the point.
What can I actually do about it?
Three things, and none of them is a better forecast. Spend flexibly — skipping the inflation raise after a down year, or cutting 10% when the balance falls through a line, recovers most of the gap because it stops the forced selling at the worst moment. Hold some years of spending somewhere you would not have to sell equities to reach, which is the same fix by another route. And open at a lower rate than the 4.50% of the portfolio this run withdraws, which buys room for whatever sequence you actually get. What this page cannot do is tell you which sequence that will be.