Why the order of returns matters

Published August 16, 2026

Reorder the same ten yearly returns and the ending balance never moves while nothing is taken out, because a product ignores the order of its factors. The set ends at 1.53 times the starting balance in every order. Take 6 percent of the start out each year and worst years first ends 55 percent below best years first.

Nothing taken out

$152,799

Reorder the years and this figure does not move at all.

Taking out 6.0% of the start each year

$81,290

Order: the order they came in.

Ending balance after 10 years, nothing taken out

Worst first: $152,799
Best first: $152,799
Gap: none at all

Same years, taking 6.0% out each year

Worst first: $45,230
Best first: $101,336
Gap: $56,106

Illustrative teaching figures. The ten returns and the $100,000 starting balance are a fixed teaching set, the return lands before the withdrawal each year, and the amount taken out is a flat sum rather than a share of the balance. Nothing here is a forecast.

In short

Drag the order handle from worst years first to best years first, or shove the bars of returns above it.
Watch the top figure, the balance with nothing taken out, stay exactly where it is.
Drag the lower rail to change how much comes out each year, then drag the order again.
Set the amount taken out to zero and watch both extreme orders land on the same balance.

Why the order changes nothing when nothing comes out

A balance left alone is the starting sum multiplied by one plus each year's return.

$B_n = B_0 \prod_{t=1}^{n}(1 + r_t)$

Multiplication is commutative, so the product is the same whatever order the factors arrive in. The ten years here compound to about 1.53 times the starting balance, an annualised return of about 4.33 percent a year, and that holds worst years first, best years first and at every setting in between. The path wanders, the destination does not. That is why the gap between the two extreme orders in the top row of the table is not merely small at every setting, it is nothing at all.

Why withdrawals hand the order control

Take a fixed sum out each year and the balance stops being a plain product.

$B_n = B_0\prod_{t=1}^{n}(1+r_t) - W\sum_{t=1}^{n}\prod_{s=t+1}^{n}(1+r_s)$

The second term is the one that depends on order, and it holds for as long as there is a balance to take the withdrawal from. Each withdrawal is scaled only by the returns that come after it, so an early withdrawal is scaled by everything and a late one by almost nothing. After a fall, a fixed sum is a larger share of what is left, so more of the holding goes to fund it and less remains to recover. At 6 percent of the starting balance a year, the best-first order finishes 2.24 times as high as the worst-first order, which is 55 percent below it. That is sequence risk, and it bites hardest in the early years of drawing an income, where a deep drawdown and a withdrawal land together.

What the picture assumes

One fixed set of ten yearly returns, chosen as an illustrative teaching set rather than measured from any market. The return lands first and the withdrawal comes out at the end of the year. The amount taken is flat: it is set as a share of the starting balance and then held there, with no inflation rise, no tax and no fees. Nothing is paid in. The balance stops at zero, because once it is spent there is nothing left to take, and the tool says which year that happened in.

Real plans differ on every one of those, and the shape survives all of them. Take nothing out and the order is irrelevant to where you finish. Take money out and the order of the very same returns can decide the outcome. This is educational material rather than financial advice.

Common questions

Does the order matter while I am still paying money in?

Yes, as the mirror image. A contribution is a withdrawal with the sign flipped, so each one is scaled by the returns that follow it. While money is going in, the balance is largest at the end, so the good years are worth most late and a strong finish beats a strong start. Only a balance with nothing going in or out is free of the order.

Is this the same thing as sequence risk?

Yes. Sequence of returns risk is the risk that the order of the returns, rather than their average, decides the outcome once money is being taken out. Both the average of the ten returns and their compounded total are the same in every order, so neither can explain the gap on its own.

Does taking a fixed percentage of the balance instead avoid it?

For the ending balance, yes. A percentage of the current balance is another multiplication, so the path becomes a product again and the order stops deciding where you finish. What moves instead is the income: the same percentage of a smaller balance is a smaller payment, so early bad years cut what you can spend rather than what you end with.

Keep reading

This page is educational material, not financial advice. The figures come from the formula shown and assume the inputs you enter hold for the whole term. Your own rate, fees, taxes and timing will differ, so treat the output as arithmetic to check a decision against, not as a recommendation.