Sequence of Returns Calculator

Sequence of returns risk is the difference the order of returns makes once money is being withdrawn. On the sample figures a 1,000,000 portfolio drawing 40,000 a year and earning -20%, 5% and 25% ends at 905,500 when the bad year comes first, and 942,400 when it comes last. The average return is 3.33% either way; the gap of 36,900 comes from the timing alone.

Taking those figures year by year with the bad year first: the first withdrawal leaves 960,000, which falls 20% to 768,000. The second leaves 728,000, which grows 5% to 764,400. The third leaves 724,400, which grows 25% to 905,500. Reversing the returns and running the same three withdrawals ends at 942,400 instead.

The reason withdrawals make order matter is that a withdrawal in a down year sells a larger share of the holding to raise the same cash, so less capital remains to participate in the recovery. Without withdrawals the order is irrelevant, since the same three factors multiply to the same product whichever way round they are applied. That is why the effect belongs to drawdown rather than to accumulation, and why it is concentrated in the years when the balance is largest relative to what is left to come.

Run it with sensible defaults

Using a starting balance of 1,000,000, an annual withdrawal of 40,000 and returns of -20%, 5% and 25%, the calculation works out to 36,900.00. That is the gap between the two orderings rather than an ending balance: bad-first finishes at 905,500 and good-first at 942,400. The defaults are a starting point rather than a recommendation.

The levers in this calculation

The headline has a closed form: the withdrawal multiplied by the spread between the last and first returns, multiplied by two plus the middle return. At the sample figures that is 40,000 x 0.45 x 2.05, which is 36,900 exactly.

Two things follow from that. The starting balance does not enter the gap at all, because the same three returns applied in either order produce the same compound factor on the opening capital, so it cancels and only the withdrawals are left to be timed differently. Enter 1,000 or a billion and the gap is still 36,900, though the balance rows beneath it move. The withdrawal, meanwhile, is exactly proportional rather than approximately so.

Among the three returns the order of influence follows the formula. A 1% relative move gives 0.56% for the third year and 0.44% for the first, since both shift the spread between them, against 0.02% for the middle year, which only nudges the two-plus term. The middle return is the weakest lever on the page by a wide margin.

How the math works

Each year the withdrawal is taken first and the remaining balance is grown at that year's return, so the balance after a year is the previous balance less the withdrawal, multiplied by one plus that return. The tool runs that three times in the order entered, runs it again with the returns reversed, and reports the difference between the two ending balances. Both runs use the same three returns, so both carry the same average.

What this doesn't capture

Steady-rate math ignores real-world volatility. Actual returns are lumpy; sequence-of-returns risk matters most in drawdown; fees and taxes drag on compound growth; and behaviour changes in drawdowns can reduce outcomes below the projection. The number represents one scenario rather than a forecast.