How to use the sequence of returns risk calculator
- Enter your starting balance, the withdrawal in year 1 and, if you want withdrawals to rise, a growth percent per year.
- Choose whether you withdraw at the start or the end of each year.
- Enter a list of yearly returns in percent, separated by commas, spaces or new lines. Negative numbers are losses.
- Compare the ending balance for the four orders: as entered, reversed, worst years first and best years first. The year by year table shows where each path went.
Formula
Start-of-year withdrawals: balance = (balance - withdrawal) x (1 + return)
End-of-year withdrawals: balance = balance x (1 + return) - withdrawal
Withdrawal next year = withdrawal x (1 + withdrawal growth)
Without withdrawals: the product of (1 + return) is the same in every order
If the balance reaches zero after a withdrawal, it stays at zero and the tool reports the year it ran out.
The same ten years in four orders
Start with $500,000 and withdraw $30,000 at the start of each year. The ten yearly returns are -18, -8, 4, 12, 20, 9, -2, 15, 7 and 11 percent. They average 5% and compound at 4.4021% a year, and that is true in every order.
As entered, the ending balance is $300,434.58. Reversed, it is $445,606.29. With the worst years first it is $251,825.31, and with the best years first it is $477,254.43. The gap between best and worst is $225,429.12, caused only by the order. With withdrawals rising 3% a year the as-entered path ends at $239,135.70.
Why order matters when you withdraw
Without withdrawals, multiplication does not care about order, so a bad year at the start hurts the same as a bad year at the end. With withdrawals, a loss early in the list hits a balance that is still large and then leaves less money to recover when the good years come. The withdrawals you take in those low years also sell shares at low prices, which the numbers capture.
This is called sequence of returns risk. It is the main reason a fixed average return is a poor guide to whether savings will last. The Retirement Withdrawal Calculator shows how long a balance lasts for a steady return and rising withdrawals, and the Retirement Calculator looks at saving up to the start.
How to use the four orders
Real markets are neither best-first nor worst-first, so the two extremes bracket what is possible for the numbers you enter, and the as-entered and reversed lines show two ordinary cases. Try your own list, for example returns from a period of history you want to test, and look for the point at which the lowest path runs out.
The tool does not predict returns. It only reorders the ones you give it. For a single compounded figure from a list, see the Compound Interest Calculator, and for returns on accounts with deposits use the Time-Weighted Return Calculator.
Assumptions and limits
- Returns are applied once per year to the balance after (or before) the withdrawal, as chosen.
- Withdrawals are fixed amounts that grow only at the rate you set. Spending does not change when the balance falls.
- Fees, taxes and income from other sources are not modeled. Include fees in the yearly returns if you want them counted.
- The list of returns is limited to 60 years and each return must be above -100%.
Frequently asked questions
What is sequence of returns risk?
It is the risk that poor returns arrive early in the years you are drawing money out. Because you are withdrawing while prices are low, the balance has less left to benefit from later gains, even if the long run average is the same.
Why is the average return the same in every order?
Adding the same list of numbers in a different order gives the same sum, and multiplying the growth factors gives the same product. Only the path of the balance, and therefore the effect of the withdrawals, changes.
Does start of year or end of year matter?
Taking the withdrawal at the start leaves less money invested for the year, so it usually ends lower than taking it at the end. The tool lets you pick so you can test both.
Does this tell me how much I can safely withdraw?
No. It shows how the order of the returns you supply changes outcomes. It is not a forecast, and a safe amount depends on many things this page does not model.