Sequence of Returns Calculator
Compare portfolio balances when fixed annual withdrawals are paired with the same return series sorted from lowest first or highest first.
How It Works
Enter the starting portfolio, annual withdrawal, and number of years. The calculator compares the bundled annual return series in lowest first and highest first order.
The model first truncates the bundled series to the entered horizon. If fewer returns remain than years requested, it appends 7% returns. It then sorts the same values in ascending order for the bad start and descending order for the good start.
Each year, the model subtracts the fixed withdrawal before applying the annual return. It reports the final balance for each ordering, the year by year balance table, and a break even withdrawal for the lowest first ordering.
Set the annual withdrawal to zero to compare compounding alone: reordering this series leaves the final balance unchanged. Restore the withdrawal to see how taking money out changes the effect of return order.
Step by step
- Enter a starting portfolio, annual withdrawal, and horizon
- Compare final balances for ascending and descending return order
- Review the annual table and the break even withdrawal result
Worked example
On a fresh visit, the bundled return series starts with −9.1% and −11.9%. Enter a $100,000 starting portfolio, $10,000 annual withdrawal, and 2 years.
The first two preset returns are −9.1% and −11.9%. Sorted from lowest to highest, the ending balance is $62,984.61; sorted from highest to lowest, it is $63,264.61. The arithmetic withdraws $10,000 before applying each year’s return. This constructed comparison is not an observed retirement outcome.
When to use this calculator
Use this calculator to isolate how return order changes balances when the same annual withdrawals are taken from a portfolio.
The balance gap isolates the effect of return order within the bundled series. It does not describe all possible return paths or establish whether a withdrawal amount is sustainable.
Common mistakes
Calling the bad start a historical retirement result can overstate what the preset represents. The tool sorts a bundled series and does not retain its original year order as a historical path.
Reading the break even withdrawal as a safe rate or a probability can mislead. It is a binary search result for one sorted series, one horizon, and the model’s withdrawal timing.
The Formula
For each year: balance = (balance − withdrawal) × (1 + return).
Bad start: bundled returns sorted from lowest to highest.
Good start: the same returns sorted from highest to lowest.
The break even withdrawal is found by binary search on the bad start ordering.
The withdrawal occurs before annual growth. The calculator truncates the bundled return series to the chosen horizon and adds 7% returns if it runs short.
Limitations and assumptions
The visible calculator uses a fixed default return series and has no preset selector or custom return inputs. This deterministic comparison is not a historical backtest or a probability model, and some bundled returns are illustrative. Withdrawals stay fixed in nominal terms and occur before each return. The series is truncated to the chosen horizon or padded with 7% returns when it runs short.
Key terms
- Sequence of returns risk
- A difference in portfolio outcomes caused by the order of returns when withdrawals are made during the period.
- Bad start and good start
- The same bundled annual returns sorted from lowest to highest, then from highest to lowest.
- Break even withdrawal
- The withdrawal amount found by binary search that leaves the balance above zero through the horizon in the bad start ordering.
Compare alternatives
Sequence of Returns compares two orderings of the same bundled annual return series during fixed withdrawals. Use Monte Carlo FIRE to see a separate model’s frequency of surviving independently drawn returns, or the Maximum Drawdown Calculator to inspect portfolio declines without withdrawals.
The tools do not produce interchangeable results. This calculator sorts its bundled series from lowest to highest and highest to lowest; it does not estimate a probability of retirement success or replay a household’s actual investment history.
FAQ
What is sequence of returns risk?
It is the effect that return order can have when withdrawals occur during a portfolio drawdown. With withdrawals held fixed, a loss early in the period leaves less capital participating in later growth than the same loss after stronger returns.
How are good and bad sequences determined?
The calculator takes its bundled series, sorts one copy from lowest to highest for the bad start, and another from highest to lowest for the good start. It does not simply reverse the original series, and each result is specific to that reordered set of returns.
How is the annual withdrawal applied?
The model subtracts the full annual withdrawal at the start of each year, then applies that year’s return. Withdrawals stay fixed in nominal terms and are not adjusted for inflation.
Does this show what happened to a historical retiree?
No. The tool compares two mathematically sorted orderings of a preset return series. The bundled presets are constructed scenarios, so their labels and returns should not be read as a household backtest or a record of actual retirement outcomes.
Does the result give a retirement success probability?
No. It reports final balances, a year by year table, and a break even annual withdrawal for the lowest first ordering. It does not sample many return paths, so it does not calculate a survival probability.
Related Tools
Use Monte Carlo FIRE for a simulated survival frequency under a separate return model. The Maximum Drawdown Calculator measures declines without the annual withdrawal sequence modeled here. Dynamic SWR Calculator explores spending rules that can change over time. Each calculation answers a different question.