Sequence-of-returns backtest
A projection with one average return hides the thing that actually breaks a withdrawal plan: the order of the bad years. This engine replays your plan against every contiguous window of real US equity returns since 1926 and reports how many survived, what the median outcome was, and which starting year hurt most.
| Start | End | Ending balance | Outcome | Depleted |
|---|---|---|---|---|
| 1929 | 1958 | $0.00 | Depleted | 1950 |
| 1930 | 1959 | $0.00 | Depleted | 1957 |
| 1928 | 1957 | $752,301 | Survived | — |
| 1931 | 1960 | $2,510,674 | Survived | — |
| 1965 | 1994 | $2,899,462 | Survived | — |
| 1927 | 1956 | $2,909,110 | Survived | — |
| 1962 | 1991 | $3,119,109 | Survived | — |
| 1966 | 1995 | $3,154,462 | Survived | — |
Withdrawals are indexed to 3% inflation and taken at year end; fees are deducted from the blended return.
rₜ = w·rₑ,ₜ + (1 − w)·r_b − fee · Equity return for the year, the bond assumption, and the fee drag.
Bₜ = Bₜ₋₁·(1 + rₜ) + Cₜ − Wₜ · Contributions and withdrawals happen at year end.
B_T(i) for every start index i · One trial per contiguous block of n years in the record.
B_T(i) ≥ 0 for all t · A window fails the first year the balance reaches zero.
A clear path from inputs to results.
A retirement projection usually assumes one average return, which quietly assumes the good years and the bad years arrive in a convenient order. They don't. This backtest replays a plan against every contiguous 30-year window of real US equity returns since 1926 and reports how many survived, so the risk you see is the risk of an actual sequence, not an average.
How to use
- Enter the starting balance and the annual withdrawal you plan to take.
- Set the plan length — 30 years is the standard retirement horizon.
- Choose the equity allocation and the bond return you want to assume.
- Add the annual fee in basis points so the drag is included.
- Read the success rate first, then the worst starting year and the drawdown.
The formula
Reference: Bengen (1994), “Determining Withdrawal Rates Using Historical Data”; Kitces on sequence-of-returns risk. Equity data: S&P 500 total return, 1926–2025.
Worked example
$1,000,000, $40,000 a year, 30 years, 70/30
- Starting balance $1,000,000.
- Withdrawal $40,000, indexed to 3% inflation.
- 30-year horizon, 70% equity, 4.5% bond assumption, 30 bp fee.
- 1
Every contiguous 30-year block of the 1926–2025 series is replayed: 100 − 30 + 1 = 71 trials.
- 2
Each year the balance grows by the blended return (0.7 × equity + 0.3 × 4.5% − 0.30%), then the indexed withdrawal is taken.
- 3
69 of the 71 windows end with a positive balance: a 97.2% historical success rate.
- 4
The median ending balance is $6.31M; the 10th percentile is $3.15M and the 90th is $9.88M.
- 5
The worst window starts in 1929 and is exhausted in 1950. The best starts in 1975.
- 6
The median peak-to-trough drawdown across all windows is 29.8%.
97.2% of historical 30-year windows survive · median $6.31M · worst start 1929 (depleted 1950).
Interpreting the result
The success rate is a historical frequency, not a probability. A 97% figure means two of the seventy-one starting years in the record failed — and both failures began just before a crash. That is the point of the exercise: the plan does not fail because the average return is too low, it fails because a poor first decade compounds against a fixed withdrawal. Raising the equity allocation increases the median but usually widens the left tail, so read the 10th percentile alongside the median.
Assumptions & limitations
- Equity returns are real annual US large-cap total returns (1926–2025). The bond return is a constant assumption you control, so a 70/30 result is a stress test, not a multi-asset historical simulation.
- Withdrawals are taken at year end and indexed to 3% inflation. Contributions, if any, follow the same convention.
- Fees are deducted from the blended return each year. Taxes, fund expenses beyond the fee input, and advisory fees are not modelled.
- A window fails the first year the balance reaches zero; later years in that window are carried at zero so every window spans the same horizon.
- This is a historical replay, not a forecast. Past sequences include conditions that may never repeat, and exclude conditions that have not happened yet.
Frequently asked questions
What is sequence-of-returns risk?
It is the risk that the order of returns, not their average, determines whether a withdrawal plan survives. Two investors with identical average returns can end with very different balances if one meets a bear market in the first five years, because withdrawals during a drawdown permanently remove capital that would otherwise have recovered.
Why does the bond return not use historical bond data?
The equity series is a verified total-return series; a second series transcribed without verification would undermine the result. Instead the bond return is an explicit assumption shown on the page, so you can test 3%, 4.5% or 6% and see how sensitive the outcome is.
Should I pick the allocation with the highest success rate?
Not on its own. Higher equity usually raises the median and can lower the failure count over long horizons, but it also deepens drawdowns — the median drawdown here is already 29.8%. Match the allocation to the withdrawal you actually need and to how you would behave in a 30% fall.
Why is the success rate described as historical rather than a probability?
Because it is a count: the share of actual starting years in the record that ended with money left. It is not a model of future returns, so it should be read as evidence about sequence risk rather than a guarantee.
How is this different from a Monte Carlo simulation?
Monte Carlo draws returns from a distribution and can produce sequences that never happened. A historical backtest only uses sequences that did happen, which makes it a useful complement: if a plan fails the historical record, it is failing on real data, not on a model assumption.
Methodology last reviewed 2026-10-20. Results are informational and not financial or engineering advice — see our disclaimer.