Sequence of Returns Calculator — Methodology

How This Calculator Works

Two portfolios with the same average return can end very differently if one suffers its losses early in retirement, while withdrawals are being taken. This calculator shows that risk two ways:

• Monte Carlo simulation — 5,000 randomly generated return sequences, plus a stress test in which the first three years of retirement are a bear market, and two common mitigations (a bond tent and a cash bucket).
• Historical backtest — the same plan run against every actual US retirement start year from 1871 onward, using real (after-inflation) returns.

They are shown side by side on purpose: independent random draws never reproduce the clustered bad decades real markets have produced, so the backtest is the harder test.

Inputs and Assumptions

• Portfolio balance at retirement: Used as you enter it; every simulation starts on your retirement day. If you are not yet retired, enter the balance you expect to have then.
• Annual withdrawal or withdrawal rate: The first year's withdrawal, as a dollar amount or as a percentage of that balance. Later years rise with inflation.
• Retirement length: How many years the money must last.
• Stock allocation: The rest is in bonds; rebalanced every year.

Formula — Monte Carlo

// Each year, each simulation (nominal, normal distribution)
stock  ~ Normal(10%, 17%)
bond   ~ Normal(5%, 6%)
return = stock% × stock + (1 − stock%) × bond

withdrawal(year) = withdrawal × (1 + 3%)^(year − 1)
balance = balance × (1 + return) − withdrawal(year)
failure if balance ≤ 0 before the final year

survival = simulations that last the full period / 5,000

// Bear-market-first stress test (then random as above)
year 1: stocks −30%, bonds −5%
year 2: stocks −15%, bonds +2%
year 3: stocks −5%,  bonds +3%

// Bucket strategy
cash = min(2 × withdrawal, 15% of portfolio), earns 0%,
       spent instead of selling in years with a negative return,
       never refilled: once it is spent, withdrawals sell again

// Bond tent (default peak 70% bonds, 5 years)
bond share moves linearly from your allocation to the peak,
reaching it in year 5 of retirement, back at your
allocation from year 10. A tent only adds bonds: if your
bond share is already at or above the peak, it changes
nothing and shows the same survival as your plan

// Sustainable withdrawal rate
binary search 2%–8% (10 steps, 1,000 simulations each)
for the highest rate with ≥ 90% survival

Formula — Historical Backtest

for every start year Y with a full window in 1871–2025:
  each year: balance −= withdrawal          // start of year (Bengen)
             balance ×= 1 + realReturn(Y + i)
  withdrawal is constant in real terms (returns are already real)

successRate = surviving start years / start years tested

Data Sources

• Robert J. Shiller, "Irrational Exuberance" online data (shillerdata.com) — real total returns for US large-cap stocks and 10-year Treasuries, 1871–2025, January to January, used by the historical backtest.
• Monte Carlo parameters — the means and standard deviations above are conventional long-run US figures we assume, not fitted to a particular dataset. The Monte Carlo is parametric; it does not resample history.
• Bengen, W. P. (1994), "Determining Withdrawal Rates Using Historical Data," Journal of Financial Planning — the historical-cohort method and start-of-year withdrawal convention.
• Cooley, Hubbard & Walz (1998), "Retirement Savings: Choosing a Withdrawal Rate That Is Sustainable" (the Trinity Study).
• Pfau & Kitces (2014), "Reducing Retirement Risk with a Rising Equity Glide Path," Journal of Financial Planning — the idea behind the bond tent.

Limitations

• Monte Carlo results are random. Running the same inputs twice gives slightly different survival rates and a slightly different sustainable withdrawal rate.
• Returns are drawn independently each year from normal distributions, which understates both the fat tails and the multi-year clustering of real losses. Stocks and bonds are drawn independently, with no correlation.
• Inflation is a fixed 3% a year in the Monte Carlo. The historical backtest uses actual inflation through real returns.
• The bond tent in this calculator peaks in year 5 of retirement, not at the retirement date as in the research it is based on, so it may understate what a tent that peaks at retirement would achieve.
• Taxes, fees, Social Security, pensions and flexible spending rules are not modelled. Withdrawals never adjust to market conditions.
• US data only. US markets had an unusually strong century, and future returns may be lower.

Last Updated

July 2026 — Historical backtest added (Shiller data); the earlier claim that the Monte Carlo used historical returns was corrected.

October 2026 — Methodology page published. The calculator had been linking to this page before it existed.

October 2026 — Two corrections. The balance you enter is the balance at retirement, but it was grown again for the years to retirement you entered, while the withdrawal was taken from the balance you typed: after 10 years at the 8% blended return a "4%" withdrawal was really 1.85%. The balance is now used as entered, and the years-to-retirement field is gone. And the bond tent moved a portfolio with less than 30% in stocks up to 30% stocks; a tent only adds bonds, so it now leaves such a portfolio unchanged.

October 2026 — A withdrawal of $0 typed in dollar mode was run at the 4% rate instead; it is now run as $0. The cash-bucket tip said the bucket means you never sell stocks in a downturn, but the bucket holds two years of withdrawals at most (less when 15% of the portfolio is smaller) and is not refilled, so a third down year sells stocks. The tip now shows the cash actually set aside and how many years of withdrawals it covers.