How it works
Each simulation starts with your balance. At the start of each year it takes your withdrawal, then applies a random yearly return and removes inflation, so every figure stays in today's dollars:
The run "lasts" if every withdrawal is paid in full. After all the runs, Calcist sorts the balances for each year and reads off the 10th, 50th (median) and 90th percentiles.
Return models. The lognormal model draws ln(1 + return) from a normal distribution, with its settings chosen so the average yearly return and its standard deviation match what you enter. Returns can't fall below −100%. The normal model draws the return itself from a bell curve and caps losses at −100%. Returns are independent from year to year.
Reproducible. The random numbers come from a seeded generator (Mulberry32 with Box–Muller), so the same inputs and seed always give the same answer. "Re-run" just adds 1 to the seed, letting you see how much the result moves between batches.
Sequence-of-returns risk
Two retirees can earn the same average return and end up in very different places. If the bad years come first, you're selling investments while prices are low to fund withdrawals, and that money isn't there when markets recover. The same bad years late in retirement do far less harm, because the balance has already done most of its work. That's why the spread between the 10th and 90th percentile lines grows so wide, and why a fixed average return can't show this risk.
Checks you can do by hand
Set volatility to 0 and every run is identical. $1,000,000, $40,000 a year at 5% for 30 years with no inflation ends at 1,000,000 × 1.05³⁰ − 40,000 × 1.05 × (1.05³⁰ − 1) ÷ 0.05 = $1,531,511. At a 0% return the same withdrawal runs out in year 26, and a $0 withdrawal always lasts.
Limitations
- Real markets have streaks, crashes and recoveries that independent draws don't capture, and the future may differ from any assumption you enter.
- Inflation is fixed, and there are no taxes or fees. Enter a return after fees.
- Real retirees adjust: they cut spending after bad years, or collect Social Security. A fixed withdrawal is the strictest test.
A planning estimate, not financial, tax or investment advice. Every assumption is listed under the result.
Sources
- Bengen, W. P. (1994), Determining Withdrawal Rates Using Historical Data, Journal of Financial Planning (FPA reprint)
- Cooley, Hubbard and Walz (1998), Retirement Savings: Choosing a Withdrawal Rate That Is Sustainable, AAII Journal (the Trinity study)
- U.S. Bureau of Labor Statistics: Consumer Price Index