One plan, three models of the market: 82%, 85% and 93%

Historical start years

1929 and 1966 survive; 1973 to 1977 do not

The historical engine lines the whole life up with history: "retire in 1929" means saving from 1911 to 1928 and drawing down from 1929. For a 30-year retiree with a fixed pot, 1929 and 1966 are the classic failures. For this plan they are not, because the decades before them built large balances: the 1966 retiree arrives with $2.77 million after saving through 1948 to 1965, when the 75/25 mix returned 10.7% a year after inflation. The 1973 to 1977 retirees saved through weaker years, reach retirement with $0.85 to $1.5 million, and then meet 6.6 to 8.7% a year inflation in their first decade. They run out between 83 and 95. The 1917 retiree runs out at 92.

Why history is kinder here

Long runs of years carry information that single draws throw away

The bootstrap draws runs of consecutive real years, stock and bond together. With one-year blocks it is close to the normal engine (82.6% against 82.2%), so fat tails alone do little to this plan. Longer blocks raise the success rate, and full historical replay raises it most. Over a 63-year plan, bad decades in US history have tended to be followed by better ones, and independent draws cannot reproduce that.

Benchmark

The 4% rule on this data lands a few points under the Trinity study

Before trusting the engine I ran the textbook case: $40,000 a year from $1 million, adjusted for inflation, for 30 years, replayed through every start year. The Trinity study (Cooley, Hubbard and Walz, 1998) reported 95% success at 50/50 and 98% at 75/25 for start years 1926 to 1966. Bengen (1994) found 4.15% the highest rate that survived every 30-year period with 50 to 75% stocks.

This data fails about one more start year than Trinity at each mix: 1965 and 1966 at 75/25, 1964 to 1966 at 50/50. They run out late, in their 25th to 29th year (the 1965 retiree at 94, a year short), and the safe maximum comes out at 3.75% for 75/25 against Bengen's 4.15%. Both studies used different bonds from mine: Trinity long-term corporate bonds and Bengen intermediate Treasuries, where I use 10-year Treasuries derived from yields. I have not tested how much of the gap that explains.

Spending rules

Flexible spending buys success with lower spending in bad stretches

The app has three spending rules. Constant spending withdraws $60k every year. The percentage rule spends 4% of the portfolio, held between a floor of 75% and a ceiling of 150% of the target. Guardrails, after Guyton and Klinger, start at $60k and cut 10% when the withdrawal rate rises 20% above where it started (except in the last 15 years) or raise 10% when it falls 20% below, within the same floor and ceiling. A pension or Social Security payment reduces what the portfolio has to cover from the age it starts.

Under the bootstrap, guardrails lift the default plan from 84.8% to 90.0%. The price is that about a quarter of the paths spend at least one year at the $45,000 floor. In history neither flexible rule ran out in any of the 90 windows, but the percentage rule's median path dropped to the floor at some point.

Solver

What gets the plan to 90%

For the plan on screen, the solver searches each lever on its own: the first later retirement age that reaches the target, the highest spending (to $500), the lowest yearly saving (to $500), and the fixed stock share closest to the current one. Under the bootstrap the default plan needs one of: retire at 52, spend $51,500, or save $48,500 a year. No fixed mix gets it there; 100% stocks reaches 88%. Under historical replay it already clears 90%, and the solver reports the slack instead: spending can rise to $62,500 or saving fall to $38,000. Normal and bootstrap searches reuse the same 5,000 seeded paths for every candidate, so the comparison is between plans, not between random draws, and the search runs in a Web Worker in under a second.

Method

Data and engine

scripts/build_returns.py reads Shiller's monthly ie_data.xls. Stock returns chain his monthly total return, (P_m+1 + D_m/12) / P_m, from January to January. Bond returns are a constant-maturity approximation: buy a 10-year bond at par at January's yield, collect a year's coupon, and sell it as a 9-year bond at the next January's yield. Before 1953 the yield column is Shiller's long-term government rate. Each series is deflated by the change in January CPI. Shiller's file runs to September 2023, with estimated CPI for its last two months, so the last full year is 2022.

Against Damodaran's histretSP.xls for 1928 to 2022, the series agree on average (real stocks 8.33% against 8.26% a year, real bonds 1.88% against 1.87%) and correlate at 0.97 year by year. Single years differ because Damodaran uses December 31 closes and Shiller monthly averages: 1987 is -6.2% here and +1.4% there, because a sharp rally in January 1987 put that month's average 6% above December's, so this window starts higher. The bond approximation matches Shiller's own monthly bond-return column to 0.34 points a year on average.

Data

Shiller, S&P Composite, CPI and GS10, 1871 to 2022 (152 years), real, January to January

Normal

Independent bivariate normal stock and bond draws with the data's means, standard deviations and correlation (0.19); stock mean and volatility adjustable

Bootstrap

Moving blocks of consecutive years with wraparound, stock and bond drawn together; block length 1 to 20, default 10

Historical

One window per retirement year; working years use the years just before it; windows that pass 2022 are shown but not counted

Timing

Savings added at year end while working; spending withdrawn at the start of each retirement year; rebalanced yearly

Checks

scripts/engine.py ports the engine to Python; scripts/check_engine.py --js runs both and the benchmarks

Stack

Static files, vanilla JavaScript and a Web Worker, no libraries, no backend, no analytics