Historical Bootstrapping

Let the historical returns be your distribution. Resample a year, apply its return, and repeat.

One year · with replacement

Your scenario

INPUTS

Change an input to start again at year 0.

Starting portfolio

Annual withdrawal

Beginning of each year; fixed nominal amount, not inflation-indexed.

Simulations

Years

Choose one historical marketUS · S&P 500 1928–2025Japan · Nikkei 225 1950–2025

US includes dividends; Japan is price-only.

SELECTED MARKET HISTORY

Reproducibility & settings

Random seed

Same settings and seed replay the paths. Increasing the simulation count keeps existing paths. R seeds do not reproduce these draws.

First historical year

Last historical year

Animation speed

Ready at year 0. Click Next to begin.

Back and Reset replay your current draw. New random draw changes the seed.

Current year0 / 30

Before the first withdrawal

Success so far100.0%

100 of 100 portfolios above zero

Median balance$1.00M

At the current year

Depleted portfolios0

Zero stays zero

Portfolio paths

Each line is one possible retirement.

Line opacity

Teaching model: success means a positive ending balance. Withdrawals stay fixed in nominal terms; inflation reduces their purchasing power. Use up to 2,000 simulations when comparing scenarios.

Sort by

Simulation	Year	Return	Market / year	Ending balance	Status

Click a row to focus that simulation. CSV includes every simulation from year 0 through the displayed year.

Explore a yearYear 0 / 30

0 · Start30 · Retirement horizon

Follow the calculation

Sim

Where the return comes from

SIM 1

Actual draws: simulation 1 only. Other simulations draw separately.

Try this:

What happens to historical order?

Follow simulation 1: are historical years chronological, and can a year repeat? Then use 2,000 simulations to compare US and Japan separately. Inspect each market’s arithmetic mean, geometric mean, and SD. Why do dividends and return currency limit a direct comparison?

How this model works

Each simulation independently samples one historical year from the selected market, uniformly with replacement, for every simulated year. A historical year can repeat. No normal distribution is assumed; original chronological dependence is discarded. The return distribution cannot generate outcomes absent from the selected history.

Withdrawals occur at the beginning of each year and stay fixed in nominal currency units. They are not inflation-indexed: with positive inflation, purchasing power declines over time. There are no contributions, taxes, or fees. “Success” means the ending balance is strictly positive; paying the final withdrawal and ending at exactly zero counts as depleted. Zero is absorbing.

Increasing Simulations reduces Monte Carlo sampling noise; it cannot fix return assumptions or create more historical evidence.

Each path has its own seeded Mulberry32 stream. Changing the simulation count or horizon preserves the earlier paths and years when other settings are unchanged.