Parametric Monte Carlo

Draw annual returns from a normal distribution. Watch one retirement become many possible futures.

r ~ Normal(μ, σ²)

Current year0 / 30

Before the first withdrawal

Success so far100.0%

100 of 100 portfolios above $0

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	Source 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:

Same mean. Different SD.

Set Simulations to 2,000. Compare mean 5% / SD 12% with mean 5% / SD 20%, keeping the seed fixed. This uses common random numbers (the same standardized draws) for a paired comparison. What happens to spread, success, and typical compound growth?

How this model works

Each annual simple return is an independent normal draw with your arithmetic mean and SD. The defaults, 5% and 12%, are illustrative nominal assumptions, not historical equity estimates (the embedded US series in the bootstrap apps is about 11.9% / 19.4%). A normal simple-return model can draw losses below −100%; the balance is floored at zero. With SD = 0, every return equals the mean.

For small returns and moderate volatility, compound growth without withdrawals is approximately μ − σ²/2, with μ and σ in decimals. At 5% / 12%, this is 4.28%; at 5% / 20%, 3.00%. This approximation is not exact; at high volatility or returns near −100% it is unreliable, and normal draws at or below −100% prevent a finite long-run log-growth interpretation.

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.