FIRE glossary
Monte Carlo Simulation
Running your retirement plan through thousands of randomly sampled market-return sequences to see what share of them leave your portfolio intact.
How Ember runs it
Ember's Monte Carlo engine draws a return sequence for each simulated run from a sampler — real historical data resampled in blocks, or a normal-distribution approximation — then plays out the full save-then-spend path for that sequence, year by year. The result reports a success probability (the share of runs that never fully depleted the portfolio) plus percentile bands showing the range of portfolio values at each year and at the end of the horizon, so you see the spread of outcomes, not just one number.
Reading a success probability honestly
A percentage on its own tells you little. Ember's own simulation trace explicitly ties the number to its drivers — how many runs, what horizon, which historical data source and version, what block length, what inflation basis — because changing any of them moves the result. Two Monte Carlo results are only meaningfully comparable when those settings match.
What it doesn't tell you
Any single simulated run is a hypothetical history built from resampled historical blocks, not a forecast of what will actually happen to markets. An 85% success rate doesn't mean an 85% chance of this specific future — it means 85% of the sampled historical sequences, replayed against your plan, never ran the portfolio to zero. The other 15% is worth understanding, not just the headline percentage.
Percentiles, not just pass/fail
Beyond the single success percentage, Ember also reports percentile bands — the 10th, 25th, 50th, 75th and 90th percentile portfolio value at each year of the simulation. That range shows what a merely mediocre outcome looks like, not just the binary of ran-out versus didn't, which matters because a plan that "succeeds" by ending with almost nothing left is a very different result from one that succeeds with plenty to spare.
Worked example
A $1,000,000 pot, $40,000/yr spend, 1,000 simulated 35-year retirements
Never ran out
89%
share of the 1,000 sampled sequences
Median ending value
US$4,810,186
Fixed illustrative inputs, not your data — for the exact maths behind your own numbers, use the free calculator or build a plan. Educational modelling, not financial advice.
Across borders
The historical series behind the simulation carries UK, US and global-equity returns plus currency moves between them, so a cross-border plan's Monte Carlo result captures market sequence risk and currency sequence risk together, rather than market risk in isolation.
Common questions
How many runs does Ember use?
It's configurable. More runs narrow the sampling noise on the estimate itself; they don't change the underlying market risk being estimated.
Where does the return data come from?
Real historical return blocks, resampled (block bootstrap) rather than assumed to follow a smooth statistical distribution — so the simulation reuses actual sequences of historical years.
Can a plan reach 100% success?
It depends entirely on the inputs. A low withdrawal rate against a well-diversified pot can get close, but no assumption set removes market risk entirely.
Related terms
See monte carlo simulation in your numbers
The free calculator gives a rough estimate; the full planner models your actual accounts, pensions, residency moves and taxes — with the maths behind every figure shown.