The five regimes
Independent annual draws from one return distribution do not look like markets. Bad years cluster. Inflations arrive with recessions. Killion's projection engine is a five-state Markov model — expansion, recession, stagflation, crisis and recovery — so the next year's distribution depends on this year's state. Asset-class shocks are correlated (a Cholesky factorisation of the covariance), and inflation surprises move with those returns.
Default runs use 1000 paths over a 60-year horizon. That is the same engine the public demo and the paying product share.
Seeds and reproducibility
Every run carries an integer seed. The same household, the same seed and the same engine version produce the same 1,000 paths. That is why a published study on this site can name a seed (the 4% article uses 20260622) and a later reader can, in principle, replay it. Unseeded Monte Carlo is a random number generator with a marketing department.
Historical backtests
Alongside the simulated paths, the product replays an allocation through every market start year since 1928 using real monthly returns. Simulation answers “how often does this fail in a world like the one the model believes in.” History answers “would this have survived the actual past.” They disagree, and that disagreement is information — see Monte Carlo vs historical backtesting.
Limitations
- No taxes, Roth conversions, RMDs or IRMAA.
- No shared household login.
- Cash and bank balances are entered manually while bank linking moves provider.
- The five regimes are a model of US-like market history, not a forecast of the next decade.
- 1000 paths is enough to stabilise a success rate to about a percentage point; it is not a law of nature. See how many simulations are enough.
- Killion is software, not an adviser, and simulated outcomes are hypothetical.
Reproduce a run
- Use the public demo or a paid account on the same engine version.
- Enter the household: balances, spend, allocation, retirement age, withdrawal rule.
- Note the seed shown on the run (studies on this site publish theirs).
- Re-run. The distribution should match to displayed precision.
The free calculators use the same identities without the full regime model, plus an optional 1,000-path lognormal band so a single line is not the only number. They are teaching tools; this page is the product engine.