Original simulation studies from the people building the engine. Every article states its method, uses seeded runs that reproduce, and reports the trade-off rather than only the headline.
We run these simulations to answer questions we had about our own plans, then publish what came out — including when the result is inconvenient. Method, path counts and assumptions are stated in each piece.
New here? The retirement planning guide pulls all of it together in reading order, and the glossary defines the vocabulary as it comes up.
A 4%-of-balance rule never ran out across 5,000 retirements and spent under $30k a year in 72.6% of them. Vanguard dynamic clamps the cuts, which is why it can fail. Paired worlds, parameter stress, and the 1928-2025 tape.
One projection is a point. 1,000 simulated lifetimes are a range. How to read the cone, what the p10 floor means, and why a 7% every-year sheet implies 100% success against a measured 89.6%.
On a rigid withdrawal grid, 90% success sits near a 3.95% rate. Nothing from 2% to 6% prints 100%. 100% is empty, not nearby.
Success rate and median leftover are different meters on the same 1,000 worlds. On a rigid grid they both fall as the rate rises, and they still are not interchangeable.
Rigid 4% from $1 million lasts in 93.5% of 25-year lives from 65 and 78.7% of 50-year lives from 40. The rate is the same. The sentence is not.
Coast is a contribution-stop date plus a compounding bet. Keep saving until 65 and 56% of paths still hold $1.5M. Stop at 45 and 32.5% do.
Lump finishes ahead in 56.3% of 1,000 regime worlds and in 67.0% of overlapping 12-month windows on the 1928+ tape. Independent n is 97, not 1,161.
Arithmetic mean 5.01% versus geometric 3.27% on a no-spend 30-year companion. Compounding the average prints $4.33M against a $2.62M median.
On a rigid 4% retiree, 100% stocks raises the median terminal and lowers success versus 60/40. The split is the result. Neither word is a ranking.
We will not name a best leverage. We ran every constant multiple from 1.00× to 3.00× in 0.01 steps — 201 overlays — on one 1928–2025 US monthly tape and through overlapping 40-year starts. Peak multiples are in-sample.
The 4% rule is a 30-year sentence. We ran rigid and Guyton-Klinger policies across 30-, 35-, 40-, 45- and 50-year horizons on 200 seeded paths.
A success rate is a binomial proportion. Here is the standard error at 100, 1,000, 5,000 and 10,000 paths, and which integer Killion actually runs.
History asks whether a plan survived the actual past. Simulation asks how often it survives in a world the model believes in. Killion runs both.
Yes, when the market model is too gentle or the household is too obedient. A 90% from independent annual draws is not a 90% from a regime-switching engine.
The 4% rule sounds settled. We ran flexible and rigid withdrawal policies through 5,000 identical market lifetimes to see what "safe" actually means, and what it costs.
One percent sounds trivial. We simulated 5,000 forty-year saving lifetimes at 0%, 0.5%, and 1% fee drag to measure what that annual charge actually removes at the finish line.
The same market crash is a footnote at 48 and a crisis at 65. A look at sequence of returns risk, and why a crash the year you retire does the most damage.
Everyone has a favorite investing strategy. We ran six through 5,000 identical market lifetimes — same household, same markets — to see which actually wins.
Monte Carlo simulation is the gap between a financial projection and a real plan. We ran one household through Killion’s full simulation engine to show why the odds, not the number, are what you actually plan against.
Timing the market can win on paper. Here is what forty years of real S&P 500 returns say about why staying invested almost always wins in practice.