# Under the hood: how the simulator computes this book Every chapter of this book leans on pofo's FIRE simulator. The last article returns the favor: here is what the machine computes, with no black box left in it. Where its data comes from (the backfilled histories, the century-long panel, the living CAPE). How the central model gets built, from your own holdings to parameters fitted and then blended. What each column of the results table draws on, in a technical rundown of the six lenses. How the simulation core runs a plan month by month: spending rules, the tax that grosses up every sale, the buffer and its thresholds, the flows. And what each section of the page computes. Then, in the spirit of the whole book, the **limits**, owned up to. A tool whose simplifications you cannot see is an oracle, and this book has said enough against oracles ([[simulator-traps]], [[monte-carlo-strengths-and-limits]]). This is also the most version-dependent chapter in the book, because the machine keeps changing. The page's own "How this machine works" panel is the authority on its exact state on any given day ([[using-the-fire-simulator]]). ::: cle The design philosophy, in three choices **One**: everything in **real** terms. The series are deflated by the HICP and withdrawals are set in constant purchasing power. Average inflation is in the machine by construction, and the risk of an inflationary episode shows up in the regime columns ([[inflation-and-withdrawal-rates]]). **Two**: the weight of the evidence rather than a verdict. Four families of models run side by side, two of which your dials cannot touch, so the data keeps the last word ([[historical-vs-parametric]]). **Three**: the real plan rather than a caricature. The simulation runs your actual spending rules, the actual tax on sales, the actual buffer. Plan complexity is free in a simulation, so the machine does not skimp on it ([[making-monte-carlo-relevant]]). ::: ## The data: what the machine knows about the world **The long history of your funds.** In portfolio mode, pofo extends every holding back beyond its quoted history. The SIM extensions splice on documented backcasts: long indices, reconstructed composites. Each recipe is calibrated and versioned. Managed futures, to take one, are a vol-targeted TSMOM backcast ([[managed-futures]]). Everything is then converted into euros and **deflated** by the HICP (`^HICP-FR`). What comes out is a matrix of **monthly real returns** for your holdings, decades deep. **A century across sixteen countries.** The broad-sample model carries the Jorda-Schularick-Taylor academic panel (annual real stock and bond returns for 16 developed countries, 1870 to 2020): the raw material for replaying national fates ([[anarkulova-cederburg]]). **A living CAPE.** Shiller's series (1881 to today) is kept current. §00 of the simulator and the CAPE anchor both feed on it ([[valuations-and-cape]]). ## The central model's pipeline Five steps run from your holdings to the central Student-t model ([[making-monte-carlo-relevant]] argues each one). 1. **The monthly real panel**, at the weights your holding sliders sit at **right now**. 2. **The fit.** The machine computes μ (the realized mean, annualized), σ (the monthly dispersion scaled to a year) and df (the inverse of the monthly kurtosis, so the tails of **your** funds, [[fat-tails]]). Computed that way, σ lands below the annualized daily volatility the brochures quote. 3. **Blending.** The fitted parameters are pulled toward a cautious world prior (μ 4.5%, σ 13%, df 4), in proportion to the share of the horizon your history does not cover, and never past 50/50. Your portfolio reaches the central model through its statistics, never through its sequence. 4. **The optional anchors.** The CAPE anchor replaces the mean with what today's valuations imply; the broad-sample prior overwrites all three dials. 5. **The draw.** Independent Student-t years are drawn and then compounded, so volatility drag falls out on its own ([[arithmetic-vs-geometric-returns]]). **The six columns, exactly what each one does** ([[historical-vs-parametric]] for how to read them): - **Historical windows**: every possible start month in your panel opens a window replayed as it happened (with an honest refusal when your history is shorter than the horizon). - **Block bootstrap**: a stationary bootstrap of your panel, with random block lengths averaging 24 months. - **Student-t**: the central case of the pipeline above. - **Sequence stress**: a calibrated two-state Markov chain (sticky bears: about 19% of years in a bear market, in episodes of roughly three years, volatility 1.5 times higher inside them, **mean preserved**; the gap to the central case isolates what a bad sequence costs, [[sequence-of-returns]]). - **Broad-sample**: a per-country block bootstrap of the JST panel, in a domestic 60/40 (your portfolio and your dials are ignored, deliberately). - **Lost decade**: the long Japan-style bear regime, with a mean degraded on purpose. This is the crash test. ## The core: a plan run month by month Every simulated path is exact accounting ([[monte-carlo-strengths-and-limits]]). At each time step, a year by default and a month when monthly withdrawals are switched on, the core does four things, in this order. 1. **The return** for the period is applied to the sleeves. 2. **The need** for the period is set by whichever rule is active, then reduced by the flows arriving at that date (the pension from its start year, side income until its end year, an annuity if part of the capital was converted). Each rule has its own formula: the fixed inflation-adjusted rule serves the same real need every year; the flexible cut bites when drawdown crosses its threshold; guardrails move spending by plus or minus 10% at the edges of the corridor, with their floor; VPW takes a share of the current portfolio; ABW reprices the annuity on wealth plus discounted pensions; the bounded rule follows the Vanguard corridor; the ratchet and the retirement smile ride on top of whatever comes out ([[withdrawal-strategies-overview]]). 3. **The source** of the withdrawal is picked. The buffer pays first when drawdown is past its threshold (10% by default), the sleeves otherwise. The buffer then refills gradually as calm returns, never above its ceiling, and stops refilling in the year you chose ([[refilling-the-buffer]]: the mechanics described there are literally the ones in the code). 4. **Tax** is applied. Every sale is **grossed up** so the net lands where it should: the rate on the dial hits the gain share of the sale. That share starts low and drifts up as unrealized gains compound, which is how a weighted-average cost basis behaves. Optional tax wrappers, each with its own rate and its own place in the selling order, refine how the sales are spread. Ruin is recorded when the money runs out, with its date. Everything else is recorded too: wealth, the spending delivered, time spent underwater. The machine draws 2,000 paths by default, and the dial goes to 10,000. ## The sections: what each one computes A quick tour, with the reading advice for each one in the manual ([[using-the-fire-simulator]]). - **§00**: today's CAPE against its own century. - **§01**: the wealth fans under the four lenses (percentiles date by date, eight paths at regular ranks, the red ones counting ruin, the axis clipped at 10x, [[reading-a-fan-chart]]). - **§02**: your plan replayed at the famous start dates on the long data (1929, 1966, 2000, Japan 1990). - **§03**: ruin broken out by what the first decade of each path returned (the sequence made visible). - **§04**: the distribution of the standard of living actually **delivered**, and who pays for it (the judge of flexible rules). - **§05**: a couple's mortality crossed with ruin ("alive, broke or gone"; the page uses French life tables), the distribution of bequests, and the **causes** of failure (an early crash, a slow grind or longevity, the diagnosis that picks the defense). - **§06**: the frontier of the rules (ruin against how much the lived standard of living swings) and the sensitivity of each lever. - **§07**: the buffer trade-off (a sweep from 0 to 10 years) and the histogram of years spent underwater. - **§08 and §09**: the plan in numbers under the selected model, then the **solver**, the equivalent moves that each bring ruin back under your threshold (the anti-OMY menu, [[one-more-year]]). ::: attention The limits, faced head on Here is the list the page's "Method & honest caveats" panel shows, with a comment on each. - The **portfolio is aggregated** before the simulation runs. There is no fine rotation between asset classes along a path; the regime grid belongs to the design stage, and the machine then tests the mix you settled on ([[market-regimes]]). - The **central model is i.i.d.** The stress and broad-sample columns exist precisely for that limit. - **Tax** is one blended effective rate, which you calibrate yourself, with no account-by-account tax engine. - Your funds' **history** is a kind window. Blending says so and the warnings say so, but no correction turns a short window into the whole story. - **Mortality** is ignored by default, and §05 puts it back in. - The usual items stay **out of scope**: divorce, long-term care, political tail risk, all left to named margins and to the chapters that deal with them ([[hyperinflation-and-extremes]]). One reading rule follows from the whole book: decide on the pessimistic columns, push the horizon past your life expectancy, and read the decimals as a ranking ([[failure-probability]]). ::: ## Checking it yourself There are three ways to audit the machine. The engine is Go code you can read: in the pofo repository, the models, the withdrawal rules and the backcast recipes are all legible and all tested, and the golden tests compare the computations against frozen external references. The book's **headline results** reproduce there in a few minutes. A SAFEMAX near 4% over 30 years falls out of the historical windows; the Trinity cliff appears when you sweep the withdrawal rate; what a bad sequence costs shows up as the gap between the central case and the stress column; the pension effect shows up the moment you move its dial. The matching chapters give the recipe each time. And **disagreements** with other tools are explained by the audit checklist: tails, memory, frictions, sample ([[simulator-traps]]). This simulator ticks boxes that most consumer tools leave empty, and it shows the ones it leaves empty itself. That is the final test to apply to **any** tool, this one included. The question is not "is it right?", because nobody is right about 45 years, but "do we know what it does, and does it say so?". ## The essentials - Three design choices: everything in real terms (deflated by the HICP), the weight of the evidence rather than one verdict (two columns ignore your dials, so the data keeps the last word), and the real plan simulated month by month (rules, tax, buffer, flows). - The central model is built in five steps: the monthly real panel of **your** holdings, then the fit (μ, long-horizon σ, df for the tails), then blending toward the world prior (capped at 50/50), then the optional anchors (CAPE, broad sample), then Student-t draws compounded over the horizon. - The six columns: your own windows replayed, your panel bootstrapped, the central case, the mean-preserving stress (what a bad sequence costs), the JST century in a domestic 60/40, and the lost decade. Every disagreement between them is a diagnosis ([[historical-vs-parametric]]). - The core grosses up every sale for tax (with a gain share that keeps rising), draws on the buffer at its thresholds, and books pensions and side income on their dates: the machinery this book describes is literally the machinery in the code. - The limits are on display: aggregation, an i.i.d. central model, one blended tax rate, short windows, what is out of scope. And that is the test worth applying to any tool: not being right, but saying what it does. --- ## Going further - The "How this machine works" and "Method & honest caveats" panels of the FIRE simulator itself: the machine's exact, current state. - The manual: [[using-the-fire-simulator]]. The reasoning behind each choice: [[making-monte-carlo-relevant]], [[historical-vs-parametric]], [[fat-tails]]. - Jorda-Schularick-Taylor (the broad-sample panel) and Shiller's website (the CAPE): the public data the machine ships with ([[the-library]]).