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fire-planner/docs/adr/0001-fire-number-monte-carlo-threshold.md
Viktor Barzin edb4d11352
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feat(fire-target): per-Case FIRE-number solver for the retirement countdown 
Add a Monte-Carlo "FIRE number" solver so the wealth dashboard can show a £
countdown to retirement across life-stage cases, in today's money.

Viktor wants to see, per country, how far his net worth is from being able to
retire for good under three cases — Solo (his spend ×1.5), Household (+Anca
×1.5), Family (+2 kids) — with cost-of-living re-scaling per country and a 99%
Guyton-Klinger success bar.

- spend_model: per-Case real-GBP spend, COL-scaled (rent + non-rent essentials
  scale by country; Holidays fixed), ×1.5 safety. Constants sourced live from
  actualbudget (Viktor) / on-record (Anca).
- geo: city -> tax jurisdiction (nomad fallback).
- fire_target: binary-search the smallest LIQUID net worth where GK reaches the
  bar; pension modelled as a tranche unlocking at ~57, kids ramp + optional home
  as cashflows. New fire_target table (migration 0007) + idempotent upsert.
- recompute-fire-targets CLI: solve every Case x country and persist for Grafana.
- CONTEXT.md glossary + ADR-0001 (why MC-threshold on liquid NW, not 25x spend).

Reuses the existing simulator unchanged (its cashflow hooks already supported
pension/kids/home). 345 tests pass; mypy + ruff clean.

Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>
2026-06-28 11:49:23 +00:00

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FIRE number via Monte-Carlo NW-threshold on the liquid pot

We compute each Case's target net worth (its "FIRE number") by searching net worth for the smallest value at which Guyton-Klinger reaches a 99% Monte-Carlo success rate — not a fixed safe-withdrawal-rate multiple (e.g. 25× spend).

A fixed multiple cannot honour the structure the engine already models: the rising 30→70 equity glide, per-jurisdiction taxes drained from the portfolio, the kids-cost ramp, an optional one-time home purchase, and a workplace pension that is locked until ~57. Our block-bootstrap's empirical perpetual SWR is also ~2.5–3%, materially below the textbook 4%, so a 25× multiple would understate the number anyway.

The solver seeds on liquid net worth — it excludes the Fidelity workplace pension (inaccessible until ~57) and injects that pension as a grown lump at age 57. Early-retirement sequence risk is funded only by spendable assets, so seeding total net worth would overstate safety exactly where the 99% bar is decided.

Consequences

  • A vectorised NW search (binary search over initial_portfolio, monotone because the GK year-0 draw is an absolute real amount) populates a fire_target table, one row per (Case × country × with-home).
  • Targets vary by country through both COL-scaled spend and the destination tax regime (the simulator drains tax from the portfolio since 2026-05).
  • The Grafana countdown reads fire_target for the selected country and diffs it against current liquid net worth from account_snapshot.
  • Pension growth to age 57 is modelled deterministically (current value compounded at an assumed real rate), not per-path — a conservative simplification, revisitable if it ever binds.