Monte carlo excess funding rate

Across all path-years, excess spending funded divided by excess spending intended.

Field: Excess-layer funding rate Unit: probability Basis: no dollar basis Computed by: Engine Status: Complete chain

Appears in: monte-carlo-page (Layered success tile "Ideal / excess funded" (second percent))

Calculation records

• Ideal and excess funding rates, and the flexible-goal totals Formula record, justified by derivation

  Purpose: How much of the intended ideal and excess spending the paths actually funded, and the flexible-goal outcomes summed over them.

  Statement: idealFundingRate = sum(idealFunded) / sum(idealIntended) and excessFundingRate = sum(excessFunded) / sum(excessIntended), each a ratio of totals across paths and each 1 when its total intended amount is not positive. Every flexibleGoals count and amount is the plain sum across every path, never an average. For the worksheet's four paths the ideal totals are $150 / $500 = 0.3 and the excess totals $350 / $500 = 0.7, with flexibleGoals { funded 3, partiallyFunded 2, deferred 2, skipped 1, fundedAmount $500, unfundedAmount $300 }; when every path intends nothing, both rates are 1. Units: rates dimensionless, counts in goals, amounts in usd. Rounding: none; rates at absolute 1e-9 and every sum exactly.

  Formula: rate = sum_p funded_p / sum_p intended_p when sum_p intended_p > 0, else 1; goal_field = sum_p goal_field_p

  • intended_p, funded_p: One path's intended and funded amount for the ideal or excess layer (unit: usd) (domain: worksheet ideal 100/300/100/0 intended)
  • rate: Funding rate for that layer (unit: 1) (domain: worksheet 0.3 and 0.7; 1 with nothing intended)
  • goal_field: One flexible-goal count or amount (unit: goals or usd) (domain: worksheet 3, 2, 2, 1, $500, $300)

  Timing: once per aggregation, over the completed path set

  Rounding: none

  Limits:

  • A ratio of totals, not a mean of per-path rates: averaging the four per-path rates under the zero-intended convention would give 0.625 for both
  • A path that intended nothing adds nothing to either side of its ratio, so it moves neither rate
  • The convention tests "intended total > 0", so a zero or negative total intended amount yields 1 rather than a division
  • The flexible-goal figures are sums; averaging them would give 0.75, 0.5, 0.5, 0.25, $125 and $75
  • The evidence supplies the four funding fields and flexibleGoals only; every other MonteCarloPath field is at the test’s neutral (no depletion or shortfall, floor and target met, attainment 1, no guardrail activity, zero balances, no bequest target)

  Provenance: derived by codex, implemented by claude.

  Independent review: cursor

  Gates (6 of 6 pass): fixture registers a test: pass; pins resolve: pass; families exist: pass; worksheet exists: pass; mutation receipt exists: pass; provenance independent: pass

  Worksheet: monte-carlo-funding-rates.md Mutation receipt: monte-carlo-funding-rates.mutation.md

  Evidence tests: run.evidence.test.ts

  Implemented in: run.ts

  Is the number of: monte-carlo-ideal-funding-rate, monte-carlo-excess-funding-rate, monte-carlo-flexible-goal-outcome-counts

Engine source: engine/src/montecarlo/run.ts (MonteCarloSummary.excessFundingRate)