Reserve simulator

How this is computed

Monthly steps m = 1..N. The reserve's stable assets are simulated month by month and checked against coverage required, computed the way the program computes it (spec §4, ADR 0016, mirrored from clients/js/src/math.ts in base units). Only free capital, the stable assets above coverage required, can back new guarantees or pay redemptions. Figures with no on-chain equivalent (net gain, yield vs Selic, MUTAV take economics) are the business view.

// capital: fulfil_deposits enforces max_tvl
capital_in(m)        = min(starting_capital [m = 1] + monthly_raise [from ≤ m ≤ until, until 0 = N],
                           max_tvl − stable_assets(m−1))         // the rest is refused

// coverage (on-chain)
cover_per_lease      = rent × (default_leg + exit_leg)              // default_cover + exit_cover
remaining_cover(m)   = Σ over active leases (cover_per_lease − claims paid on that lease)
coverage_required(m) = max(ceil(c × remaining_cover(m) / 10_000),              // c in bps, c ≥ 1_000
                           provisions + min(stress_buffer, remaining_cover(m) − provisions))   // ADR 0022
                       provisions ≈ 0 here: claims are paid in the month they arise
free_capital(m)      = max(0, stable_assets − coverage_required)

// register_guarantee, in the program's order (one agency holds the whole book)
refused if           cover_per_lease > max_cover_per_guarantee                       // GuaranteeCapExceeded
                     remaining_cover + new_cover > max_cover_per_agency              // AgencyCapExceeded
                     ceil(c × (remaining_cover + new_cover)) > stable_assets         // InsufficientFreeCapital
new(m)               = most of new_per_month that pass, one after another; refused leases are not carried over
active(m)            = leases signed in the last lease_term months with cover left

// flows
guarantee_fees(m)    = active(m) × rent × fee × fee_periods_per_year / 12
mutav_take(m)        = guarantee_fees(m) × min(take, 30%)            // fee_take_bps ≤ MAX_FEE_TAKE_BPS
net_fees(m)          = guarantee_fees(m) − mutav_take(m)
claims_paid(m)       = active(m) × expected_claims / 12 × ramp(m)    ramp(m) = min(1, m/4) if on
                     + active(m) × (bad_year_claims − expected_claims) / 12   in the 12 months from the bad-year month
                       each lease's payment is capped at its remaining cover; a lease at 0 is exhausted and leaves the book
brs_income(m)        = opening(m) × brs_share × brs_yield / 12          // Nora pays BRS to the income inbox; sweep_income books it monthly
// adapter what-if: one adapter asset, e.g. TESOURO (the pilot holds BRS only: adapter_share = 0, brs_share = 1)
adapter_share        = min(adapter_share_wanted, 1 − min_settlement)    // claims and redemptions pay out in BRS (the settlement token)
brs_share            = 1 − adapter_share
adapter(m)           = opening(m) × adapter_share × adapter_rate / 12
net_gain(m)          = net_fees(m) + brs_income(m) + adapter(m) − claims_paid(m)
stable_assets(m)     = stable_assets(m−1) + capital_in(m) + net_gain(m) − redemptions(m)

// redemptions (only ever from free capital, like strict FIFO fills)
none                 = 0
kept above coverage  = max(0, free_capital(m) − buffer × coverage_required(m))
share of net gain    = min(free_capital(m), share × max(0, net_gain(m)))

// claim caps (pay_claim)
flag month m         if claims_paid(m) > max_claim_per_period   → the excess goes through pay_claim_admin
flag                 if one eviction (min(eviction_cost, exit_leg) × rent) > max_claim_per_call

// bad-year check (off-chain planning signal; never changes coverage required)
bad_year_claims      = expected_claims × bad_year_multiplier
bad_years_covered    = stable_assets(N) / (active(N) × bad_year_claims)    study: grow ≥ 2,0×, never < 1,0×

// expected claims per lease per year (event level)
default_leg          = min(12 × delinquency, default_leg_cover) × rent
evictions            = eviction_rate × min(eviction_cost, exit_leg_cover) × rent
exit_debts           = A: other_exit_debts × rent · B: (other_exit_debts − penalty) × rent · C: 0
claims_to_fees       = expected_claims / (rent × fee × fee_periods_per_year)

// at-a-glance answers
leases_backed        = most leases at full cover with ceil(c × k × cover_per_lease) ≤ stable_assets(N)
new_leases_from_gain = net_gain(N) / (c × cover_per_lease)
raise_to_avoid_refusals = smallest monthly raise (R$1.000 steps, same window) with 0 refused months, max_tvl lifted
payback_month        = first m with Σ net_gain ≥ starting_capital (projected at month-N pace if beyond N)

// reserve yield (business view)
avg_stable_assets    = mean opening(m)
reserve_yield        = Σ brs_income / avg × 12/N  +  Σ (net_fees − claims_paid) / avg × 12/N  +  Σ adapter / avg × 12/N
return_on_capital    = Σ net_gain / capital_in   (annualized × 12/N)
selic_benchmark(m)   = opening(m) × selic / 12       // the same capital at Selic

// Compare c & sizing (steady state, book full for a year, stable assets = stable_assets(N))
normal_net_gain      = net fees − leases × expected_claims + stable × (brs_share × brs_yield + adapter_share × adapter_rate)
bad_year_net_gain    = net fees − leases × bad_year_claims + stable × (brs_share × brs_yield + adapter_share × adapter_rate)

Sources and defaults

• Pilot parameters: mutav/docs/operation/02-parameters.md on origin/main (reviewed 2026-09-19, the single source of business numbers): rent R$2.200, guarantee fee 10% (modelled value inside 9–15% by score), default-leg cover 12× rent (working value, under legal review), exit-leg cover 6× as a separate sublimit, capitalized reserve R$300.000, ~6-month pilot, ~28 new contracts/month to a 170-lease book. The pilot scenarios use the founders' pilot parameters instead (ADR 0028, amended 2026-10-12, the path to R$1M): guarantee fee 12%, R$120.000 start plus R$170.000 a month from month 2, 17 new leases a month (97 by month 6, at the R$1M max_tvl), c = 0,25, issuer income 70% of CDI (≈ 9,6% a year, planning assumption), redemptions above a 25% buffer. 02's “reserve ~80% TESOURO once an adapter exists” is superseded: the pilot reserve is BRS-only (2026-10-07), with TESOURO as the first adapter candidate once Etherfuse has a BRS leg. Fee charged 12× a year: agencies are billed one boleto a month.
• Coverage ratio (c): ADR 0016 and 40-reserve.md 9w. The program holds coverage_required = max(ceil(c × remaining cover), provisions) with c ≥ 0,10 (MIN_COVERAGE_RATIO_BPS = 1_000); devnet and the pilot run at 0,25 (ADR 0028). Filed claims stay fully covered at any c. At R$39.600 of cover per lease, R$100.000 backs 10 leases at c = 0,25 and 2 at c = 1,0; R$300.000 backs 30 at c = 0,25; 170 leases need R$1.683.000 at c = 0,25.
• Caps (devnet config): the caps are off by default in the simulator (0 = no limit); the Devnet caps scenario turns them on. Devnet values: coverage_ratio_bps 2.500; max_tvl R$1M; max_cover_per_guarantee R$120k; stress_buffer R$19k (ADR 0028); max_cover_per_agency R$10M in the simulator only (no program cap since ADR 0019; well above max_tvl ÷ 0,25 plus fee growth, so it never binds: one reserve may serve a single agency); max_claim_per_call / max_claim_per_period R$15k / R$20k per 31 days (a 6×-rent eviction, R$13.200, fits the per-call cap); min_settlement_bps 100% (claims and redemptions pay out in BRS, the settlement token; the pilot holds BRS only, so adapter income is a what-if until the floor is lowered); fee take ≤ 30% (MAX_FEE_TAKE_BPS). Request limits (R$1k–R$100k, R$500 minimum fill) do not affect this model.
• Bad-year check: 40-reserve.md 9w asks the reserve to grow to 2,0 bad years of claims and never hold fewer than 1,0. It is not enforced on-chain yet (a later ADR), so it is shown as an off-chain planning signal next to the coverage figures.
• Delinquency: base 2,5% of annual rent, the founders' working figure for the starting region (2026-10-11): a round number set above the measured anchors for the pilot's segment. Measured: Superlógica IIL, RS apartments, average of the three latest prints (abr/jun/jul 2026), 2,01%, verified at source 2026-09-08; South region 2,67%. Stress 2,87% (IIL RS aggregate). Tail 5,93% (Loft IIA RS, 15-day threshold). Applied as an annual rate on annual rent: 12 × rate × rent.
• Evictions: 12-eviction-cost-south.md. While the fiança is live the art. 59 §1º IX liminar is unavailable, so a forced exit costs about 6× rent (capped at the exit leg). If the fiança extinguishes once the default leg is exhausted, the liminar becomes arguable: base 5,5×, low 2,5×. Eviction rate: 12-eviction-rate-south.md, measured filings, adjusted (not MUTAV data). CNJ DataJud first-instance despejo filings (all 27 state courts, own query 2026-10-02) ÷ IBGE PNAD rented households give 0,5–0,7% of South leases facing a suit per year; about a third end in a court-ordered exit. Adjusted for an underwritten, agency-managed book: low 0,10% / base 0,25% / high 0,60% per year.
• Other exit debts: 12-exit-costs-non-eviction.md §9, base case per lease-year: damage incl. painting 0,056×; accessory charges 0,024×; early-termination penalty 0,077×; abandonment 0,020×; alterations 0,010×; total ≈ 0,19×. All [inference].
• Bad-year multiplier 2,33: calibrated to 40-reserve: R$1.894 per lease per year in scope B (R$321,9k / 170) against R$813 of expected claims.
• Debts covered: A = all tenant debts incl. the termination penalty; B = excluding the penalty (default); C = evictions and abandonment only. In C, abandonment is handled through the eviction event (despejo / imissão, art. 66).
• Take rate 20%: simulator default (the config placeholder; the value is still open, 06-business-model). Lease term 30 months: typical lease (06, PY:109). Issuer income (Nora), % of TVL a year: BRS itself pays no yield. Nora pays the reserve issuer partnership revenue as an annual rate on the reserve's TVL, in BRS, to the reserve's income inbox; the operator's sweep_income moves it into reserve and books it on-chain (ADR 0017), all of it to NAV since the income take is 0, so it counts in stable assets and NAV from then on. It is CDI-linked and tiered on the whole balance: each month the TVL selects the tier whose threshold it is strictly above, and income = TVL × (tier % × CDI) / 12. Public default: CDI 13,65% (Selic − 0,10 pp) and one tier at 70% of CDI (≈ 9,6% a year), a planning assumption until the agreement is signed; whole-balance vs marginal tiers and holding-period rules are to be confirmed with the issuer. A flat brsYieldPct in an older link overrides the tiers. Selic 13,75%. TESOURO 11,58% (adapter what-if only): Etherfuse on-chain accrual, unconfirmed.
• Changed vs earlier versions: 2026-10-12 (latest): the path to R$1M is the pilot plan (founders): Pilot · path to R$1M is 17 leases and R$170k a month from month 2; the earlier 10-a-month plan is kept as a scenario; the conservative variant keeps R$100k a month. Old links that relied on the earlier defaults now load the new plan. 2026-10-11: every numeric input has a slider beside its box, over a range meant for exploring scenarios; the box still takes any value. 2026-10-11: new “Path to R$1M · 6 months” scenario (17 leases and R$170k a month). 2026-10-11: pilot capital R$100k start + R$100k a month from month 1 → R$120k start + R$100k a month from month 2 (founders), so no capital comes in and goes back out in month 1; R$620k by month 6. 2026-10-11: base delinquency 2,01% → 2,5% (founders' working figure for the starting region; the stress scenario doubles it to 5,0%). Old links that relied on the 2,01% default now load 2,5%. 2026-10-11: the founders' pilot parameters (ADR 0028). Default follows the new devnet config: c = 0,25, max_tvl R$1M, R$120k per guarantee, per-call claim cap R$15k (was R$10k, so a 6×-rent eviction fits it), R$20k per 31 days unchanged. Pilot · recommended: R$100k start plus R$100k a month from month 1, 10 leases a month to 60, 12% guarantee fee, redemptions above a 25% buffer; Pilot · conservative is the same at c = 0,50 and 5 leases a month. The “BRS yield” input is renamed “Issuer income (Nora), % of TVL a year” and is now CDI-linked and tiered on the whole balance (CDI plus up to 4 tiers, link keys issuerCdiPct, tier1Min/tier1Pct … tier4Min/tier4Pct); the public default is one tier at 70% of CDI (≈ 9,6% a year), replacing the flat 12,75%. An older link's brsYieldPct still works as a flat override. Old links that relied on the earlier defaults (c = 0,10, max_tvl R$300k) now load the new defaults (c = 0,25, R$1M). The yield vs Selic view shows the effective annual rate. Saved inputs from earlier versions are not reused. 2026-10-07: the pilot reserve is BRS-only. BRS yield defaults to 12,75% (Selic − 1 pp), the adapter share wanted to 0; the TESOURO-specific share cap became the minimum held in the settlement token (min_settlement_bps, 100% BRS), and one generic adapter asset (e.g. TESOURO) is the what-if; those scenarios moved to “Expansion (adapters, what-if)”. Saved inputs from earlier versions are not reused. 2026-10-07 (later): BRS income added (BRS yield, default 0) and a Reserve yield tab holding the BRS yield, the BRS / TESOURO split, the TESOURO yield and Selic. 2026-10-07: the simulator now computes what the program enforces. Coverage required is ceil(c × remaining cover), and paid claims reduce remaining cover; the gate and the caps (max_tvl, per guarantee, per agency, asset split, fee take, claim caps) are inputs, enforced as on-chain; the bad-year floor became an off-chain check; the sizing-rule switch became “Compare c”; labels use the program's terms. Saved inputs from earlier versions are not reused. Earlier: delinquency 2,46% → 2,01%, rent R$2.000 → R$2.200, fee 12% → 10% per 30-day period, cover 3+6 → 12+6, eviction rate 2% prior → 0,25% measured-adjusted, single loss ratio → event-level claims.

Simplifications

• Claims are paid as a smooth expected monthly flow in the month they arise, so open provisions are about 0 and coverage_required is the c term. No subrogation recoveries, no TESOURO price moves, constant rates.
• A single agency holds the whole book, so every lease counts against max_cover_per_agency.
• Yield accrues on the opening stable assets: Issuer income at BRS share × issuer income rate / 12 (the whole reserve in the pilot), and, as an adapter what-if, an adapter asset (e.g. TESOURO) at min(adapter share, 1 − settlement floor) × rate / 12, booked in the same month (the monthly sweep_income; the days between Nora's payment and the sweep are ignored).
• The gate admits as many of the month's planned leases as the caps and free capital allow; refused leases are not carried over. A lease leaves the book at the end of its term (the claims tail is not modelled).
• Selic is the opportunity cost of the same capital, not a target.

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