Libor Transition And Fallbacks

LIBOR transition and fallbacks

Everyone remembers the five statutory tenor spread adjustments. Almost nobody remembers that the base rate they attach to depends on what kind of contract it is. "SOFR + 26.161 bp" is ambiguous as written in US law: 12 CFR 253.4 gives five different base rates for the same spread.

Every figure below is printed by scripts/fallbacks.py (runs in 0.3 s; no optional dependencies). ✅ Measured means this file produced it on 2026-09-09. Every rule is quoted from eCFR 12 CFR part 253 (Regulation ZZ), fetched 2026-09-09.

The rule: the tenor spread adjustment in 12 CFR 253.4(c) is the SAME for every contract type; the base rate is not. Name the contract type before you name the rate.

1. ✅ The five statutory tenor spread adjustments — 12 CFR 253.4(c)

Verbatim: "(1) 0.00644 percent for overnight LIBOR; (2) 0.11448 percent for one-month LIBOR; (3) 0.26161 percent for three-month LIBOR; (4) 0.42826 percent for six-month LIBOR; and (5) 0.71513 percent for 12-month LIBOR."

• ✅ 12 CFR 253.2 covers only those five tenors. The definition of LIBOR there says it "Does not include the one-week or two-month tenors of U.S. dollar LIBOR." 🚨 A 1-week or 2-month LIBOR contract has no Board-selected replacement and is outside the statute.
• ✅ The LIBOR replacement date is "the first London banking day after June 30, 2023" — 2023-07-03.

2. 🚨 One spread, FIVE base rates

✅ From 12 CFR 253.4:

🚨 Read the last two rows again. A six-month LIBOR contract held by an FHFA-regulated entity falls back to 30-day Average SOFR + 42.826 bp: a six-month forward rate is replaced by a thirty-day backward-looking average, and the spread is still the six-month one. The statute says so.

✅ Four administrators publish those five rates (12 CFR 253.2, "Relevant benchmark administrator"):

⚠️ CME Term SOFR is licensed and not redistributable, which is why fallback_rate takes it as an argument rather than computing it. The other four are free.

3. 🚨 What the base rate costs — measured

✅ One 3-month LIBOR contract, 10,000,000 notional, period 2026-07-01 → 2026-10-01, on a seeded SOFR path around 4.30% with a +25 bp step on 2026-06-18 and a −25 bp step on 2026-09-17. CME Term SOFR is stood in with a perfect forward (4.540911%) — the friendliest possible assumption for the cash contract:

✅ Over four quarterly resets across 2026:

• 🚨 The largest single-reset gap is 19.56 bp — against a statutory spread adjustment of 26.161 bp. The base rate is worth as much as the number everyone argues about.
• 🔑 The sign flips. A backward-looking average lags: it is below the in-arrears rate after a hike and above it after a cut. That is why the year total nets down to −1,805 while single quarters are ±20 bp. A hedge sized on the annual number will be wrong every quarter.
• ✅ The cash contract matches the derivative here only because Term SOFR was given perfect foresight. A real forward-looking term rate does not know about an unscheduled move, and the gap is whatever the surprise was.

4. ✅ The consumer transition is a ramp, not a step — 12 CFR 253.4(b)(2)(i)

For a consumer loan, during the one-year period beginning on the LIBOR replacement date, the spread "transitions linearly for each business day" from the difference between the relevant CME Term SOFR and the relevant LIBOR tenor determined as of the day immediately before the LIBOR replacement date to the statutory adjustment.

✅ The arithmetic, with an illustrative day-before difference of 15.0 bp (⚠️ not a quoted value — the endpoint, 26.161 bp, is the statutory one) over 252 business days:

🚨 A consumer loan and an otherwise identical business loan carried different spreads on every day between 2023-07-03 and 2024-07-03, converging only at the end. Any historical repricing, restatement or interest-recalculation over that window has to know which one it is holding. ✅ Reg ZZ also deems Refinitiv's published "USD IBOR Cash Fallbacks" for "Consumer" products equal to those rates, so there is a published series and you should use it rather than re-derive the ramp.

5. What Regulation ZZ does and does not do

• ✅ It applies only where the contract has no workable fallback of its own — 253.3(b) lists the exceptions, including a contract that already specifies a non-LIBOR replacement.
• ✅ Benchmark replacement conforming changes (253.5) become "an integral part of the LIBOR contract" automatically, and for a non-consumer contract the calculating person may make further technical changes in their reasonable judgment. Two counterparties can therefore make different conforming changes to the same trade and both be compliant.
• ✅ For derivatives the fallback is determined on the derivative transaction fallback observation day, and if the rate is unavailable then, "the most recently available publication ... shall be used" — a stale-rate rule that is in the regulation and not in most implementations.
• ⚠️ This is US dollar LIBOR only. Sterling and yen "synthetic LIBOR" ran under FCA powers on a different timetable and are not covered by anything here.

6. What the script gives you

scripts/fallbacks.py — numpy only at import; no optional libraries.

Where this sits

• ../sofr-and-rfr-compounding/SKILL.md — how each of these SOFR bases is actually computed: the index, the averages, and 🚨 the four few-bp errors in compounding one.
• ../ois-discounting-and-multi-curve/SKILL.md — repricing a legacy swap after the fallback, and 🚨 why the par rate check passes while the annuity is 1.461% wrong.
• ../yield-measures-and-bill-quotes/SKILL.md — the other family of quotes that are not what they look like.
• ../../../fin-core/skills/us-market-rules/SKILL.md — the US regulatory and calendar layer this sits inside.
• ../../../fin-models/skills/term-structure-models/SKILL.md — building the curve these rates project off.
• ../../../fin-core/skills/derivatives-pricing/SKILL.md — 🚨 rateslib is not open source; QuantLib is the permissive route for repricing the swaps this skill describes.