Compounded SOFR is the rate you get when you take each business day’s Secured Overnight Financing Rate over an interest period, chain the daily rates together so each day earns interest on the prior days’ interest, and annualize the result. It converts a stream of overnight rates into one number that covers a full loan or bond period. The calculation is mechanical; the wrinkles are in how contracts schedule the observation window so the rate is known in time to bill.
What SOFR Measures Before You Compound It
SOFR is a broad measure of the cost of borrowing cash overnight against U.S. Treasury collateral.1Federal Reserve Bank of New York. Secured Overnight Financing Rate Data The New York Fed publishes it each business day at roughly 8:00 a.m. ET, drawing on tri-party repo, GCF Repo, and cleared bilateral Treasury repo transactions. The rate is backward-looking by design: today’s published SOFR is a summary of yesterday’s overnight funding cost.
A single overnight rate is fine for overnight transactions. Almost nothing else in the loan and bond world settles overnight, though, so contracts need a way to turn a run of daily rates into one rate for a 30-, 90-, or 180-day period. Compounding is that way.
How the Calculation Works
For every business day in the interest period, you build a daily rate factor, multiply all the factors together, subtract 1, and annualize.2Federal Reserve Bank of New York. ARRC Syndicated Loan Conventions Technical Appendices
Building the Daily Rate Factor
For business day b, the factor is (1 + rb × nb / 360), where rb is that day’s published SOFR and nb is the number of calendar days the rate applies. The 360-day denominator is the U.S. money-market day-count convention.
The nb value is where weekends and holidays enter. SOFR only publishes on business days, so Friday’s rate covers three calendar days (Friday, Saturday, Sunday) and nb equals 3. If Monday is a holiday, Friday’s rate covers four days.3Federal Reserve Bank of New York. ARRC SOFR Syndicated Loan Conventions Misweighting non-business days is the most common implementation error, and it corrupts every step that follows.
Chaining the Factors
Multiply the daily factors across the whole period. Subtract 1 from the product to isolate the total interest for the period. Multiply by 360 divided by the total calendar days in the period to annualize.2Federal Reserve Bank of New York. ARRC Syndicated Loan Conventions Technical Appendices
A short worked example makes the mechanics concrete. Take a three-business-day period, all weekdays, no holidays, with published SOFR rates of 5.00%, 5.05%, and 5.10%:
- Day 1 factor: 1 + (0.0500 × 1/360) = 1.00013889
- Day 2 factor: 1 + (0.0505 × 1/360) = 1.00014028
- Day 3 factor: 1 + (0.0510 × 1/360) = 1.00014167
The product is about 1.00042084. Subtract 1 to get 0.00042084, then multiply by 360/3 to annualize, giving roughly 5.05%. Because the factors multiply rather than add, higher rates late in the period carry slightly more weight than they would in a simple arithmetic average.
The SOFR Index and Published Averages
Running that product over 60 or 90 business days with weekend weighting is tedious. The New York Fed publishes two tools that most servicers and desks actually use in place of the manual calculation.
The SOFR Index
The SOFR Index is a cumulative measure that started at 1.00000000 on April 2, 2018 and compounds forward each business day using the same mechanics described above.4Federal Reserve Bank of New York. SOFR Averages and Index Data To get compounded SOFR for any custom window, divide the index value at the end of the period by the value at the start, subtract 1, and annualize with the 360/days multiplier. Two published numbers replace the entire product-of-factors calculation.
30-, 90-, and 180-Day Averages
The New York Fed also publishes pre-calculated compounded averages over rolling 30-, 90-, and 180-calendar-day windows.4Federal Reserve Bank of New York. SOFR Averages and Index Data For contracts with matching interest periods, these plug in directly. The ARRC’s working group on adjustable-rate mortgages pointed to these published averages as what makes compounded SOFR workable in consumer lending, where servicers need a rate they can look up rather than compute.5Federal Reserve Bank of New York. Options for Using SOFR in Adjustable Rate Mortgages
Timing Conventions Contracts Use
Compounded SOFR has one awkward property: the final rate isn’t known until the interest period ends, which is too late for a servicer to invoice on time. Contracts solve this with one of three conventions, each trading a bit of rate accuracy for administrative lead time.
Lookback
A lookback shifts the observation window backward by a fixed number of business days, usually five. On June 10, the contract applies the SOFR published on June 3. By the last day of the interest period, every rate needed for the calculation has already been published, so the agent knows the compounded rate with enough time to bill. The ARRC recommends this convention for syndicated loans and specifies a lookback without observation shift, meaning the earlier rate is applied to the current day’s principal balance, which avoids problems if a loan is prepaid mid-period.3Federal Reserve Bank of New York. ARRC SOFR Syndicated Loan Conventions The cost is a small basis mismatch: the rate paid doesn’t perfectly match secured funding costs for the exact days of the period.
Lockout
A lockout, sometimes called a suspension period, lets compounding run normally for most of the period, then freezes the rate for the last few days. Whatever SOFR was on the cutoff day gets carried forward through the end. Two-to-five-day lockouts have appeared in SOFR floating-rate notes. Most of the period uses the freshest rate, which keeps discounting close to par, but the frozen tail creates a small hedging basis against standard SOFR swaps. The ARRC’s user guide notes lockouts fit less well for loans that can be prepaid at any time, because advance notice only arrives at the scheduled period end.6Federal Reserve Bank of New York. An Updated Users Guide to SOFR
Payment Delay
Under a payment delay, the observation window covers the full interest period exactly, with no shifts or freezes, so the rate reflects secured overnight funding for every day of the period. Time for the calculation comes from pushing the payment date back a fixed number of business days after the period ends.7Federal Reserve Bank of New York. Appendix to SOFR Floating Rate Notes Conventions Matrix A period ending March 31 might pay on April 7. Rate accuracy is best under this convention; cash flow timing moves. Payment delay has seen more use in floating-rate notes than in syndicated loans, where fixed payment dates are usually preferred.
Compounded SOFR Is Not Term SOFR
Compounded SOFR and Term SOFR share the same underlying overnight rate but answer opposite questions. Compounded SOFR measures what actually happened, in arrears. Term SOFR is a forward-looking rate published daily by CME Group in 1-, 3-, 6-, and 12-month tenors, derived from SOFR futures.8CME Group. CME Term SOFR Rates Term SOFR gives borrowers a rate known at the start of the period, which is why some bilateral business loans and trade finance deals prefer it.
The ARRC does not support Term SOFR for most of the derivatives market and recommends overnight SOFR and SOFR averages over Term SOFR for floating-rate notes, adjustable-rate mortgages, student loans, and most securitizations.9Federal Reserve Bank of New York. ARRC Recommended Scope of Use for SOFR Term Rates If a contract references SOFR without qualification, it almost always means compounded SOFR in arrears.
Legacy LIBOR Contracts Add a Fixed Spread
If the compounded SOFR number is showing up in a contract that originally referenced LIBOR, the replacement rate is not bare SOFR. LIBOR reflected unsecured interbank lending and carried a credit premium; SOFR is Treasury-secured and sits lower. To keep the switch from moving economic value between borrower and lender, a fixed credit spread adjustment was added on top of SOFR when legacy contracts transitioned. The March 2021 LIBOR cessation announcement locked these in:
- 1-month tenor: 0.11448% (about 11.4 basis points)
- 3-month tenor: 0.26161% (about 26.2 basis points)
- 6-month tenor: 0.42826% (about 42.8 basis points)
The spreads were set as the five-year historical median difference between each LIBOR tenor and the corresponding compounded SOFR rate. They are fixed for the life of the contract. A legacy 3-month LIBOR loan now pays 3-month compounded SOFR (or Term SOFR, depending on the fallback language) plus 0.26161%. New contracts written after transition don’t carry these adjustments, because their pricing was built around SOFR from origination.