Compounded SOFR is the annualized interest rate you get when you string together the daily Secured Overnight Financing Rates published over an interest period and let them compound. It answers a practical question: if you borrowed cash overnight, repaid it the next morning, and immediately borrowed again at the new day’s rate for every day in a 30-, 90-, or 180-day period, what single rate describes the total interest? The math is a product of daily rate factors, annualized on a 360-day basis. The complications are almost entirely about timing.
What SOFR Measures Before You Compound It
SOFR is a broad measure of the cost of borrowing cash overnight collateralized by U.S. Treasury securities.1Federal Reserve Bank of New York. Secured Overnight Financing Rate Data It comes from the Treasury repo market, where one party temporarily sells Treasuries for cash and buys them back the next day at a slightly higher price. That price difference, expressed as an annual rate, is SOFR.
The New York Fed publishes SOFR each business day at roughly 8:00 a.m. ET, reflecting activity from the prior day. Because it looks backward at what actually happened overnight, a single day’s SOFR is only directly useful for overnight exposures. Compounding is how you extend it to cover a full loan or bond interest period.
How the Compounding Calculation Works
For each business day in the interest period, you build a daily rate factor. Take that day’s published SOFR, multiply by the number of calendar days the rate applies to, divide by 360, and add 1. Written out, the factor for business day b is (1 + rb × nb / 360), where rb is that day’s SOFR and nb is the number of calendar days it covers.2Federal Reserve Bank of New York. ARRC Syndicated Loan Conventions Technical Appendices
That nb is where weekends and holidays enter the calculation. SOFR is only published on business days, so Friday’s rate applies for three calendar days (Friday, Saturday, and Sunday), making nb equal to 3. A three-day holiday weekend pushes it to 4.3Federal Reserve Bank of New York. ARRC SOFR Syndicated Loan Conventions Weighting non-business days incorrectly is the most common implementation mistake, and it distorts every step that follows.
Once you have a factor for every business day in the period, multiply them all together. Subtract 1 from the product to isolate the total interest for the period. Then annualize by multiplying that number by 360 divided by the total calendar days in the period.2Federal Reserve Bank of New York. ARRC Syndicated Loan Conventions Technical Appendices
A Worked Example
Take a simplified three-business-day period with no weekends or holidays. If SOFR prints at 5.00%, 5.05%, and 5.10% on those three days, the daily factors are:
- Day 1: 1 + (0.0500 × 1/360) = 1.00013889
- Day 2: 1 + (0.0505 × 1/360) = 1.00014028
- Day 3: 1 + (0.0510 × 1/360) = 1.00014167
Multiply the three factors and you get roughly 1.00042084. Subtract 1 for a period rate of 0.00042084, then multiply by 360/3 to annualize. The result is about 5.05%. The geometric averaging naturally pulls the answer toward the higher end of the daily series, which is why compounded SOFR differs slightly from a plain arithmetic average of the same rates.
The Shortcut Almost Everyone Actually Uses
Running the full product-of-daily-factors calculation by hand for a 90-day period, weekend adjustments included, is tedious. Two published tools eliminate the work.
The SOFR Index
The SOFR Index is a running cumulative measure, starting at a base value of 1.00000000 on April 2, 2018, and incorporating each new day’s SOFR through the same compounding mechanics described above.4Federal Reserve Bank of New York. SOFR Averages and Index Data To compute compounded SOFR over any custom window, divide the index value at the end of the period by the value at the start, subtract 1, and annualize using 360 divided by the calendar days in between. Two lookups and light arithmetic replace the daily-factor loop entirely. This is how most servicers and trading desks compute compounded SOFR in production.
SOFR 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 Contracts with matching interest periods can reference these values directly. The ARRC’s working group on consumer products noted that having a trusted public administrator publish these averages makes compounded SOFR feasible even for adjustable-rate mortgages and other mass-market lending, where operational simplicity matters.5Federal Reserve Bank of New York. Options for Using SOFR in Adjustable Rate Mortgages
Timing Conventions: Why the Rate You Pay Isn’t Always the Period You Pay For
The awkward reality of compounded SOFR is that you don’t know the final rate until the interest period ends. Borrowers need invoices before their payment date. Servicers need lead time. Financial contracts bridge that gap through one of three conventions, each with its own trade-off.
Lookback
A lookback shifts the observation window backward by a set number of business days, typically five. On June 10, you apply the SOFR rate that was published on June 3. This is the ARRC’s recommended convention for syndicated loans.3Federal Reserve Bank of New York. ARRC SOFR Syndicated Loan Conventions
Because the last day’s applicable rate was actually published five business days before the period ends, the administrative agent knows the full compounded rate in time to invoice and settle. The ARRC specifically recommends a lookback without an observation shift, meaning the earlier rate is applied to the current day’s principal balance rather than to the earlier day’s balance. That structure avoids mismatches if the loan is prepaid mid-period. The cost is a small basis mismatch: the borrower isn’t paying for the exact overnight funding cost of the actual period. Five days of slippage on a 90-day period is usually a fair trade for operational certainty.
Lockout
Under a lockout, sometimes called a suspension period, compounding runs normally through most of the interest period, but the SOFR rate is frozen for the last few days. The rate observed on the cutoff day carries forward for every remaining day. Two-to-five-day lockouts have been used in several SOFR floating-rate notes.6Federal Reserve Bank of New York. An Updated Users Guide to SOFR
For most of the period, the rate used each day is the most recent SOFR print, which keeps discounting and net asset value calculations close to par. The frozen tail creates a small hedging basis against standard SOFR swaps. Because a lockout only produces advance notice at the scheduled end of an interest period, the ARRC’s user guide notes it fits less naturally with loans that can be prepaid at any time.6Federal Reserve Bank of New York. An Updated Users Guide to SOFR
Payment Delay
Payment delay is the structurally cleanest option. The observation window covers the full interest period with no shifts or frozen rates, so the compounded rate reflects the exact overnight funding cost of every day. To give the servicer time to calculate, the payment date is pushed back by a set number of business days after the period ends.7Federal Reserve Bank of New York. Appendix to SOFR Floating Rate Notes Conventions Matrix An interest period ending March 31 might not settle until April 7. The rate is perfectly accurate; the cash flow timing shifts. This convention shows up more in floating-rate notes than in syndicated loans.
Compounded SOFR vs. Term SOFR
The two rates come from the same underlying overnight rate but answer opposite questions. Compounded SOFR tells you what actually happened during a past period. Term SOFR tells you what the market expects for a future period.
Term SOFR is a forward-looking rate published daily by CME Group in 1-, 3-, 6-, and 12-month tenors, derived from SOFR futures activity.8CME Group. CME Term SOFR Rates Because borrowers know the rate at the start of the period, cash management is simpler, which appeals to corporate treasurers and middle-market borrowers.
The ARRC has drawn a firm line on scope. It does not support Term SOFR for the bulk of the derivatives market, where compounded SOFR in arrears is already the standard, and it recommends limiting Term SOFR derivatives to end-user hedges of cash products already referencing Term SOFR. For floating-rate notes, adjustable-rate mortgages, student loans, and most securitizations, the ARRC recommends overnight SOFR or SOFR averages, not Term SOFR.9Federal Reserve Bank of New York. ARRC Recommended Scope of Use for SOFR Term Rates Term SOFR has found its widest adoption in bilateral business loans and trade finance, where operational simplicity outweighs structural purity.
The Spread Adjustment on Legacy LIBOR Contracts
If you hold a floating-rate instrument that originally referenced LIBOR and fell back to SOFR, the rate you pay is not just compounded SOFR. LIBOR reflected unsecured interbank lending and carried a built-in credit premium; SOFR is Treasury-secured and sits lower on the yield curve. To keep the transition economically neutral, a fixed credit spread adjustment was added.
The permanent adjustments, triggered by the March 2021 cessation announcement, were set as the five-year historical median difference between each LIBOR tenor and the corresponding compounded SOFR rate:
- 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)
These spreads are fixed for the life of the contract. A legacy loan that referenced 3-month LIBOR now pays 3-month compounded SOFR (or Term SOFR, depending on the fallback language) plus 0.26161%. Contracts originated fresh on SOFR do not carry these adjustments, because their pricing was built around SOFR from the start.