Compounding SOFR in arrears: lookback, observation shift, lockout and payment delay

Four conventions solve the same problem: compounded SOFR is not known until the interest period is over. Here is how each one works, where the ARRC said to use it, and what each produced on a real quarter of 2026 data.

Updated October 10, 2026 · Data through October 8, 2026 · Sources & method

Compounded SOFR in arrears is only final once the last overnight rate of the interest period is published, at about 8:00 a.m. ET on the next business day, which is usually the payment date itself. Each convention buys time in a different way. A payment delay keeps the exact rate and pays later. A lookback borrows each day's rate from a few business days earlier but keeps the interest period's day weights. An observation shift moves the whole observation window back, weights included. A lockout stops taking new rates for the last few days. On the quarter from June 30 to September 30, 2026, they produced compounded rates between 3.66177% and 3.68250% on identical underlying data, a spread of about 2 bp, mostly because the Fed's target range moved up on September 17 and the lagged conventions caught less of it.

The problem the conventions solve

Under plain arrears, every calendar day of the interest period accrues at that day's SOFR (weekends and holidays at the previous business day's rate), and the daily factors are multiplied together. The New York Fed's SOFR Averages and SOFR Index use the same arithmetic:

compounded rate = [ Π (1 + SOFRᵢ × nᵢ / 360) − 1 ] × 360 / d SOFRᵢ SOFR for business day i in the observation window nᵢ calendar days SOFRᵢ applies (1 on most days, 3 over a weekend) d calendar days in the observation window

The catch is timing. SOFR for a value date is published the following business day, so the rate for the period's last business day arrives on the morning interest is due. The ARRC's Updated User's Guide to SOFR (February 2021) says plain arrears "is often not operationally practical" and names the fixes: "payment delays, lookbacks, and lockouts." The observation shift is a variant of the lookback. The four differ in which rate each day uses and which days' weights apply to it.

The four conventions

Payment delay

Interest is computed exactly as in plain arrears and paid k days after the period ends. The rate is the true compounded rate for the period, with no lag. The ARRC guide notes this is how standard SOFR overnight index swaps work: they "generally use a payment delay to settle 2 days after the end of the interest period (often referred to as 'T+2')." Because the payment, not the observation, moves, the next period still starts on the original date.

Lookback without observation shift

In the guide's words: "For each day in the interest period, the SOFR rate from k business days earlier is used to accrue interest." The calendar of accrual is untouched. A Friday in the interest period still accrues for three days, and a Thursday before a holiday weekend for four, even though the rate it borrows came from a business day k days earlier that may have covered only one night. The ARRC recommended this form, with a 5-business-day lookback, for syndicated and business loans.

Lookback with observation shift

Both ends of the window move back k business days, and each rate is weighted by the days it actually covered in that shifted window. The result is a genuine compounded average of SOFR over a real stretch of the calendar, so it can be reproduced from two SOFR Index values. The ARRC's floating-rate note conventions call it a "Two-Day Backward Shifted Observation Period and No Lockouts." The ISDA fallback for legacy USD LIBOR derivatives also compounds SOFR with a two-day backward shift.

Lockout

Rates are observed with no lag until the last k business days of the period; those days repeat a single earlier print. The guide says "A 2-5 day lockout has been used in some SOFR FRNs," and cautions that a lockout may not suit loans that can be repaid at any time.

What changes under each convention. Source: ARRC User's Guide to SOFR (2021) and SOFR FRN Conventions Matrix (2019).
Convention	Rate for each day	Day weights nᵢ from	How notice is gained
Plain arrears	That day's SOFR	Interest period	None
Payment delay (k)	That day's SOFR	Interest period	Pay k days after period end
Lookback (k)	SOFR k business days earlier	Interest period	Last print needed is k business days old
Observation shift (k)	SOFR k business days earlier	Shifted observation window	Window ends k business days early
Lockout (k)	That day's SOFR, frozen for the last k business days	Interest period	Last k days need no new print

What the ARRC recommended

The ARRC's guidance split along product lines, and derivatives kept their own market conventions:

Business and syndicated loans: lookback without observation shift, with its loan conventions contemplating a 5-business-day lookback. The guide's reasons are that loan principal can be repaid on any day and that loans trade between lenders without clean coupons, so every calendar day needs to keep its own weight in the interest period.
Floating-rate notes: the observation shift was among the conventions the ARRC recommended. The guide observes that FRNs "have tended to have a shorter lookback period of 2-3 business days." The August 2019 FRN Conventions Matrix documents three structures: a lockout with a one-day lookback, a five-day lookback with no lockout, and the two-day backward-shifted observation period.
Derivatives (market practice, not an ARRC recommendation): SOFR OIS generally settle T+2 through a payment delay, as the guide notes, and ISDA's IBOR fallback uses a two-day backward shift (see the LIBOR fallback calculator).

None of this is binding. The Matrix states it is "not intended in any way to mandate, prescribe, or limit the ways in which SOFR may be used," and the ARRC itself was terminated in November 2023. The conventions survive in the documents that adopted them, so the governing text is always the contract's definition of the observation period.

Worked example: June 30 to September 30, 2026

Take a $25,000,000 quarterly interest period from Tuesday, June 30, 2026 (inclusive) to Wednesday, September 30, 2026 (exclusive): 92 days on ACT/360. It is a useful test because it contains two holidays with no SOFR print (Friday, July 3 and Monday, September 7) and a change in policy rates. From June 30 through September 16, SOFR stayed between 3.53% (July 9) and 3.68% (June 30 and August 31). The federal funds target range was raised from 3.50%–3.75% to 3.75%–4.00% effective September 17, and SOFR printed 3.85% that day and between 3.85% and 3.90% for the rest of the period (see SOFR in 2026 and the target-range history).

Each row below was computed from the New York Fed's daily SOFR with the same routine that runs the compounded SOFR calculator. Interest is the annualized rate × $25,000,000 × 92 / 360 in every row, including the shifted ones.

Compounded SOFR for June 30 – September 30, 2026 under each convention, $25 million notional, ACT/360. Source: computed from Federal Reserve Bank of New York SOFR data.
Convention	SOFR value dates used	Compounded rate	vs plain	Interest	Last print published
Plain arrears	Jun 30 – Sep 29	3.68228%	—	$235,257.00	Sep 30 (payment day)
Payment delay, 2 days	Jun 30 – Sep 29	3.68228%	0.00 bp	$235,257.00	Sep 30; paid Oct 2
Lookback, 2 days	Jun 26 – Sep 25	3.67307%	−0.92 bp	$234,668.31	Sep 28
Lookback, 5 days	Jun 23 – Sep 22	3.66243%	−1.99 bp	$233,988.51	Sep 23
Observation shift, 2 days	Jun 26 – Sep 25 (window Jun 26 – Sep 28, 94 days)	3.67588%	−0.64 bp	$234,847.64	Sep 28
Observation shift, 5 days	Jun 23 – Sep 22 (window Jun 23 – Sep 23, 92 days)	3.66177%	−2.05 bp	$233,946.47	Sep 23
Lockout, 2 days	Jun 30 – Sep 25 (Sep 25 repeated)	3.68250%	+0.02 bp	$235,271.02	Sep 28

Three things drive the spread of results.

The lag decides how much of the rate rise is captured. Plain arrears accrues 13 of the 92 days at post-change prints (September 17 through 29). A 5-day lookback or shift captures only 6: the September 17 print first reaches accrual on September 24 under the lookback, and the shifted window ends on September 23. In a rising-rate quarter the lag saves the borrower $1,268.50 (lookback) or $1,310.54 (shift) against plain arrears; in a falling-rate quarter it works the other way.

The lockout barely matters here. September 28 and 29 accrue at September 25's 3.90% instead of their own 3.90% and 3.88%, adding 0.02 bp, or $14.02. A lockout only bites when SOFR moves inside the last few days.

The payment delay changes the date, not the amount. It is the only row that gives notice and still charges the exact period rate.

Two rows can be checked against published figures. The SOFR Index was 1.24910242 on June 30 and 1.26085682 on September 30, 2026: (1.26085682 ÷ 1.24910242 − 1) × 360 ÷ 92 = 3.68228%, matching plain arrears. For the 5-day shift, the Index was 1.24822289 on June 23 and 1.25990358 on September 23: (1.25990358 ÷ 1.24822289 − 1) × 360 ÷ 92 = 3.66177%, matching again. The SOFR Index calculator does this ratio for any pair of dates. No pair of Index values reproduces the lookback or lockout rows.

Which day count? With a 2-day shift, the observation window here runs 94 days (June 26 to September 28) while the interest period is 92. The table annualizes the compounded rate over the 94 observed days and applies it to the 92 interest-period days. The ARRC guide calls this an "interest-period weighted observation shift" and says some parties in the FRN market choose it. Under the guide's basic observation shift, interest instead accrues over the days of the observation period: $25,000,000 times the raw 94-day compounding factor, or $239,953.02, which is $5,105.38 more. Consecutive shifted windows tile the calendar without overlap, so neither method counts a day twice; they spread the same rates over different day counts. The guide adds that the interest-period weighted version can at times produce a negative daily accrual even when SOFR is positive, which is one reason it was discussed but not recommended for business loans. The contract decides which method applies. For the 5-day shift the two agree, because that window (June 23 to September 23) is also 92 days.

Why lookback and observation shift weight days differently

Both conventions use exactly the same SOFR value dates. In the example, a 5-day lookback and a 5-day shift draw on the prints from June 23 through September 22, and differ by only 0.066 bp. The difference is entirely in the weights.

Under a lookback, the weight belongs to the accrual day. Thursday, July 2 accrues for four days (July 2 to July 6, across the July 3 holiday and the weekend), and five business days before it is Thursday, June 25. So June 25's 3.64% is applied for four days, although June 25 itself was an ordinary one-night rate. Under a shift, the weight belongs to the observed day. June 25 counts once, because the next business day was June 26, and the four-day weight falls on July 2's own print inside the shifted window.

Every SOFR print whose weight differs between a 5-day lookback and a 5-day observation shift, June 30 – September 30, 2026 interest period. Source: computed from Federal Reserve Bank of New York SOFR data.
SOFR value date	SOFR	Days, lookback	Days, shift	Why
Thu Jun 25	3.64%	4	1	Borrowed by Jul 2, a four-day accrual day
Fri Jun 26	3.62%	1	3	Borrowed by Mon Jul 6; covers a weekend when observed
Thu Jul 2	3.64%	3	4	Borrowed by Fri Jul 10; covers the July 3 holiday when observed
Fri Aug 28	3.65%	4	3	Borrowed by Fri Sep 4, a four-day accrual day (September 7 holiday)
Thu Sep 3	3.66%	3	1	Borrowed by Fri Sep 11
Fri Sep 4	3.65%	1	4	Borrowed by Mon Sep 14; covers the long weekend when observed

Holidays cause the mismatch: they put a different number of business days between the accrual day and the observed day, so long weights land on the wrong prints. In this quarter the misplaced weights sit on rates within 4 bp of each other, so the effect is tiny. It grows when SOFR moves sharply around holidays. For the interest period December 2, 2025 to January 2, 2026, which spans Thanksgiving, Christmas and New Year's Day as well as a reduction in the target range effective December 11, 2025, a 5-day lookback gives 3.84726% and a 5-day shift 3.86516%, a gap of 1.79 bp. There, the shifted window (November 24 to December 24) is 30 days long while the interest period is 31. The shift gives Wednesday, November 26's 4.05% two days because of the Thanksgiving holiday. The lookback hands those long weights to December 17–23 prints of 3.66% to 3.69%, borrowed by the multi-day accrual days around Christmas and New Year's.

Neither weighting is wrong. The lookback keeps accrual tied to the loan's own calendar, which is what lets a loan be repaid or traded on any date. The shift keeps each rate paired with the nights it actually measured, which is what makes the result equal to an Index ratio and to a published SOFR Average when the windows coincide (see SOFR Averages vs the SOFR Index).

Trade-offs side by side

Practical strengths and weaknesses of each convention.
Convention	Strengths	Weaknesses
Payment delay	Exact period rate; matches the T+2 settlement of SOFR OIS, so a swap hedge lines up	Payment falls after the period ends, outside the interest period it pays for
Lookback, no shift	Every accrual day has a known rate, so prepayment or a trade on any date can be settled; ARRC loan convention	Weights and rates come from different days; cannot be checked against the SOFR Index
Observation shift	A true compounded average, reproducible from two Index values; matches the ISDA fallback with a 2-day shift	Window dates are counted in business days, so the observation and interest periods can differ in length around holidays
Lockout	Rates stay current until close to the end; little lag in a rate move	Repeats one print; the ARRC cautioned it may not suit loans that can be repaid at any time

Read the definitions, not the labelTwo documents that both say "lockout" or "lookback" can still differ by one business day. In the table above, the 2-day lockout freezes the last two business days at the print immediately before them (September 25). That is one reading. The ARRC guide describes the last k days as frozen at the rate observed k days before the period ends, which for a September 30 end and k = 2 points to September 28: September 28 keeps its own print and September 29 takes September 28's 3.90% instead of its own 3.88%. Here both readings give 3.68250%, because September 25 and September 28 both printed 3.90%; they diverge whenever those two prints differ. Some documents also combine conventions, such as the Matrix's lockout with a one-day lookback, or add a floor or rounding. The calculation agent's determination under the contract governs; figures here illustrate the arithmetic.

To rerun this example or test your own period, enter June 30 and September 30, 2026 into the compounded SOFR calculator and switch conventions; its daily table shows which value date and weight each accrual day used. For how these rates feed a loan's margin, floor and payment schedule, see floating-rate loans on SOFR, and for the forward-looking alternative that avoids arrears altogether, Term SOFR vs overnight SOFR.