Lookback, observation shift, weekend and holiday weights, and why the margin is added after compounding rather than inside it.
Compounded SOFR in arrears multiplies together one plus each day's SOFR times its day weight over 360, across an observation period shifted back by the lookback, subtracts one and annualises over the period's days. The margin is then added simply, not compounded. On an illustrative $150 million term loan at SOFR plus 3.25 per cent for a 92-day period with a five business day lookback, compounded SOFR is 4.30397 per cent and interest is $2,895,689.29, $8,814.29 more than a simple average of the same rates would charge.
Worked in full in How to Read a Credit Agreement by Julian R. Sterling, with every figure reproduced in a free workbook.See the book on Amazon →
A term rate such as EURIBOR or the old LIBOR is fixed at the start of the interest period, so the borrower knows what it owes for three months. An overnight rate is published each morning for the previous business day. A loan that references it can only know its rate once the period has run, and the interest has to be calculated from a string of daily fixings. The lookback exists so the number is known a few business days before it must be paid: here, on 24 September for a payment on 1 October. Credit agreements describe the mechanics in a schedule of rate terms; the arithmetic below is the standard compounded in arrears method with an observation shift.
| Input | Value |
|---|---|
| Principal | $150,000,000 |
| Margin | 3.25% |
| Interest period | 1 July to 1 October 2026, 92 days |
| Lookback, with observation shift | 5 business days |
| Observation period | 24 June to 24 September 2026, 92 days |
| SOFR, illustrative | 4.30%, then 4.05% from 17 September |
| Holidays in the window | 3 July, 7 September |
Compounded rate = [ Π (1 + SOFRi × ni / 360) − 1 ] × 360 / d
ni = calendar days from business day i to the next business day; d = calendar days in the observation period
Interest = principal × (compounded rate + margin) × days in the interest period / 360
Excel, with rates in B2:B65 and weights in C2:C65: =(PRODUCT(1+B2:B65*C2:C65/360)-1)*360/SUM(C2:C65), entered as an array formula in older versions
Step 1, shift the window. Count five business days back from each end of the interest period. 1 July becomes 24 June and 1 October becomes 24 September. With an observation shift, both the rates and the day weights are taken from this window, which here also runs 92 days.
Step 2, weight each fixing. The window holds 64 business days whose weights add up to 92. Most weigh one day. Each Friday weighs three, because Friday's rate applies over the weekend, and the two business days before a holiday weigh four: Thursday 2 July and Friday 4 September. A fixing that weighs four moves the product four times as much as a midweek one.
Step 3, compound. 85 of the 92 days are at 4.30 per cent and 7 are at 4.05 per cent, because only five business days of the cut fall before the window closes. The product of the 64 factors is 1.01099904. Subtract one and multiply by 360/92: 4.30397 per cent. The simple day-weighted average is 4.28098 per cent; compounding adds 2.30 bp.
Step 4, interest. Add the margin to get 7.55397 per cent and apply it for 92/360 of a year, 0.255556. SOFR contributes $1,649,855.96 and the margin $1,245,833.33: $2,895,689.29 in all.
The compounding uplift grows with the square of the rate, so it is a rounding error at low rates and a real number at high ones.
| Flat SOFR | Compounded rate | Uplift, bp | Extra interest, $ |
|---|---|---|---|
| 2.00% | 2.0050% | 0.50 | 1,920 |
| 4.30% | 4.3232% | 2.32 | 8,893 |
| 6.00% | 6.0452% | 4.52 | 17,339 |
| 8.00% | 8.0805% | 8.05 | 30,875 |
The lookback also changes which rates are seen. Observed over the interest period itself, the same loan would pick up more days after the 25 bp cut: compounded SOFR of 4.28475 per cent and interest $7,370.10 lower. When rates are falling, a lookback costs the borrower a few days of the old rate; when they are rising, it saves them.
Compounding the margin. If the 3.25 per cent is added to each daily SOFR before compounding, the all-in rate becomes 7.60233 per cent, 4.84 bp above SOFR compounded plus the margin, and the borrower is overcharged $18,535.97 for the quarter. Standard drafting compounds the reference rate only and adds the margin afterwards; an agent's spreadsheet that does otherwise is wrong against the agreement. The second error is to weight every business day as one: it drops the weekends and holidays, which on this window are 28 of the 92 days of interest.
Check which method the agreement uses. A lookback without observation shift weights each fixing by the days in the interest period rather than in the observation window; a payment delay or a lockout uses different days again. On a smooth rate path the answers differ by fractions of a basis point; around a policy move they do not.
The interest provisions, the break costs on a fixed-period loan and the fees around them are read clause by clause in How to Read a Credit Agreement; the free workbook for this case carries the complete facility. For what a prepayment in the middle of a fixed interest period costs, see how break costs are calculated.
Because each day's interest earns interest on the following days. Over a 92-day window with SOFR flat at 4.30 per cent, the compounded rate is 4.3232 per cent, 2.32 bp higher, or $8,893 on $150 million. The uplift grows with the square of the rate: 0.50 bp at 2.00 per cent and 8.05 bp at 8.00 per cent.
The rates and their day weights are taken from a window that starts and ends a set number of business days before the interest period, five here. An interest period from 1 July to 1 October 2026 is observed from 24 June to 24 September, so the rate is known a week before the payment. Without the shift, the rates are lagged but the weights come from the interest period.
Not under standard drafting: SOFR is compounded and the margin is added afterwards. Compounding a 3.25 per cent margin with the daily rates would give 7.60233 per cent rather than 7.55397 per cent on the illustrative loan, overcharging the borrower $18,535.97 for one 92-day period on $150 million.
This article is one calculation from How to Read a Credit Agreement. The book takes the same case from first principles to the decision, chapter by chapter, and every figure it prints is a live formula in the free companion workbooks.
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