Reader question: If SOFR is an overnight rate published for individual business days, how can a system calculate the compounded rate over an arbitrary 37-day, 92-day or other custom period without manually multiplying every daily observation?
The New York Fed’s SOFR Index solves this by storing the cumulative effect of compounding SOFR from a fixed starting point. Instead of rebuilding every factor from the beginning, a calculation can divide the index value at the end of a period by the index value at the start. That ratio isolates the growth produced by SOFR over the chosen interval. The growth factor is then annualised using the actual number of calendar days and a 360-day year.
The important distinction is page role. This article does not own loan-specific lookbacks, floors or fallback language. BukitTimahTutor already has a page for floating-rate loan SOFR calculations. This page owns the official cumulative index as a computational shortcut, control and reconciliation object.
What this page owns — and what it does not
This page owns:
published SOFR Index values + start/end value dates → custom-period compounded growth → annualised compounded average.
It does not replace the SOFR benchmark-production algorithm, which explains how overnight transaction data become one daily SOFR; the loan coupon algorithm, which owns contractual observation conventions; or the interest-rate swap valuation page.
This is benchmark arithmetic and financial-computation education, not a recommendation involving any loan, bond, swap or interest-rate position.
What the SOFR Index represents
The Federal Reserve Bank of New York states that the SOFR Index measures the cumulative impact of compounding SOFR on a unit of investment over time. Its initial value is:
1.00000000 on April 2, 2018,
the first value date of SOFR.
Each later index value carries forward the prior cumulative growth and multiplies in the newest applicable overnight SOFR factor.
Conceptually:
It = Iprevious × (1 + SOFR × calendar-days-applicable / 360).
The New York Fed publishes the index to eight decimal places.
Why weekends do not create three separate SOFR observations
SOFR is produced for business-day value dates. Over a normal weekend, Friday’s SOFR observation applies across the weekend accrual interval.
The New York Fed’s published example shows a Friday SOFR compounded once with a factor such as:
1 + SOFRFriday × 3/360
for Friday, Saturday and Sunday together.
This is not equivalent to inventing Saturday and Sunday market observations. It is one observed overnight rate applied over the number of calendar days for which that rate accrues under the methodology.
The direct compounding formula
Suppose a calculation period contains business-day SOFR observations indexed by i. Let:
- ri = SOFR applicable to business day i;
- ni = number of calendar days for which that SOFR applies;
- N = total calendar days in the calculation interval.
The cumulative growth factor is:
G = ∏i(1 + ri ni/360).
The annualised compounded average is then:
R = (G − 1) × 360/N.
This direct formula is the reference arithmetic behind the index.
The index-ratio shortcut
Because the index is cumulative, the growth over a subperiod can be isolated by division.
Let:
- IS = SOFR Index at the start value date;
- IE = SOFR Index at the end value date;
- N = calendar days from start to end under the intended period definition.
Then the period growth factor is:
GS,E = IE / IS.
And the annualised compounded rate is:
RS,E = (IE/IS − 1) × 360/N.
This calculation is powerful because hundreds of overnight observations can be compressed into two published numbers and one calendar-day count.
A simple numerical example
Suppose:
- start Index = 1.24000000;
- end Index = 1.24500000;
- calendar days = 30.
Growth:
1.245 / 1.240 − 1 ≈ 0.004032258.
Annualised compounded rate:
0.004032258 × 360/30 ≈ 4.8387%.
The example is stylised. A production calculation must use the exact official index values and correct value-date interval.
Why the denominator is calendar days
The New York Fed methodology uses the actual number of calendar days in the calculation period with a 360-day year.
This matters because a 30-calendar-day period can contain a different number of business-day SOFR observations depending on weekends and holidays.
The denominator is therefore not:
number of SOFR observations × 1 day.
It is the actual calendar length of the compounded period.
Business-day observations and calendar-day accrual are different dimensions
A useful mental model separates:
- observation dimension: when a new SOFR fixing exists;
- accrual dimension: how many calendar days that fixing applies to.
Most business days have ni = 1. A Friday before a normal weekend often has ni = 3. A holiday can create a longer or differently positioned accrual interval.
Confusing these dimensions is one of the most common sources of “almost correct” compounded rates.
Publication date is not the same as SOFR value date
The New York Fed publishes SOFR after the underlying overnight transactions occur. Its public methodology distinguishes the publication date, the SOFR value date and the index value date.
A system that joins data only by webpage publication timestamp can shift every observation by one business day.
For calculation, the important question is:
Which value date does this published observation belong to?
The data model should preserve both publication and value dates instead of overwriting one with the other.
Holiday calendars matter
The New York Fed’s reference-rate publication schedule interacts with U.S. government-securities market holidays. For example, it announced that there would be no SOFR or SOFR Index publication for Friday, April 18, 2025 because of the market closure, with subsequent publication arrangements on Monday, April 21.
This provides a useful falsifier for naive code. An algorithm that assumes “every weekday has a SOFR fixing” will fail on such dates.
The SOFR Index can validate a direct daily compounding engine
There are two mathematically equivalent paths for a standard custom interval:
Path A: multiply the individual daily factors.
Path B: divide the official end Index by the official start Index.
If both use the same date interval and methodology, their growth factors should agree to the tolerance implied by published rounding.
This creates an unusually strong operational control because one method can independently verify the other.
Why exact equality may fail at very fine precision
The published Index is rounded to eight decimal places. Daily SOFR and published compounded averages also have their own publication precision.
An internal engine carrying more precision can therefore differ by a tiny amount from a calculation reconstructed only from published rounded Index values.
The correct diagnostic is not “bit-for-bit equality.” It is:
difference within the expected tolerance created by official publication rounding.
SOFR Averages and the SOFR Index are related but not interchangeable
The New York Fed publishes backward-looking compounded SOFR Averages for standardized 30-, 90- and 180-calendar-day windows.
The Index is more general because it allows a user to compute a compounded average over a custom interval by taking an index quotient.
If the required period is exactly aligned with a published standard average, the two approaches should be consistent subject to methodology and rounding.
The Index does not encode contractual lookbacks
This boundary is essential.
A loan may use a five-business-day lookback, observation shift, lockout, floor or credit-spread adjustment. The official SOFR Index does not automatically know those contract rules.
If a contract’s observation period differs from its interest-accrual period, a simple start/end Index quotient over the accrual dates can be wrong.
The floating-rate loan algorithm owns those contractual transforms.
When an Index quotient is appropriate
The Index is strongest when the desired calculation exactly corresponds to the standard SOFR compounding period represented by the selected start and end value dates.
It is also useful as:
- a reconciliation control;
- a benchmark-data quality check;
- a custom historical compounded-rate calculator;
- a way to avoid rebuilding long histories for simple standard intervals.
When direct daily reconstruction is safer
Direct reconstruction is safer when a contract applies:
- lookbacks without observation shift;
- observation shifts;
- lockouts or rate cut-offs;
- interest-rate floors;
- spread adjustments inside or outside compounding;
- non-standard day-count treatment;
- partial-period special rules.
Those features change the mapping between daily observations and accrued days. The official Index can still be a useful external control, but it may not directly equal the contractual coupon rate.
Inputs and outputs
A robust SOFR Index calculation can require:
- start value date;
- end value date;
- official SOFR Index values for both dates;
- actual calendar-day count;
- 360-day annualisation convention;
- publication/value-date metadata;
- precision and rounding policy;
- contractual observation-period mapping if the result is used downstream.
Outputs can include:
- index growth factor;
- period compounded return;
- annualised compounded average;
- calendar-day denominator;
- official-data provenance;
- difference from direct daily compounding;
- reconciliation status.
Evidence polarity: what supports confidence?
Evidence for the calculation includes official New York Fed Index values, correct start/end value dates, calendar-day denominators that reproduce known periods, direct-compounding reconciliation within publication-rounding tolerance and correct treatment of weekends and holidays.
Evidence against confidence includes using business days in the annualisation denominator, shifting index values by publication date, assuming every weekday has a fixing, treating weekends as three independent rates, or obtaining a custom rate that disagrees materially with direct daily compounding over the same standard interval.
Counterexample: average of daily SOFR is not compounded SOFR
The arithmetic mean:
(r1 + r2 + … + rn)/n
is not generally equal to the compounded average.
Compounding multiplies growth factors. The difference can be small over short periods and modest rates, but the two calculations are conceptually different.
Counterexample: Friday’s rate is not simply copied three times and compounded three times
The official methodology treats the calendar-day span as one factor:
1 + r × 3/360.
Compounding three separate factors:
(1 + r/360)3
creates a small but real difference. The New York Fed’s published methodology owns the correct convention.
Counterexample: index quotient alone cannot reproduce a five-day loan lookback
If a loan accrues interest from June 10 to July 10 but uses SOFR observations shifted five business days earlier, an Index quotient over June 10–July 10 does not represent the contractual observation set.
The date transformation must occur before the appropriate compounding calculation.
Counterexample: a missing publication is not automatically a zero rate
On a holiday or market closure, lack of a newly published SOFR does not mean overnight interest is zero. The methodology determines how the last applicable fixing spans calendar days.
Substituting zero silently understates the compounded factor.
Weak links in implementation
Publication/value-date confusion. Index records are shifted by one business day.
Calendar denominator bug. Business-day count is used instead of actual calendar days.
Weekend overcompounding. Friday’s rate is compounded three separate times instead of using the methodology’s day multiplier.
Holiday fabrication. Missing fixings are filled with zero or invented observations.
Index precision loss. Eight-decimal index values are truncated further before division.
Wrong interval orientation. Start/end values are reversed.
Contract leakage. A standard Index quotient is used for a non-standard lookback/lockout contract.
Diagnostics: how to test the engine
- New York Fed example replay: reproduce the published early-April-2018 Index sequence.
- weekend test: verify a Friday rate applies with the correct multi-day factor.
- holiday test: use a known market closure and verify no fictitious fixing is created.
- index/direct equivalence test: compare Index quotient with direct daily compounding over the same standard interval.
- 30/90/180-day comparison: compare custom Index calculations with official SOFR Averages when dates align.
- date-shift test: deliberately offset one endpoint by one business day and confirm the control catches the difference.
- precision test: carry extra internal precision and quantify the effect of official eight-decimal Index rounding.
- denominator test: compare calendar-day and business-day annualisation and require the calendar convention.
- contract-boundary test: feed a lookback loan and ensure the plain Index shortcut is rejected or transformed appropriately.
- provenance test: trace each endpoint to an official New York Fed record.
What would falsify confidence?
Confidence should be withdrawn if the calculation cannot reproduce official examples, if Index and direct compounding disagree beyond expected rounding, if known holidays generate fabricated rates, if results depend on server timezone rather than financial value dates, or if a non-standard contract is priced from an unadjusted Index quotient.
Alternatives and limits
The alternative is direct daily compounding from individual SOFR observations. That method is more verbose but more flexible for bespoke observation conventions. The Index is computationally elegant because it turns a long product of factors into one ratio.
Neither method forecasts future SOFR. The Index is backward-looking. Future cash-flow valuation requires a forward curve or scenario model, which belongs to the interest-rate valuation layer.
How this connects to the surrounding knowledge estate
The overnight benchmark page explains how transaction data become one daily SOFR. This page begins after that publication step and compresses the historical compounding path. The day-count article explains why ACT/360 matters. The floating-rate loan page owns contractual observation transforms. SOFR futures convexity adjustment belongs to the forward-looking market-curve layer rather than the realised historical compounding layer.
Verification and update triggers
Preserve official endpoint values, publication/value dates, calendar-day counts, methodology version and rounding policy. Revalidate after New York Fed methodology changes, publication-calendar changes, data-vendor remapping, benchmark corrections, calendar-library upgrades or any persistent mismatch with official SOFR Averages/Index values.
Primary and high-quality references
- Federal Reserve Bank of New York, Reference Rates, defining SOFR, SOFR Averages and the SOFR Index.
- Federal Reserve Bank of New York, Additional Information about Reference Rates, including current SOFR Index methodology and the cumulative-compounding example.
- Federal Reserve Bank of New York, Statement Regarding Publication of SOFR Averages and a SOFR Index, documenting the index formula, calendar-day treatment and publication precision.
- Federal Reserve Bank of New York, 2019 request for comment on SOFR Averages and Index, explaining the design logic for business-day compounding and weekend/holiday accrual.
- Federal Reserve Bank of New York, Statement Regarding Publication of Reference Rates on Friday, April 18, 2025, illustrating a real publication-calendar exception.
Educational boundary: This article explains published benchmark-index arithmetic. It does not recommend an interest-rate product, specify a contractual fallback or provide personalized financial advice.