A Four-Week Bill Shows 3.83 and 3.89 on the Same Treasury Rate Page

On Friday, September 18, 2026 — the most recent business day before this was written — the U.S. Treasury published the four-week bill at 3.83. One column to the right, on the same row of the same file, it published the same four-week bill at 3.89. On the par yield curve file for that identical date, the one-month point read 3.97.

None of those three numbers is a typo, a revision, or a stale print. They are three different units applied to an overlapping slice of the same market. A spreadsheet that subtracts one from another without converting is not measuring a spread. It is measuring its own bookkeeping, and the answer it produces is stable enough to look like a signal.

This matters well beyond the bill market. Short Treasury rates get dropped into the risk-free slot of option models, into carry and basis calculations, into financing assumptions for leveraged positions, and into the cash leg of nearly every backtest. The series are free, official, and daily, which is exactly why they get pasted in without anyone reading the column header. The same failure appears whenever a time series arrives without its units written down next to it.

Two Columns on One Page, Two Different Years

Treasury states both definitions plainly on its Daily Treasury Bill Rates page. The bank discount rate is "the rate at which a bill is quoted in the secondary market and is based on the par value, amount of the discount and a 360-day year." The coupon equivalent is "the bill's yield based on the purchase price, discount, and a 365- or 366-day year."

Two differences are hiding in those two sentences, and both push in the same direction.

Element	Bank discount rate	Coupon equivalent
Denominator of the return	Par value (100)	Purchase price (below 100)
Days in the year	360	365 or 366
Stated purpose	Secondary market quoting convention	Comparison against a coupon security

Treasury adds what the second column is for: the coupon equivalent "can be used to compare the yield on a discount bill to the yield on a nominal coupon security that pays semiannual interest with the same maturity date." Note the boundary in that sentence. It licenses a comparison at the same maturity date. It does not promise that the number will line up with an interpolated curve point carrying a round label like "1 Mo."

The Federal Reserve uses the same convention in its H.15 release, where the Treasury bill footnote reads, in full, "On a discount basis." This is not one agency's quirk. Discount quoting is the market convention for bills, and the burden of conversion sits with whoever is reading the file.

One Price, Two Annualizations

The cleanest way to see that these are the same fact in two costumes is to take a single auction and run Treasury's own arithmetic. Treasury's Office of Financing publishes the formulas in a bill calculation document:

• Price from the discount rate: P = 100 ( 1 - dr / 360 )
• Discount rate from the price: d = ( ( 100 - P ) / 100 ) * ( 360 / r )
• Investment rate, meaning coupon-equivalent yield, for bills of half a year or less: i = ( ( 100 - P ) / P ) * ( y / r )

Here r is days to maturity and y is the number of days in the year. Treasury's own worked example in that document runs "From Jan. 22, 2004 to Feb. 19, 2004 (28 days)" and computes d = ( ( 100 - 99.937778 ) / 100 ) * ( 360 / 28 ), giving d = 0.800%.

Now take a live one. Treasury's Fiscal Data auction records show a four-week bill, CUSIP 912797VM6, auctioned on September 17, 2026, issued September 22 and maturing October 20 — a 28-day bill. The record carries a high discount rate of 3.82%, a high investment rate of 3.885%, and a price per $100 of 99.702889.

Feed 3.82% and 28 days into the first formula and the price comes back as 99.702889, matching the published price to all six decimals. Feed that price into the third formula with a 365-day year, and the investment rate comes back as 3.8846%, which is the published 3.885% at Treasury's stated display precision of three places. One price, two annualizations, six and a half basis points apart before any market view enters the picture.

The Spread Between the Columns Is Not a Constant

If the two columns differed by a fixed amount, a lazy model would still work after a one-time offset. They do not. Here is the full September 18, 2026 row, with the difference between the published coupon equivalent and the published bank discount rate for each tenor.

The gap more than triples from the front of the bill curve to the back of it. The structure is readable straight off the formulas. Divide the investment rate formula by the discount rate formula and the common term cancels, leaving a ratio of (100 / P) * (y / 360). The second factor is a fixed 365/360 in a non-leap year. The first factor is not fixed: the longer the bill, the larger the accumulated discount, the lower the price P, and the larger the ratio of par to price.

One caveat keeps that tidy explanation honest. Treasury's document specifies the simple formula for bills of half a year or less, and a separate quadratic for longer bills: i2 [ r / 2y - .25 ] + i ( r / y ) + ( ( P - 100 ) / P ) = 0. The 52-week line at the bottom of the chart comes out of the quadratic, not the simple ratio, because a one-year bill has to be put on a semiannual-compounding footing before it can stand next to a coupon security. The direction is the same; the algebra is not.

The Par Yield Curve Is a Third Unit

The third number from the opening — 3.97 at the one-month point — comes from a different construction entirely. Treasury's par yield curve methodology describes inputs as "indicative, bid-side market price quotations (not actual transactions) for the most recently auctioned securities obtained by the Federal Reserve Bank of New York at or near 3:30 PM each trading day."

Three things in that sentence deserve to be written into a data dictionary.

• Indicative, not executed. The parenthetical "not actual transactions" is Treasury's own. Anyone reconciling these levels against fills is comparing a quote survey to a trade tape.
• Bid-side. Not a mid. Not an offer.
• A 3:30 PM snapshot. Not a session close, and not the futures settlement window.

The inputs are specific: "4-, 6-, 8-, 13-, 17-, 26-, and 52-week bills; the most recently auctioned 2-, 3-, 5-, 7-, and 10-year notes; and the most recently auctioned 20- and 30-year bonds." Fourteen observed points. Everything else on the published curve — including the "1 Mo" and "1.5 Month" columns — is interpolated, using "monotone convex interpolation performed on forward rates midway between the input points." That method is recent enough to matter for long histories: it "replaced the previous quasi-cubic hermite spline method as of December 6, 2021."

The output is a par yield, not a spot yield and not a bill discount rate. Treasury says the fitting "minimizes the price error on the initial price input points, resulting in true par rates." And the bills do not enter the curve in discount form: "The inputs for the bills are bid discount rates corresponding to their bond equivalent yields."

There is also a maturity-label problem sitting underneath the column headers. The four-week bill in the auction above runs 28 days. The curve's "1 Mo" point is a constant maturity, not that bill. The 52-week bill runs 364 days; the "1 Yr" point does not. That gap between a round label and an actual instrument is the same one that makes a reopened ten-year get recorded as a nine-year eleven-month security, and it is why a par curve's tenor labels describe positions on a fitted curve rather than the cash flows of any one bond.

For completeness, Treasury publishes a fourth family on the same site: the par real yield curve, "which relates the par real yield on a Treasury Inflation Protected Security (TIPS) to its time to maturity." Real yields and nominal par yields are not the same unit either, and they share a page layout.

What the Unit Mismatch Does to a Spread

Here is the practical consequence, using nothing but published values from that same Friday. Take each bill tenor against the nearest labeled curve point, first in discount form, then in coupon-equivalent form.

Read in discount form, the bills sit 11 to 22 basis points below the curve across four tenors — a persistent, one-directional gap that a screen would happily label as cheapness. Read in coupon-equivalent form, the same four comparisons collapse to 8, 6, negative 3, and 3 basis points. Most of the apparent spread was the 360-day year.

The residual is the interesting part, and it is worth refusing to explain away. At 26 weeks the sign flips: the coupon equivalent of 4.27 sits above the 6-month curve point of 4.24. Converting the day count does not make the two series identical, because they are still not the same object — one is a quoted bill, the other an interpolated par yield at a constant maturity, fitted from fourteen points under a specific interpolation method. Anyone who claims a clean conversion between them should be asked to reproduce that negative three.

Concrete Framework

A short protocol, applied once per data source, removes this class of error permanently.

1. Name the series in the column header, not the tenor. "4W_BANK_DISCOUNT" and "4W_COUPON_EQUIV" are acceptable. "4W" is not. The single most common version of this failure is a column named after a maturity with the convention discarded.
2. Record three attributes next to every rate series you ingest: day-count denominator (360 or 365/366), the base the return is measured against (par or price), and the snapshot time (3:30 PM for these files).
3. Never difference two series until both are in the same unit. For bills of 26 weeks or less, convert using i = ( ( 100 - P ) / P ) * ( y / r ). For 52-week bills, use the quadratic form; the simple ratio will be wrong.
4. Match the maturity, not the label. A 28-day bill is not the "1 Mo" curve point and a 364-day bill is not the "1 Yr" point. If the comparison must be made, write the date mismatch into the output so it travels with the number.
5. Set a materiality floor at 1 basis point. Treasury publishes these to two decimals, so one basis point is the finest distinction the files can support. A model that acts on a difference smaller than that is acting on rounding.
6. Re-derive one published value per source, once. Take an auction record, run the price formula, and confirm you land on the published price. If you cannot reproduce 99.702889 from 3.82% and 28 days, your pipeline has the wrong convention and you have found it before it reached a position.
7. Break the histories at known methodology dates. December 6, 2021 is a hard seam in the par curve series. A backtest that spans it is stitching two construction methods together.

What Would Invalidate This

Several conditions make the analysis above either wrong or irrelevant, and they should be checked before it is used.

If the methodology changes again. The monotone convex method replaced quasi-cubic hermite spline on a specific date, which is proof the construction is not permanent. Any conversion rule derived here has a shelf life ending at the next methodology notice.

If the year contains February 29. Treasury's definition says a 365- or 366-day year. The reproduction above used 365 because the year following the September 2026 issue date does not include a leap day. Hard-coding 365 will produce a small, systematic, and very hard to spot error in the wrong year.

If the bill runs longer than half a year. The simple investment-rate formula does not apply, and the (100 / P) * (y / 360) ratio that explains the widening gap does not hold at 52 weeks. The chart's bottom bar is consistent with the story but is not produced by the same equation.

If a single day is treated as a regularity. Every figure here comes from one date, September 18, 2026. The 6-to-19 basis point progression is that day's row. The mechanism is structural, but the magnitudes are not constants and should be recomputed, not memorized.

If the residual is assumed away. The negative three basis points at 26 weeks is the strongest evidence in this piece against treating the coupon equivalent as a drop-in substitute for a curve point. Converting units narrows the gap. It does not close it.

If executable prices are what the model actually needs. Both families are built from indicative bid-side quotations — Treasury's methodology says "not actual transactions" in as many words. For anything that has to survive contact with a fill, this entire set of files is the wrong source, correctly converted or not.

If the model only ever compares a column to itself. A strategy that differences the 13-week bank discount rate against its own thirty-day average is internally consistent and untouched by any of this. The error appears at the seams between series, not inside one.

This article is for informational and educational purposes only. It is not investment advice, and it is not a recommendation to buy or sell any security. Treasury rate series are revised and republished, and conventions and methodologies change; verify current figures and definitions against the primary sources before relying on them. Trading and investing involve risk of loss.