Methodology
Treasury Curve Methodology
Safe Rate fits one discount curve to Treasury's end-of-day prices for every fixed-rate note and bond, every business day since September 2008. Across 31,521 tenor-days, its par yields differ from the Federal Reserve's published curve by 2.28 basis points root mean square, with an average difference of 0.01 basis points.
What goes in
Treasury's end-of-day prices (FedInvest) for every marketable Treasury, every business day. The coupon curve is fitted to fixed-rate, non-callable notes and bonds with at least three months to maturity.
Held out, each for a stated reason: TIPS, whose yields are real rather than nominal (they get their own real curve); floating-rate notes, which have no fixed coupon to discount; callable bonds, whose redemption date is uncertain; and anything inside three months, where money-market effects dominate. Bills go to a separate money-market curve on their own day-count basis.
The model
A Nelson-Siegel-Svensson curve, fitted as a zero-coupon discount curve against each security's observed dirty price, the same object the Federal Reserve publishes. Every cashflow is discounted at its own zero rate, so zero rates, par yields and forward rates all come from one discount function and agree with each other.
Price errors are weighted by inverse modified duration, so they behave like yield errors and long bonds do not dominate simply because their prices move more. A penalty on the roughness of the forward curve, with its strength chosen by held-out cross validation, keeps the curve smooth between securities, and the fourth Svensson factor is used only when the data clearly calls for it.
What comes out
For each business day, at 1, 2, 3, 5, 7, 10, 15, 20, 25 and 30 years: the continuously compounded zero rate, the par yield on a semiannual coupon basis, and the instantaneous forward rate.
Par or zero? A par yield is the coupon that prices a new bond at 100, and it is what the market quotes. Spreads such as 2s10s and 5s30s are differences in par yields, so the 2s10s and 5s30s pages use par. Zero rates are the discount rates themselves, for pricing cashflows and building forwards.
How closely it tracks the Federal Reserve's curve
The comparison is with the Gürkaynak, Sack and Wright curve the Federal Reserve publishes, matched on every date and tenor both cover. Measured October 8, 2026, in basis points:
| Series | Fed series | Points | Mean | Mean abs | RMSE | Tolerance |
|---|---|---|---|---|---|---|
| Par yield | SVENPY | 31,521 | 0.01 | 1.28 | 2.28 | 6 |
| Zero rate | SVENY | 31,521 | −0.15 | 1.68 | 3.44 | 6 |
| Real zero rate (TIPS curve) | TIPSY | 27,018 | 0.00 | 1.73 | 2.81 | 12 |
The mean difference is close to zero in each case: the curve is scattered around the Federal Reserve's, not biased against it. The tolerance is a gate in the build: if any of these drifts past it, the daily run fails rather than publishing.
The 30-year instantaneous forward is the exception, at 60.85 basis points RMSE. No traded cashflow pins a forward rate thirty years out, and the authors of the Federal Reserve's curve disclaim that region themselves. It is published with that limit stated, not as a figure to rely on.
How it differs from Treasury's constant-maturity yields
Treasury's official constant-maturity yields, republished by the Federal Reserve in its H.15 release and on FRED (for example DGS2 and DGS10), are a third curve with its own method: a par curve built from bid-side quotes for the most recently auctioned securities, taken in the afternoon rather than at the end of the day. This curve is fitted to end-of-day prices for all eligible notes and bonds, and the Federal Reserve's research curve to off-the-run securities.
Three methods and three times of day mean the curves differ from day to day without any of them being wrong. The spread pages show the H.15 constant-maturity spread as a labeled reference line beside this one.
Sources
- Prices: U.S. Department of the Treasury, FedInvest end-of-day prices, a U.S. government publication.
- Comparison: Gürkaynak, Sack and Wright (2007), "The U.S. Treasury Yield Curve: 1961 to the Present," and the Federal Reserve Board's published data (feds200628).
- Model: Svensson (1994); calibration after Gilli, Grosse and Schumann (2010); roughness penalty after Fisher, Nychka and Zervos (1995).