U.S. KRED-Estimated 1-Year Risk-Neutral Yield without Persistence Correction

KRED splits the US Treasury zero curve into an expected average future short rate and a residual premium and serves both halves at one, three, five and ten years. The estimation uses excess-return regressions with state dynamics estimated by ordinary least squares, and applies no small-sample persistence correction before the premium is formed, the configuration the published methodology states for its own estimation (Adrian, Crump, and Moench 2013; Bauer, Rudebusch, and Wu 2012). Because that correction is absent, these series are a different estimand from the corrected family KRED publishes beside them, not a second reading of the same quantity.

The estimation sample begins in 1980, where the six-parameter regime of the input curve starts, so no earlier date can be evaluated on the same construction. The published decomposition draws on a longer window reaching decades further back, which KRED does not replicate, and a term-structure split of this class depends on the span it is estimated over (Bauer, Rudebusch, and Wu 2012; Bauer and Rudebusch 2020). Every gate-derived statistic quoted in these notes comes from a pinned comparison sample of 558 month-ends running from 1980-01 to 2026-06; the series themselves update on the pipeline cadence.

Agreement with the published decomposition was measured maturity by maturity against bars committed before the measurement existed. At one year the level correlation is 0.8996, the correlation of monthly changes is 0.4706 and the mean absolute deviation is 14.14 basis points, at three years 0.9633 and 0.7777 and 18.29 basis points, at five years 0.9764 and 0.8631 and 19.75 basis points, and at ten years 0.9889 and 0.9576 and 21.23 basis points. Against the pre-committed minima of 0.95 on levels and 0.90 on changes, together with the per-maturity deviation bounds, that leg is recorded as failed at one, three and five years and passed at ten. No external validation of the expected-path and premium split exists for either configuration, since two pre-registered attempts to establish one returned an outcome licensing no such claim, and that absence is a property of the design rather than a finding about the world (Conover 1999).

Five statements bound what these series are. Neither half is the term premium or the expected path, since both are model-identified quantities that exist only relative to a stated estimator, and the term-structure tradition writes a long rate as an expected path of short rates plus a premium precisely because the second piece is the residual of that identity (Hicks 1939; Kim and Wright 2005). Neither is a replication, a validation, a check, or a correction of the published decomposition, and neither is evidence for or against it in either direction. Neither validates, corroborates, or outranks the corrected family published beside it, and that holds in both directions. Neither is comparable with the Korean constructions as a like-for-like pair, because the input curve, the sample, and the market all differ. And neither carries any claim about its values as first published, since a re-estimation rewrites the whole history and no dated vintage panel is kept (Orphanides and van Norden 2002).

KRED evaluates the published Svensson parameters of the US Treasury zero curve analytically at monthly points from one month to one hundred and twenty months, in continuously compounded percent, and hands that panel to the same excess-return-regression estimator the platform runs for its corrected families. The pricing factors are the leading principal components of the panel. The state follows a first-order vector autoregression whose persistence enters exactly as ordinary least squares estimates it, and the premium at each maturity is the gap between the model yield and the yield implied by the expected average short rate under the no-arbitrage restriction (Adrian, Crump, and Moench 2013; Bauer, Rudebusch, and Wu 2012). The input curve extends the parsimonious Nelson and Siegel (1987) form to six parameters (Svensson 1994; Gürkaynak, Sack, and Wright 2007), and the family of methods that recovers a zero curve from coupon prices has been compared in the literature (McCulloch 1971; Vasicek and Fong 1982; Bliss 1997).

The accuracy legs that do not depend on the estimation span pass with large headroom. The analytic reconstruction of the published curve columns differs from them by 0.0018 basis points on average, and internal pricing errors average between 0.61 and 1.47 basis points across the four maturities. The pre-committed agreement leg against the published decomposition, by contrast, fails as measured at twelve, thirty-six and sixty months and passes at one hundred and twenty months, a split of verdicts that is not evidence of a defect in the computation and not evidence about the corrected family in either direction (Bauer, Rudebusch, and Wu 2012; Orphanides and van Norden 2002).

Three properties of the input bear on the reading. The one-month and two-month points of the curve sit below the shortest maturity its publishers state it is estimated for, so those two columns are an extrapolation rather than an evaluation inside the estimated range; the gap is disclosed rather than repaired, and no figure is attached, because no statistic of this family's own producer measures it. A screen drops daily rows whose short end is degenerate. On the pinned sample it removes 14 of the 11622 daily rows since 1980, or 0.12 % of the panel, and none of the 559 month-ends in the estimation panel trips it, which is coverage composition rather than data loss. The input curve is republished on a weekly cycle, so the trailing edge of the panel lags the calendar by several business days and the latest value is not a same-day quotation.

Re-estimating the same specification from a 1990 start and setting it against the full-sample estimate over the overlap gives a correlation of 0.9753 on the ten-year premium and a mean absolute difference of 54.13 basis points across 438 month-ends. Those numbers are reported as they came out. They carry the standing caveat that a model holding its long-run endpoint fixed attributes movements in a slowly moving trend to the premium, so a split of this kind is expected to move with the sample it is estimated on (Bauer and Rudebusch 2020; Andrews 1993).

A term premium is the compensation a holder of a long bond earns for bearing the risk that short rates turn out differently than expected. A long yield read without the split therefore confuses a change in what markets expect with a change in what they charge (Hicks 1939). The split matters for policy analysis because the stance is set at the shortest maturity while transmission runs through long rates (Bindseil 2004; Borio 1997). That premiums move rather than sit at a constant is what the return-forecasting literature established, with excess bond returns predictable from the shape of the curve (Cochrane and Piazzesi 2005; Hansen and Hodrick 1980).

The difference between this estimate of the ten-year premium and the published one is a trend rather than an offset, so the two do not stand in any stable relationship. Read as era means of the signed difference in basis points, over the segments a break search places at 1982-10, 1984-11, 1988-11, 1990-12 and 2017-12, it runs 58.42 from 1980-01, then 25.91, then 15.22, then 39.68, then 4.55 from 1991-01, and 24.25 from 2018-01. A sample mean of such a difference cannot assert its own constancy (Andrews 1993). No trend coefficient, correlation, or significance statement is attached to it anywhere, because the difference of two near-integrated series is exactly the object on which such a regression misleads (Granger and Newbold 1974; Phillips 1986).

Over the 97 month-ends on which the published ten-year premium is negative, spanning 2015-01 through 2024-09, this estimate sits on the opposite side of zero in 15 of them; across those months the published series averages −53.42 basis points and this one −32.78 basis points. KRED publishes no explanation of why the two allocate the yield differently there. It publishes none because the literature it cites documents the persistence correction's effect on the estimated dynamics and on risk-neutral volatility, not on the level of the premium (Bauer, Rudebusch, and Wu 2012; Bauer and Rudebusch 2020), so any account of the direction would have to be supplied rather than cited.

Two limits bound the economic reading. The level of a premium of this class depends on the span it is estimated over and on the estimated persistence of the state, so a difference between two such estimates is a statement about measurement rather than a finding about the world (Orphanides and van Norden 2002). A slope or premium reading taken from these series is likewise a reading of this estimator in this configuration alone. A decomposition built from different machinery on the same curve answers the same question differently, and the corrected family published beside these series is one such difference, not a check on them (Kim and Wright 2005; Estrella and Mishkin 1998).

For a bond desk the premium is the part of a long yield that carries expected excess return, so it enters relative-value work differently from the expected-path part. Where the premium is wide, holding duration is being paid for; where it is narrow, the same duration earns a smaller expected reward. That is the practical content of predictable excess returns (Cochrane and Piazzesi 2005; Hansen and Hodrick 1980). A position taken on such a reading is executed through the curve, not through the premium itself, since the premium is not a traded instrument. Exposure is measured by the duration that maps yield changes into price changes and managed by immunization defined on the whole term structure (Macaulay 1938; Fisher and Weil 1971).

Four facts bound that use. The history is rewritten whenever the model is re-estimated, so a backtest that treats today's series as what was visible at each past date overstates what a desk could have acted on (Orphanides and van Norden 2002; Kim and Orphanides 2012). Both halves come from one estimation on one curve; they sum to the model yield at the same maturity by construction, they are not two independent readings, and the four maturities are columns of that single estimation rather than four separate measurements. The corrected family published beside these series is a second configuration of the same estimator, not a second measurement of the same quantity, so a spread taken between the two is a specification difference and not a relative-value signal, since comparing two outputs is not comparing two models (Diebold 2015). And because the curve is estimated rather than quoted, these series inherit its estimation conventions and the differences among curve-estimation methods the literature has compared (McCulloch 1971, 1975; Nelson and Siegel 1987; Svensson 1994; Bliss 1997; Gürkaynak, Sack, and Wright 2007).

USACMRNY1 is the expected-average-short-rate half of a decomposition KRED estimates on the US Treasury zero curve in the published methodology's configuration, with ordinary least squares state dynamics and no small-sample persistence correction. The statistical object is therefore an estimated yield, not a price observed in a market or a survey of expectations (Adrian, Crump, and Moench 2013). The archetype's deterministic pre-test places a constant and a linear trend in the test regression, the specification a secularly declining rate level requires. Over the 11608 daily observations spanning 1980-01-02 to 2026-07-24 the three procedures agree. The augmented Dickey-Fuller test of Dickey and Fuller (1979), in the lag-augmented form of Said and Dickey (1984) with lag length chosen by an information criterion as in Ng and Perron (2001), does not reject a unit root with a statistic of −2.86471 at p = 0.174192. The nonparametric Phillips and Perron (1988) test concurs, with a statistic of −2.40704 at p = 0.375884. The KPSS test rejects stationarity with a statistic of 1.91021 at p < 0.01 (Kwiatkowski et al. 1992). All three agree honestly, the agreement carries a clean I(1) verdict, and with no lone dissent the GLS-detrended escalation of Elliott, Rothenberg, and Stock (1996) is not required.

Because the level carries a stochastic trend, the serial-correlation and break diagnostics run on the first difference. The Ljung and Box (1978) portmanteau, which refines the original Box and Pierce (1970) form, rejects the no-autocorrelation null at lags 10 and 20, with Q = 111.29 at p = 0.000 and Q = 171.438 at p = 0.000. The automatic portmanteau of Escanciano and Lobato (2009), which selects its own lag order rather than taking a fixed ladder, does not reject at the same level, with a statistic of 0.0000856596 at p = 0.992615. The two portmanteau procedures part company on the differenced series, and the disagreement is reported as it stands, not settled by preference. The multiple-break procedure of Bai and Perron (1998), computed by the dynamic-programming algorithm of Bai and Perron (2003), finds no break in the mean of the differenced series (Perron 1989), read with the parameter-instability perspective of Andrews (1993) in mind.

Three limits belong with the verdict. The tested object is model output, not a quoted price, so the reading describes an estimated expected path and inherits every assumption of the estimator behind it, including the choice to leave the state dynamics uncorrected (Bauer, Rudebusch, and Wu 2012). A re-estimation rewrites the whole history and no dated vintage panel is kept, so nothing here is a claim about the series as first published (Orphanides and van Norden 2002; Kim and Orphanides 2012). And the verdict belongs to this decomposition in this configuration alone. The other maturities of the same estimation are columns of one model, not separate readings, and an expected path produced by different machinery, or by the corrected configuration of the same estimator, is a different estimand whose reading is neither independent evidence nor support in either direction (Kim and Wright 2005; Cochrane and Piazzesi 2005).

The series is daily and has no low-integer seasonal period, so the seasonal-unit-root machinery of Hylleberg et al. (1990) and the Canova and Hansen (1995) seasonal-stationarity test are inapplicable and deliberately not run, the seasonal auxiliary regression being degenerate at a daily period (Beaulieu and Miron 1992; Ghysels and Osborn 2001).