U.S. KRED-Estimated 10-Year Risk-Neutral Yield

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 estimator is a set of excess-return regressions, with a small-sample persistence correction applied to the state dynamics before the premium is formed (Adrian, Crump, and Moench 2013; Bauer, Rudebusch, and Wu 2012).

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

Four statements bound what these series are. Neither half is the term premium or the expected path; 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 counts as evidence for or against it in either direction. Neither can be set beside the Korean term-premium construction 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).

A second KRED configuration of the same estimator, which omits the small-sample persistence correction, is published beside these series at the same four maturities. It is a different estimand rather than a second measurement of this one, and neither family validates, corroborates, or outranks the other in either direction.

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 excess-return-regression estimator the platform already runs for Korea. The pricing factors are the leading principal components of the panel. The state follows a first-order vector autoregression whose persistence is bias-corrected before the premium is formed, 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 is a six-parameter extension of the parsimonious Nelson and Siegel (1987) form (Svensson 1994; Gürkaynak, Sack, and Wright 2007), and the broader family of methods for recovering a zero curve from coupon prices has a comparative literature of its own (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 bp on average, internal pricing errors average between 0.61 and 1.47 bp across the four maturities, the ten-year model yield differs from its published counterpart by 0.647 bp on average, and the bias correction moves estimated persistence and risk-neutral volatility in the direction the correction's own authors document. The pre-committed agreement leg on the term premium itself, by contrast, fails as measured at twelve, thirty-six and sixty months, and that failure is not evidence of a defect in the computation (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 lie below the shortest maturity the curve's publishers state it is estimated for, so those two columns are an extrapolation rather than an evaluation inside the estimated range; the gap between the extrapolated short point and the observed one-month Treasury constant-maturity rate, measured at 25.0 bp, is disclosed rather than repaired. 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, so this is coverage composition rather than data loss. Finally, 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 most recent 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 0.9494 on the ten-year premium and a mean absolute difference of 39.35 bp across 438 month-ends. Those numbers are reported whatever they turn out to be. They are read with 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 collects 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 distinction matters for policy analysis because the stance is set at the shortest maturity while transmission runs through long rates (Bindseil 2004; Borio 1997). And premiums move rather than sitting at a constant, a point the return-forecasting literature established by showing that excess bond returns are 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, it runs −104.74 in the 1980s, −8.69 in the 1990s, +56.87 in the 2000s, +118.00 in the 2010s and +93.88 over 2020 to 2026. The mean over the first sixty month-ends of the sample is −147.63, against +77.52 over the last sixty, and the largest single difference reaches −231.58. 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 93 of them; across those months the published series averages −53.42 basis points and this one +53.74 basis points. KRED publishes no explanation of why the two allocate the yield so 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 be supplied rather than cited.

Two limits therefore bound the economic reading. The level of a premium of this class depends on the span it is estimated on and on the estimated persistence of the state, so a difference between two such estimates is a statement about measurement, not a finding about the world (Orphanides and van Norden 2002). And a slope or premium reading taken from these series is a reading of this estimator alone, since a decomposition built from different machinery on the same curve answers the same question differently (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 is held for 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).

Three 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, so by construction they sum to the model yield at the same maturity; they are not two independent readings. And the curve is estimated rather than quoted, so these series inherit its estimation conventions along with 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).

USRNY10 is the expected-average-short-rate half of a decomposition KRED estimates on the US Treasury zero curve. The object under test is therefore an estimated yield, not a price observed in a market or a survey of expectations (Adrian, Crump, and Moench 2013). The deterministic pre-test for this archetype puts a constant and a linear trend in the test regression, the specification a secularly declining rate level calls for. 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), run in the lag-augmented form of Said and Dickey (1984) with the lag length chosen by an information criterion as in Ng and Perron (2001), does not reject a unit root with a statistic of −2.46865 at p = 0.343809. The nonparametric Phillips and Perron (1988) test concurs with a statistic of −2.17167 at p = 0.505807, and the KPSS test rejects stationarity with a statistic of 2.13931 at p < 0.01 (Kwiatkowski et al. 1992). All three point the same way, an honest agreement that carries a clean I(1) verdict. With no lone dissenter to adjudicate, 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 = 106.735 at p = 0.000 and Q = 145.982 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 0.661618 at p = 0.415989. The two portmanteau procedures part company on the differenced series; that disagreement is reported as it stands rather than 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 (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 is a property of this decomposition alone, since an expected path produced by different machinery on the same curve is a different estimand whose reading is neither independent evidence nor support in either direction (Kim and Wright 2005; Cochrane and Piazzesi 2005).

This 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 not applicable and are deliberately not run, the seasonal auxiliary regression being degenerate at a daily period (Beaulieu and Miron 1992; Ghysels and Osborn 2001).