South Korea 3-Year Zero-Coupon Bond Risk-Neutral Yield without Persistence Correction

KRED decomposes the Korean 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 runs excess-return regressions on ordinary least squares state dynamics 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). The absence of that correction is the only difference from the corrected Korean family published beside these series, since both run on one shared input panel, and it makes the two families different estimands rather than two readings of one quantity.

The estimation panel is the platform's existing Korean zero-curve panel, and the sample span is determined by that input. It opens on 2000-12-18 and carries 6307 daily observations through 2026-06-09 at the pinned vintage. The curve rests on five market knots, at three months and at one, three, five and ten years, and is interpolated by a shape-preserving piecewise cubic rule onto a monthly maturity grid running from one month to one hundred and twenty months. Every maturity between the knots is therefore an interpolated point on the curve, not a quoted one.

No official decomposition of the Korean curve exists, so nothing outside this estimation measures the same object. The family therefore carries no validation of its expected-path and premium split that is independent of its own construction. KRED states that absence rather than filling it. The cross-configuration comparison with the corrected family beside it measures the two configurations against each other and never validates either, because comparing two outputs is not comparing two models (Diebold 2015; Campbell and Thompson 2008; Goyal and Welch 2008).

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

KRED loads the same daily Korean zero-curve inputs its corrected decomposition uses, interpolates them with a shape-preserving piecewise cubic rule from five market knots onto a monthly maturity grid running from one month to one hundred and twenty months, and hands that panel to the excess-return-regression estimator. The pricing factors are the five 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 difference 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 identity that the premium equals the model yield less the risk-neutral yield holds on every row of every served maturity.

The short leg of the panel is fitted less closely than the rest. Over the 6307 daily observations from 2000-12-18 to 2026-06-09, the mean absolute difference between the model yield and the observed zero-coupon yield is 4.99 basis points at twelve months, 1.05 at thirty-six months, 2.11 at sixty months and 1.04 at one hundred and twenty months. These figures are a property of the input panel the estimation runs on, not of any one configuration of the estimator, and the same measurement on the same panel returns the same values to two decimal places when the small-sample persistence correction is applied. The twelve-month figure is therefore disclosed as a panel property and carries no comparative reading of any kind.

Re-estimating the same specification from a 2011-01-03 start and setting it against the full-sample estimate over the overlap gives a correlation of 0.9943 on the ten-year premium and a mean absolute difference of 39.92 basis points across 186 month-ends. Those numbers are reported whatever they turn out to be. 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).

The whole history is re-estimated whenever the series refreshes, so a value read today for a past date can differ from the value read for that same date earlier. No dated vintage panel is kept, the size of such a revision cannot be quantified here, and nothing on this page is a claim about the series as first published (Orphanides and van Norden 2002; Kim and Orphanides 2012).

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). And premiums move rather than sitting at a constant, a fact 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).

This family and the corrected Korean family are estimated on one shared panel, so the difference between them isolates the configuration rather than mixing it with a difference in inputs. That is a measurement the Korean record can state and the US record cannot. Over 307 month-ends, the level correlation between the two configurations' premiums is 0.9699 at one year, 0.9428 at three years, 0.9521 at five years and 0.9682 at ten years. The correlation of monthly changes is 0.9954, 0.9630, 0.9702 and 0.9451, and the mean absolute difference is 7.00, 21.75, 32.67 and 49.62 basis points. The signed mean of the corrected estimate less this one is 0.00 basis points at one year, 0.20 at three years, 0.76 at five years and 3.76 at ten years, against dispersions of 8.40, 26.69, 39.71 and 59.24 basis points. The two configurations run close in changes and apart in level.

The signed difference is a trend rather than an offset. Read as era means in basis points over the segments a break search places at 2002-12, 2008-12, 2011-08, 2014-10 and 2022-04, it runs −104.82 from 2000-12, then −49.26, then −24.24, then 17.83, then 74.57 from 2014-11, and 14.15 from 2022-05. A sample mean of such a difference cannot assert its own constancy (Andrews 1993), and 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). The dispersion of the ten-year expected-path half also differs across the two configurations, 1.0313 percentage points under the corrected one against 0.4415 under this one, the direction the correction's own authors document for estimated persistence and for risk-neutral volatility (Bauer, Rudebusch, and Wu 2012). KRED publishes no explanation of the correction's effect on the level of the premium, because that effect is not what the cited literature establishes.

Two limits bound the economic reading. Every quantity above is descriptive of the pair and is never evidence for or against either configuration in either direction, since a benchmark-relative quantity is an artifact of the comparison rather than a decision input (Campbell and Thompson 2008; Goyal and Welch 2008). And 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; Kim and Wright 2005).

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 rather than 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, so they are not two independent readings, and the four maturities are columns of that one estimation, not 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. A spread taken between the two is therefore a specification difference, not a relative-value signal, since comparing two outputs is not comparing two models (Diebold 2015). And the underlying curve is interpolated from five market knots rather than quoted at every maturity, so a reading at a maturity between those knots inherits the interpolation as well as the estimation (Macaulay 1938; Bliss 1997).

KRACMRNY3 is the expected-average-short-rate half of a decomposition KRED estimates on the Korean Treasury zero curve in the published methodology's configuration, with ordinary least squares state dynamics and no small-sample persistence correction. 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 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 6307 daily observations spanning 2000-12-18 to 2026-06-09, 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 −1.83265 at p = 0.688805. The nonparametric test of Phillips and Perron (1988) concurs, with a statistic of −1.89693 at p = 0.65626. The KPSS test rejects stationarity, with a statistic of 1.48982 at p < 0.01 (Kwiatkowski et al. 1992). All three return the same reading, an honest agreement that carries a clean I(1) verdict. This is not a lone-dissent reading, so 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) statistic, rejects the no-autocorrelation null at lags 10 and 20, with Q = 91.4671 at p = 0.000 and Q = 130.948 at p = 0.000. The automatic portmanteau of Escanciano and Lobato (2009), which selects its own lag order rather than taking a fixed ladder, concurs with a statistic of 9.08033 at p = 0.00258373, so the two portmanteau procedures read the differenced series the same way. The multiple-break procedure of Bai and Perron (1998), computed with 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 attach to the verdict. The tested object is model output rather than a quoted price, so the reading describes an estimated expected path and inherits every assumption of the estimator that produced 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 rather than 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, a sampling frequency at which a low-integer seasonal period cannot arise. The seasonal-unit-root machinery of Hylleberg et al. (1990) and the seasonal-stationarity test of Canova and Hansen (1995) are therefore not applicable and are deliberately not run, since the seasonal auxiliary regression is degenerate at a daily period (Beaulieu and Miron 1992; Ghysels and Osborn 2001).