South Korea Treasury Bond 3Y Par Yield

KRKTB3 is the raw three-year Korean Treasury benchmark par yield, recorded as reported without any transformation. The recorded value is the annualized yield at which the on-the-run three-year sovereign coupon bond would trade at par.

This par yield coincides with the yield to maturity that reconciles a bond's promised coupons and principal with its market price, following the discounting concept that Macaulay (1938) formalized. Its three-year point sits on the term structure to which the forward-rate decomposition of Hicks (1939) applies.

Its level reflects the zero-coupon discount function recovered from coupon-bond prices. This recovery originates with McCulloch (1971) and was refined by McCulloch (1975), who corrected for differential coupon taxation. The same surface is summarized parsimoniously by a level-slope-curvature form or by exponential splines (Nelson and Siegel 1987; Vasicek and Fong 1982).

The three-year point is read against the full curve of zero rates, as duration analysis requires (Fisher and Weil 1971). The extended forward-curve parameterization and the daily off-the-run construction place the same maturity within a continuously estimated surface (Svensson 1994; Gürkaynak, Sack, and Wright 2007). The estimation methods themselves were catalogued by Bliss (1997).

The three-year tenor lies above the corridor of the overnight operating target, so the recorded number is a market price rather than an administered value (Bindseil 2004).

KRED applies no transformation to KRKTB3 and stores the reported par yield exactly as quoted, so the only methodology that bears on it is the measurement basis by which such a yield comes to exist. That basis is the yield-to-maturity convention of Macaulay (1938), under which the par yield is the single rate equating discounted coupons and principal to a par price, equivalently the coupon rate that makes the three-year bond trade at face value.

The benchmark par yield is read off a fitted term structure. The discount function is recovered from coupon-bond prices by the cubic-spline approach of McCulloch (1971), the tax-adjusted variant of McCulloch (1975), the exponential splines of Vasicek and Fong (1982), the parsimonious level-slope-curvature curve of Nelson and Siegel (1987), and the forward-augmented extension of Svensson (1994). Its operational daily form was documented by Gürkaynak, Sack, and Wright (2007), and the comparison across methods was carried out by Bliss (1997).

Because the three-year node is one point on this surface, its consistency with neighboring zero and forward rates follows the immunization arithmetic of Fisher and Weil (1971) and the forward-rate decomposition of Hicks (1939). The underlying transaction prices are quoted in a dealer market whose microstructure resembles the identification framework of Furfine (1999). No smoothing, deflation, or seasonal adjustment is imposed.

The three-year yield is a forward-looking price, decomposing into the average short rate expected over three years plus a term premium (Hicks 1939). Its level therefore conveys where the market sees the policy path settling.

The short-rate anchor is the overnight operating target steered through the corridor and standing facilities, a mechanism surveyed across regimes (Bindseil 2004; Borio 1997). The day-to-day volatility of that target around its setting was analyzed by Bartolini, Bertola, and Prati (2002), and its determination in the overnight interbank market was modeled by Hamilton (1996).

The transaction-level identification of those overnight rates underpins the front end from which the curve extrapolates (Furfine 1999). The cost of financing a three-year bond position is set in the secured repo market (Duffie 1996).

The par yield is a maturity-specific summary of expected rates and risk. The level-slope-curvature reading, the forward-rate construction, and the daily estimated curve let analysts locate the three-year point relative to expectations (Nelson and Siegel 1987; Svensson 1994; Gürkaynak, Sack, and Wright 2007). The duration logic then translates its movements into the macroeconomic transmission of monetary policy (Macaulay 1938).

For pricing and risk management, the three-year par yield is the discount rate that values won fixed-income cash flows at that horizon. Its sensitivity is summarized by the duration concept and by full-term-structure duration, the latter used to immunize portfolios against rate moves (Macaulay 1938; Fisher and Weil 1971).

Traders read this yield against the forward-rate decomposition and finance their positions at the special rate of the secured repo market (Hicks 1939; Duffie 1996). The carry on a three-year benchmark therefore depends jointly on the yield and on its collateral value.

Relative-value desks fit the surrounding curve and then judge whether the on-the-run three-year point is rich or cheap to that fitted curve. The fit uses discount-function splines, the level-slope-curvature form, the forward extension, exponential splines, and daily off-the-run estimates, with the construction method chosen among evaluated alternatives (McCulloch 1971; Nelson and Siegel 1987; Svensson 1994; Vasicek and Fong 1982; Gürkaynak, Sack, and Wright 2007; Bliss 1997).

The same yield anchors both swap spreads and the front end where overnight steering operates, so it serves as a core hedging and benchmark instrument (Bartolini, Bertola, and Prati 2002).

On the 6,832 daily observations spanning 1998-11-13 to 2026-06-10, fit with a constant and trend, the unit-root battery agrees that the three-year Treasury par yield is integrated of order one. The augmented Dickey-Fuller test of Dickey and Fuller (1979), in the ARMA-consistent lag-augmented form of Said and Dickey (1984) and with lag length set as in Ng and Perron (2001), does not reject a unit root with p = 0.657, the nonparametric Phillips and Perron (1988) test concurs with p = 0.4439, and the Kwiatkowski et al. (1992) stationarity test rejects its trend-stationary null at p < 0.01, so the verdict is an unambiguous I(1). The GLS-detrended power escalation of Elliott, Rothenberg, and Stock (1996) is reserved for ambiguous outcomes under the house protocol and is not required on this clean reading.

Because the level is integrated, the mean-shift and serial-correlation diagnostics are run on the first difference, the stationary object those procedures require, since a break search or a portmanteau on an integrated level would spuriously segment and read near-unit autocorrelations (Bai and Perron 1998; Perron 1989). 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, consistent with the parameter-instability inference of Andrews (1993). The Ljung and Box (1978) portmanteau statistic, refining the original Box and Pierce (1970) form, is computed on the first difference and rejects the white-noise null at lags 10 and 20, with Q = 33.29 and Q = 78.29 and p = 0.000 and p = 0.000, and the automatic portmanteau test of Escanciano and Lobato (2009) concurs with a statistic of 4.29 at p = 0.038.

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 are deliberately not run, the degeneracy of the seasonal auxiliary regression at a daily period being the standard ground (Beaulieu and Miron 1992; Ghysels and Osborn 2001).