U.S. Treasury 3Y Constant Maturity Yield

USTSY3 is the raw series that records the three-year U.S. Treasury constant maturity yield exactly as published, in percent per annum and without any transformation. A constant maturity yield is read at a fixed remaining maturity from a fitted yield curve, so the value is not the yield of any particular outstanding security.

What is read is a par yield, the single discount rate equating a security's remaining cash flows to a price of par, which is the yield-to-maturity construct of Macaulay (1938), and a level that decomposes into the average short rate expected over the term plus a premium (Hicks 1939). Curves of this kind are recovered from observed Treasury prices by spline estimation of the discount function (McCulloch 1971, 1975; Vasicek and Fong 1982) or by imposing a parametric level-slope-curvature form and its second-term extension (Nelson and Siegel 1987; Svensson 1994), and a daily construction of that class is specified by Gürkaynak, Sack, and Wright (2007), with the competing estimators compared by Bliss (1997). KRED neither fits the curve nor interpolates the maturity point, and the fitting method behind the published value is not restated here.

A par curve is not the zero-coupon term structure that underlies the duration measure of Fisher and Weil (1971), so the recorded value is not a spot rate and is a different object from the zero-coupon and forward curves KRED estimates elsewhere. At three years the expected policy path still dominates the level, while the premium for holding the claim is no longer negligible. The rate being expected is an operating target, whose corridor and standing-facility mechanics Bindseil (2004) sets out.

KRED applies no transformation to USTSY3 and stores the published constant maturity yield exactly as recorded, with no rescaling, deflating, smoothing, annualizing, or differencing, and it neither fits the curve nor interpolates the maturity point. What follows is therefore the measurement basis by which such a value comes to exist rather than a procedure KRED carries out.

A par yield is the single discount rate equating a security's coupons and principal to a price of par (Macaulay 1938), and the timing of those cash flows is summarized by the zero-coupon-based duration of Fisher and Weil (1971). From one year out the inputs are coupon-bearing notes, whose prices carry the coupon and accrual conventions of the market. A three-year point sits among coupon maturities whose remaining coupon streams are still short. Recovering a continuous discount function from observed prices proceeds by cubic spline, by its refinement for differential coupon taxation, or by exponential splines (McCulloch 1971, 1975; Vasicek and Fong 1982), while parametric construction instead imposes a level-slope-curvature form or its forward-rate extension (Nelson and Siegel 1987; Svensson 1994). A daily version of that class, producing par, zero-coupon, and forward rates at any maturity, is specified by Gürkaynak, Sack, and Wright (2007), and the estimators are evaluated against one another by Bliss (1997).

Fits of this kind are commonly estimated from off-the-run prices, since an issue trading special in the secured financing market prices richer than the curve, a specialness defined by Duffie (1996). The identity tying a fitted par curve to expected future short rates and a term premium is that of Hicks (1939).

At this tenor the level is an average of the policy rate expected over the coming years plus a premium, which is the decomposition of Hicks (1939), so it moves with revisions to the expected sequence of decisions rather than with the setting in force today. The rate being averaged is the overnight operating target whose corridor Bindseil (2004) sets out and whose design across frameworks Borio (1997) surveys, steered as modelled by Bartolini, Bertola, and Prati (2002) and determined day to day as characterized by Hamilton (1996). Three years reaches beyond most such phases, so part of the level compensates for holding the claim rather than for the path.

The legs of a curve position are weighted by the zero-coupon-based duration of Fisher and Weil (1971) on the common yield concept of Macaulay (1938), which is what makes this region the one where a view on the cycle is expressed. It is also where the curvature term of a fitted form does most of its work (Nelson and Siegel 1987; Svensson 1994; Gürkaynak, Sack, and Wright 2007), and the same level discounts medium-dated cash flows through the discount function of McCulloch (1971).

In fixed-income practice this level is the discount rate for medium-dated exposure, and the rate sensitivity it implies is the duration of Macaulay (1938) in the zero-coupon-consistent form of Fisher and Weil (1971). This is where a duration-neutral curve trade begins to earn the premium rather than the path.

Relative value is judged by reading the node against a fitted curve, whether a parametric form and its extension (Nelson and Siegel 1987; Svensson 1994), exponential splines (Vasicek and Fong 1982), or a spline discount function and its tax-adjusted variant (McCulloch 1971, 1975), so a cheapness measured against one fit need not survive another (Bliss 1997).

Positions are financed in the secured market, where collateral and specialness set the repo rate below the general riskless rate (Duffie 1996), and the forward rates implied by the curve price the carry and roll-down on the holding (Hicks 1939; Gürkaynak, Sack, and Wright 2007).

On the 16,125 daily observations spanning 1962-01-02 to 2026-07-24, fit with a constant and trend, the unit-root battery agrees that the three-year constant-maturity 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 = 0.2722, the nonparametric Phillips and Perron (1988) test concurs with p = 0.3063, 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 = 202.024 and Q = 250.219 and p = 0.000 in both cases, and the automatic portmanteau test of Escanciano and Lobato (2009) concurs with a statistic of 48.7309 at p = 0.000, the short-horizon dependence expected of a daily yield change.

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 not applicable 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).