U.S. Treasury 20Y Constant Maturity Yield

USTSY20 is the raw series that records the twenty-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). A curve of this kind may be summarized by a parametric level-slope-curvature form and its second-term extension (Nelson and Siegel 1987; Svensson 1994), or recovered as a discount function by cubic and exponential splines and by the refinement for differential coupon taxation (McCulloch 1971, 1975; Vasicek and Fong 1982). Bliss (1997) sets those estimators against one another, and a daily construction of the class is specified by Gürkaynak, Sack, and Wright (2007). 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 twenty years the same long-horizon expectation and premium are at work, and the point lies between the two most heavily traded long maturities. The rate being expected is an operating target, whose corridor and standing-facility mechanics Bindseil (2004) sets out.

KRED applies no transformation to USTSY20 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). At long maturities the inputs are coupon-bearing notes and bonds whose long streams of remaining coupons the recovered discount function has to price consistently. A twenty-year point falls between the two long benchmarks, so its level is read from the fitted shape between them. 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 the long end the premium for holding a long-dated claim is a substantial part of the level, which is the liquidity-premium reading of the term structure given by Hicks (1939), while the expectations part is an average of future settings of the operating target described by Bindseil (2004) and surveyed across operating frameworks by Borio (1997). The long-yield record against which such readings have been checked is the one assembled by Macaulay (1938). The twenty-year point is read between the two long benchmarks that surround it.

A long-dated claim carries long duration, so the level governs the relation between yields and realized bondholder returns set out by Fisher and Weil (1971), and it fixes the level factor of a fitted form (Nelson and Siegel 1987), whose extension adds a second term where one hump cannot match the observed shape (Svensson 1994), read from a daily construction of the kind specified by Gürkaynak, Sack, and Wright (2007). The same level discounts long-horizon cash flows through the discount function of McCulloch (1971), and because it is a fitted point rather than a traded yield its level depends on the estimator chosen (Vasicek and Fong 1982; Bliss 1997).

In fixed-income practice this level is the discount rate for long-dated liabilities, and the rate sensitivity it implies is the duration of Macaulay (1938) in the zero-coupon-consistent form of Fisher and Weil (1971). Twenty-year exposure is used where a liability profile falls between the ten- and thirty-year benchmarks.

Relative value is judged against a fitted curve, and the fit may be a spline discount function or its tax-adjusted variant (McCulloch 1971, 1975), an exponential spline (Vasicek and Fong 1982), or a parametric form with its extension (Nelson and Siegel 1987; Svensson 1994), so what looks cheap on one fit need not look cheap on 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 14,436 daily observations spanning 1962-01-02 to 2026-07-24, fit with a constant and trend, the unit-root battery agrees that the twenty-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 = 0.5893, the nonparametric Phillips and Perron (1988) test concurs with p = 0.5964, 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. The observation count is smaller than the calendar span would imply, because the series was not published for a stretch of years in the middle of the sample, so the count is taken from the battery rather than inferred from the endpoints.

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 = 48.7774 and Q = 66.2163 and p = 0.000 in both cases, and the automatic portmanteau test of Escanciano and Lobato (2009) concurs with a statistic of 12.9322 at p = 0.000323, 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).