U.S. Treasury 10Y − 2Y Yield Spread

USTSY10Y2Y is the raw series that records the difference between the ten-year and the two-year U.S. Treasury constant maturity yield, in percentage points and without any transformation. The difference is published as a series in its own right and is recorded as published, so KRED does not subtract one leg from the other.

Both legs are par yields read at fixed maturities from one fitted curve, so the value measures a par-yield slope rather than a forward spread or a slope of the zero-coupon term structure that underlies the duration measure of Fisher and Weil (1971), a distinction that follows from the par-to-zero-coupon transformation of McCulloch (1971). Each leg is separately a yield to maturity in the sense of Macaulay (1938), which is what makes the two commensurable.

A slope carries information because each leg is the average short rate expected over its own term plus a premium (Hicks 1939), and slope is also a named factor of the fitted form itself (Nelson and Siegel 1987; Svensson 1994). Because both legs come from the same fit, whether a tax-adjusted spline, an exponential spline, or a daily construction of the kind specified by Gürkaynak, Sack, and Wright (2007), the recorded difference inherits that fit's dependence on the estimator (McCulloch 1975; Vasicek and Fong 1982; Bliss 1997).

The short leg sits at the horizon over which a full easing or tightening phase is priced, so the difference sets long-horizon pricing against the sequence of decisions the market already expects, a sequence anchored on the operating target described by Bindseil (2004).

A fall in the recorded value therefore means the long leg has moved down relative to the short one, and the number itself does not say whether expectations or the premium moved.

KRED applies no transformation to USTSY10Y2Y and performs no subtraction. The difference is recorded exactly as published rather than computed from the two legs, so no rescaling, deflating, smoothing, annualizing, or differencing is applied, and what follows is the measurement basis by which such a difference comes to exist.

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). Each leg is a par yield in that sense, and both are nodes of one such fit read on the same day. 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). An operational daily version of that class is specified by Gürkaynak, Sack, and Wright (2007), and the competing 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 relating a difference between two par yields to the forward rates spanning the interval between them is that of Hicks (1939).

A slope carries information because each leg is an average of expected short rates plus a premium (Hicks 1939), so the difference records what is priced over the interval between the two maturities. The short leg is anchored on the overnight operating target whose corridor and standing facilities Bindseil (2004) sets out and whose design across operating frameworks Borio (1997) surveys, a rate steered as modelled by Bartolini, Bertola, and Prati (2002) and determined day to day as characterized by Hamilton (1996). At two years what the short leg holds is the expected sequence of settings rather than the one in force today.

When the value is negative the arithmetic content is that the long leg is priced below the short one, which is a statement about two points of one curve. Both legs are read on the common yield convention of Macaulay (1938) from a single daily construction of the kind specified by Gürkaynak, Sack, and Wright (2007), and slope is the second named factor of the fitted form (Nelson and Siegel 1987; Svensson 1994).

Two measurement caveats bear on any reading. The value is a par-yield difference rather than the difference of zero-coupon rates that underlies the duration measure of Fisher and Weil (1971), a distinction fixed by the transformation of McCulloch (1971), and because both legs come from one fit the recorded difference moves with the estimator chosen (Bliss 1997). KRED estimates a near-term recession probability elsewhere from a model-decomposed slope and a near-term forward spread, which is a different object from this recorded difference.

A position expressing a view on this value is a duration-weighted holding of the two legs, sized so that a parallel move in the level nets out and only the change in shape remains. The weights come from the duration of Macaulay (1938) in the zero-coupon-consistent form of Fisher and Weil (1971).

What such a position trades is the slope factor of the fitted curve (Nelson and Siegel 1987; Svensson 1994), and since the par-to-zero-coupon transformation of McCulloch (1971) shows that a par-yield difference is not the forward spread the position earns, the two are reconciled through the curve rather than read off this series. The measured value also shifts with the fitting method, whether a tax-adjusted spline or an exponential spline (McCulloch 1975; Vasicek and Fong 1982; Bliss 1997).

Carry is set by financing, and the two legs finance at different secured rates whose specialness varies by maturity (Duffie 1996), so a curve position that looks flat on yield can be strongly positive or negative on carry. The forward rates implied by the curve price the roll-down as each leg ages (Hicks 1939; Gürkaynak, Sack, and Wright 2007).

The ten-year minus two-year Treasury yield spread is published as its own series and is served as recorded, so the statistical object is the published spread rather than any difference KRED forms from two yield legs. As a mean-reverting premium it is fitted with a constant and no trend, since a fitted trend on a premium of this kind is a specification error. On the 12,534 daily observations spanning 1976-06-01 to 2026-07-27 every procedure rejects its own null, so no clean order of integration is assigned. The augmented Dickey-Fuller test of Dickey and Fuller (1979), in the lag-augmented form of Said and Dickey (1984) with lag length set as in Ng and Perron (2001), rejects the unit root with a statistic of −3.14298 at p = 0.0235314, the nonparametric Phillips and Perron (1988) test also rejects with a statistic of −3.20856 at p = 0.0194947, and the Kwiatkowski et al. (1992) test rejects stationarity with a statistic of 1.40952 at p < 0.01, the near-unit-root pattern of a highly persistent mean-reverting signal under which neither null survives. This is not a lone-dissent case, since the two same-null procedures agree with each other and the disagreement lies with the opposite-null test. The GLS-detrended escalation of Elliott, Rothenberg, and Stock (1996) was not computed for this member, so the ambiguity is reported as it stands rather than adjudicated by a further test.

On the level the first-order autocorrelation is 0.998742 with an implied half-life of 550.468 observations, a descriptive persistence summary and not an integration claim. The Ljung and Box (1978) portmanteau on the level, refining the original Box and Pierce (1970) form, rejects the no-autocorrelation null at lags 10 and 20, with Q = 123625 and Q = 243672 and p = 0.000 in both cases. The multiple-break procedure of Bai and Perron (1998), computed by the dynamic-programming algorithm of Bai and Perron (2003), runs on the level because the level is the object this archetype fixes unless the protocol certifies a clean integrated reading, and it locates five mean shifts, at 1983-12-16, 1993-09-27, 2001-03-30, 2008-10-06, and 2016-04-13, consistent with the parameter-instability inference of Andrews (1993). Since the verdict is ambiguous rather than clean, the level portmanteau and the level break dates are read as descriptive of a persistent signal and carry no claim about its order of integration (Perron 1989).

This spread is daily and has no defined 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).