And similarly for the Two Year Treasury?

A standard decomposition of the ten year rate is (for quarterly data):

Where the first term on the right hand side (call it * z’*) would be a representation of the expectations hypothesis of the term structure – the long term interest rate is the average of the expected future short rates.

We don’t observe the expected values, but we do observe the ex post realizations. Calculate the average of the ex post realizations, to obtain * z*.

Figure 1 plots the *i _{10y,t }* (black line),

**(red line), and**

*z*where the estimated *rp* is the Kim-Wright estimate (blue line) or the Adrian-Crump-Moench estimate (orange).

**Figure 1:** Ten year constant maturity Treasury yield (black), ten year minus Kim-Wright term premium (blue), ten year minus Adrian-Crump-Moench term premium (orange), and average of future three month Treasury yields on secondary market (red). NBER defined recession dates peak-to-trough shaded gray. Sources: Treasury via FRED, Shiller, Fed via FRED, NY Fed, NBER and author’s calculations.

If full information rational expectations held, and the estimates of the 10 year term premium on a zero coupon bond were accurate, then the light blue line or orange line should match the red line, more or less. This characterization does not hold, although it does better for the Adrian-Crump-Moench estimates than the Kim-Wright.

A similar point applies to the two year horizon.

**Figure 2:** Ten year constant maturity Treasury yield (black), ten year minus term premium (blue), ten year minus Adrian-Crump-Moench term premium (orange), and average of future three month Treasury yields on secondary market (red). NBER defined recession dates peak-to-trough shaded gray. Sources: Treasury via FRED, Shiller, Fed via FRED, NY Fed, NBER and author’s calculations.

The finding that long yields — even after adjusting for risk premia — are too high are consistent with market observers overestimating how high interest rates will go. For some concrete evidence, see the Survey of Professional Forecasters expectations of future 3 month Treasury yields, vs. the actual.

**Figure 3:** Three month Treasury yield (blue line) and Survey of Professional Forecasters mean forecast (red +) as of Q3, in %. Green shading denotes early, late periods. Source: Federal Reserve Board, Philadelphia Fed.

None of the foregoing invalidates the expectations hypothesis of the term structure (which relies upon expected future rates). But it does cast into doubt whether future short rates will actually go as high as implied by the current long rates (even after adjusting for estimated term premia).