The pure expectations hypothesis (PEH) states that a long-term bond yield equals the average of current and expected future short-term rates over the bond's life. Under this theory, the yield curve's shape reflects only the market's forecast of the path of short-term rates, with no risk premium.
If the PEH held perfectly:
In reality, the PEH fails empirically. Research by Fama and Bliss (1987), Campbell and Shiller (1991), and others shows that long-term yields systematically overpredict future short rates. The Salomon Brothers yield curve primer series documents that forward rates are biased predictors of future rates, consistently overstating the magnitude of future rate increases.
The failure of the PEH implies the existence of a term premium, extra compensation investors demand for bearing duration risk. The yield curve's shape therefore reflects both rate expectations and a time-varying risk premium, and disentangling the two requires a model such as the ACM model.
The PEH carries a precise algebraic implication. If the EH holds, the 2-year spot rate s2 must equal the geometric average of today's 1-year spot rate s1 and the 1-year forward rate one year from now f(1,2):
(1 + s2)^2 = (1 + s1) * (1 + f(1,2))
Solving for the forward rate:
f(1,2) = [(1 + s2)^2 / (1 + s1)] - 1
You can observe s1 and s2 directly from the Treasury curve, then solve for the implied f(1,2). Under the PEH, this forward rate is an unbiased forecast of the future 1-year spot rate. You can extract these implied forwards for any horizon on YCP's Forward Rates page, which updates daily from the on-the-run Treasury curve.
The empirical record contradicts the unbiasedness claim directly. Fama and Bliss (1987) tested the prediction across multiple horizons and found that when f(1,2) exceeds s1, the subsequent change in the 1-year rate is actually negative more often than positive. The forward rate fails to predict the direction of rate moves. It points in the wrong direction. This is the opposite of what the PEH requires, and the finding has proved robust across samples and countries in the decades since.
If the PEH fails, then the gap between the observed long yield and the pure expectations component must represent compensation for risk. That gap is the term premium:
Term premium = Long yield minus average expected short rates
As a concrete example, suppose the 10-year yield is 4.50% and the average of expected 1-year rates over the next ten years is 3.80%. The term premium is +70 basis points. Investors who buy the 10-year note earn that 70 bps above the return they could expect from rolling 1-year bills, in exchange for accepting duration risk.
The term premium is not directly observable, because expected future short rates are not observable either. Estimating it requires a term structure model. The Adrian-Crump-Moench (ACM) model, developed at the Federal Reserve Bank of New York, decomposes the yield at every maturity into an expectations component and a term premium component. YCP's Term Premia page plots the ACM decomposition daily so you can see both components across the curve in real time.
The PEH's failure has direct consequences for how policymakers read the curve. A steeper yield curve admits two interpretations with opposite implications.
If the steepness reflects a high expectations component, markets anticipate that short rates will rise. That signal may justify further tightening by the Fed. If the steepness instead reflects a high term premium, the expected path of short rates may already be low or declining, and tightening on top of a high-term-premium curve risks overdoing it.
The Fed's ability to disentangle the two in real time is imperfect. This is why Fed economists rely on the ACM decomposition and similar models rather than reading the raw yield level as a policy signal.
A clear example arose in late 2023. After the 10-year yield climbed above 5.00% in October 2023, Fed Chair Powell noted publicly that the move appeared to reflect higher term premium rather than higher rate expectations. That distinction directly informed the Fed's decision to hold rates steady at subsequent meetings rather than hike further. For portfolio managers, it was a case where knowing the decomposition, not just the yield level, was the actionable insight.
Does the expectations hypothesis hold in practice?
No. The empirical evidence is consistently negative. Fama and Bliss (1987) and Campbell and Shiller (1991) both document that forward rates are biased predictors of future spot rates. The bias implies a non-zero term premium, which the PEH rules out by construction.
What is the difference between the pure expectations hypothesis and the local expectations hypothesis?
The pure expectations hypothesis (PEH) says that expected total returns are equal across all maturities over any holding period. The local expectations hypothesis (LEH) makes the weaker claim that expected returns are equal only over the next infinitesimally short period. The LEH is consistent with arbitrage-free term structure models. The PEH is not. In practice, the distinction matters because PEH implies that forward rates are unbiased forecasts of future spot rates, while LEH makes no such claim.
How does the expectations hypothesis relate to forward rates?
Under the PEH, every forward rate is an unbiased estimate of the future spot rate for the same period. If f(1,2) = 4.20%, the PEH says the market expects the 1-year rate one year from now to be 4.20%. YCP's Forward Rates page shows all implied forward rates so you can compare them directly against current spot rates to assess what the curve is pricing in.