A yield is observable; its explanation is not
A Treasury yield can be observed in market data, but the division between expected future short rates and a term premium cannot be read directly from a screen. The New York Fed describes the premium as compensation for the risk of interest-rate changes over a bond’s life and publishes estimates using the Adrian–Crump–Moench, or ACM, model. Its data include fitted yields, expected average short rates and term premia for maturities from one to ten years. These are research estimates rather than official Federal Reserve policy forecasts. [1]
The distinction matters whenever a long yield rises. One interpretation is that short rates are expected to remain higher. Another is that holding long-duration exposure has become less attractive at the old price. Both can happen together. A quoted yield by itself cannot allocate the move between the two explanations.
What compensation for risk means
A long-term bond fixes contractual payments while its market value changes as discount rates change. A person who sells before maturity faces price risk; a person holding to maturity still faces an opportunity-cost comparison with rolling shorter securities. A positive estimated premium says that the model assigns extra expected compensation to that exposure. It is not a separately paid fee, and it does not guarantee a positive realized return over the next month.
A negative estimate is conceptually possible. If an asset is especially valuable in unfavorable economic states, an investor can be willing to accept less expected return for its hedging value. This is an economic interpretation, not proof that a particular negative estimate was caused by a flight to safety. Model misspecification or an overstated short-rate expectation can also generate a low residual. The Board’s model documentation explicitly allows either sign. [3]
The familiar word premium can therefore mislead. It need not be positive, is not directly collectible independently of the bond position, and is not the same as the spread between a ten-year and a two-year Treasury. That curve spread compares two yields, each with its own expectations and risk components.
How ACM extracts an unobserved component
The ACM research uses a three-step regression approach. In accessible terms, it estimates how yield-curve factors evolve, relates bond excess returns to those factors and their surprises, then estimates the prices of the risks. The paper’s preferred specification uses five principal components, statistical summaries of common movements across yields. No-arbitrage restrictions connect the fitted bond prices across maturities. [2]
This is more disciplined than labeling every unexplained daily move a premium. It makes the decomposition consistent with a chosen model of yield dynamics and bond pricing. But the model’s factors are statistical summaries, not five independently observed economic causes. A component cannot automatically be renamed fiscal fear, inflation uncertainty or foreign demand merely because that story sounds plausible.
The original staff report dates to August 2008 and was revised in April 2013; the maintained data product applies the approach beyond the original research sample. [1][2] A historical paper’s fit and robustness results are evidence about that study, not a warranty that every later market regime is captured equally well.
Worked example: rising yields with falling expected short rates
Assume a hypothetical model fits a ten-year yield of 4.50%, divided into an expected-average-short-rate component of 3.70% and a term premium of 0.80%. At a later date, the fitted yield is 4.80%, the expectations component is 3.65% and the premium is 1.15%. The 30-basis-point yield increase equals a 5-basis-point fall in expected rates plus a 35-basis-point increase in the premium. One is one-hundredth of a percentage point.
Under those assumptions, calling the entire yield increase a forecast of tighter monetary policy would be wrong. Yet calling the increase entirely a premium move would also miss the offsetting expectations change. The decomposition is informative because it distinguishes mechanisms, not because its estimates are observations.
Now suppose a different admissible model splits the original 4.50% into a 4.30% expectations component and a 0.20% premium. Both models can fit the same yield while disagreeing about its composition. Market-price fit alone cannot determine which unobserved split is correct. All figures here are invented and use a common, internally consistent decomposition; none describes current Treasury pricing.
Scroll horizontally to see all columns.
| Hypothetical fitted quantity | Initial date | Later date | Change |
|---|---|---|---|
| Ten-year yield | 4.50% | 4.80% | +30 basis points |
| Expected-rate component | 3.70% | 3.65% | −5 basis points |
| Term-premium component | 0.80% | 1.15% | +35 basis points |
Why another published model can disagree
The Federal Reserve Board’s three-factor implementation uses survey forecasts of three-month Treasury bill rates alongside yields to help address persistent-data estimation problems. Its documentation warns that a close yield fit does not guarantee plausible expectations or premia. It also describes re-estimation after earlier parameters produced undesirable behavior near the effective lower bound. Changes in assumptions can therefore change the interpretation of history. [3]
Definitions differ too. The Board defines its yield premium as the yield minus expected average short rates and includes a convexity component arising from the nonlinear relationship between price and yield. Its documentation distinguishes this from a pure premium excluding convexity. [3] Two series with the same maturity label need not be exactly like-for-like.
An illustrative sensitivity makes the issue concrete: holding a fitted yield at 4%, a 3% expected-rate component leaves a 1% residual, while a 3.5% component leaves 0.5%. That half-point difference could reflect a different assumption about persistent future rates rather than new evidence that investors suddenly changed their risk tolerance.
Surveys offer a cross-check, not a perfect answer
New York Fed researchers in September 2022 compared model estimates with gaps between market-implied short-rate paths and survey forecasts. Their dated example found small negative survey-based estimates at some horizons. The article also explained that these estimates need matched horizons and careful timing of survey and market observations. Those 2022 results are historical evidence about a method, not a current reading. [4]
Surveys introduce different limitations: respondents may disagree, answer at different times, or differ from the investors setting marginal prices. Market-implied forwards likewise contain risk compensation rather than being pure forecasts. Agreement between independently constructed measures can strengthen an interpretation, but a disagreement is often information about uncertainty rather than a reason to erase one series.
A yield premium over an entire ten-year horizon also differs from a premium for a forward interval starting five years ahead. Similar labels conceal different exposures. An explanation that moves between them without identifying the horizon can attribute short-run policy news to long-run risk, or the reverse.
What a model estimate can support
A sustained increase across several well-specified premium estimates is more persuasive evidence of repriced duration risk than a single model’s one-day jump. A causal claim about borrowing supply, inflation risk or investor demand needs additional evidence connecting that mechanism to the move. A premium series alone cannot identify all three.
The decisive distinctions are observation versus estimation, expected compensation versus realized profit, and common movement versus causal attribution. Term-premium estimates make the more interpretable when those distinctions remain visible. They do not turn a bond-market narrative into a certain forecast or imply a particular investment decision.
Sources
- Federal Reserve Bank of New York; Treasury Term Premia, ACM data and methodology overview; checked October 4, 2026Official sourceBack to text: ↑1↑2
- Adrian, Crump and Moench, Federal Reserve Bank of New York; Pricing the Term Structure with Linear Regressions, Staff Report 340; August 2008, revised April 2013Official source · PDFBack to text: ↑1↑2
- Federal Reserve Board; Three-Factor Nominal Term Structure Model, methodology and Q&A; November 5, 2019, current documentation checked October 4, 2026Official sourceBack to text: ↑1↑2↑3
- Crump, Smith and Van Tassel, Federal Reserve Bank of New York; Short-Dated Term Premia and the Level of Inflation; September 28, 2022Official sourceBack to text: ↑