The ACM model (Adrian, Crump, and Moench, 2013) is the most widely referenced term premium estimate, published by the Federal Reserve Bank of New York. It decomposes each Treasury yield into two components:
The model belongs to the class of no-arbitrage affine term structure models. It uses five pricing factors extracted from Treasury yields via principal components and estimates the market price of risk using excess bond return regressions.
The ACM term premium is available on this site's term premia tool, which visualizes both the time series of term premium estimates by maturity and the decomposition of any yield into its expectations and premium components.
Key insights from the ACM model:
The model has limitations: it is estimated in-sample, estimates are sensitive to the sample period, and it cannot distinguish between true expectations and risk-neutral expectations. Competing models (Kim-Wright, Christensen-Rudebusch) produce different point estimates but generally agree on the direction of changes.
Three assumptions do the work, and each one is a place where the output can go wrong.
A few factors explain the whole curve. The model extracts five principal components from the cross section of yields. The first three correspond closely to level, slope, and curvature, and together they account for nearly all the daily variation. Everything the model knows about the curve arrives through these factors.
The factors follow a stable process. Their evolution is estimated from history and assumed to continue. This is where the expected path of short rates comes from. If the process changed, the estimated path describes a world that no longer exists.
No arbitrage links the tenors. Bonds of different maturities must be priced consistently with one another. This constraint is what turns a statistical description of yields into a decomposition, because it forces the expected path and the premium to add up to the observed yield at every tenor at once.
The estimation itself is a regression of excess bond returns on the lagged factors. That regression measures how much investors were actually paid for bearing each kind of risk, and the fitted compensation is the term premium.
The model publishes three series for each maturity, and confusing them is the most common misreading.
The useful discipline is to read the two components together. A term premium that rose 30 bps while the yield rose 30 bps means the expected path did not move at all, and the entire increase was investors demanding more compensation. The same 30 bps rise in the premium alongside a 10 bps fall in the yield means the expected path dropped 40 bps, which is a materially different market.
Changes are also more trustworthy than levels. The premium is a residual, so it absorbs every error in the estimated expected path. Its level inherits those errors. Its direction over a short window is far less sensitive to them.
The model is a research tool published for transparency, and its authors are explicit about what it cannot do.
Estimates are revised. The parameters are re-estimated as new data arrives, so a published history changes over time. A chart of the term premium drawn today will differ from the same chart drawn a year ago, including for dates in the distant past.
Sample dependence is severe. The estimated process for the factors is dominated by whatever regime supplied most of the data. Models fitted through a long period of falling rates carried that experience into their expected paths, and their premium estimates were revised when the pattern broke.
The zero lower bound is not modeled. The affine structure allows rates to go arbitrarily negative. During periods when policy rates were pinned near zero, the model's expected path could imply outcomes that policy would not have permitted, which pushes error into the premium.
Risk neutral is not the same as expected. The decomposition separates a yield into a risk neutral component and a premium. Reading the risk neutral component as the market's genuine forecast requires an additional assumption that the model does not supply.
Competing estimates are the practical check. When ACM, Kim-Wright, and Christensen-Rudebusch agree on direction, the signal is worth acting on. When they disagree, the disagreement is the information.
Because the model is re-estimated on the full sample each time it is updated. New observations change the fitted parameters, and the fitted parameters determine the decomposition at every historical date. The observed yields do not change. Only the split between expectations and premium does.
No. A negative estimate means investors accepted less yield than the expected policy path alone would justify, which can happen when a long bond is valued for something other than its yield. Regulatory demand, hedging value against equity risk, and large scale central bank purchases all produce this. Sustained negative readings were a normal feature of the years of heavy asset purchases.
Use more than one. ACM is the most widely cited and is updated frequently, which makes it the practical default. Comparing it against at least one alternative guards against treating a single model's assumptions as fact. The premia tool on this site charts the ACM series by maturity.