Term Premium Estimation With the ACM Model

A 10-year Treasury yield is a single observed number, but it's really the sum of two things an investor can't directly see separately: the average short-term rate the market expects over the next decade, and an extra sliver of compensation for the risk of holding a long bond instead of just rolling over short-term ones. Pulling those two pieces apart from one observed number is impossible without a model — and the ACM model, named for its authors Adrian, Crump, and Moench, is one of the most widely used tools for doing exactly that, published regularly by the Federal Reserve Bank of New York.

The basic decomposition

Every yield the model produces is split the same way:

$$y_n = \underbrace{\frac{1}{n}E\left[\sum_{t=0}^{n-1} r_t\right]}_{\text{expectations component}} + \underbrace{TP_n}_{\text{term premium}}$$

In words: the observed $n$-year yield equals the average short rate the model believes the market expects over that horizon, plus whatever extra yield is left over once that expectation is accounted for — that leftover is the term premium.

The ACM approach estimates this using a linear regression-based affine term structure model: it summarizes the yield curve's movements with a handful of statistical factors (roughly, level, slope, and curvature-like combinations of yields), estimates how those factors evolve over time and how they're priced (their "market price of risk"), and uses those estimated dynamics to compute, at each point in history, what portion of each yield reflects pure rate expectations versus compensation for risk.

Worked example

Suppose the ACM model estimates that the 10-year Treasury yield of 4.30% splits into an expectations component of 3.60% and a term premium of 0.70%.

1. Interpretation of the expectations component: the market is, on average, expecting short-term rates to run around 3.60% over the coming decade.
2. Interpretation of the term premium: investors require an extra 0.70 percentage points of yield, on top of pure rate expectations, to compensate for the risk of holding a 10-year bond rather than continuously rolling over short-term instruments.
3. A shift to watch: if the observed yield rises to 4.60% while the model's expectations component stays at 3.60%, the entire increase is attributed to a rising term premium (now 1.00%) — a signal that investors are demanding more compensation for duration risk, not that the market suddenly expects higher future short rates.

What this means in practice

Central banks and macro researchers watch the ACM term premium closely because it helps distinguish two very different stories behind a rising long yield: "the market expects tighter policy" versus "investors are demanding more compensation to hold duration," which call for very different policy or portfolio responses. A negative estimated term premium — which has occurred historically — implies investors were, on the model's terms, accepting less than the pure expectations component would justify, often attributed to strong safe-haven demand or regulatory-driven buying of long bonds.