The curve is measured, the split is a choice

The ten-year Treasury yield is part expectation and part compensation. Some of it is the average short rate markets expect over the next decade. The rest is the term premium, the extra yield demanded for holding a long bond instead of rolling bills. The New York Fed publishes that split monthly, back to 1961, from the Adrian-Crump-Moench model, and commentary quotes the result to the basis point.

Rebuilding the model from the yield curve up gives two numbers that sit very badly together. The fitted curve comes back to within half a basis point. The premium drawn out of that same curve comes back to fourteen.

median error on the published fitted yields

0.45 bp

median error on the published fitted yields

median error on the risk-neutral yield, and so on the premium

14 bp

median error on the risk-neutral yield, and so on the premium

correlation with the Fed's published ten-year premium

0.9997

correlation with the Fed's published ten-year premium

movement in the premium from the start date alone

81 bp

movement in the premium from the start date alone

Verify before interpreting

Nothing the model says about the term premium means anything if it cannot reproduce the yields the premium is extracted from, so that is the first thing to check. It reproduces them. Across every maturity from one to ten years and every month from 1961, the fitted yields match the published series to a median of 0.45 basis points, a 99th percentile of 2.8, and a worst case of 9.

That is the part of an affine term structure model which is identified. The cross-section of the curve is over-determined, and a sound estimator nails it.

Where the certainty runs out

With prices of risk in hand the model runs two bond-pricing recursions. One compensates investors for risk and gives the yield. The other sets the prices of risk to zero and gives the risk-neutral yield, which is what the curve would be if duration carried no premium at all. The term premium is the gap between them.

The risk-neutral yield reconstructs to a median of 14 basis points against the published series. That is roughly thirty times looser than the fitted yield it is subtracted from, and the premium, being the complement, inherits exactly that error. The ten-year premium still tracks the Fed’s at a correlation of 0.9997, so the shape and the timing are right. It is the level that floats.

The level is a choice, not a measurement

The clearest way to see how soft the level is: hold the model and the data fixed, change only where the estimation sample begins, and watch.

So the level of the term premium is not a number the data hands you. It is a number a modelling decision hands you, and different defensible decisions hand you numbers that disagree by most of a percentage point. Reproducing the Fed’s exact level would mean matching a set of estimation choices to the basis point. It would not mean the level was any better identified.

Why it matters

A single figure, quoted to the basis point in commentary and used to argue about whether long rates are too high or too low, turns out to be identified only to within tens of basis points, even when the curve it comes from is fit almost perfectly.

The uncertainty is not sampling noise that more data would shrink. It is specification dependence, and it is largest at exactly the long maturities the number is quoted for. That is the same lesson as the CPI reconstruction in a different market: a headline everyone treats as measured turns out to depend on a choice, and the choice is where the story is.