Term Premium, Issuance and the Balance Sheet

Decomposing the long yield

The ten-year yield is the average of the expected overnight rate over the ten years plus a term premium. That is not an approximation of convenience, it is the definition that comes out of the no-arbitrage argument: an investor can hold a rolling series of overnight deposits or one ten-year bond, and for both to be held the ten-year has to offer the same expected return plus whatever compensation the investor requires for not being able to change their mind. The expected-path component is therefore a forecast — the market’s average view of policy — and the premium is a price for bearing the risk that the forecast is wrong over a horizon long enough that the investor cannot do much about it. The practical consequence is that an announcement can move the long yield in either direction. The path reprices almost instantly in short-dated futures, because a change in the expected path is a statement about policy that can be priced; the premium moves more slowly and for different reasons — how credible the committee now looks, how uncertain the inflation outlook has become, and how much paper the market has to absorb. A hike that is read as a firm commitment to the target can therefore lower the long yield, because it reduces inflation uncertainty by more than it raises the expected path, and that is the most common source of the “hawkish decision, lower long rates” puzzle. The estimation is worth one honest sentence, because it is easy to over-trust. With one price and two unknowns, the decomposition is only identified by imposing a model, and every published estimate is a model output rather than an observation. That does not make the framework useless — it makes it a lens. The claims that survive are the qualitative ones: a yield close to the average expected policy path implies almost no premium and therefore no compensation for duration, which is what the early twenty-twenties looked like; a yield far above a plausible path implies either a much higher expected path or a substantial premium, and those two hypotheses can be distinguished by looking at the front of the curve, where expectations dominate. The ten-year, split in two — 10-year yield: 4.20% · Average expected short rate over ten years: 3.55% · Term premium: 0.65pp — about 15% of the whole yield ← · Same expected path, premium at 1.60pp: a 10-year at 5.15% · A 50bp rise in the expected path: 4.70%, if the premium is unchanged Every published term-premium estimate is a model output. It is defensible to say the premium is low or high relative to its own history, and it is not defensible to act on a single decimal place — the models disagree with each other by more than most trading decisions can tolerate.

Who holds the duration, and what happens when they stop

A term premium exists because someone has to hold the bond to maturity, and the willingness to do that is a balance-sheet question. Four holders matter. Pension funds and insurers buy long duration to match long liabilities and are comparatively insensitive to price, which makes them a stabilising buyer — until their funding improves and their need to buy falls. Foreign reserve managers buy for policy rather than return and can step away for reasons unrelated to price. Banks and dealers warehose duration using financing, so their capacity moves with the cost of leverage and with regulation that penalises balance-sheet size. And households and mutual funds buy for yield, which makes them the most price-sensitive and therefore the marginal buyer when the others step back. Issuance is the other side. A government that finances itself at the long end puts duration into the market and requires one of those four groups to hold it; one that finances at the short end does not. That is why the composition of the deficit matters as much as its size (MR9 for the arithmetic): a deficit funded with bills is a money-market problem, while the same deficit funded with ten- and thirty-year bonds is a duration problem, and it shows up in the premium rather than in the expected path. When the supply of duration rises while the balance-sheet capacity of the buyers is flat or falling, the price has to fall for the market to clear, which is a rise in yield that has nothing to do with the growth or inflation outlook. Central-bank balance sheets are the third mover, and they work by changing who holds the duration rather than by changing the expected path. When a central bank buys long-dated bonds, it takes duration off private balance sheets and replaces it with a reserve balance, which is the shortest liability in the system. If the buyers were charging a premium for holding that duration, and the supply disappears into the central bank, the premium compresses — and the effect is largest when the buyers were most constrained. Runoff is the mirror image: as the balance sheet shrinks, the private sector has to absorb the duration it had sold, so the same expected path can support a higher long yield than it did before. That is the mechanism by which “the same economy” can carry two different ten-year rates, and it is the reason the size and composition of a balance sheet is a policy instrument rather than a footnote. • A term premium is what the marginal holder charges to hold duration to maturity. • Four buyer groups: pension and insurance, foreign reserves, banks and dealers, price-sensitive funds. • Long-end issuance adds duration; bill issuance does not — composition matters as much as size. • Large-scale purchases replace duration with reserves and compress the premium; runoff does the reverse. • The expected path prices growth and inflation; the premium prices supply, uncertainty and buyer capacity. The decomposition explains an apparent contradiction that recurs every cycle: a central bank can be tightening the policy rate while buying or holding long bonds, because the two instruments act on different terms of the same yield. Judging the stance from the policy rate alone misses whichever half of the yield the balance sheet is setting.

Estimating something you cannot observe

The decomposition in this lesson is conceptually clean and computationally awkward, because splitting a long yield into expected short rates and a term premium requires knowing the expected short rates — which are not observable either. Both halves are estimates, and the published numbers come with a precision they have not earned. The standard estimates come from the affine term-structure family of models, which use the joint behaviour of yields across maturities to back out the two components. They are fitted to data, so they move when the data is revised, and — more importantly — they disagree with each other. The disagreement is not a rounding error; it can be a large fraction of the estimated premium itself, which is why a single model’s output printed to two decimal places is a presentation choice rather than a measurement. There are simpler alternatives, and each trades something away. A **survey-based** measure subtracts what professional forecasters expect for short rates from the current long yield: transparent, and dependent on forecasters being right, which they are not reliably. A **forward-rate decomposition** takes the gap between successive forward yields as a proxy: model-free and contaminated by expected-path effects, because a rising expected rate path looks the same as a premium. And a rough **average-expected-rate** approach compares the current yield with the average short rate expected over the horizon: crude and honest about being crude. The historical pattern is worth knowing even with the uncertainty attached. The estimated premium declined through most of the 2010s to near or below zero, then rose as central banks reduced their bond holdings and the supply of duration shifted back toward private balance sheets. The direction of that movement matters more than the level: a premium rising means the compensation for holding long bonds has increased, which raises the discount rate applied to anything with distant cash flows — the same statement as the equity-duration read, arriving from the government bond market instead of the equity market. The usable conclusion is a procedural one. Quote a range across at least two methods, use it to answer a directional question — is the term premium adding to or subtracting from the long yield — and resist using it to fine-tune a duration position. And remember what the range itself is telling you: when the uncertainty around an input exceeds the size of the decision it is meant to inform, the decision should be made on the risk appetite rather than on the estimate. • Both components of the long yield are estimates, so the split carries a range. • Model estimates disagree with each other by a material fraction of the premium. • Survey, forward-rate and averaging approaches each trade precision for transparency. • Use the direction of the premium rather than its level to inform a duration decision. A useful habit for reading commentary that cites the term premium: ask which model, and what the range across models is. Where the answer is a single number from a single model, the sentence is describing a model output as though it were a market observation.

Sources

• Affine term-structure models and the estimated term premiumAdrian, Crump & Moench (ACM) term-premium series, Federal Reserve Bank of New York; Kim & Wright (2005)
• Balance-sheet policy and duration extractionStandard portfolio-balance and preferred-habitat literature on large-scale asset purchases
• The supply of duration, issuance and the premiumTreasury issuance data and the literature on duration supply and long yields
• Balance-sheet runoff: the mechanics and the capsFederal Reserve statements on the balance sheet and principles for reducing the size of the balance sheet