Why do long bonds usually pay more — expectations, or compensation?
The curve normally slopes upward. There are two rival explanations for that, they are both partly right, and knowing how they mix is what separates a careful reader of the curve from a headline-repeater.
Explanation one: pure expectations
In the pure expectations view, a 10-year yield is nothing but the average of the one-year rates the market expects over the next ten years. Under that story:
- An upward slope means only "short rates are expected to rise."
- Rolling one-year bills for a decade would have the same expected return as buying the ten-year outright.
- The forward rates from the last-but-one lesson would be genuine forecasts.
Clean, elegant, and not quite how lenders behave.
Explanation two: the term premium
Lenders demand something extra for locking money up. That extra is the term premium, and it compensates for:
- Inflation and policy uncertainty over a long horizon.
- Price risk — precisely the thing you spent Unit 2 learning to measure. A 10-year bond has a duration around 8; a 1-year bill around 1. One of these can lose 8% of its value on a 100bp move; the other cannot.
- Liquidity and the cost of being unable to change your mind cheaply.
The decomposition
Put them together and you get the working equation of the modern curve:
10-year yield ≈ average expected future short rate + term premium
If the 10-year yields 4.0% and the market's expected average short rate over the decade is 3.0%, the term premium is about 1.0%.
The catch that makes this professional-grade
Only the left-hand side is observable. Nobody publishes "the market's expected average short rate" — it has to be estimated, either from surveys of forecasters or from affine term-structure models (the Adrian–Crump–Moench and Kim–Wright estimates are the best-known).
Which means every term-premium figure you will ever read is a model output with error bars. Different models produce different numbers for the same day, sometimes differing by half a percentage point or more. Treat a term-premium estimate the way this Academy treats a DCF output: as a made-visible assumption, never a measured fact.
It can go negative
Nothing forces the premium to be positive. If investors want long duration badly enough — regulation obliging pension funds to hold long bonds against long liabilities, large-scale central-bank purchases, a flight to safety — they may accept less than the expected path of short rates.
That matters for reading an inversion. A downward-sloping curve can come from expected rate cuts, from a compressed or negative term premium, or from both. "The curve inverted, so the market expects cuts" is at best half the story, and the missing half is not observable.
What it means for your duration
Loosely, the term premium is the market's price for bearing duration risk. A high premium means duration is being generously compensated; a low or negative one means it is being given away cheaply. That is an observation about the state of the market — not a strategy, not a signal, and not a forecast. We describe how the number is constructed and how uncertain it is; what anyone does about it is outside what this Academy teaches.
In the data
Two curves are published for the same dates: the nominal Treasury curve, first, and the curve of inflation-linked Treasuries (TIPS), second.
Their difference at a maturity is breakeven inflation, an observable the market prices. The term premium appears in neither table and in no quote anywhere: it is a model output, and different models produce different answers from identical inputs. The real curve also starts at five years, so there is no short-end breakeven to compute at all.
Try it now
In the nominal curve in the section above, take the 3-month and 10-year yields and write down what that gap would imply if the pure expectations view were the whole story. Then subtract the 10-year real yield from the 10-year nominal one for breakeven inflation at ten years.
Open a published term-premium estimate: the Federal Reserve Bank of New York posts the ACM ten-year term premium on its website, and FRED carries the Kim-Wright estimate as series
THREEFYTP10. Note the sign and size of each for the same date. Two models, one unobservable quantity, and two different numbers.State the decomposition in one sentence and name which of its two terms can never be directly observed.