Duration Is Not Priced by the Year: What This Curve Pays for Each One

On 25 August 2026 the Treasury curve sloped upward at every point measured, from four weeks out to thirty years. The usual reading of that shape is that term premium has returned and longer maturities are being paid for again.

That reading is not wrong, but it stops one division short. The curve says how much extra yield each maturity carries. It does not say how much extra yield each year of maturity carries, and those two questions have very different answers on this curve. Dividing one into the other takes a minute and changes what the shape appears to be offering.

The Curve, in Order

From the Federal Reserve's H.15 release for that business day:

• 4-week bill 3.64%, 3-month 3.71%, 6-month 3.79%, 1-year 3.84%
• 2-year note 4.17%
• 10-year note 4.64%
• 30-year bond 5.17%

Two features of that list are worth naming before any arithmetic touches it. The gaps between the points are not even — four weeks to three months is about nine weeks, while ten years to thirty is two decades — and no chart of seven evenly spaced labels can show that. Any plot of these points at equal intervals, including the one below, compresses the right-hand side enormously. That compression is the visual reason the far end of a curve tends to look steeper than it is being paid for.

Bills are quoted on a secondary-market discount basis and the notes and bonds are constant maturity, so the two halves of that list are not strictly the same measurement. The comparisons below stay inside the constant-maturity series wherever the distinction would matter.

Read left to right, the notable steps are similar in size. Two years to ten years adds 0.47 percentage points. Ten years to thirty adds 0.53. On the bill side, three months to two years adds 0.46 — a figure kept separate below, because it crosses the quote basis.

The Same Gain, Divided by Time

Inside the constant-maturity series — the three points that are measured the same way — the two stretches cost very different amounts of time.

• Two years to ten is 8 years of extension for 0.47 points — 0.059 points per year
• Ten years to thirty is 20 years for 0.53 points — 0.027 points per year

Nearly the same yield gain, and the second one costs 2.5 times the time. Per year of maturity accepted, the middle eight years pay about 2.2 times as much as the last twenty. Neither the H.15 release nor the curve itself states this; it is the only arithmetic in this article, and it is division.

Taken as one move, two years out to thirty is 1.00 point over 28 years, or 0.036 points per year. That single figure conceals the fact that the first eight of those years are paid at about 2.2 times the rate of the last twenty.

Inside the Front End, the Rate Is Not Even Either

The same division applied between the four short points shows that the front stretch is not one uniform thing.

• 4 weeks to 3 months — +0.07 points over about 0.17 years — 0.40 points per year
• 3 months to 6 months — +0.08 over 0.25 years — 0.32 per year
• 6 months to 1 year — +0.05 over 0.5 years — 0.10 per year
• 1 year to 2 years — +0.33 over 1 year — 0.33 per year

The sequence is 0.40, 0.32, 0.10, 0.33. It falls, drops sharply, and then rises again. The flattest stretch on the front of this curve, per year of extension, is the half-year between six months and one year, and the step after it is paid at more than three times that rate.

Nothing about the curve's overall upward slope suggests that. Read as a line, the front looks like a gentle and steady climb from 3.64 to 3.84. Read per year, it contains the cheapest stretch on the near end and one of the more expensive ones immediately after.

Two cautions attach to these four figures, and they are the reason this section is kept apart from the one above. The first is the basis. The four short points are bills, quoted on a secondary-market discount basis, while the two-year is constant maturity. A discount-basis quote and a coupon-equivalent yield are not the same number for the same security, so the last step in that list — and any figure built from it — is not directly comparable to the constant-maturity stretches. The direction of that difference is known but its size is not established here. The headline comparison in this article is therefore made only within the constant-maturity series. Where a figure inside this section is built from the bill quotes — including the step from one year to two — this caution applies to it and it should not be set against the constant-maturity figures.

The second caution is magnitude. Differences of 0.05 and 0.07 points are small in absolute terms. This ordering describes one day's curve, and the figures should be recomputed rather than remembered.

Nearly the Same Gain, Very Different Commitments

Two rows describe the two constant-maturity stretches. One barely changes and the other changes by a factor of two and a half.

• Yield gained: 0.47 and 0.53 — six hundredths of a point apart
• Years committed: 8 and 20 — the second asks for two and a half times the time of the first

The bill stretch alongside them gains 0.46 points for 1.75 years, but it is quoted on a different basis and is placed here for reference rather than comparison.

A shape described only by the first row looks like a curve that rewards patience evenly. A shape described by both rows looks like something else: purchases at different prices, quoted in the same units.

This is not an argument that the long end is mispriced. Term premium, inflation expectations and the supply of long paper all sit inside that 0.53 points, and none of them are visible in a division. It is an argument that the yield number alone is not the price, because the yield number does not carry the denominator.

How the Figure Moves

Because it is a ratio, the per-year number responds to changes in the numerator and denominator differently, and that is worth knowing before reading it on another day.

The denominator never changes. The distance from two years to ten years is eight years regardless of what yields do. Every movement in the per-year figure comes from the numerator alone, which means the figure moves exactly in proportion to the yield gain across that stretch.

The consequence is that the same absolute move in yields registers very differently at different parts of the curve. A gain of 0.10 points added to the two-to-ten stretch raises its per-year figure by 0.0125. Shorter stretches divide by smaller numbers, so the same gain moves them further.

How stable any of this is over time is not a question a single day's release can answer. Everything above describes the curve of 25 August 2026. Whether the 2.2-times relationship between the middle and the long end persists, widens or inverts is a matter for a series of these observations, not for one of them, and no claim about its persistence is made here.

What the Division Does Not Settle

Two things follow, and a third does not.

What follows is a way of stating a position. A holding described as "picking up half a point by going out to thirty years" and one described as "picking up 0.027 points per year of maturity accepted" are the same holding. The second phrasing makes the denominator visible, and any comparison across maturities that does not carry the denominator is comparing different things.

What also follows is where small changes matter most, and this part depends only on the denominators. A given move in yields divided by 8 years registers 2.5 times larger than the same move divided by 20. Shorter stretches are where the per-year figure is most sensitive to a shift, for the arithmetic reason that they are dividing by a smaller number. No comparison of quote bases is involved in that statement.

It is also worth restating both stretches in the units the market usually quotes. Ten years to thirty pays 2.65 basis points for each additional year of maturity accepted, and twenty of those are the 53 basis points separating the two yields. Two years to ten pays 5.88 basis points a year, and eight of those are its 47.

That is the finding in one comparison: 5.88 against 2.65, in the same market, on the same day, on the same quote basis, in the same units.

What does not follow is which maturity to hold. Yield per year of extension says nothing about price sensitivity to a change in yields, which runs in the opposite direction and is larger at long maturities, and nothing about whether a position will be held to maturity at all. A figure that ignores both cannot decide anything on its own. It is one input, and it is one that most descriptions of a curve leave out.

What Would Invalidate This

The arithmetic above holds for one curve on one day. Several things would break it.

• A flatter middle. The 2.2-times relationship rests on the 0.47 points between two and ten years. If ten-year yields fell toward the two-year level, the middle stretch would pay less per year and the relationship would narrow or reverse without the long end moving at all.
• An inverted or humped curve. Every figure here assumes each stretch has a positive gain. On an inverted curve the division produces negative numbers per year, and the framing above stops describing anything useful.
• Any attempt to rank the bill stretch against the note stretches. The two are quoted on different bases, which is why the headline comparison here is kept inside the constant-maturity series. A ratio built across that boundary would not mean what it appears to mean, and the figures in the front-end section carry that caution with them.
• Any use as a return estimate. Yield per year of extension is a description of a curve's shape at one moment. It is not a projection of what a position would earn, and treating it as one imports assumptions this arithmetic does not make.

Concrete Framework

A four-step version of what this article did, applicable to any curve on any day.

1. Take the yields as published, with the basis noted. Record which points are bills and which are constant maturity, and do not mix them silently.
2. Compute the gain for each stretch you actually care about. Adjacent points only. Differences between non-adjacent points hide what happened in between.
3. Divide each gain by the years of extension it costs. This is the step that is almost never taken and the one that produces a comparable number.
4. Write both rows down, not one. Yield gained and years committed. A description that carries only the first row is not describing a price.

The fourth step is the one that survives contact with a different curve. Yields change daily and any specific figure here is stale within a session, but the habit of carrying the denominator does not go stale. A curve read only as a set of levels will always look like it is offering the same thing at every maturity, because levels are quoted in the same units regardless of what they cost in time.

Repeating this on a different day answers a question the level cannot: not whether the curve is steeper, but whether the steepness is being paid at a different rate per year than it was.

This article describes published interest rate data and arithmetic on it. It is not investment advice, does not recommend any security or maturity, and makes no projection of returns. Figures are from the Federal Reserve H.15 release for the business day 25 August 2026 and change daily.