The Yield Curve, Explained · Lesson 5 of 6
Which end moved: decomposing a month's change in the curve
One concept: decomposing a curve move by end
Why it matters
Kitalpha’s yield curve page sets today’s curve, as of 2026-09-15, beside the curve from 2026-08-14. Over that month the 2-year went from 4.17% to 4.67% and the 10-year from 4.68% to 5.00%. The previous lesson showed that the difference between those moves is a change of slope. This one asks the next question: which end did the work, and what do the labels traders attach to the answer describe?
The concept
Any change in the curve between two tenors can be taken apart into two moves: how much the shorter yield changed and how much the longer yield changed. The change in the slope is the second minus the first. If the two are equal the curve shifted in parallel between those tenors; if they differ the shape changed; and which one is larger says which end of the curve did the work over the period.
Traders name the combinations with four labels, and the labels are descriptions, not verdicts. The first word says which way yields moved, in the vocabulary of bond prices: bull when yields fell, because bond prices rose, and bear when yields rose. The second word says what the gap did: steepening when it widened, flattening when it narrowed. A bull steepening is yields falling with the short end falling by more. A bear steepening is yields rising with the long end rising by more. A bull flattening is yields falling with the long end falling by more. A bear flattening is yields rising with the short end rising by more. Each label is read from two numbers and cannot be read from one; it says which end moved and in which direction, and it says nothing about what comes next.
The reason the ends part company is the same as in the previous lesson. The short end follows the policy rate, so a change in what the central bank is expected to do moves the 2-year more than the 10-year. The long end carries expectations about growth and inflation over years, plus the extra price lenders ask for a long commitment, so news about the longer run moves the 10-year more. A month in which the policy outlook shifted and the long-run outlook did not tends to move the short end; a month with the opposite news tends to move the long end; and a month with both can move the ends in opposite directions.
The curve record holds the comparison at three horizons, a week, a month and a year, and each is the same decomposition over a different period: two moves, one per end, and their difference. A tenor’s own record adds the shortest horizon, one trading day to the next, where the same arithmetic applies to a single day’s change at each end of the curve. The chart below draws today’s curve as a solid line and the curve a month ago as a dashed one. Look at the two ends: the end where the lines are further apart is the end that did the month’s work, and the direction of the gap gives the label’s first word.
- Latest (2026-09-15)
- One month ago (2026-08-14)
| Tenor | Latest (2026-09-15) | One month ago (2026-08-14) |
|---|---|---|
| 1M | 3.93% | 3.79% |
| 1.5M | 4.00% | 3.80% |
| 2M | 4.06% | 3.81% |
| 3M | 4.11% | 3.86% |
| 4M | 4.19% | 3.88% |
| 6M | 4.17% | 3.95% |
| 1Y | 4.39% | 3.98% |
| 2Y | 4.67% | 4.17% |
| 3Y | 4.76% | 4.24% |
| 5Y | 4.83% | 4.36% |
| 7Y | 4.91% | 4.51% |
| 10Y | 5.00% | 4.68% |
| 20Y | 5.40% | 5.25% |
| 30Y | 5.36% | 5.25% |
Worked example
Take the curve record with its two dates, 2026-09-15 and 2026-08-14. The steps below read the 2-year’s and the 10-year’s changes over the month in basis points, take the difference as the change in slope, find which move was larger, and read today’s 2s10s spread. Every figure comes from the curve record’s two dated curves.
Record: U.S. Treasury par yield curve · as of · Source: U.S. Department of the Treasury
- 2-year yield: change over the last month, in basis points, from the curve record 50 bp Today's curve against the curve on the record's one-month comparison date.
- 10-year yield: change over the last month, in basis points 32 bp
- Long end's move minus short end's move: the change in the 2s10s slope, in basis points -18 bp Positive: steepening; negative: flattening; zero: a parallel shift between these tenors.
- The larger of the two moves, in basis points, ignoring sign 50 bp The end with the larger move is the end that did the work; its sign gives the label's first word.
- 2s10s spread today, in basis points 33 bp
What to read off the steps. The third line is the shape change: positive is steepening, negative is flattening. The fourth line says which end did the work, and the sign of that end’s move gives the label’s first word, bull for a fall and bear for a rise. Put together, the first four lines produce one of the four labels for this month’s move. The last line is where the slope stands now. None of the lines says why the ends moved as they did, and the label they produce describes a completed move and predicts nothing.
Faded example
Now the far end of the curve on its own record: the 30-year par yield as of 2026-09-15. Today’s yield and the previous trading day’s are given. Complete the last step: the one-day change in basis points.
Second record: 30-Year Treasury Par Yield · as of
- 30-year par yield today, from its own record5.36%
- 30-year par yield on the previous trading day5.34%
- bp Tolerance ±1 bp
Reveal the answer and the explanation
2 bp — Subtract the previous day's yield from today's and multiply by 100. The 30-year is the curve's far end; its move on a day, set beside the 2-year's, is the same decomposition the worked example made over a month, at the shortest horizon the record offers.
Stored on this device only; not graded.
Retrieval check
Mark your confidence before each answer. Every option carries an explanation; read the ones you rejected too.
-
1. Over the month, the curve record shows the 2-year yield moving by a different amount from the 10-year. A headline that reports only the 10-year's move has left out:
Choose your confidence first. -
2. Using the curve record, compute the 2-year yield's change over the last month in basis points. Enter a whole number, negative if it fell.
Source record: U.S. Treasury par yield curve (as of 2026-09-15)
Tolerance ±1 bpChoose your confidence first. -
3. Using the curve record, subtract the 2-year yield's change over the month from the 10-year yield's change over the month. Enter the difference in basis points, negative if the curve flattened.
Source record: U.S. Treasury par yield curve (as of 2026-09-15)
Tolerance ±1 bpChoose your confidence first. -
4. Suppose over a month the 2-year yield fell by 30 basis points and the 10-year yield fell by 10 basis points. Using the descriptive labels traders use, the move is:
Choose your confidence first.