The Yield Curve, Explained · Lesson 3 of 6
Inversion, described
One concept: inversion as a described shape
Why it matters
The 2s10s spread record on Kitalpha reaches back to 2002-01-02, and across that history it counts the trading days on which the 2-year yield exceeded the 10-year: 782 of them, in 17 separate episodes, the last of which ended on 2024-09-05. That shape has a name, inversion, and a reputation as an omen. A reader who meets the word tends to hear a forecast. What the record actually holds, a count of days on which two yields stood in an unusual order, is what this lesson reads.
The concept
A yield curve usually slopes upward: the longer the loan, the higher the yield, because lending for longer carries more uncertainty and the lender charges for it. When a shorter tenor yields more than a longer one, the curve between those two tenors is inverted. On a spread record, which is the longer yield minus the shorter, inversion shows as a value below zero. It is a shape, computed from two published yields on a date, and the record’s history is a day-by-day account of when the shape held.
That history can be read in three ways, and each is a fact about the record. The inverted-day count says how many trading days the spread spent below zero. The episode count says how many separate runs of such days there were, so that one long inversion counts once as an episode and many times as days. The minimum says how deep the spread went. Dividing the day count by the total days in the history gives the share of the record’s past spent inverted, a frequency that describes the past and only the past. Together these say that inversion is a recurring shape with a known history, neither unprecedented nor constant.
Why the shape occurs is a matter of explanation rather than record, and the explanations are the subject of later lessons in this course: short yields follow the policy rate closely, long yields carry expectations about growth and inflation over years, and when the first is high and the second is low the curve inverts. Those are hypotheses about causes, held with varying confidence; the record does not contain them.
Two readings go beyond the record, and they are the ones to refuse. The first is that an inversion means a recession is happening: a recession is a fall in output measured on other records, and a spread is two prices, which say nothing about output on the day. The second is that inversion causes recession. Whether past inversions were followed by recessions is a question answered by putting the spread’s history beside an output record, and even a regular sequence is not a cause; a spread reflects expectations and policy, and so does the economy that follows, which is a different relation from one producing the other. The record can describe a shape and count its occurrences. It cannot say what the shape will be followed by, and it cannot say why.
The chart below draws six years of the 2s10s with a rule at zero. Count the stretches below the rule as episodes, read their length as days, and read nothing from them about what came next.
The table lists about every 63th observation; the chart plots all 1500.
| Date | 2s10s Spread (10-Year minus 2-Year) |
|---|---|
| 2020-09-15 | 0.54% |
| 2020-12-16 | 0.79% |
| 2021-03-19 | 1.58% |
| 2021-06-17 | 1.29% |
| 2021-09-16 | 1.11% |
| 2021-12-17 | 0.75% |
| 2022-03-21 | 0.18% |
| 2022-06-21 | 0.10% |
| 2022-09-20 | -0.39% |
| 2022-12-21 | -0.53% |
| 2023-03-24 | -0.38% |
| 2023-06-23 | -0.97% |
| 2023-09-22 | -0.66% |
| 2023-12-22 | -0.41% |
| 2024-03-26 | -0.32% |
| 2024-06-26 | -0.39% |
| 2024-09-25 | 0.26% |
| 2024-12-27 | 0.31% |
| 2025-03-31 | 0.34% |
| 2025-07-01 | 0.48% |
| 2025-09-30 | 0.56% |
| 2026-01-02 | 0.72% |
| 2026-04-03 | 0.51% |
| 2026-07-06 | 0.35% |
| 2026-09-15 | 0.33% |
Worked example
Take the 2s10s record and its history from 2002-01-02. The steps below read the inverted-day count and the total day count, take the share of the history spent inverted, read the episode count and the lowest value the spread reached, then read today’s spread in basis points with its sign. Every figure comes from the spread record, itself computed from the Treasury’s daily par yields.
Record: 2s10s Spread (10-Year minus 2-Year) · as of · Computed by Kitalpha from U.S. Department of the Treasury par yields
- Trading days the 2s10s spread was below zero, across the record's history 782
- Trading days in the record's history 6,180
- Share of the history spent inverted, in percent 12.7% A frequency across the record's own past, not a probability for any future day.
- Separate inversion episodes: runs of consecutive days below zero 17
- The lowest value the spread has recorded, in percentage points -1.08 pp
- Today's spread, in basis points 33 bp Read the sign: below zero is the inverted shape, at or above zero is not.
What to read off the steps. The third line is a frequency across the record’s own past: it says how common the shape has been, and it is not a probability that tomorrow will show it. The fourth and fifth lines are the shape’s texture, how many times it occurred and how deep it went. The last line is where the curve stands today, and its sign is the only thing about today that the record can report. None of the six lines says what any inversion was followed by, and none says why.
Faded example
Now the second computed spread: the 3m10y record, the 10-year minus the 3-month, whose history counts its own inverted days and episodes. Its day counts are given. Complete the last step: the share of its history spent inverted.
Second record: 3m10y Spread (10-Year minus 3-Month) · as of
- Trading days the 3m10y spread was below zero, across its history981
- Trading days in its history6,177
- % Tolerance ±0.1 %
Reveal the answer and the explanation
15.9% — Divide the inverted-day count by the total days and multiply by 100. The 3m10y and the 2s10s invert on different days, because the 3-month tenor tracks the policy rate more closely than the 2-year does; both shares are frequencies across each record's own past.
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. The 2s10s record shows a stretch of days below zero. Factually, those days record:
Choose your confidence first. -
2. Using the 2s10s record, divide the days spent below zero by the total days in the history and multiply by 100. Enter the share in percent to one decimal.
Source record: 2s10s Spread (10-Year minus 2-Year) (as of 2026-09-15)
Tolerance ±0.1 %Choose your confidence first. -
3. The record counts inversion episodes separately from inverted days. An episode is:
Choose your confidence first. -
4. Past inversions of the 2s10s spread have sometimes been followed by recessions. From the spread record alone, the claim that inversion causes recession is:
Choose your confidence first.