The Yield Curve, Explained · Lesson 6 of 6
A spread against its own history: percentile as position, not prediction
One concept: percentile as position in a record's history
Why it matters
The 2s10s spread record on Kitalpha does not stop at today’s value. As of 2026-09-15 it places that value at the 27.5% percentile of its history since 2002-01-02, and at the 59.5% percentile of the last five years. A reader who has only seen the value hears either that it is unprecedented or that, being high, it must be about to fall. A percentile says neither, and reading what it does say is this lesson’s idea.
The concept
A percentile locates one value inside a set of values. Take every trading day in a record’s history, sort the spread’s values from lowest to highest, and ask what share of them lie below today’s. That share is today’s percentile. At the 50th percentile half the past days were lower; at the 90th, nine in ten. The median is the value at the 50th percentile, the middle of the record’s past, and the distance between today’s value and the median is a plain way of saying how far from the middle today sits.
Three things follow from the definition, and each corrects a common reading. First, a percentile is a position among days that have already happened. It is descriptive: the record counts the days below today’s value and reports the share. It contains nothing about tomorrow, because the order of past values does not constrain the next one; a spread at the 95th percentile is not thereby due to fall, and one at the 5th is not due to rise. Turning a position into a probability about the future adds a claim the count does not make.
Second, a high percentile is not unprecedented. Below the 100th percentile some past days were higher, and the record’s maximum names the highest of them; a value inside the range between minimum and maximum has company in the past. Unprecedented means outside the range, which the record would show as a new maximum or minimum.
Third, a percentile depends on the window it is taken over. The same value sits at one percentile of the whole history and at a different one of the last five years, because the two windows hold different distributions of days; a spread that was typical of the last five years can be high against two decades, or the reverse. Neither number is the true percentile. Each answers the question against a stated stretch of the past, and the record states both so that a reader can see how much the choice of window changes the answer; a lesson earlier in this track made the same point about impact tiers, which are also cut on a trailing window.
The distribution behind the percentile can be drawn. Sorting six years of daily levels into bins gives a histogram: tall bars where the spread spent many days, tails where it visited rarely, and the mean and median marked. A percentile is a position along that shape. Look at the histogram below for where the bulk of the days sits, then read today’s percentile as how far along the shape today falls, counted in days to its left.
| Bin from | to | Count |
|---|---|---|
| -1.250 | -1.000 | 5 |
| -1.000 | -0.750 | 79 |
| -0.750 | -0.500 | 119 |
| -0.500 | -0.250 | 256 |
| -0.250 | 0.000 | 82 |
| 0.000 | 0.250 | 134 |
| 0.250 | 0.500 | 229 |
| 0.500 | 0.750 | 307 |
| 0.750 | 1.000 | 80 |
| 1.000 | 1.250 | 120 |
| 1.250 | 1.500 | 69 |
| 1.500 | 1.750 | 20 |
Worked example
Take the 2s10s record as of 2026-09-15. The steps below read today’s value, its percentile across the whole history and across five years, the historical median, today’s distance from that median in basis points, and the record’s full range. Every figure comes from the spread record, 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
- 2s10s spread today, in percentage points 0.33 pp
- Percentile of today's value across the whole history, in percent 27.5% The share of past trading days on which the spread was lower than today's value.
- Percentile across the last five years 59.5%
- Historical median, in percentage points 1.05 pp
- Today minus the historical median, in basis points -72 bp A distance from the middle of the record's past, not a distance the spread has to travel.
- The record's range, maximum minus minimum, in basis points 399 bp
What to read off the steps. The second and third lines are two positions for one value, and the gap between them shows how much the window matters. The fifth line places today relative to the middle of the past; it is a description, and the sign says only which side of the median today sits on. The last line is the width of the whole record, which is the yardstick against which any single distance is small or large. None of the lines says where the spread goes next, and none says that today’s position is a reason for anything.
Faded example
Now the second spread’s own history: the 3m10y record as of 2026-09-15, at the 36.4% percentile of its past. Its value and its median are given. Complete the last step: today’s distance from that median in basis points.
Second record: 3m10y Spread (10-Year minus 3-Month) · as of
- 3m10y spread today, in percentage points0.89 pp
- Its historical median1.54 pp
- bp Tolerance ±1 bp
Reveal the answer and the explanation
-65 bp — Subtract the median from today's value and multiply by 100. The 3m10y has its own history and its own median; its distance from that median places it within its own past, and says nothing about the 2s10s or about tomorrow.
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 gives today's value a percentile across its whole history. That percentile states:
Choose your confidence first. -
2. Using the 2s10s record, subtract the historical median from today's spread and express the result in basis points. Enter a whole number, negative if today is below the median.
Source record: 2s10s Spread (10-Year minus 2-Year) (as of 2026-09-15)
Tolerance ±1 bpChoose your confidence first. -
3. Using the 2s10s record, subtract the five-year percentile from the all-history percentile. Enter the difference in percentage points to one decimal, negative if the five-year figure is higher.
Source record: 2s10s Spread (10-Year minus 2-Year) (as of 2026-09-15)
Tolerance ±0.1 ppChoose your confidence first. -
4. The 2s10s record shows today's value at a high percentile of its history, and also shows the history's maximum. If today's value is below that maximum:
Choose your confidence first.