Percentiles and base rates: where today's value sits in its own history

Why it matters

A headline calls the gap between two Treasury yields “the widest in years” or “unheard of”. Kitalpha’s 2s10s spread record holds that gap: the 10-year yield minus the 2-year yield, today 0.33 pp (33 bp) as of 2026-09-15, with a daily history that starts on 2002-01-02. Is today’s level rare, or ordinary? The figure on its own cannot say. This lesson takes one idea, the percentile, and uses it to place a value inside its own history, so that “unprecedented” becomes a claim you can check against the record rather than a feeling.

The concept

A percentile is a position in a sorted list. Take every daily level a series has recorded, sort them from lowest to highest, and ask what share of them sits below today’s level. That share, written as a number from 0 to 100, is today’s percentile. A percentile of 50 says half the recorded days sat below today’s level; a percentile of 90 says nine days in ten sat below it and one in ten above. When some days sat exactly at today’s level, each such tie is counted as half a day, so a level that matches many past days is pushed to neither end of the scale.

Two things about that definition matter most. First, a percentile is a rank, not a size. It counts days, and it says nothing about how many basis points separate today’s level from any other. Two spreads can have the same percentile while one sits far from its median in basis points and the other close to it, because what decides the percentile is how many days fell on each side, not how far away they were. Second, a percentile is a percentage of days, not a percentage of a value. The all-history figure in this lesson is never “today’s spread as a fraction of its record high”; it is “the share of recorded days that sat below today’s spread”. Keeping those two apart is the single most common slip when reading one.

A base rate is the plain-language cousin of the same idea: how often something has occurred in the record. Asking for the base rate of a level like today’s is asking what share of the history sat above or below it, which is exactly what the percentile answers. A level near the 50th percentile, the median, is as common as a level gets; a level at the 99th has been matched or exceeded on about one recorded day in a hundred; only a percentile at the very top or bottom of the scale means no recorded day sat on the far side of it. “Unprecedented” is therefore a claim about the percentile, and it is a demanding one.

The window is part of the claim. The same level can be ranked against every recorded day or against only the most recent five years, and the two percentiles need not agree, because the levels that were common recently may differ from the levels that were common over decades. Neither window is the right one; each answers a different question, and an honest reading names which set of days it counted. Kitalpha’s spread pages carry the full daily history as a chart and a table; the percentiles in this lesson are worked out from that history at the moment the page is built, and the day count and start date are printed beside them so the window is never hidden.

The histogram below sorts the 2s10s spread’s last 1,500 trading days of levels into bins a quarter of a percentage point wide, covering 2020-09-15 to 2026-09-15. Look for the median line: half of those days sit in the bars to its left. A level’s percentile is how far along the bars it sits, counted from the left edge, and a level with tall bars on both sides of it has plenty of company.

Worked example

Take the 2s10s spread record as of 2026-09-15. Its history runs from 2002-01-02 and holds 6,180 trading days; the lowest level recorded is -1.08 pp, the highest 2.91 pp, and the median 1.05 pp. The steps read today’s level, rank it against the whole history and against the last five years, and turn the rank back into a count of days.

Read the steps in order. The percentile in step three is a share of the day count in step two, so multiplying the two and dividing by 100 gives about how many recorded days sat below today’s level, and 100 minus the percentile gives the share that sat above it. Those two figures answer “has this been seen before”: a level with recorded days on both sides of it has. The five-year percentile ranks the same level against a shorter window and can differ from the all-history figure; the difference is information about the window, not an error. The last step measures distance from the median in basis points, a separate figure the percentile does not contain.

Faded example

Now the second record: the 3m10y spread, the 10-year yield minus the 3-month yield, as of 2026-09-15, with a history of its own that starts on 2002-01-02. Today’s level, the day count and the all-history percentile are given below. Complete the last step: turn the percentile into a count of days.

Retrieval check

Mark your confidence before each answer. Every option carries an explanation; read the ones you rejected too.

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