Correlation is not causation: two yields that move together

Why it matters

Kitalpha’s Treasury pages hold a yield for every tenor, the length of a loan to the U.S. government. On 2026-09-15 the 2-year yield was 4.67% and the 10-year yield was 5.00%. Plot each day’s change in one against the same day’s change in the other, for the last 250 trading days, and the points form a cloud. If that cloud leans along a rising diagonal, the two moved the same way on most days, and it is tempting to conclude that one of them moves the other. This lesson is about why that conclusion does not follow from the picture, and what the picture does establish.

The concept

Start with what is plotted. A daily change is today’s yield minus yesterday’s, in percentage points: a yield that moves from 4.00% to 4.05% has changed by 0.05 percentage points. A scatter plot places one point per trading day. Its horizontal position is that day’s change in the first series and its vertical position the same day’s change in the second. The shape of those points is the whole of the evidence.

Correlation is the name for co-movement: the tendency of two series to change in the same direction on the same day (positive correlation), in opposite directions (negative), or with no consistent relation (near zero). The correlation coefficient, written r, puts a number on it. It runs from −1 to +1. At +1 every point sits on one rising straight line; at −1 on one falling line; at 0 the cloud has no lean at all. Between those limits, r measures how tightly the points hug a straight line, and its sign gives the line’s direction. It is built from the two series’ daily changes, each scaled by its own standard deviation (the typical distance of a day’s change from the series’ mean), so r carries no units and is the same in percentage points or in basis points.

Two things r does not measure deserve saying plainly. It does not measure steepness: a series that moves twice as far as another on every day is perfectly correlated with it, r = +1, though the line is steep. And it does not measure cause.

Causation is a claim about mechanism: A causes B when a change in A, with everything else held still, produces a change in B. A scatter plot holds none of the ingredients of that claim. It records no order of events, because both changes are closing figures for the same day. It records nothing about what else moved. So the same leaning cloud fits at least four accounts equally well: the first series moved the second; the second moved the first; a third factor moved both; or the two simply happened to line up in this window. The plot cannot choose between them, and neither can r.

For the two records in this lesson the third account is the natural one. The 2-year and 10-year yields are both prices of lending to the U.S. government, for different lengths of time, set by trading on the same days. When the Federal Open Market Committee announces a decision on the federal funds rate, or an inflation report or a jobs report is released, that one piece of news reaches both at once. Each yield responds to the news, not to the other yield. The co-movement is real; the link between the two is a shared cause standing outside both series.

One further caution: r is a property of the window it was computed from; a different window gives a different figure, and each describes only its own days.

The scatter below plots the last 250 daily changes of the 2-year yield against the 10-year’s. Look for three things: which way the cloud leans, the coefficient printed in the note beneath it, and the points in the two off-diagonal quadrants: days on which the two moved in opposite directions, which a leaning cloud still contains.

Worked example

The 2-year yield record carries the distribution of that tenor’s daily changes over its last 250 trading days, from 2025-09-15 to 2026-09-15: the same days the scatter plots on its horizontal axis. Two of its figures set the scale of that axis. The mean daily change is the centre of the cloud from left to right; the standard deviation is its typical half-width. The record states both in percentage points. The steps convert each to basis points, where one basis point is one hundredth of a percentage point, and then mark the band one standard deviation either side of the mean.

Read the steps against the chart. The mean says where the cloud is centred horizontally; a figure near zero means that on an ordinary day the yield ended close to where it began. The band from the fifth step to the sixth is the horizontal stretch that holds a typical day’s move; points well outside it are the large-move days, and when those days coincide with large moves in the 10-year they are the points that give the cloud its lean. Nothing in these six numbers concerns the 10-year at all, which is the point: each axis has its own scale, set by its own series, and the coefficient in the note is what remains once both scales are divided out.

Faded example

Now the 10-year yield record, the series on the scatter’s vertical axis, over the same window. Its mean and its standard deviation in percentage points are given below, with the mean already converted. Complete the last step: the 10-year’s standard deviation in basis points, which sets the vertical scale of the cloud.

Retrieval check

Mark your confidence before each answer, then read the feedback on every option, including the ones you rejected: the errors they name are the ones this lesson exists to prevent.

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