The shape and the macro backdrop that produced it.
Eight points on a line, and three numbers that summarise them: level (how expensive is money), slope (what you are paid to wait), curvature (is the belly rich or cheap against the wings). The curve runs to the last month in which every tenor was actually auctioned — a month where the long bonds did not come to market is left out rather than carried forward.
Pick any two months. The curve overlay shows what the shape did; the macro panel below shows what else moved over the same window — which is usually the more useful half of the picture.
The same macro panel, measured against the curve itself. Choose which property of the curve to correlate against — the level (whether the whole curve sits high or low), the slope (its shape), or the curvature (whether the belly is rich or cheap against the wings). Each row is then repeated across seven time offsets.
| Curve level | The average of the 3M, 1Y, 2Y, 5Y, 10Y and 20Y yields. Whether the whole curve sits high or low, regardless of shape — an upward or downward shift in the general price of money. A positive correlation means the series is high when yields across the board are high; negative means high when yields are low. |
| 3M–10Y slope | 10Y − 3M. The shape of the curve. A positive correlation means the series is high when the curve is steep; negative means high when it is flat or inverted. |
| Curvature | 2 × 5Y − 2Y − 10Y. Whether the belly sits above or below a straight line drawn between the wings. Positive readings mean the 5Y is cheap against the 2Y and 10Y; negative means it is rich. |
These three are close to independent of one another, which is why a series can correlate strongly with one and barely at all with the others. A variable that moves the level but not the slope is telling you about the general price of money; one that moves the slope but not the level is telling you about the distribution of that price across time.
One row for each macro series. One column for each time offset. Every cell holds a single number — a correlation coefficient — measuring how closely that series and the chosen curve property moved together across all the months in the sample.
The same calculation is repeated seven times per row, each time shifting one series against the other by a fixed number of months. That is what turns a single correlation into a row: it lets you see whether the relationship is tightest when the two are measured in the same month, or when one is measured earlier than the other.
A correlation coefficient runs from −1 to +1. The sign is the direction; the size is the strength.
Square the coefficient to get the share of variation the two have in common. A reading of 0.50 means a quarter of the movement lines up; 0.80 means about two thirds.
The column heading is the offset between the two readings being paired. The convention here: a plus sign means the macro series is measured earlier than the curve.
Shifting costs observations. A twelve-month offset drops twelve months from the pairing, so the columns furthest from zero rest on the smallest samples. Panel D reports the exact count for whichever cell you have selected.
Which side moved first is a statement about timing in this dataset, not about cause. Two series can line up at an offset because a third thing drove both.
| Levels | Each series is used exactly as reported, paired against the curve measure as reported. This is the raw reading. |
| Δ 3-month | Both sides are converted to their change over the previous three months before correlating. Instead of asking whether high goes with high, it asks whether rising goes with rising. |
| Full 2009–26 | All — months, subject to when each individual series begins. |
| Post-2022 | Only the months from January 2022 onward — — observations, fewer once an offset is applied. |
| Colour | Green for positive, terracotta for negative. Intensity tracks the size of the coefficient, so a pale cell is a weak relationship whatever its sign. |
| Outline | The largest coefficient in that row, by absolute size — the offset at which that series and the curve measure line up most closely. |
| Em dash | Fewer than 24 paired observations remain after the offset and any gaps in the series, so no coefficient is reported. |
For a given series x, the chosen curve measure y, and an offset k months, pair every month t where both readings exist: x at month t against y at month t+k. Drop any pair with a missing value. Then take the Pearson coefficient over what remains — the covariance of the two, divided by the product of their standard deviations. Panel D rebuilds exactly this for whichever cell you select.
Every number in the matrix is produced the same way. Pick a cell above and this panel rebuilds it from scratch — the scatter of paired observations, the count, and the sentence the number is making.