Which leg of index-plus-spread moves, and how often

Track 1 lesson 13 established that your rate is an index plus a spread, and Track 8 lesson 16 set out what each leg is paying for. Neither answered the question this lesson asks: across a long period, how much of the movement in the rate came from each leg?

The two legs run on different clocks. The index is republished every business day and is free to change on every one of them. The spread is written into an agreement and changes when a lender rewrites a pricing grid, which happens on a timescale of years. So the legs are not two comparable sources of variation. They are a continuous one and a rare one.

Take an illustrative twenty-four months. The index takes fifteen distinct values, changing in fourteen of the twenty-three month-to-month steps, and travels from 3.88 percent to 6.04 — a range of 2.16 points. The spread changes once, from 1.85 to 2.35, a range of 0.50. The resulting rate runs from 5.73 percent to 8.22, a range of 2.49 points.

Attributing that variation is more informative than the ranges. Of the total variance in the monthly rate, 80.1 percent came from the index, 9.6 percent from the spread, and the remaining 10.3 percent from the two moving in the same direction at the same time. That last term is not a rounding artefact. It is the signature of a lender widening a spread during the same cycle in which the index was rising, which is the mechanism lesson 23 takes apart.

For a borrower this sets where to look. If your cost rose and you want to know whether anything about your particular facility changed, the published index history will explain roughly four fifths of it by default. The residual is where a spread revision hides, and a residual of half a point on a two-and-a-half point move is easy to miss when the whole increase feels like a market event.