Lesson 20 of 25 · 7 min

Why the two arrive together rather than in sequence

Neither leg causes the other; both are functions of one number, and a shared input has no transmission delay to introduce.

A natural reading of the last lesson is that one leg triggered the other — that the higher interest cost somehow pushed the collateral down, or that the falling collateral pushed the rate up. Neither happened, and the reason the two arrived together is more mechanical than a chain of cause and effect.

There is no channel running from your interest cost to a share price; your accrual is not an input to anybody's valuation model. There is no channel running the other way either, because a published index is computed from transactions between third parties and knows nothing about your collateral. The two legs are connected to one third thing, which is the level of the risk-free rate.

Write both as functions of that one variable. Interest cost is roughly linear in it: a point more rate is a point more accrual on the balance. Collateral value is roughly linear in it too, through duration, but with a coefficient several times larger. Feed one number into both expressions and the outputs change at the same moment, because they share the input rather than because one drives the other.

The table below does exactly that on one facility: a $1,988,000 portfolio with an effective duration of 6.6, a $734,000 balance, a 68 percent threshold, a starting rate of 5.40 percent and one year of accrual. Rate changes of zero, one, two and three points give headroom of 42.73, 38.09, 32.75 and 26.53 percent.

The practical consequence is that there is no interval between the legs. They are not two events with a gap in which a borrower could respond to the first before the second arrives. Where a gap does appear it is contractual rather than causal, and it runs in the direction people least expect, which is the subject of lesson 22.

Two outputs of one input are simultaneous by construction. Looking for the causal arrow between them is looking for something that is not there.

Key terms

Common factor: One variable feeding two outputs. It produces perfectly synchronised movement with no causal link between the outputs themselves.
Simultaneity: Two effects arriving at the same moment because they share a cause, rather than because one followed the other.
Rate sensitivity of headroom: How many points of headroom are lost per point of rate change, once both legs are included. It grows as the rate move grows.

Worked example

One input, four outcomes

Portfolio $1,988,000 at an effective duration of 6.6, balance $734,000, threshold 68 percent of market value, starting rate 5.40 percent, one year of accrual on an Act/360 basis.

Rate change of 0.00: Headroom 42.73%
Rate change of +1.00: Headroom 38.09%
Rate change of +2.00: Headroom 32.75%
Rate change of +3.00: Headroom 26.53%
Headroom lost on the first point: 4.64 points
Headroom lost on the third point: 6.22 points

Four rows, one variable. Both columns moved on every row and neither column was ever computed from the other.

Check yourself

On the facility above, the first point of rate rise costs 4.64 points of headroom and the third costs 6.22. The input is the same size both times. Why is the third more expensive?

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Educational only. Nothing in this lesson is investment, legal or tax advice, or a recommendation to enter into any transaction. Figures are illustrative and computed from the inputs stated in the lesson.