Lesson 24 of 25 · 8 min

One facility, one rate path, twenty-four months

The index came back to within a quarter point of where it started, and ten points of headroom did not come back with it.

This lesson runs the mechanisms of the whole track through one facility, month by month, for two years. The arithmetic is the point, so every figure below reconciles against every other one.

The facility: a pledged portfolio worth $1,865,000, a drawn balance of $742,000, a threshold of 68 percent of market value, a spread of 2.05 percent over a monthly-reset index, Act/360, interest capitalised, and collateral with an effective duration of 5.4. Twenty-four months is 730 days. The trigger value starts at 742,000 ÷ 0.68 = $1,091,176.47, so headroom starts at 41.49 percent.

The shape of what follows, all figures illustrative:

Months 1 to 12: the index climbs from 3.94 percent to 6.42, and the rate with it, from 5.99 to 8.47.
Months 13 to 15: a plateau. The index peaks at 6.44 in month 14 and the rate at 8.49.
Months 16 to 24: the index falls back to 4.18 and the rate to 6.23.
Collateral, moving 5.4 percent for each point the index travels from its month-1 level, bottoms at $1,613,225 in month 14 and ends at $1,840,829.60 — 1.30 percent below where it began.
The balance never falls. It ends at $862,855.61, having absorbed $120,855.61 of capitalised interest.

Headroom starts at 41.49 percent, bottoms at 25.76 percent in month 15, and ends at 31.07. The index round-tripped to within 0.24 of a point of its starting level and the collateral to within 1.30 percent of its starting value. Headroom finished 10.42 points below where it began.

The two do not match because the legs are different kinds of object. Collateral value is a level, so when the rate comes back the level comes back. The balance is a running total: every month added interest, and nothing in a falling index reverses a figure already added. The trigger value rose $177,728.84 across the two years while the collateral fell only $24,170.40.

A full round trip in the rate is not a round trip in the facility. One leg is a price and the other is a ledger, and only one of them knows how to go back.

Key terms

Round trip: A rate path that returns close to where it started. Restores the collateral leg approximately and the cost leg not at all.
Running balance: A total that only accumulates. It has no mechanism for reversing, which is what makes the cost leg irreversible within a cycle.
Trough headroom: The lowest headroom reached across a cycle. It arrives after the rate peak, because the balance keeps growing while the collateral is recovering.

Worked example

Twenty-four months, six milestones

Portfolio $1,865,000, balance $742,000, threshold 68 percent of market value, spread 2.05 percent, effective duration 5.4, Act/360, interest capitalised, 730 days.

Month 0: Balance $742,000, collateral $1,865,000, headroom 41.49%
Month 6, rate 7.43%: Balance $767,358.60, collateral $1,719,977.60, headroom 34.39%
Month 12, rate 8.47%: Balance $799,965.93, collateral $1,615,239.20, headroom 27.17%
Month 15, rate 8.44%: Balance $817,002.62, collateral $1,618,260.50, headroom 25.76%
Month 18, rate 7.73%: Balance $833,643.15, collateral $1,689,764.60, headroom 27.45%
Month 24, rate 6.23%: Balance $862,855.61, collateral $1,840,829.60, headroom 31.07%

$120,855.61 of interest on a facility drawn once and never touched again. The rate ended 0.24 of a point above where it started and headroom ended 10.42 points below.

Check yourself

In month 24 the rate is 6.23 percent, only 0.24 of a point above the 5.99 percent of month 1, and the collateral is within 1.30 percent of its starting value. Why is headroom 10.42 points lower than it was?

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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.