Lesson 15 of 25 · 7 min

How the multiple changes with the threshold

A generous threshold delays the first call and enlarges the cure, and both effects come from one term.

A higher maintenance threshold is usually described as a better term, and on one dimension it plainly is. The trap is that the same term governs a second quantity in the opposite direction, and the second one only shows up on the worst day.

The multiple 1 ÷ (1 − t) at a range of thresholds:

50 percent: 2.00 dollars sold per dollar of gap.
58 percent: 2.381.
65 percent: 2.857.
72 percent: 3.571.
80 percent: 5.00.
88 percent: 8.333.
92 percent: 12.50.

The growth is not linear. Raising the threshold from 50 to 58 adds 0.38 to the multiple; raising it from 84 to 92 adds 6.25. The multiple grows in proportion to one over the square of the remaining margin, so the last few points before a full advance are where almost all of the effect lives.

Now see both directions at once on one balance of $300,000. At a 65 percent threshold the call arrives when collateral value reaches $300,000 ÷ 0.65 = $461,538.46. At 80 percent it arrives at $300,000 ÷ 0.80 = $375,000, which is 18.75 percent lower — genuinely more room. But suppose in each case the collateral then falls a further 5 percent below the trigger. The shortfall becomes 5 percent of the balance either way, or $15,000. The cure at 65 percent is $15,000 ÷ 0.35 = $42,857.14. The cure at 80 percent is $15,000 ÷ 0.20 = $75,000.

So the two effects are exact mirror images of each other in their source and asymmetric in their timing. The later trigger is enjoyed on every ordinary day. The larger cure is paid once, on a day when prices have already fallen far enough to reach a lower trigger.

Key terms

Trigger value: The collateral value at which the ratio equals the threshold exactly. A higher threshold puts it lower.
Convexity of the multiple: The way the multiple accelerates as the threshold rises, because it depends on the reciprocal of the remaining margin.
Overshoot: How far collateral falls past the trigger before anything is done. It sets the shortfall as a share of the balance.

Worked example

Two thresholds, one balance, one overshoot

Balance $300,000 in both cases. Collateral falls to the trigger and then 5 percent further.

Trigger at 65 percent: $461,538.46
Trigger at 80 percent: $375,000
Shortfall after a further 5 percent: $15,000
Cure by sale at 65 percent: $42,857.14
Cure by sale at 80 percent: $75,000

The 80 percent borrower absorbed 18.75 percent more decline before the first call and then faced a cure 75 percent larger for the same overshoot.

Check yourself

The same $19,000 shortfall arises in two accounts, one with a 62 percent threshold and one with a 76 percent threshold. How much must each sell?

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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.