The forced-sale multiple: why selling a dollar does not cure a dollar

Selling collateral to fix a shortfall shrinks the collateral, so the cure costs more than the gap.

This is the lesson people most often have never seen, and it is pure arithmetic. When you repay a shortfall by selling pledged securities, the sale does two things at once: it reduces your balance, and it reduces your collateral. Both sides of the ratio move. That is why a $13,000 shortfall is not cured by selling $13,000 of stock.

Work the algebra once and it will stay with you. Let S be the amount of collateral sold. After the sale the balance is B − S and the collateral value is V − S. You need that ratio to equal the threshold t. Solving gives a formula whose shape is the whole lesson: the denominator is (1 − t), which is small when the threshold is high, which makes S large.

S = (B − t × V) ÷ (1 − t)

S: Collateral you must sell to bring LTV exactly back to the threshold.
B: Current loan balance, including accrued interest.
V: Current collateral value on the basis your agreement uses.
t: The maintenance threshold as a decimal. A higher t makes (1 − t) smaller and S larger.

The ratio S divided by the raw shortfall is the forced-sale multiple, and it equals 1 ÷ (1 − t). At a 70 percent threshold the multiple is 3.33. At 75 percent it is 4. At 80 percent it is 5. So an $80,000 gap at an 80 percent threshold requires selling $400,000 of stock. The multiple is a property of the threshold alone, which means it is knowable in advance, before anything goes wrong.

The multiple explains why forced sales feel disproportionate. They are disproportionate — by exactly 1 ÷ (1 − t).

Key terms

Forced-sale multiple: How many dollars of collateral must be sold per dollar of shortfall. Equals 1 ÷ (1 − threshold).
Shortfall: The amount by which your balance exceeds what the threshold permits at current collateral value.
Self-defeating cure: The general problem that fixing a ratio by shrinking both its numerator and denominator requires a larger action than the gap suggests.

Worked example

A $13,000 shortfall and a $43,333 sale

Balance $300,000, collateral value $410,000, threshold 70%.

Permitted balance: $287,000
Shortfall: $13,000
Forced-sale multiple: 3.33×
Collateral to sell: $43,333
Check: after the sale: $256,667 ÷ $366,667 = 70.0%

The gap was $13,000. The sale was $43,333 — more than three times the number that appeared in the notice.

Check yourself

Balance $500,000, collateral value $600,000, threshold 80%. How much must be sold, and what is the multiple?

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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.