Lesson 13 of 25 · 7 min

Why a lender becomes conservative exactly when room is needed

The fall and the revision multiply rather than add, so a 30 percent decline removes 44 percent of borrowing capacity.

The complaint is that the lender tightens at the worst possible moment. The more useful statement is that the two things working against a borrower do not add together — they multiply, and the multiplication is where almost all of the damage is.

LV1 / LV0 = (1 - d) x (1 - h1) / (1 - h0)

LV0: Lending value before: market value times the original advance rate.
LV1: Lending value after both the price fall and the revision.
d: The decline in market value, as a decimal.
h0: The haircut before the revision, as a decimal. One minus it is the advance rate.
h1: The haircut after the revision.

Work the case. A $1,860,000 holding at a 65 percent advance rate supports $1,209,000 of lending value. A 30 percent fall takes market value to $1,302,000. The haircut is then revised from 35 percent to 48, so the advance rate becomes 52 percent and lending value becomes $677,040. That is 0.70 times 0.52 divided by 0.65, which is 0.70 times 0.80, or 0.56 of where it started. Lending value fell 44 percent — not the 30 percent of the price move, and not the 43 percent an additive reading of thirty percent plus thirteen points would suggest.

Headroom fares worse still, because the balance does not fall with the collateral. Against a $780,000 balance, the account had $429,000 of room and now has a $102,960 shortfall. The whole $531,960 of lost lending value came out of headroom, because headroom is a residual and only one of its two inputs moved.

State the same event as a survivable decline and it becomes sharper. Before the revision, the balance stayed covered down to $780,000 divided by 0.65, which is $1,200,000 of market value — a 35.5 percent fall. After it, only down to $780,000 divided by 0.52, which is $1,500,000, a fall of 19.4 percent. The revision did not merely shrink the cushion. It moved the line to a place the price had already passed on its way down.

Key terms

Compounding: Two reductions applied in sequence multiply rather than sum, so their combined effect is larger than adding the two percentages suggests.
Survivable decline: The fall in market value a balance can absorb before cover fails. It moves when the balance moves and when the advance rate does.
Advance-rate revision: A change in the percentage of market value credited as collateral. It acts on the post-decline value, so it arrives magnified.

Worked example

Thirty percent down, forty-four percent gone

Illustrative figures. A $1,860,000 holding at a 65 percent advance rate, a $780,000 balance, a 30 percent price fall followed by a haircut revision from 35 percent to 48.

Lending value before: $1,209,000
Market value after the fall: $1,302,000
Lending value after the revision: $677,040
Combined effect: A 44 percent fall
Headroom before and after: $429,000 to minus $102,960
Survivable decline before and after: 35.5% to 19.4%

The threshold that could absorb a 35.5 percent fall in the morning could absorb 19.4 percent by the evening, and the price had already fallen 30.

Check yourself

A $2,240,000 holding at a 60 percent advance rate falls 24 percent, after which the advance rate is cut to 49 percent. By what percentage does lending value fall, and why is the answer not 24 percent plus 11 points?

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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.