Margin, mortgages and the forced sale

Before taking a borrowed position there is one number worth more than every forecast about it: the price at which somebody else decides you are selling.

It takes two minutes to compute and almost nobody computes it, because it belongs to a version of the future that the person taking the position is not thinking about.

The trigger price

The arithmetic is short. Call the position value A, the borrowing D, and the share of the position the lender insists remain yours m.

You are inside the agreement while the equity is at least m of the position: A minus D, over A, at least m. Rearranged, that says the position can fall to D divided by one minus m before you are outside it.

So the trigger price is D / (1 − m), and the fall that gets you there is one minus that number divided by A.

Three positions in the same asset, each with a lender who wants a quarter of the position to remain yours:

• Borrow 50,000 against 100,000. Trigger at 66,667. The asset can fall about a third.
• Borrow 70,000 against the same 100,000. Trigger at 93,333. The asset can fall about seven percent.
• Borrow 30,000 against it. Trigger at 40,000. The asset can fall sixty percent.

Same asset, same lender, same rules. The distance between comfortable and finished is set entirely by how much was borrowed, and it does not change in proportion — going from 50,000 of borrowing to 70,000 does not halve your buffer, it cuts it by four fifths.

Predict

Two people hold the same asset. One has borrowed half its value; the other has borrowed roughly 70% of it. The lender requires a quarter of the position to stay theirs. The asset falls 10% over a fortnight. What happens?

Choose one answer

Both are fine — a tenth is well inside a quarterThe first is fine; the second is sold out or must find cashBoth must add cash, in proportion to how much they borrowedIt depends on whether the fall was fast or slow

Lock in answer

The property version, where the buffer has a familiar name

Property borrowing usually has no daily trigger, which makes it feel like a different animal. It is the same animal with a longer fuse.

The deposit is the buffer. Put down a fifth and the price can fall a fifth before your equity is gone. Nothing happens on that day — no call arrives, and if the payments are being made, nobody is interested. The consequence is delayed and it is real: you cannot sell without bringing cash, cannot move without selling, and cannot usually refinance on decent terms. The position holds you rather than the other way round.

Property loan

≈ Hypothetical model, not a forecast

A long-dated secured loan: the payment, the interest bill, and what paying extra each month changes.

It assumes

• The price fall being tested happens immediately, before any capital has been repaid.
• The lender applies no charge and takes no action while payments continue.
• The rate is fixed for the whole term, which most long loans are not.
• Nothing is spent on the costs of buying, holding or selling the property.

It ignores

• Purchase taxes, legal costs, survey fees and lender fees
• Insurance, maintenance, and anything else the property costs to hold
• Any change in the value of the property itself
• Rate resets, which is how most long loans actually behave

Find the smallest deposit that would leave you with equity intact after a fall of one fifth in the price — a loan of no more than four fifths of the value, and no more than two points below that.

Deposit1,500%

Annual interest rate500%

Amount borrowed

255,000

Deposit paid up front

45,000

Loan as a share of the price

0.85

Scheduled monthly payment

1,491

Total handed over, scheduled payments only

447,211

Total handed over, paying extra

447,211

Total interest, scheduled payments only

192,211

Total interest, paying extra

192,211

Months taken when paying extra

300

Months removed from the term

0

Interest avoided

0

• Balance outstanding

◷ Not there yet — keep moving the controls.

Look at the balance line in the chart before moving on. In the early years it barely moves — the payments are mostly interest — so the buffer is at its thinnest for the longest stretch, and it is thin during precisely the years when the buyer is most likely to need to move.

Why the forced seller gets the worst price available

The trigger is only half the damage. The other half is who you become when it fires.

A forced seller has three properties, and each one costs money. Their deadline is short, so they cannot wait for a better bid. Their deadline is known — the requirement is in the agreement and the counterparty can see the position — so nobody needs to bid generously. And their deadline arrives at the same time as everybody else's, because the price move that triggered you triggered every similarly positioned holder on the same afternoon.

That last one is the mechanism behind the shape of sharp falls. Selling triggered by a fall causes a further fall, which triggers more selling. Nobody in that chain wanted to sell at that price; every one of them had a rule written months earlier that said they would.

Check

An asset falls 30% and recovers fully over the following eighteen months. Two holders: one unleveraged, one who was sold out at the bottom of the fall. Where does each end up?

Choose one answer

Both recover — the price came back to where it startedThe unleveraged holder is level; the forced seller has a permanent lossThe forced seller does better — they were out during the worst of itBoth have a permanent loss, since the leverage cost interest

Check answer

›Three ways the trigger moves without the price movingOptional

The calculation at the top assumed the only variable is the asset price. Three other things move the line, and each has ended positions that the price alone would not have.

The requirement itself can change. The share the lender insists you keep is usually theirs to raise, and it is most likely to be raised in exactly the conditions where raising it hurts. A position that was inside the line at breakfast can be outside it at lunch with the asset unchanged.

The debt grows. Interest that is added to the balance rather than paid in cash moves the trigger towards you every month, quietly, with no news attached.

The valuation can be revised. For anything not priced on a screen, the number the lender uses is a mark, and the mark can be re-cut by the lender's own valuer at a moment of their choosing.

None of these is unfair or unusual. They are all in the agreement. They are merely absent from the version of the future most people picture when they take the position.

Worth remembering

• A borrowed position has a trigger price: the debt divided by one minus the share of the position the lender requires you to keep.
• Raising the borrowed share cuts the tolerable fall far faster than in proportion.
• On a property loan the deposit is the buffer: the price can fall by roughly the deposit percentage before equity is gone.
• A forced seller has a short deadline, a visible one, and one shared with everyone else in the same position.
• Leverage converts a temporary fall into a permanent loss by removing you from the asset before the recovery.