Lesson 25 of 25 · 8 min

Seven patterns that repeat in every episode

The arithmetic of a forced sale is scale-invariant: the same percentage of the same book, at any size.

Twenty-four episodes, running from 1993 to 2022, across futures, repo, swaps, notes, funds and retail margin accounts. They share seven features, and the seven are worth stating plainly because each one is checkable against a position rather than being a matter of judgment.

The seven patterns:

The position was concentrated, correlated, or both, so the diversification on paper did not exist in the event.
The leverage was invisible to at least one party — off the balance sheet, inside a margin percentage, or spread across lenders who could not see each other.
The collateral and the obligation moved together, because a haircut is raised in the same conditions that cut the price.
A cure required selling the thing that was falling, which is the one transaction that makes the fall worse.
The clock belonged to somebody else: an exchange's daily settlement, a counterparty's morning deadline, a clearing house's overnight recalculation.
The discount widened exactly when it hurt, because the cost of immediacy rises with the number of people who need it.
The sequence ran faster than the decision process it had to pass through.

Two of them deserve a second sentence. The invisible leverage is not always concealed — in 2022 the pension hedges were disclosed and conventional, and the leverage still lived inside a margin percentage rather than in anything labelled borrowing. And the clock is the feature most often left out of the retelling, because a deadline is not a number and does not appear in a risk report.

The final pattern is that none of this is about size. The arithmetic of a forced sale is a ratio, and a ratio has no units. An account with a few thousand in it and a book with hundreds of millions, at the same leverage and under the same maintenance rule, are required to sell the same percentage of themselves on the same day.

Key terms

Scale invariance: The property that a forced-sale calculation depends only on ratios, so the answer in percentage terms is identical at every account size.
Invisible leverage: Borrowing that appears as a margin percentage, a derivative notional or an off-balance-sheet financing rather than as a loan. It behaves as leverage regardless.
Cost of immediacy: The discount accepted for selling now rather than later. It rises with the size being sold and with the number of others selling the same thing.

Worked example

The same arithmetic, one hundred thousand times apart

Illustrative figures scaled down so the arithmetic is followable; they are not the reported amounts. A retail account with $6,400 of equity holding a $32,000 position, and an institutional book with $640,000,000 of equity holding a $3,200,000,000 position. Both at 5.0x, both under a rule requiring equity of 20 percent of value, both facing a 13 percent fall.

Retail equity after the fall: $2,240
Retail requirement and shortfall: $5,568 required, $3,328 short
Retail sale needed to cure: $16,640
Institutional equity after the fall: $224,000,000
Institutional requirement and shortfall: $556,800,000 required, $332,800,000 short
Institutional sale needed to cure: $1,664,000,000

The two books are one hundred thousand times apart in size. Both lost 65 percent of their equity, both are short 52 percent of it, and both must sell 59.8 percent of what they hold. The arithmetic does not know how big you are.

Check yourself

A retail account holds a $13,750 position with $2,750 of equity. An institutional book holds $1,375,000,000 with $275,000,000 of equity. Both face an 11 percent fall under a rule requiring equity of 20 percent of value. Compare the shortfalls.

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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.