Lesson 10 of 25 · 7 min

The liquidity spiral, one turn at a time

Each turn is small and each is reasonable, and the total sold comes to twenty-four times the shortfall that began it.

The spiral is usually described in a single sentence: prices fall, haircuts rise, selling follows, prices fall again. Put that way it sounds like a metaphor. It is arithmetic, and whether it converges depends on numbers that can be written down.

One turn, in four steps, each of which is somebody following a stated rule:

The price falls, so lending value falls and a shortfall appears.
Measured volatility rises, so the buffer rule raises the haircut, and the shortfall grows.
The shortfall is cured by selling collateral and applying the proceeds to the balance.
The sale moves the price, so the holdings that were not sold are marked lower, and the turn begins again.

Step three has an arithmetic property that drives everything. Selling collateral reduces both sides of the test: a sale of S cuts the balance by S and cuts lending value by (1 minus the advance rate) times S, so the net improvement is the haircut times S. Curing a shortfall of D therefore requires selling D divided by the haircut, which Track 9 works through line by line. The larger the haircut, the larger the sale — so the same revision that creates the shortfall also enlarges the sale needed to fix it.

Run it. A portfolio of $2,140,000 carries a 30 percent haircut and a balance of $1,402,000, leaving $96,000 of room. An 8 percent fall produces a $23,840 shortfall. The haircut is revised to 34 percent and the shortfall becomes $102,592. Curing that requires selling $345,267, which marks the rest down by 0.4 percent for each $100,000 sold. Two further revisions, to 37 and then 39 percent, require sales of $144,121 and $81,237.

The shortfall that started it was $23,840. The collateral sold to chase it was $570,625, which is 23.9 times as much, and no step in the sequence was unreasonable.

Key terms

Liquidity spiral: A loop in which selling to meet a collateral requirement lowers prices, which raises the requirement, which forces more selling.
Cure multiple: How many dollars of collateral must be sold to close one dollar of shortfall. It is one divided by the haircut, so it rises as terms tighten.
Convergence: Whether each turn of the loop is smaller than the one before. A property of the numbers rather than of anybody's composure.

Worked example

Three turns, with every figure carried

Illustrative figures. Market value $2,140,000, balance $1,402,000, haircut 30 percent. Each $100,000 sold marks the remaining holdings down by 0.4 percent.

After an 8 percent fall: Shortfall $23,840
Haircut revised to 34 percent: Shortfall $102,592
First sale: $345,267
Haircut to 37 percent, second sale: $144,121
Haircut to 39 percent, third sale: $81,237
Total collateral sold: $570,625

Market value ended at $1,362,910 against $2,140,000, a 36.3 percent fall, of which the market itself supplied 8 points.

Check yourself

A portfolio worth $980,000 carries a $545,000 balance at a 42 percent haircut. The haircut is revised to 47 percent. How large a sale of collateral is needed to restore cover, and why is it more than twice the shortfall?

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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.