Lesson 20 of 25 · 7 min

Why one borrower's cure is another borrower's shortfall

The sale that fixes one account marks down that holding everywhere, and the total removed can exceed the problem solved.

A cure is a private act with a public price. The shares go into a market where other people's collateral is valued at whatever the last trade said.

The chain has four links and none of them requires anybody to behave unusually. A shortfall is closed by selling collateral, and the sale must be the shortfall divided by the haircut. That sale has a price impact. The impact sets the closing price. Every other pledged holding of the same name is remarked to that price overnight, and each one's lending value falls by the markdown multiplied by its advance rate.

Give it arithmetic. A $96,400 shortfall at a 38 percent haircut requires a $253,684 sale. In a name trading $9,400,000 a day at 2.6 percent daily volatility with a constant of 0.90, that is an impact of 0.3844 percent. If the lender's other accounts hold $46,800,000 of the same name at a 62 percent advance rate, $179,905.53 of market value and $111,541.43 of lending value disappeared that night. The problem solved was $96,400. The collateral destroyed elsewhere was 1.16 times as large.

Then the sequence continues or it does not, and which one happens is a ratio rather than a mood. If 55 percent of that destroyed lending value lands on accounts that had less headroom than their share of it, the next round's aggregate shortfall is $61,347.79, which is 0.6364 of the first. A sequence with that ratio sums to $96,400 divided by 0.3636, which is $265,127 of total shortfall, or 2.75 times the original. Had the ratio been above one, the sum would not converge at all.

Nobody in this sequence did anything unusual and no lender exercised any discretion. Each account cured its own shortfall in the ordinary way, on the ordinary timetable.

Key terms

Spillover: The effect one account's forced sale has on the collateral value of unrelated accounts holding the same security.
Second round: The shortfalls created by the first round's selling. It exists whenever some accounts had less headroom than the markdown they received.
Convergence ratio: Each round's shortfall divided by the previous round's. Below one the sequence dies out; at or above one it does not.

Worked example

Curing $96,400 and destroying $111,541

Illustrative figures. A $96,400 shortfall, a 38 percent haircut, a name trading $9,400,000 a day at 2.6 percent daily volatility, constant 0.90, and $46,800,000 of the same name held across other accounts at a 62 percent advance rate.

Sale required to cure: $253,684
Price impact of that sale: 0.3844%
Market value removed from other accounts: $179,905.53
Lending value removed from them: $111,541.43
Ratio to the shortfall cured: 1.16 times
Total shortfall across all rounds: $265,127

One account is now compliant. The pledged collateral behind the lender's whole book is $179,905.53 smaller, and the first account's own remaining shares were marked down too.

Check yourself

An account cures a $48,000 shortfall at a 30 percent haircut. The sale carries an estimated 0.21 percent price impact, and other accounts hold $28,500,000 of the same security at a 58 percent advance rate. How much collateral value does the cure remove from them?

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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.