Lesson 23 of 25 · 7 min

Why a quiet regime accumulates leverage

Borrowing capacity is computed from volatility, so a calm year hands out room that a noisy one takes back without asking.

Leverage is usually described as something a borrower chooses. Part of it is not. The amount available is computed from a volatility figure, so it rises when volatility falls, whether or not anybody requests an increase.

Take $2,140,000 of market value with the model this track uses — a 3.5 multiple and an 18-session exit. At 16.2 percent annualised volatility the daily figure is 1.0205 percent, the haircut is 15.15 percent and the advance rate is 84.85 percent, giving $1,815,710.55 of capacity. At 34.1 percent the daily figure is 2.1481 percent, the haircut is 31.90 percent and the advance rate is 68.10 percent, giving $1,457,390.73. The difference is $358,319.82, or 19.73 percent of the larger figure.

There is a second effect, and it is the one borrowers notice less. The same headroom is worth less protection in a noisier regime. Express headroom in daily standard deviations rather than in percent: 22 percent of headroom against a 12.4 percent volatility, whose daily figure is 0.7811 percent, is 28.16 daily standard deviations. The same 22 percent against 38.1 percent volatility, daily 2.4001 percent, is 9.17. Nothing about the loan changed and the protection fell by two thirds.

Put the two together and the direction is one-way. A quiet regime raises the capacity on offer and simultaneously makes whatever headroom remains look comfortable in movement terms. Both push towards using the capacity, and there is no corresponding mechanism pushing the other way while the quiet lasts.

So the stock of borrowing outstanding against a given portfolio is largest at the end of a long quiet stretch, which by construction is the session before the haircuts widen. Lesson 6 rejected the mystical version of quiet preceding violence; this is the mechanical version, and it requires nobody to have made a mistake. It is what a volatility-driven advance rate does when applied over time.

Key terms

Headroom in volatility units: The distance to a maintenance threshold expressed in daily standard deviations rather than in percent. It shrinks when volatility rises even if the percentage is unchanged.
Procyclicality: The property of a rule that loosens in calm conditions and tightens in stressed ones, amplifying the cycle it is measuring rather than damping it.
Volatility-driven capacity: Borrowing capacity that moves because a statistic moved. It grows without being requested and shrinks without being withdrawn.

Worked example

Capacity and protection, both moving with one statistic

$2,140,000 of market value, coverage multiple 3.5, 18-session exit. Headroom figures use a separate illustrative case with 22 percent of headroom.

Volatility 16.2%: Advance 84.85%, capacity $1,815,710.55
Volatility 34.1%: Advance 68.10%, capacity $1,457,390.73
Capacity withdrawn: $358,319.82
22% headroom at 12.4% volatility: 28.16 daily standard deviations
The same 22% at 38.1% volatility: 9.17 daily standard deviations
Protection lost, in movement terms: Two thirds

The quiet regime offered $358,319.82 more capacity and made the remaining headroom look three times as safe. Both figures were reversed by the same print.

Check yourself

A borrower has 22 percent headroom. Volatility on the collateral goes from 12.4 percent to 38.1 percent annualised. How much protection does that 22 percent represent in each regime?

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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.