Lesson 12 of 25 · 7 min

Procyclicality: the same rule tightening at the worst moment

Any buffer sized from a risk measurement must grow when risk grows; a rule without that link is stable and permanently expensive.

The word procyclical sounds like an accusation about a particular lender. It is a description of a class of rules, and every rule in the class behaves this way whether or not anyone intends it to.

The general form is short. A buffer meant to cover a plausible adverse move over a liquidation window is a multiple of a volatility estimate, scaled by the square root of the window's length.

h = z x sigma x sqrt(T / 252)

h: The haircut the rule produces, as a decimal fraction of market value.
z: How adverse a move is covered, in standard deviations. A 2.33 corresponds to a one-in-a-hundred day.
sigma: The annualised volatility estimate for the asset. The only term that moves day to day.
T: The assumed liquidation window in trading days.
252: Trading days in a year, converting the annual volatility figure to the window's length.

Because volatility enters linearly, the haircut is proportional to it. With z of 2.33 and a ten-day window, an asset at 22 percent volatility gets a 10.21 percent haircut and the same asset at 47 percent gets 21.81 percent. The ratio 2.1364 is exactly 47 divided by 22. No appetite changed, no committee met, and no view was formed about the borrower. One input moved and the function returned what it was built to return.

The generality is the part worth keeping. The same holds for a rule keyed to implied volatility, to a percentile of a trailing distribution, to a rating assessment, to a spread level, or to an internal loss model, because every one of those inputs deteriorates in a decline. A rule immune to the cycle must be keyed to something that does not move with it — a through-the-cycle floor or a fixed schedule — and such a rule is systematically too conservative in every calm period, which is the trade-off nobody escapes. Real schedules sit in the middle: a floor plus a volatility term, rounded into steps, which mutes the movement without removing it.

Procyclicality is not a policy choice. It is what necessarily happens when a buffer is sized from a measurement of the thing it is buffering against.

Key terms

Procyclicality: The tendency of a rule to tighten in downturns and loosen in expansions because its inputs move with the cycle.
Buffer rule: Any formula that sets a cushion as a multiple of a measured risk. The class of rules to which almost every haircut schedule belongs.
Through-the-cycle: A setting fixed at a level meant to hold across good and bad conditions. Stable by construction and needlessly expensive most of the time.

Worked example

One formula, two regimes, no decision

Illustrative figures. A haircut rule of 2.33 standard deviations over an assumed ten-day liquidation window, applied to the same shares in two different quarters.

Window scaling factor: 0.199205
Haircut at 22 percent volatility: 10.21%
Haircut at 47 percent volatility: 21.81%
Ratio of the two haircuts: 2.1364
Number of decisions taken in between: None

The haircut more than doubled on an unchanged rule, an unchanged schedule and an unchanged opinion of the borrower.

Check yourself

Under the same rule, volatility on a holding rises from 16 percent to 29 percent. What are the two haircuts, and how much of the change reflects a decision by the lender?

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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.