Lesson 11 of 25 · 7 min

Why a haircut rises during a decline rather than before it

The input is a backward-looking average, so the rule cannot move until the fall it measures has already happened.

It looks like opportunism: the discount goes up just as the collateral goes down. The cause is duller than that, and it is worth locating precisely, because the same mechanism also decides how long the discount stays after the decline is over.

Track 1 lesson 4 made the observation that the haircut and the drop tend to arrive together. The mechanism is the estimator. A buffer rule needs a volatility number, and a volatility number is computed over a trailing window — sixty trading days is a common choice. A trailing average cannot register anything until it is inside the window, and any single day is one sixtieth of the sample.

Put figures on it. Sixty days each moving 0.55 percent give an annualised volatility of 0.55 percent times the square root of 252, which is 8.73 percent. Add one day of minus 3.1 percent and the measure reads 10.74 percent: the price has fallen 3.1 percent and the estimate has moved two points. After five such days the price is down 14.57 percent and the measure reads 16.48 percent. The estimator arrives late because it is an average of the thing it is trying to detect.

On top of the estimator lag sits a governance lag. A monitor fires, a committee considers, a schedule version is published with an effective date. Track 8 lesson 15 describes how discretionary revisions cluster on a handful of days a year; this is why the cluster lands a few days after a market has already moved.

The consequence for a borrower is an ordering. Under an illustrative rule of a 25 percent floor plus 2.33 times volatility times the square root of ten over 252, the haircut goes from 29.05 percent to 29.98 after one day and 32.65 after five. You absorb the entire 14.57 percent price fall first, using the old cushion, and the 3.60 points of additional haircut arrive afterwards, against what is left.

Key terms

Trailing window: The fixed number of past days a volatility estimate is computed over. Everything inside it counts equally and nothing outside it counts at all.
Estimator lag: The delay between a market moving and a measure of that market registering the move. A property of averaging, not of anybody's attention.
Volatility input: The single number a buffer rule is keyed to. Whatever else a schedule contains, this is the term that moves.

Worked example

Five days of falling, one lagging measure

Illustrative figures. A sixty-day trailing window in which every prior day moved 0.55 percent, followed by five consecutive days of minus 3.1 percent. Annualising uses the square root of 252.

Measured volatility before: 8.73%
After one day: 10.74%
After three days: 13.91%
After five days: 16.48%
Haircut under the rule, before and after: 29.05% to 32.65%
Order of arrival: Price first, haircut second

The volatility measure nearly doubled and the haircut moved 3.60 points, entirely after the fourteen and a half percent fall that caused both.

Check yourself

A lender keys its haircut to a 40-day trailing window. The prior 37 days each moved 0.48 percent; the last three each fell 2.6 percent. What does the measure read before and after, and how much has the price already fallen by the time it reads the second figure?

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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.