Lesson 6 of 25 · 7 min

Why quiet periods precede violent ones

Quiet does not cause violence; it shrinks the estimate of how violent things could get, and the estimate is what gets used.

The claim that calm markets cause turbulent ones is usually stated as though something mystical were involved. Three ordinary mechanisms account for it, and all three are arithmetic.

The first is estimation error. A volatility estimate computed from n observations carries a standard error of roughly the volatility itself divided by the square root of twice n. On a twenty-session window that is 15.81 percent of the estimate. So a reading of 12.4 percent has a standard error of 1.96 points, and a conventional confidence band running from 8.56 percent to 16.24 percent. The estimate is not a fact; it is a measurement with a width, and the width is never quoted alongside it.

standard error of the estimate = volatility ÷ square root of (2 × n)

standard error of the estimate: The typical distance between a measured volatility and the underlying volatility it is measuring.
volatility: The level being estimated, expressed for the same period as the answer.
n: The number of observations in the estimation window. Larger n narrows the error.

The second is clustering read forwards in time. Lesson 5 measured a lag-one autocorrelation of +0.4289 in absolute returns. That figure says a quiet cluster tends to continue, which is why quiet periods are long — and it says exactly the same thing about turbulent clusters, which is why the first large session tends to be followed by more. The transition is not a ramp. It is a change of state that the estimate only registers after the fact.

The third is what happens while the quiet lasts, and lesson 23 works it out in full: positions, capacity and haircuts are all sized to the low figure, so the low figure and the largest stock of borrowing occupy the same window. The sequence quiet-then-violent is therefore not causal so much as selective. We notice the pairing because the violence arrives when the buffers are thinnest.

Put the three together and the honest statement is narrower than the folklore. Calm does not load a spring. Calm produces a small estimate with a wide error band, that estimate is fed into rules which then permit more exposure, and the estimate is guaranteed to be least accurate about the thing that has not happened yet.

Key terms

Standard error of a volatility estimate: How far a measured volatility typically sits from the volatility it is measuring. Roughly the estimate divided by the square root of twice the window length.
Backward-looking estimate: A figure computed entirely from observations that have already occurred. It can only register a change in conditions after the change has produced data.
Selection rather than causation: A pairing that appears because of when we notice it, not because one side produced the other. Quiet does not cause violence; it coincides with thin buffers.

Worked example

How much a twenty-session estimate can be wrong by

An illustrative reading of 12.4 percent annualised from a twenty-session window, and a reading of 38 percent from the same window length.

Standard error as a share of the estimate, n = 20: 15.81%
Same share at n = 60: 9.13%
Same share at n = 252: 4.45%
Band around a 12.4% reading: 8.56% to 16.24%
Band around a 38% reading: 26.22% to 49.78%

A quiet 12.4 percent reading is consistent with an underlying 16.2 percent, and a 38 percent reading is consistent with anything from 26 to 50. Neither band appears next to the figure a model consumes.

Check yourself

A lender's 20-session estimate reads 12.4 percent. How precise is that figure, and what does its imprecision have to do with the timing of stress?

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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.