Lesson 24 of 25 · 7 min

The volatility feedback loop, end to end

One 6.2 percent session lifts a twenty-session estimate by 13.7 points, and the estimate costs more than the price does.

Every mechanism in this track so far has been a single arrow. This lesson connects them, with one set of figures carried all the way through.

Start with nineteen quiet sessions whose standard deviation annualises to 11.17 percent. Then one session of −6.2 percent. Recomputing the twenty-session figure gives 24.87 percent — a jump of 13.70 points, or 2.227 times, from a single observation. That is the estimator doing its job, not malfunctioning: one large squared deviation in a window of twenty dominates the average.

The model responds next. With a 3.5 multiple and an 18-session exit, the volatility-driven haircut moves from 10.45 percent to 23.27 percent, a change of 12.82 points. Lesson 17 established that a published advance rate contains a conservatism wedge that does not move with volatility, so take the published rate as 78 percent before the shock and apply the change: 78 − 12.82 gives 65.18 percent.

Now both effects land on the collateral. Market value of $3,480,000 falls 6.2 percent to $3,264,240, a loss of $215,760. Lending value was $3,480,000 × 0.78 = $2,714,400. At the old advance rate the reduced market value would support $2,546,107.20; at the new one it supports $2,127,686.84. So the price took $168,292.80 of lending value and the haircut took $418,420.36, for a total of $586,713.16 — 2.719 times the market-value loss.

Against a $2,050,000 balance, loan-to-value moves from 75.52 percent to 96.35 percent in one session, and spare lending value falls from $664,400 to $77,686.84. Lessons 20, 21 and 22 then supply the rest of the circuit: the same volatility print instructs volatility-targeted pools to sell, raises margin requirements, and obliges hedgers to sell into the decline. That selling produces the next price fall, which produces the next volatility print.

The amplifier in this loop is not the price. It is the estimate, which reacts to one observation and is then read simultaneously by every rule in lesson 21.

Key terms

Feedback circuit: A chain in which each step's output becomes an earlier step's input. Here: price, then estimate, then rule, then forced selling, then price again.
Amplification ratio: Total lending value lost divided by market value lost. Above one whenever the haircut widens at the same time as the price falls.
Estimate sensitivity: How much a volatility figure moves in response to one observation. On a twenty-session window, a single large session can more than double it.

Worked example

One session, traced from return to loan-to-value

Nineteen quiet sessions annualising to 11.17 percent, then a single −6.2 percent session. $3,480,000 of market value, $2,050,000 balance, published advance rate 78 percent before. Coverage multiple 3.5, 18-session exit. Illustrative throughout.

Volatility estimate before and after: 11.17% then 24.87%
Volatility-driven haircut: 10.45% then 23.27%
Published advance rate: 78.00% then 65.18%
Market value: $3,480,000 then $3,264,240
Lending value: $2,714,400 then $2,127,686.84
Loan-to-value: 75.52% then 96.35%

A 6.2 percent session cost 2.719 times its own size in lending value, and 71 percent of the damage came from the haircut rather than from the price.

Check yourself

A single −6.2 percent session raises a 20-session volatility estimate from 11.17 percent to 24.87 percent, widening the haircut by 12.82 points. On $3,480,000 of collateral at a 78 percent advance rate, how much lending value is lost, and how much of it is the price?

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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.