Lesson 16 of 25 · 7 min

What a volatility spike does to a haircut

The advance rate falls because one figure in a formula moved, and nobody looked at the borrower, the price or the file.

Track 1 lesson 4 said a haircut scales with how much an asset moves. This is the quantitative version of that sentence, and it is the lesson the rest of the track exists to reach. A volatility figure goes in one end of a lender's collateral model and an advance rate comes out of the other. Nothing between the two is a decision about the borrower.

The model is the one Track 7 lesson 9 built: a coverage multiple times a daily volatility times the square root of an assumed exit in sessions. Track 7 held volatility fixed and varied the days, because the exit length is what changes when a position grows. This lesson does the opposite. The days are fixed at 22 and the multiple at 3.5, and only volatility moves.

The position is 9,400 shares at $128.75, so $1,210,250 of market value, against a balance of $640,000. The price does not move at any point in what follows. Neither does the number of shares, the balance, the agreement, or anything a borrower could observe.

At 23.8 percent annualised volatility the daily figure is 23.8 ÷ 15.8745 = 1.4993 percent, so the haircut is 3.5 × 1.4993 × 4.6904 = 24.61 percent. The advance rate is 75.39 percent and the lending value is $912,376.98. Against the $640,000 balance that is a loan-to-value of 70.15 percent and $272,376.98 of unused lending value.

Now let volatility print 38.5 percent. Daily 2.4253 percent, haircut 39.81 percent, advance rate 60.19 percent, lending value $728,396.59. The loan-to-value is 87.86 percent. At 57.2 percent volatility the haircut is 59.15 percent, the advance rate is 40.85 percent, and the lending value is $494,353.51 — below the balance, a deficiency of $145,646.49 and a loan-to-value of 129.46 percent.

Three loan-to-value figures, from 70.15 percent to 129.46 percent, with one unchanged price and one unchanged balance. Track 8 lesson 11 showed a holding's row changing categorically; this is the continuous version, and it needs no threshold to be crossed.

Key terms

Volatility input: The single figure a collateral model consumes to size a discount. Everything about how it was measured — window, anchor, divisor — is invisible downstream.
Advance-rate model: The arithmetic that turns a volatility figure into a percentage of market value a lender will count. Mechanical, so it applies without anybody reviewing the borrower.
Collateral deficiency: The amount by which a balance exceeds lending value. It can arise from a volatility print alone, with no change in market value.

Worked example

One holding, one price, three volatility prints

9,400 shares at $128.75, so $1,210,250 of market value. Balance $640,000. Coverage multiple 3.5, assumed exit 22 sessions, so the square root factor is 4.6904. Illustrative throughout.

Volatility 23.8%: Haircut 24.61%, advance 75.39%
Loan-to-value at 23.8%: 70.15%
Volatility 38.5%: Haircut 39.81%, advance 60.19%
Volatility 57.2%: Haircut 59.15%, advance 40.85%
Lending value lost across the three prints: $418,023.47
Change in market value: $0

The holding went from $272,376.98 of spare lending value to a $145,646.49 deficiency without trading a share.

Check yourself

12,600 shares at $74.20 are pledged against a $520,000 balance. The lender uses a 3.5 multiple and a 16-session exit. Volatility rises from 21.4 percent to 36.9 percent. What happens to the loan-to-value?

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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.