Lesson 17 of 25 · 7 min

Why a haircut is a volatility forecast wearing different clothes

Run the model backwards and a published percentage becomes readable, but only as one product of two numbers you must fix separately.

Lesson 16 ran the collateral model forwards. Run it backwards and a published advance rate turns into a statement about what the lender must be assuming. This reversal is the most useful thing in the track, because the advance rate is the one figure a borrower is actually given.

Suppose a schedule credits a single large-company equity at 65 percent. That is a 35 percent haircut. The model says 0.35 equals the coverage multiple times the daily volatility times the square root of the assumed sessions. Two of those four quantities are now known.

Say realised volatility on the name is 32 percent, so the daily figure is 32 ÷ 15.8745 = 2.0158 percent. Then the multiple times the square root of the days must equal 0.35 ÷ 0.020158 = 17.363. That is the entirety of what the published haircut tells you: a single product. It does not identify the multiple and it does not identify the exit length; it constrains them jointly.

The product admits many readings, all consistent with the same 65 percent. With the 2.33 multiple Track 7 lesson 9 used, the implied exit is 17.363 ÷ 2.33 = 7.4518 sessions squared, which is 55.5 sessions — eleven weeks. With a 3.5 multiple it is 24.6 sessions. And if the agreement states a ten-session exit, the implied multiple is 17.363 ÷ 3.1623 = 5.49.

That last reading is the informative one. A multiple of 5.49 is far beyond anything a normal distribution justifies at a 99 percent confidence level, which is about 2.33. So either the lender is assuming an exit measured in weeks rather than days, or the published haircut contains a margin of conservatism that has nothing to do with volatility. Both are entirely reasonable positions for a lender to hold. The point is that the haircut cannot distinguish them, and any reading that attributes the whole 35 percent to the asset's volatility is crediting volatility with work that a time assumption and an appetite did.

A haircut is a volatility forecast multiplied by a time assumption multiplied by an appetite for coverage. Fix any two and the third is readable. Fix none and you have one equation and three unknowns.

Key terms

Reverse engineering a haircut: Solving the discount model for its inputs instead of its output. It yields a single product of the coverage multiple and the square root of the assumed exit.
Implied exit window: The number of sessions a published haircut would correspond to, once a coverage multiple and a volatility figure are assumed. Often far longer than a borrower expects.
Conservatism wedge: The part of a published haircut not explained by volatility and a plausible exit length. It does not move when volatility moves, which matters in lesson 24.

Worked example

One published haircut, three consistent readings

A 65 percent advance rate, so a 35 percent haircut, on a name whose realised volatility is 32 percent. Daily volatility 2.0158 percent. Illustrative throughout.

What the haircut pins down: Multiple × root days = 17.363
Reading it with a 2.33 multiple: An exit of 55.5 sessions
Reading it with a 3.5 multiple: An exit of 24.6 sessions
Reading it with a stated 10-session exit: A multiple of 5.49
Multiple a normal 99th percentile would use: 2.33
What the haircut says about the asset alone: Nothing, without one of the other two

Three readings, one advance rate, and no way to choose between them from the published figure. That ambiguity is a property of the arithmetic, not of any particular lender.

Check yourself

A schedule credits a holding at 72 percent. Realised volatility on the name is 24 percent and the lender states a 3.5 coverage multiple. What exit window is the haircut consistent with?

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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.