Lesson 9 of 25 · 7 min
Why the exit window, not the price, sets the discount
The discount answers a question about days; volatility only converts those days into dollars.
Volatility is usually blamed for a large haircut, and it is only half of the explanation. The other half is the number of days from lesson 8, and it is the half that changes when a position grows.
A discount sized for a liquidation has to cover the adverse move that can occur while the sale is running. Move sizes scale with the square root of elapsed time, which is the same scaling that gives an option's time value its shape in Track 3. So the discount is a daily volatility, stretched by the square root of the days, multiplied by how many standard deviations of adverse move the lender wants covered.
haircut = k × daily volatility × square root of days
- haircut
- The percentage of market value withheld as a buffer.
- k
- How many standard deviations of adverse move the lender wants covered. An illustrative 2.33 covers roughly the worst 1 percent.
- daily volatility
- Annualised volatility divided by the square root of 252 trading days.
- square root of days
- The stretch applied for a liquidation lasting more than one session.
Hold volatility fixed at 38 percent annualised, so daily volatility is 38 ÷ 15.8745 = 2.394 percent, and let k be 2.33. A two-day exit needs 2.33 × 2.394 × 1.4142 = 7.89 percent. An eleven-day exit needs 2.33 × 2.394 × 3.3166 = 18.50 percent. A nineteen-day exit needs 2.33 × 2.394 × 4.3589 = 24.31 percent. One company, one volatility, and haircuts from 8 percent to 24 percent.
Two holders of the identical company can face haircuts three times apart, and no fact about the company distinguishes them. Only the number of sessions their exits require does.
Key terms
- Liquidation window
- The number of sessions a lender expects an exit to take. It is set by position size against volume, not by price.
- Daily volatility
- Annualised volatility divided by the square root of the number of trading days in a year, roughly 15.87.
- Coverage multiple
- How many standard deviations of adverse move a discount is built to survive. A larger multiple means a wider haircut at the same volatility.
Worked example
One volatility, three exit lengths
Annualised volatility 38%, so daily volatility is 2.394%. Coverage multiple 2.33. Illustrative figures throughout.
- Two-day exit
- 7.89%
- Eleven-day exit
- 18.50%
- Nineteen-day exit
- 24.31%
- Advance rate implied by the nineteen-day figure
- 75.69%
- Change in volatility across the three rows
- None
2.33 × 2.394 × 1.4142.
2.33 × 2.394 × 3.3166.
2.33 × 2.394 × 4.3589.
100% − 24.31%, before any other adjustment.
The haircut tripled on an unchanged asset. Days did all the work, and days are a function of size.
Check yourself
A holding has 26% annualised volatility and the lender's exit assumption is nine days with a coverage multiple of 2.33. What haircut does the formula give?
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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.