Lesson 25 of 25 · 7 min

One position, three volatility regimes, three cushions

Nothing about the holding changes across the three cases, and the decline it survives goes from 38.6 percent to 6.5 percent.

Everything in this track reduces to one arithmetic chain. Here it is, run three times on a position that never changes, so that the only thing moving is the statistic.

The position: 6,300 shares at $186.40, so $1,174,320 of market value, against a $560,000 balance. The lender uses a 3.5 coverage multiple, an 18-session assumed exit, and a maintenance test that the balance may not exceed 90 percent of lending value. So the trigger lending value is 560,000 ÷ 0.90 = $622,222.22 in all three cases. These are illustrative figures.

Quiet regime, 14.7 percent annualised volatility. Daily 0.9260 percent, haircut 3.5 × 0.9260 × 4.2426 = 13.75 percent, advance rate 86.25 percent, lending value $1,012,844.06, loan-to-value 55.29 percent. The trigger market value is 622,222.22 ÷ 0.8625 = $721,422.01, which is $114.51 a share, so headroom is (1,174,320 − 721,422.01) ÷ 1,174,320 = 38.57 percent.

Ordinary regime, 26.8 percent. Daily 1.6882 percent, haircut 25.07 percent, advance rate 74.93 percent, lending value $879,928.49, loan-to-value 63.64 percent. Trigger market value $830,394.75, or $131.81 a share, and headroom 29.29 percent.

Stressed regime, 46.3 percent. Daily 2.9166 percent, haircut 43.31 percent, advance rate 56.69 percent, lending value $665,725.72, loan-to-value 84.12 percent. Trigger market value $1,097,581.15, or $174.22 a share, and headroom 6.53 percent.

Six point five three percent. Same shares, same price, same balance, same agreement. The company was not reassessed and the borrower did not draw a dollar more. One input to a formula moved.

Key terms

Trigger market value: The market value at which the balance exactly reaches the maintenance threshold. It rises when the advance rate falls, even with the balance fixed.
Survivable decline: The percentage fall in market value the position absorbs before the maintenance test is breached. Headroom, stated as the event it corresponds to.
Regime sensitivity of headroom: How much the survivable decline changes for a change in volatility alone. Here, 32 points of headroom across 31.6 points of volatility.

Worked example

One pledged position, three regimes

6,300 shares at $186.40, so $1,174,320 of market value, against a $560,000 balance. Coverage multiple 3.5, 18-session exit, maintenance test at 90 percent of lending value, so trigger lending value is $622,222.22 throughout. Illustrative figures.

Quiet, 14.7% volatility: Haircut 13.75%, advance 86.25%
Quiet: trigger and headroom: $721,422.01, or $114.51 a share
Ordinary, 26.8% volatility: Haircut 25.07%, advance 74.93%
Ordinary: trigger and headroom: $830,394.75, or $131.81 a share
Stressed, 46.3% volatility: Haircut 43.31%, advance 56.69%
Stressed: trigger and headroom: $1,097,581.15, or $174.22 a share

The price at which a call becomes possible rose from $114.51 to $174.22 while the share traded at $186.40 the whole time. The holding was identical in all three cases.

Check yourself

The same 6,300 shares at $186.40, the same $560,000 balance, the same 90 percent maintenance test, a 3.5 multiple and an 18-session exit. Volatility is 35.5 percent. What is the headroom?

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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.