Lesson 16 of 25 · 6 min

Apply a haircut widening with a price move

The same 15-point cut costs $223,560.61 once Calder has already fallen 19 percent, because a haircut is a percentage of a smaller number.

A haircut is a percentage of current market value. Apply it after a price has already fallen and the dollar damage is smaller, because the percentage is being taken of a smaller number. Apply the 19 percent uniform move first, then cut Calder from 35 percent to 20 percent.

After the 19 percent move Calder is worth $1,490,404.05 and contributes $521,641.42 of lending value. Cutting the advance rate to 20 percent leaves $1,490,404.05 × 0.20 = $298,080.81. The cut now costs $521,641.42 − $298,080.81 = $223,560.61, which is $1,490,404.05 × 0.15. The same 15 points cost $276,000.75 on the unmoved row.

Book lending value after both shocks is $2,654,573.52 − $223,560.61 = $2,431,012.91. Market value is still the 19 percent figure, $4,886,563.95, because a haircut does not edit prices. Market LTV is still 38.03 percent. Lending-value LTV is $1,858,563.47 ÷ $2,431,012.91 = 76.45 percent.

Reverse the order and the ending totals match. Cut Calder to 20 percent on the March prices first, taking lending value to $3,001,250.50, then apply 19 percent: $3,001,250.50 × 0.81 = $2,431,012.91. Same market value, same lending value, same two LTVs. The dollar cost of the 15-point cut is path-dependent. The ending book, if nobody sells in the middle, is not.

Key terms

Stacked stress: A price move and a haircut widening applied to the same restatement. Each edits a different input on the same row.
Percentage of a smaller number: The property that a haircut applied after a decline removes fewer dollars than the same haircut applied to the unmoved price.
Commuting shocks: Two restatements whose ending totals agree regardless of order, provided no sale is forced between them.

Worked example

Nineteen percent, then fifteen points off Calder

Uniform 19 percent first. Then Calder's advance rate cut from 35 percent to 20 percent on the already-fallen row.

Calder market value after 19 percent: $1,490,404.05
Calder lending value at 35 percent: $521,641.42
Calder lending value at 20 percent: $298,080.81
Cost of the cut: $223,560.61
Book lending value after both: $2,431,012.91
Lending-value LTV: 76.45%

The cut is cheaper in dollars after the decline and more expensive as a share of the leftover lending value. The ending book matches the reversed order.

Check yourself

After a 19 percent decline, Calder is worth $1,490,404.05. The advance rate is then cut from 35 percent to 20 percent. What does the cut cost in lending value, and what is the book's lending value after both shocks?

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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.