Lesson 22 of 25 · 7 min

Sequence reversed

Reverse the order and the ending book matches — unless a sale was forced in the middle, in which case nothing matches.

The same three shocks, reversed: ten days at 8.47 percent first, then Calder cut from 35 percent to 20 percent on the March prices, then the 19 percent uniform move. If no sale is forced at an intermediate step, the ending market value, lending value and balance are the same three numbers the previous lesson ended on.

Rate first. Ten days add $4,372.79. Balance $1,862,936.26, trigger $2,661,337.51. Prices and advance rates are still the March figures, so market value is $6,032,795 and lending value is $3,277,251.25. Both tests pass easily. Haircut second. Calder's 15-point cut takes lending value to $3,001,250.50 and leaves market value at $6,032,795. Market LTV is still 30.81 percent against a slightly higher trigger. Still a pass. Price third. Market value becomes $4,886,563.95 and lending value becomes $3,001,250.50 × 0.81 = $2,431,012.91. Those are the previous lesson's ending totals.

The intermediate pictures differ. Price-first put lending value through a 70 percent lending-value line on day one. Rate-first never did: the haircut left $3,001,250.50, and only the last step took lending value to $2,431,012.91, in one jump, after the other two shocks had already been absorbed on a still-intact book.

Put a forced sale at the first lending-value fail and the two sequences stop being rearrangements of each other. Price-first would sell at a $517.15 shortfall, shrink the book, and then apply the haircut and the reset to whatever was left. Rate-first would not sell until the last step, and would then be selling a 20-percent-advance Calder inside an already-fallen book. Same three shocks, two leftover statements. The order is part of the arithmetic the moment a sale sits inside it.

Key terms

Reversed sequence: The same shocks applied in the opposite order. Ending totals agree if every intermediate test passed.
Path-dependent sale: A sale forced by an intermediate fail. It edits the book that the remaining shocks are then applied to.
Intact book: A pledged account to which no sale has yet been applied. Rate-first keeps the book intact until the last step.

Worked example

Reset, haircut, price — the same ending, a different middle

Ten days at 8.47 percent, then Calder 35 to 20 on March prices, then a 19 percent uniform move. No intermediate sale.

After the reset, trigger: $2,661,337.51
After the haircut, lending value: $3,001,250.50
After the price move, market value: $4,886,563.95
After the price move, lending value: $2,431,012.91
Ending balance: $1,862,936.26
Where the sequences would have split: A sale at the $517.15 lending-value fail

Without a sale the three shocks commute. With a sale they produce two different leftover statements from one list of events.

Check yourself

Rate, haircut, then a 19 percent price move, with no sale in between, ends at market value $4,886,563.95 and lending value $2,431,012.91. What would have to happen in the price-first sequence for those two figures to disagree?

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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.