Lesson 25 of 25 · 8 min

One call, end to end, on a single timeline

A thirty-thousand-dollar gap became a hundred-and-twenty-eight-thousand sale and a residual of two hundred and seventy-nine dollars.

Every mechanism in this track appears in one episode, and the arithmetic reconciles across it. The account holds 2,940 units of a broad equity index fund at $214.60, worth $630,924, and 5,600 shares of a large-company stock at $81.25, worth $455,000: $1,085,924 of collateral. The balance is $690,000 of principal plus thirty days of accrual at an illustrative 7.65 percent: $690,000 × 0.0765 ÷ 360 = $146.625 a day, or $4,398.75, giving $694,398.75. The threshold is 66 percent of market value.

The timeline, hour by hour:

Monday 16:00 — permitted balance $1,085,924 × 0.66 = $716,709.84 against a balance of $694,398.75. Passes, with $22,311.09 of room in balance terms, equivalent to a 3.1 percent fall in collateral.
Tuesday 16:00 — the stock falls 14.8 percent to $69.225 ($387,660) and the fund falls 1.9 percent to $210.52 ($618,928.80). Collateral $1,006,588.80; balance $694,545.38. A 7.3 percent portfolio decline.
Wednesday 02:14 — the engine computes a permitted balance of $664,348.61 and writes a shortfall of $30,196.77. The ratio is 69.0 percent.
Wednesday 07:26 — notice sent, effective on sending. Two business days stated, with the right to sell without further notice reserved. Cure by outside cash $30,196.77; by posting collateral $30,196.77 ÷ 0.66 = $45,752.68; by selling pledged collateral $30,196.77 ÷ 0.34 = $88,814.03.
Wednesday 16:00 — nothing has been done. The stock falls a further 5.2 percent to $367,501.68; the fund is unchanged. Collateral $986,430.48; balance $694,692.00; shortfall $43,647.88; sale required $128,376.12.
Thursday 10:41 — the lender sells the fund, sized from Wednesday's figure: $128,376.12 ÷ $210.52 = 609.8 units, rounded to 610, realising $128,417.20.
Friday — the sale settles and the proceeds are applied. Balance $694,985.25 − $128,417.20 = $566,568.05; collateral $490,511.60 + $367,501.68 = $858,013.28; permitted balance $566,288.76. Residual shortfall $279.29.

The residual decomposes exactly. The sale was sized from Wednesday's close but executed on Thursday, by which point one more day of accrual had raised the requirement to $128,807.38; the sale fell $390.18 short, leaving $390.18 × 0.34 = $132.66 of gap. Settlement added one further day of interest, $146.63, with no collateral change and therefore no offset. Together, $132.66 + $146.63 = $279.29.

The headline figures: a gap first reported at $30,196.77, a sale of $128,417.20, a realised multiple of 4.25 where the threshold's multiple is 2.94, and an account still $279.29 in breach after a cure executed correctly on the number it was given.

Key terms

Stale sizing: Computing the size of a cure from a valuation that has since been superseded. It leaves a residual proportional to the change.
Residual decomposition: Attributing what is left of a shortfall to specific causes: undersized sales, accrual, settlement timing, further price moves.
Realised multiple: Total sold divided by the shortfall first reported. It exceeds the threshold's multiple whenever anything moves in between.

Worked example

The residual, accounted for to the cent

The episode above: threshold 66 percent, daily interest $146.625, fund units sold at $210.52 in round hundreds.

Shortfall first reported, Wednesday 02:14: $30,196.77
Requirement at Thursday's execution: $128,807.38
Actually sold: $128,417.20
Gap left by the undersized sale: $132.66
Gap added by one day of settlement interest: $146.63
Residual shortfall on Friday: $279.29

Two causes, both timing rather than judgment: a figure computed a day early and a repayment applied a day late.

Check yourself

In the episode above, the first shortfall was $30,196.77 and $128,417.20 was sold. Why is the realised multiple 4.25 when the threshold implies 2.94?

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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.