Lesson 11 of 25 · 6 min
Why capacity is the sum of lending values, not a percent of the total
The percent is a summary of a sum that already exists. It cannot stand in for the sum.
Collateral capacity, before any facility limit, is the sum of the per-name products. On the March book that sum is $3,277,251.25. It is not 54.32 percent 'applied to the account' as a policy. The 54.32 percent is 3,277,251.25 ÷ 6,032,795, which is the sum looking at itself. Using the percent as an input reverses the dependency.
The reversal produces a working shortcut and a structural error. The shortcut: if the mix and the rates are unchanged, 6,032,795 × 0.5432 recovers the sum, give or take rounding. The error: treating 54.32 percent as a rate the lender assigned to the pool, then applying it to a new mix, or to a stressed mix, as if the schedule were one row. A stressed Calder does not keep the old blend. Lesson 13 shows the blend rising as Calder falls.
Capacity talk also picks up a second meaning, which lesson 12 separates: the amount you may still draw, after the facility limit and the current balance. That figure is not a percent of market value either. It is a minimum of two dollar amounts, minus a third. Starting from 54.32 percent of $6,032,795 lands you in the right neighbourhood this month and the wrong identity forever.
Write the identity in the order the system uses it. Look up five rates. Multiply five market values. Add the products. Compare the sum with the limit. Compare the minimum with the balance. The percent, if anyone prints it, is a caption on the third step. It is not a substitute for the first three.
A percent of a total is how a blend is reported. A sum of products is how a blend is made. Capacity lives in the second sentence.
Key terms
- Collateral capacity
- The sum of per-name lending values, before any facility limit is applied. $3,277,251.25 on this statement.
- Shortcut blend
- Reusing last month's blended percent on this month's market value. It works only while mix and rates hold still.
- Dependency order
- Products first, sum second, percent third. Reversing the last two treats an output as an input.
Worked example
The sum, then the caption
March products as in lesson 2. The blend is computed after the sum, not before it.
- Sum of the five products
- $3,277,251.25
- Caption on that sum
- 54.32%
- Shortcut: $6,032,795 × 0.5432
- $3,277,014.24
- Shortcut: $6,032,795 × 0.543239
- $3,277,251.25
- What a 54.32% 'policy rate' would be
- A category that does not exist
$3,277,251.25 ÷ $6,032,795.
Rounding drift of $237.01 against the true sum.
Needs the unrounded blend.
Even the shortcut needs the unrounded quotient. The rounded 54.32 percent is already too coarse to rebuild the sum.
Check yourself
Someone applies 54.32 percent to the March market value of $6,032,795 and books $3,277,014 as lending value. What did they use as an input that is actually an output, and what is the true sum?
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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.