Lesson 9 of 25 · 7 min
Why a variable rate can move with no change in stated capacity
Two formulas share no symbol, which makes the numbers independent on the ledger and not independent in the world.
Track 5 lesson 12 established that a rate change is not a capacity change. This lesson asks why the two are unlinked, and then why the answer is narrower than it first sounds.
The ledger reason is simple enough to check by inspection. Capacity is market value multiplied by advance rates, an expression containing no interest rate anywhere in it. The rate is an index plus a spread, an expression containing no collateral anywhere in it. Two formulas, no shared symbol. A reset writes to the accrual engine; a revaluation writes to the collateral record; neither process calls the other.
You can see the independence as an exact fact on a single day. When the rate on a facility moves from 6.35 to 7.75 percent at a reset, a portfolio worth $2,455,000 at a blended 61 percent advance rate has a lending value of $1,497,550 before the reset and $1,497,550 after it. Not approximately the same. The same number, because nothing in the calculation moved.
Then look nine months later. The same portfolio is worth $2,031,000 and carries a blended 56 percent, so lending value is $1,137,360 — a fall of 24.05 percent. Decompose it: prices did 17.27 percent of the work, since 2,031,000 ÷ 2,455,000 = 0.82729, and the advance rate cut did 8.20 percent, since 0.56 ÷ 0.61 = 0.91803. Multiply the two factors and 0.82729 × 0.91803 = 0.75948, which is the 24.05 percent fall. Neither piece was caused by your rate. Both were caused by whatever caused your rate.
A rate change does not cause a capacity change. It does not follow that capacity is unaffected by whatever moved the rate, and the rest of this track is about the second sentence.
Key terms
- Accounting independence
- Two figures computed from expressions with no symbol in common, so neither can move the other directly. True and easily over-read.
- Common cause
- A third variable that moves two figures at once. It produces correlation with no causal link running between them.
- Multiplicative decomposition
- Splitting a total change into factors that multiply rather than add. Two declines combined always come to slightly less than their sum.
Worked example
Exact on the day, irrelevant over nine months
A $2,455,000 portfolio at a blended 61 percent advance rate, on the day of a reset and nine months later. Illustrative.
- Rate at the reset
- 6.35% to 7.75%
- Lending value before and after that reset
- $1,497,550 and $1,497,550
- Market value nine months on
- $2,031,000
- Blended advance rate nine months on
- 56%
- Lending value nine months on
- $1,137,360
- Total fall
- 24.05%
$2,455,000 × 0.61. The reset touched nothing in this line.
A fall of 17.27 percent: 2,031,000 ÷ 2,455,000 = 0.82729.
A cut of 8.20 percent: 0.56 ÷ 0.61 = 0.91803.
$2,031,000 × 0.56.
0.82729 × 0.91803 = 0.75948.
On the day of the reset the independence was exact and provable. Over nine months it was true and beside the point, because both numbers answer to the same environment.
Check yourself
Market value falls 12.4 percent over a period and the blended advance rate is cut from 64 percent to 59 percent. By how much does lending value fall, and why is it not 20.2 percent?
Saved in this browser only. No account, nothing sent anywhere.
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.