Lesson 21 of 25 · 7 min
Rate cycles: how far and how long, described in shape
Two cycles with an identical peak can differ by a factor of two and a half in cost, because the peak is one parameter of three.
A rate cycle is usually described by its peak. The peak is one of three numbers that define it, and on a capitalising facility it is not the one that dominates the cost.
The three are amplitude, how far the rate travelled from trough to peak; speed, how long it took to get there; and plateau, how long it stayed. What a borrower actually pays is the area beneath the path — rate multiplied by time — rather than the height of it.
Compare two cycles with identical peaks of 5.25 points above trough. Cycle A rises across 11 months, holds 4, and falls back across 9, for 24 months in total. Its area is 5.25 × 11 ÷ 2 plus 5.25 × 4 plus 5.25 × 9 ÷ 2, which is 28.875 plus 21 plus 23.625, or 73.5 rate-months. Cycle B rises across 22 months, holds 14, and falls across 18, for 54 months. Its area is 57.75 plus 73.5 plus 47.25, or 178.5 rate-months.
On a $1,375,000 balance, the interest above the trough rate is 1,375,000 × 73.5 ÷ 1,200 = $84,218.75 for cycle A and $204,531.25 for cycle B. A ratio of 2.43, from two cycles whose peaks were identical to the basis point.
The collateral leg reads the same shape differently. Collateral tracks the level of the rate, not the area beneath it, so it is at its lowest at the peak and recovers as the path comes back down. A long plateau is therefore a large cost and a modest extra drawdown; a tall, fast spike is a large drawdown and a modest cost. The same three parameters, weighted completely differently by the two legs.
Cost is an integral and collateral value is a level. Ask one cycle shape those two questions and the answers will not rank the cycles the same way.
Key terms
- Amplitude
- How far a rate travelled from trough to peak. The number cycles are usually named by, and the least complete of the three.
- Plateau
- How long a rate stayed near its peak. Contributes nothing to the collateral drawdown and a great deal to the cost.
- Rate-months
- Points of rate multiplied by months at that level. The area under a cycle, and what a capitalising facility actually pays for.
Worked example
Same peak, two and a half times the cost
Two illustrative cycles, both peaking 5.25 points above trough. Balance $1,375,000.
- Cycle A: 11 months up, 4 flat, 9 down
- 73.5 rate-months
- Cycle B: 22 months up, 14 flat, 18 down
- 178.5 rate-months
- Interest above trough, cycle A
- $84,218.75
- Interest above trough, cycle B
- $204,531.25
- Ratio
- 2.43
- Difference in peak
- None
28.875 + 21 + 23.625, over 24 months.
57.75 + 73.5 + 47.25, over 54 months.
$1,375,000 × 73.5 ÷ 1,200.
Both peaked at 5.25 points above trough.
Naming a cycle by its peak describes the collateral leg reasonably and the cost leg barely at all. The two cycles differ by $120,312.50 on an identical balance.
Check yourself
A cycle rises 3.80 points across 8 months, holds for 6, and falls back across 10. How many rate-months is that, and what does it cost above the trough rate on a $2,050,000 balance?
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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.