Lesson 13 of 25 · 7 min
Headroom as a daily number
With prices held flat, thirty days of interest alone shave twenty-seven hundredths off the March headroom.
Headroom is usually met as a month-end percentage. It is also a daily remainder: today's book minus today's trigger, divided by today's book. Hold the March book at $6,032,795 and let only the balance move at $372.75 a day. The 31 March remainder is 55.99 percent. After one day the balance is $1,858,936.22, the trigger is $2,655,623.17, and the remainder is $3,377,171.83, or 55.98 percent.
After fifteen days the accrued interest is $5,591.18, the balance is $1,864,154.65, the trigger is $2,663,078.07, and headroom is $3,369,716.93, or 55.86 percent. After thirty days the invented April interest of $11,182.36 has taken the balance to $1,869,745.83 and the trigger to $2,671,065.47. Headroom on the frozen March book is $3,361,729.53, or 55.72 percent. Thirty days of interest, prices unchanged, is 0.27 percentage points.
That path is not a forecast of April. It is the isolated effect of the balance path on a ratio that also has a book path. A daily headroom number is the two paths evaluated on the same morning. The letter that prints 55.99 percent is the evaluation on 31 March. The evaluations on the other thirty mornings are the same subtraction performed on later balances.
Hₙ = (Mₙ − (B + n × d) ÷ t) ÷ Mₙ
- Hₙ
- Headroom as a percentage on day n after the last close.
- Mₙ
- Market value on day n.
- B
- Last closing balance.
- d
- One day's interest at the last known rate and day-count.
- t
- The maintenance threshold, here 0.70.
Key terms
- Daily headroom
- Today's book minus today's trigger, divided by today's book. A remainder that exists on mornings the letter does not cover.
- Isolated balance path
- The headroom path obtained by accruing interest and holding every last sale fixed. It measures what the numerator alone does.
Worked example
March book held flat through thirty April days
Book $6,032,795, opening $1,858,563.47, 7.22 percent Act/360, threshold 70 percent of market value.
- Day 0 headroom
- 55.99%
- Day 1 headroom
- 55.98%
- Day 15 headroom
- 55.86%
- Day 30 headroom
- 55.72%
- Movement from interest alone
- 0.27 percentage points
Trigger $2,655,090.67.
Trigger $2,655,623.17.
Trigger $2,663,078.07.
Trigger $2,671,065.47.
The book did not move. The remainder still fell by 0.27 points because the trigger is a rising numerator divided by a fixed 0.70.
Check yourself
Prices stay at the March book of $6,032,795 for thirty days. Interest of $11,182.36 posts. What is headroom on day 30?
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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.