Lesson 18 of 20 · 6 min

What a confidence interval does and does not promise

A 95% interval is a statement about a procedure under assumptions, not a guarantee about your outcome.

Confidence intervals and percentile bands are the standard way uncertainty gets reported, and they are routinely read as promises they do not make.

What a 90 percent interval from a simulation actually says is: under these assumptions, 90 percent of the generated paths fell within this range. Every word of that is conditional. Change the volatility assumption and the range changes. Change the distributional shape and the range changes, most at the edges.

Three specific misreadings are worth naming. First, the interval says nothing about the 10 percent outside it — and for a leveraged holder, that region is where every consequential outcome lives, so the interval excludes precisely what needs analysis. Second, the endpoints are not bounds; outcomes beyond them are not merely unlikely, they are exactly what the interval declined to describe. Third, an interval on the ending value says nothing about the path, so touching a threshold mid-period is invisible in it, as lesson 11 showed.

In the standard setup the 5th percentile ending value is about $402,000, comfortably below the $428,571 trigger. So even the reported band's lower edge sits in the region where a call has occurred, and everything below that edge — the part the interval does not characterise — is the part where the forced-sale multiple applies.

The useful habit: read the tail outside the interval, not the interval. That is where the events that change your position are.

Key terms

Confidence interval: A range produced by a procedure that captures the quantity a stated share of the time, under the procedure's assumptions.
Percentile band: The simulation equivalent: the range between two percentiles of the generated outcomes. Conditional on every input.
Excluded tail: The outcomes outside the interval. Uncharacterised by construction, and where leveraged consequences concentrate.

Worked example

Reading the band and then reading past it

Standard setup, 10,000 runs, three-year horizon. Trigger value $428,571.

5th percentile ending value: $402,000
95th percentile ending value: $1,267,000
What the 90% band excludes: 1,000 of the 10,000 paths
Paths ending below the trigger: 6.8%
Paths touching the trigger at any time: 14.3%
The decision-relevant figure: 14.3%

The band's own lower edge is past the trigger, and the number that matters — 14.3 percent — is not in the band at all.

Check yourself

A simulation reports a 90% band of $402,000 to $1,267,000 for ending collateral value, with a trigger at $428,571. What should you notice?

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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.