Lesson 25 of 25 · 7 min

What a model is for, and exactly where it stops

The conversion from assumptions to consequences is exact. The assumptions are the part that was never measured.

A model does one thing, and it is genuinely valuable: it converts stated assumptions into their consequences, exactly, at a level of detail no one reaches by intuition. That conversion is never the weak link. The assumptions are, and the honest way to show it is arithmetic rather than assertion.

One position, one model, two defensible choices. Collateral $1,470,000, a balance of $742,000, a 65 percent threshold, three years. The trigger value is $742,000 ÷ 0.65 = $1,141,538, a decline of 22.34 percent. They differ only in the window over which volatility was estimated: one analyst uses five years and gets 18.4 percent, the other one year and gets 27.9 percent.

Neither is wrong. A longer window is more stable and a shorter one more current, and no settled rule decides between them. Run 200,000 paths under each, identical in every other respect. The probability of touching the trigger over three years comes out at 24.12 percent on the first estimate and 48.52 percent on the second, a factor of 2.01. The first percentile of ending collateral is $805,977 against $514,342.

So the model reported two facts about two assumption sets, and neither was a fact about the market. The conclusion is not that the model is useless, nor that the cautious figure wins — picking it is still a choice made without evidence. It is that the output range across defensible assumptions is itself the result, and quoting one number from inside it discards the most informative thing the exercise produced.

What the choice did not touch is worth naming precisely. The trigger value of $1,141,538 is a division. The 22.34 percent decline is a subtraction. The cure multiple at a 65 percent threshold is 1 ÷ 0.35 = 2.857. The breach frontier from lesson 20 is two multiplications. None of those moved, because none of them requires a distribution. That is the boundary: a model converts what you told it, exactly, and stops at the edge of what you told it.

Key terms

Assumption set: The inputs and structural choices a result depends on. Two defensible sets can produce outputs a factor of two apart.
Output range: The span of results across defensible assumption sets. More informative than any figure inside it, and rarely the thing reported.
Distribution-free quantity: A figure computable from your own documents without a probabilistic assumption, such as a trigger value, a headroom percentage or a cure multiple.

Worked example

One position, two windows, two answers

Collateral $1,470,000, balance $742,000, threshold 65 percent, three years, 200,000 runs each. Only the volatility window differs.

Five-year window estimate: 18.4% volatility
One-year window estimate: 27.9% volatility
Ratio of the two answers: 2.01×
First percentile of ending collateral: $805,977 against $514,342
Trigger value, both cases: $1,141,538
Decline to the trigger, both cases: 22.34%

The probabilities differed by a factor of two and the arithmetic did not differ at all. That split is where a model stops.

Check yourself

Two analysts model the same facility. One estimates volatility over five years and gets a 24.12 percent chance of touching the trigger; the other uses one year and gets 48.52 percent. What is the most useful thing to take from the pair of results?

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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.