Lesson 20 of 20 · 7 min

The difference between a model and the world

A model is a set of assumptions with the arithmetic done; the world is under no obligation to match it.

This closing lesson is the same point as Track 3's closing lesson, arriving from the probability side. It is worth stating twice.

Every number in this track came from assumptions. The 14.3 percent touch probability assumed 20 percent volatility, normally distributed returns, monthly steps, and a stationary process for three years. Each of those is false in a documented way. The number is not therefore useless — it is a precise statement of what those assumptions imply, and stating implications precisely is genuinely valuable.

What survives the criticism, and is worth relying on:

Arithmetic identities. The forced-sale multiple, loan-to-value, headroom and recovery asymmetry are algebra, not forecasts.
Directional statements. Higher volatility raises touch probability; leverage increases path dependency; interest raises the trigger value.
Sensitivity results. Knowing that the answer moves elevenfold across plausible volatility inputs is robust knowledge.
Stress-test consequences. If collateral falls 40 percent, the required sale is $160,000. That does not depend on any probability.

What does not survive, and should not be leaned on:

Tail probabilities. Wrong by orders of magnitude, in a known direction.
Correlation estimates under stress. Measured in calm and applied in crisis.
Any single point estimate reported without its inputs.
The assumption that the largest historical decline is a bound.

Take the risk you can measure. The measurable part is the arithmetic: your trigger value, your headroom, your multiple, and how the answer moves when you change an assumption. The probability that it happens is the part nobody can hand you.

Key terms

Model: A set of assumptions with their implications worked out. Reliable exactly to the extent its assumptions hold.
Robust conclusion: A result that holds across a wide range of assumptions. Arithmetic identities and directional statements qualify; tail probabilities do not.
Measurable risk: The part of an exposure you can compute from your own documents: trigger value, headroom, forced-sale multiple, and stress consequences.

Worked example

Sorting one simulation's outputs by how much weight they bear

The standard setup's results, classified by robustness.

Trigger value $428,571: Arithmetic
Forced-sale multiple 3.33×: Arithmetic
Headroom 28.6%: Arithmetic
Touch probability rises with volatility: Robust direction
Touch probability is 14.3%: Assumption-dependent
A 20% one-day decline is a 1-in-10⁴⁵ event: Wrong

Three of these are facts about your position, two are conditional statements, and one is an artefact of a bad assumption. Knowing which is which is the skill.

Check yourself

Which of these is the most reliable: your 28.6% headroom, the 3.33 forced-sale multiple, or the 14.3% probability of touching your trigger?

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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.