Lesson 15 of 25 · 6 min

Narrative, and the story a concentration needs

A sentence has no error bars, and four conditions that are each very likely are jointly close to a coin flip.

A large single holding tends to come with a sentence attached. The sentence is short, it is repeatable, and it survives contact with other people, which is most of what a sentence is selected for.

What a sentence cannot carry is a conjunction. A claim that reads as one proposition is usually several, each of which has to hold for the whole to hold, and joint probability multiplies. Four conditions at illustrative likelihoods of 0.85, 0.80, 0.75 and 0.90 give 0.85 × 0.80 × 0.75 × 0.90 = 0.459. Every individual condition looked comfortable. The conjunction is 45.9 percent, and the chance that at least one fails is 1 − 0.459 = 54.1 percent.

The four conditions, of the kind a single sentence compresses into one clause:

The demand that drove the last decade continues at a similar rate.
No competitor takes a material share of it.
Margins hold rather than compressing as the market matures.
The financing to fund the growth stays available on similar terms.

The arithmetic runs the other way from the intuition. Adding a condition can only lower the joint figure, yet adding a condition to a story makes it more detailed, and a more detailed story is more persuasive. Three of these conditions give 0.51; the fourth takes it to 0.459. Each extra clause of specificity buys conviction and costs probability.

Under a pledge the relevance is narrow and direct. The size of a draw is set against the confidence in the position, the confidence is carried by the sentence, and the sentence rounds a 45.9 percent conjunction up to something that sounds like a near-certainty. The maintenance test, by contrast, has no view on the story at all.

Key terms

Conjunction: A claim that requires several things to be true at once. Its probability is the product of the parts, so it is always lower than the weakest-sounding part suggests.
Joint probability: The chance that all of a set of conditions hold together. Multiplication, not averaging.
Narrative compression: Reducing a multi-part claim to one sentence. The parts survive; the requirement that all of them hold does not.

Worked example

Four comfortable conditions, one uncomfortable product

A single-sentence case for a holding, decomposed into four conditions with illustrative probabilities.

Demand continues: 0.85
No material share lost to a competitor: 0.80
Margins hold: 0.75
Financing stays available on similar terms: 0.90
Chance all four hold: 45.9%
Chance at least one fails: 54.1%

No single condition was even close to a coin flip. Their conjunction is worse than one, and the sentence contains no trace of it.

Check yourself

A case for a holding requires four conditions with probabilities 0.85, 0.80, 0.75 and 0.90. What is the chance that the case holds in full, and why does adding detail lower it?

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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.