Law of Large Numbers

mechanism

A broad enough random sample starts to resemble the population it came from because stock-specific surprises partly cancel one another. That is why a randomly chosen basket of 30 stocks can roughly track the market’s return.

Pick 30 stocks at random—without identifying the next great company—and their combined return can still come out roughly the same as the entire market’s.

How randomness begins to reproduce the market

Each stock can surprise you, but a basket does not depend on any one surprise. As the sample widens, unusually strong and weak outcomes partially offset each other, reducing the influence of company-specific luck. What remains increasingly resembles the average outcome of the population from which the stocks were drawn. In this investing example, the population is the market and the random basket is its rough miniature.

Where it shows up

Thirty stocks as a miniature market

The episode’s random 30-stock basket shows the mechanism in its simplest form: breadth can approximate the market return even without successful stock selection. This supplies part of the logic behind Index Investing—capture a broad baseline instead of assuming that choosing individual winners is necessary.

Large is not the same as representative

The cancellation depends on a genuinely broad random sample. Thirty stocks chosen from one fashionable sector, or selected through a hidden bias, need not resemble the whole market. Nor does a market-like average eliminate risk: individual outcomes still vary, and highly uneven Power-Law Returns can leave a basket unusually sensitive to whether it includes a few exceptional performers.

Test the basket before trusting its average

Before treating a portfolio as market-like, write down the population it is meant to represent, then check whether its holdings were selected broadly and without a shared sector, size, or theme bias. If you cannot defend that sampling process, compare it with a broad index rather than calling it diversified.

Episodes that teach this

The Only Investment Advice You Ever Need - Future IQ · explained at 5:36 8,910 views
"If you randomly pick any 30 stocks... those 30 stocks will have roughly the same return as the entire market."