law of large numbers

noun phrase
Updated on: 15 Nov 2017

Definition of law of large numbers

:a theorem in mathematical statistics: the probability that the absolute value of the difference between the mean of a population sample and the mean of the population from which it is drawn is greater than an arbitrarily small amount approaches zero as the size of the sample approaches infinity

First Known Use of law of large numbers

1911


Financial Definition of LAW OF LARGE NUMBERS

law of large numbers

What It Is

The law of large numbers states that as additional units are added to a sample, the average of the sample converges to the average of the population.

How It Works

Applied to finance, the law of large numbers implies that the more a company grows, the harder it is for the company to sustain that percentage of growth.

For example, let's assume recently founded Company XYZ has a market capitalization of $10 million. In year 1, XYZ grows 100% from $10 million to $20 million. Shareholders love XYZ's growth story, and would like the company to continue growing at 100% per year.

But to do so XYZ would have to grow its market capitalization by $20 million in year 2, $40 million in year 3, $80 million in year 4, etc.  If XYZ was able to grow 100% each year, within 20 years XYZ would be larger than the entire $14 trillion U.S. economy! As companies grow larger, their growth rates must slow.

Why It Matters

Large cap stocks cannot have the growth rates that small cap stocks have. The law of large numbers tells investors that companies with a small market capitalization have much more room to grow (at a much faster rate) than companies with large market capitalizations.

But a company will not grow forever. Eventually, a successful company will have to transition away from growth and toward income generation on its way to becoming a cash cow.


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