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Law of Large Numbers

Written By
Paul Tracy
Updated August 12, 2020

What is the Law of Large Numbers?

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 Does the Law of Large Numbers Work?

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 Does the Law of Large Numbers Matter?

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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