Law Of Large Numbers

DEFINITION of 'Law Of Large Numbers'

A principle of probability and statistics which states that as a sample size grows, its mean will get closer and closer to the average of the whole population. The law of large numbers in the financial context has a different connotation, which is that a large entity which is growing rapidly cannot maintain that growth pace forever. The biggest of the blue chips, with market values in the hundreds of billions, are frequently cited as examples of this phenomenon. 

BREAKING DOWN 'Law Of Large Numbers'

As an example, assume that company X has a market capitalization of $400 billion and company Y has a market capitalization of $5 billion. In order for company X to grow by 50%, it must increase its market capitalization by $200 billion, while company Y would only have to increase its market capitalization by $2.5 billion. The law of large numbers suggests that it is much more likely that company Y will be able to expand by 50% than company X.

The law of large numbers makes logical sense. If a large company continues to grow at 30-50% every year, it would eventually become bigger than the economy itself! Obviously, this can't happen and eventually growth has to slow down. As a result, investing in companies with very high market capitalization can dampen the potential for stock appreciation.

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