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/Example:

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

Best execution refers to the imperative that a broker, market maker, or other agent acting on behalf of an investor is obligated to execute the investor's order in a way that is most advantageous to the investor rather than the agent.