Confronting a Law Of Limits

These days, it’s hard to find a superlative that adequately describes Apple. But maybe simplest is best: biggest. Measured by market capitalization, Apple is the world’s biggest public company. This week it solidified its lead over Exxon Mobil, the previous titleholder, as Apple’s shares hit a record high of $526.29, which gave it a market capitalization of just under $500 billion. Apple becomes only the 11th company to reach the top spot since 1926, according Howard Silverblatt, a senior index analyst for Standard & Poor’s.

Here is the rub: Apple is so big, it’s running up against the law of large numbers. Also known as the golden theorem, with a proof attributed to the 17th-century Swiss mathematician Jacob Bernoulli, the law states that a variable will revert to a mean over a large sample of results. In the case of the largest companies, it suggests that high earnings growth and a rapid rise in share price will slow as those companies grow ever larger. If Apple’s share price grew even 20 percent a year for the next decade, which is far below its current blistering pace, its $500 billion market capitalization would be more than $3 trillion by 2022. That is bigger than the 2011 gross domestic product of France or Brazil. Put another way, to increase its revenue by 20 percent, Apple has to generate additional sales of more than $9 billion in its next fourth quarter. A company with $1 billion in sales has to come up with just another $200 million.