Is there a connection between portfolio theory and statistics?

Question

In my finance textbook, it says that owning 30 individual stocks is considered diversified. Is there a connection between this assertion and the statistical concept that a random sample size needs to be at least 30 to be distributed normally around the mean? If so, why is 30 this magic number? Is it special like Pie and E?

Answer 1

There is definitely a connection between portfolio theory and statistics; portfolio theory is little but applied statistics.

As to your actual question, 30 is not a magic number, it's a rule of thumb.

It's possible to have a diversified portfolio with less than 30 securities in it, provided that correlations between their returns are sufficiently low. But, since correlations are generally positive, 30 is considered a reasonable number that would generally allow you to lower portfolio volatility to near-market level.

As to your assertion that "a random sample size needs to be at least 30 to be distributed normally around the mean", it's simply wrong. You generally need 30 or more observations to conclude with high degree of certainty whether they are distributed normally...