The Quest for the Perfect Sample

Most investment advisors will tell you that you should diversify your portfolio. Many statisticians have spent years trying to find the perfect sample size that accurately reflects the population. Some claim that 20 is the "magic number" while others claim 30 or even 50. The problem with this approach is that in searching for the magic number, we tend to forget that these numbers are built on assumptions. Let me explain:

Suppose we have 26 stocks (labeled A-Z). Below represents our holding in each stock. Are we perfectly diversified?

But the magic number is 20...we have 26 stocks!

The magic numbers make certain assumptions. One of them is that you are investing an equal amount in each security. If one stock (stock C) goes bust, almost a third of the portfolio is lost. Does this look like a perfectly diversified portfolio to you?

Ok, so we invest an equal amount in each stock and our problem is solved, right?

Not quite...let's assume we invest $1,000 in each stock. What happens if we are over-invested in one particular industry?

Even though we invested the same in each stock, if the Financial Services industry falls, we put almost half our portfolio at risk. We're still not diversified.

I see what you're doing here! You won't fool me! We put an equal amount in each stock and then equally distribute by industry and we've solved the problem!

You could say that. However, let's take this example:

We just invested $2,000 in one stock in thirteen different industries. If we break down our portfolio by cap size (small, medium, large cap stocks), we can see that we are over-invested in small cap stocks. If a market force causes hardship on small cap stocks, our portfolio can take a huge hit.

Ok, I give up, you will find a problem with every solution I come up with...

You're absolutely correct! Next time you look to diversify your assets or try and find the perfect sample size, be cognizant of the fact that these principles make certain assumptions. Anyone that tells you that numbers never lie doesn't fully understand that numbers are meaningless when out of context.