30 stocks is NOT all you need for diversification

According to statistics, by holding a higher number of stocks, the portfolio variance will be lower. Thus, the risk of the entire portfolio is brought down. Researchers have said that 30 stocks, or even 18 stocks, is all you need to get the effect of diversification.

In 1970, Lawrence Fisher and James H. Lorie did a study "Some Studies of Variability of Returns on Investments In Common Stocks", which was published in The Journal Of Business. They showed that a randomly created portfolio of 32 stocks could reduce the distribution by 95%, compared to a portfolio of the entire New York Stock Exchange.

However, is it entirely true that you just need 32 stocks to be within 95% of the market?

A study by William Bernstein

According to William Bernstein, in his book "The Four Pillars of Investing", when you hold a smaller number of stocks in your portfolio, you will incur a higher chance of outperforming and underperforming the market. Thus, to be as close as possible to the market, you should hold as much as possible of the entire market.

I will quote verbatim from William Bernstein.

From The Pillars of Investing

But there is a much more important reason why you should not attempt to build your own portfolio of stocks, and that is the risk of buying the wrong ones. You may have heard that you can obtain ade- quate diversification by holding as few as 15 stocks. This is true only in terms of lowering short-term volatility. But the biggest danger fac- ing your portfolio is not short-term volatility—it’s the danger that your portfolio will have low long-term returns.

In other words, you can buy a 15-stock portfolio that has low volatility, but it may put you in the poorhouse just the same. In order to demonstrate the risks of not owning enough stocks, Ronald Surz of PPCA Inc., a provider of investment software, kindly supplied me with some data he generated on the returns of random stock portfolios, which I plotted in Figure 3-6. Mr. Surz examined 1,000 random port- folios of 15, 30, and 60 stocks. What you are looking at is the final wealth of these portfolios relative to the market. For example, look at the cluster of bars on the left—the 15-stock portfolios.

First, note the middle black bar and the thick horizontal line through it, which represents the market return at the 50th percentile (the medi- an performance). By definition, this returned $1.00 of wealth after 30 years relative to the market—that is, it got the market return. The bar at the extreme left, representing 5th percentile performance, beating 95% of all of the random portfolios, returned two-and-one-half times the wealth of the market portfolio. At the 25th percentile—the top quarter of performance—you got almost 50% more than the market’s final wealth.

Figure 3-6 shows us just how much luck can contribute to portfolio performance. The 60-stock portfolios are about the size of a small mutual fund. Notice that, purely by chance, one out of 20 of the port- folios had a 30-year wealth of $1.77 or more, relative to the market’s $1.00. This means that, by accident, these portfolios beat the market by more than 2% per year over 30 years—enough to put any manag- er in the Mutual Fund Hall of Fame. (The 95th-percentile-by-accident portfolios would similarly be expected to beat the market by more than 10% in any one-year period.)

Now, go back to the 15-stock portfolios on the left. If you were unlucky and got bottom quarter performance (the fourth bar), after 30 years you only received 70 cents on the dollar. And if you were real- ly unlucky and got bottom 5% performance (95th percentile), then you received only 40 cents on the dollar.

Note how adding more stocks (the 30-stock and 60-stock portfolios) moderates the differences in returns—the lucky picks don’t do quite as well, and the bad draws don’t do quite as badly. Finally, if you own all the stocks in the market, you will always get the market return, with no risk of failing to obtain it.

Figure 3-6 demonstrates the central paradox of portfolio diversification. Obviously, a concentrated portfolio maximizes your chance of a superb result. Unfortunately, at the same time, it also maximises your chance of a poor result. This issue gets to the heart of why we invest. You can have two possible goals: One is to maximize your chances of getting rich. The other is to minimize your odds of failing to meet your goals or, more bluntly, to make the likelihood of dying poor as low as possible.

In short

The entire post is summed up nicely by this paragraph in the book.

In other words, concentrating your portfolio in a few stocks maxi- mizes your chances of getting rich. Unfortunately, it also maximizes your chance of becoming poor. Owning the whole market—indexing—minimizes your chances of both outcomes by guaranteeing you the market return.

What we can draw from this is that we should choose an index fund which owns as much as possible the total number of shares in the entire index, for this will give us the least tracking error, "minimising your chance of becoming poor".
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