According to their latest annual report, Vanguard’s S&P 500 Index Fund holds 503 unique stocks. The S&P 500, of course, has just 500. As most of you know, the S&P 500 is the most well known stock index, and anyone that reads personal finance literature on a regular basis knows they an index fund such as Vanguard’s should be one of their core holdings (note: this is not an endorsement of Vanguard’s fund).
But why do we invest in index funds? The answer is that many (most?) of us recognize that we can’t consistently beat the market, so we might as well try to follow with the market is doing.
What is the S&P 500?
The S&P 500 is an index of the 500 largest US companies. Investing in any one of these companies instead of all 500 could yield better results, but that also comes with more risk. If the risk level of the S&P 500 was a 4 out of 10 (with 10 being the most risky) then the risk associated with a particular company might be a 7. When you diversify with an index, you remove that additional risk.
Systematic vs. unsystematic risk
The risk that is removed by diversifying is called “unsystematic risk.” Unsystematic risk is the risk associated with a particular stock or company. Systematic risk, on the other hand, is the risk associated with overall market returns (in this case the S&P 500).
Unfortunately, you cannot reduce systematic risk (also called “market risk”) by diversifying within a certain investment class. Thus, someone invested in the S&P 500 is subject to the systematic risk of the market but, isn’t subject to the unsystematic risk of one particular stock.
Minimizing unsystematic risk
So… How many stocks does it take to remove unsystematic risk? In order to answer that question, we must first remember exactly how diversification works. If you invested in two stocks, Bank of America (BAC) and Wells Fargo (WFC), you would be still subject to unsystematic risk. The reason for this is that anything that affects the banking industry as a whole will affect these two banks. Their returns are strongly correlated.
In other words, companies in the same industry tend to rise and fall together. In this particular case, the actual correlation is about 0.69, with 1 being perfectly correlated and 0 meaning no correlation at all. But if you were to purchase Bank of America and Waste Management (WM) stock, the correlation is much lower at 0.25.
The whole point of diversification from a mathematical standpoint is to select stocks with correlations as close to 0 as possible. The less correlation you have, the more unsystematic risk you remove. The simplest way to achieve this is, of course, to buy a broad index fund.
How many stocks does it take?
As it turns out, you can actually remove unsystematic with many fewer than 500 stocks. What do you think it takes? 300? 200? 100? The number is actually closer to 30.
The exact number depends on whether or not you randomly select stocks or actually research and make well-informed decisions about the companies themselves. In the end, I’d be willing to bet that with enough time and energy (and computing power), I could find 10-12 stocks that collectively diversify away most of the unsystematic risk.
Risk is measured by the standard deviation of the returns. I won’t bore you with what that means, but after about 20 or 30 stocks you have diversified about 70% of all risk away. By adding more stocks to your portfolio you would only be able to diversify fractions of a percent more away. The 30% that remains is the market risk, and without investing in other asset classes, you can’t diversify away that market risk.
So what does this mean for you and me? Nothing really. Thankfully we can purchase broad index funds with very cheap fees. And even if we couldn’t, discount brokers have gotten so cheap that you could easily purchase 30 or stocks if you wanted.
The research behind the magic number of stocks to hold mattered much more back when index funds didn’t exist and transaction costs were high. But still… Understanding the number of stocks it takes to diversify does help you understand (and appreciate) the benefits of diversification and broad market index funds.