How Many Stocks Do You Need to Be Diversified?

How Many Stocks Do You Need to Be Diversified?This is a guest post from Philip (a.k.a., The Weakonomist) of Weakonomics. If you like what you see here, please consider subscribing to his RSS feed.

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.

15 Responses to “How Many Stocks Do You Need to Be Diversified?”

  1. Anonymous

    I think 20 stocks would represent a diversified portfolio. Picking stocks from different sectors also increases the diversification exercise. Picking 20 stocks from different sectors involves a lot of fundamental analysis, if you’ve not got the time like me its better to just invest in a index fund. Great post, very informative.

  2. Anonymous

    Question.. When diversifying a portfolio, do you want to do it in accordance with an index or do you want to invest equally in each industry sector? If I were to invest in 20 stocks in seven industry sectors, do I want to invest more in bigger industry sectors or equally across the board?

  3. Anonymous

    One corollary to this argument that should be mentioned is that the statistical correlation is calculated based on historical data. The issue with that is the fundamentals of the market place change over time, the interconnectedness of industries can change as the world changes. A good example of this might be the latest US housing boom and bust (or the tech bust where the internet distorted the marketplace). Historically financials and real estate were probably less correlated than in the run up to this last bust (same with tech and everything else). That might lead one to believe that one is more diversified than one actually is. So, to be on the safe side you probably want to lean toward more rather than fewer. Given Buffet-like prescience 6 stocks may be enough, and 12 might be enough given normal circumstances, but considering how booms and busts seem to occur due to marketplace distortions, a little extra insurance is probably advisable.

  4. Anonymous

    In my opinion the beginning of the article needs to emphasize more that unsystemmatic risk also includes industry risk it’s not just a numbers thing. During the internet bubble people would say they were well diversified when in fact they were heavily overweighted in a single sector. More recently we saw the same thing happen for the finance sector.

  5. Anonymous

    Last time I looked, 12 stocks was near the optimal point for getting away from company-related risk. Obviously the more you add the more diversified you get, but it’s very much a case of diminishing returns.

  6. Anonymous

    The higher the number does not necessarily mean that it is better diversified. The key indeed lies in correlation. Picking the least correlated stocks would protect your basket from being swayed into one direction simply because an industry is doing well (or otherwise).

    But as an individual investor, I still prefer to pick my own stocks and not to invest in index funds. But I guess, that’s just the gambler in me.

  7. Anonymous

    Statistically, they say 15 – 20 well-selected stocks in different lines of business. But why take the chance that you might pick a bunch of duds. Make it easy on yourself and just buy the whole damn market (VTI). You won’t make a fortune overnight, but over 30 years you’ll beat at least 75% of the pros.

  8. Anonymous

    This is a great article that does a terrific job of explaining diversification within asset classes. It also is a good application of statistical analysis where 30 is a sample size that does a relatively good job of approximating the larger population from which the sample was taken.

    @Smarter Spend – I’m guessing that the 4 out of 10 and 7 numbers are relative numbers based on standard deviation measurements. Philip probably didn’t want to get into a discussion of sigmas with this post, but I’d say it’s a good relative scale with these numbers. The S&P 500 is usually just below the average of individual issues (stocks) and investors picking a stock touted on CNBC, in SmartMoney, etc. will frequently pick one that has above average risk…a 7.

  9. Anonymous

    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.

    Where are you getting these numbers?

  10. Anonymous

    Great article, and right on. Take home message? More risk for more reward… only after you have removed unsystematic (specific) risk.

  11. Anonymous

    (A different Dan)

    Truth be told, there is market risk in every asset class, too. In the end, there is *some* correlation between ALL classes.

    If it was truly possible to diversify away risk by holding multiple asset classes, we’d all be rich, because there would be a perfect mix.

  12. Nickel

    Dave: While it’s possible to statistically reduce risk with a relatively small number of stocks, it’s not easy to identify them, and hardly worth the trouble. I would go a step further, and say to go with a Total Market fund instead of the S&P 500, or do S&P 500 *plus* a small cap index of some sort.

    Dan: The premise of the article is not flawed. Philip says right there in the article that you can’t diversify away systematic risk without including multiple asset classes:

    “The 30% that remains is the market risk, and without investing in other asset classes, you can’t diversify away that market risk.”

  13. Anonymous

    If you want to be diversified you can’t just invest in stocks. Plain and simple. The premise of the article is flawed. You need to also go into bonds, real estate, cash. Maybe some gold, oil… baseball cards…

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