The Illusion of Diversification: The Myth of the 30 Stock Portfolio

Jim Cramer, the star of CNBC's Mad Money use to do a segment called "Am I Diversified?" in which viewers would call in, give Cramer their top five holdings and Cramer would let them know if they were well diversified.

The idea of five stock diversification is quite low and mostly refuted by the "stock picking" community, which tends to believe the number of individual stocks needed to be diversified is actually closer to 30. While 30 is no doubt better than five, it just isn't good enough.

Key Takeaways

  • It has long been known that diversification can help reduce one's portfolio risk while also boosting returns.
  • Just how many stocks are enough to achieve a properly diversified portfolio has been a subject of research and debate.
  • Owning 30 stocks across a range of industry sectors has become a rule of thumb for achieving diversification. But how good is this rule of thumb? Read on to find out.

Where Does the Magical Number 30 Come From?

In 1970, Lawrence Fisher and James H. Lorie released "Some Studies of Variability of Returns on Investments In Common Stocks" published in The Journal Of Business on the "reduction of return scattering" as a result of the number of stocks in a portfolio. They found 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.

From this study came the mythical legend that "95% of the benefit of diversification is captured with a 30 stock portfolio." Of course, no self-respecting stock jock would tell people they create a random portfolio so the investment managers adjusted this to "We pick the best 30 and achieve max diversification at the same time." In this statement, they are essentially saying, "we can capture the return of the market and capture the diversification to the market by picking the 30 best stocks," and they often use something like Figure 1 to prove their claims. Unfortunately, neither point is really true.

Figure 1: Total portfolio risk as a function of the number of stocks held (%)

The Reduction of Risk Is Not the Same As Increasing Diversification

The Fisher and Lorie study was primarily focusing on the 'reduction of risk' by measuring standard deviation. The study was not actually about any improvements in diversification. A more recent study by Surz & Price addressed the shortcomings of the Fisher and Lorie study by using proper diversification measurements. Specifically, they looked to R-squared which measures diversification as the percent of variance which can be attributed to the market as well as tracking error which measures the variance of portfolio returns versus its benchmark.

The results of their study, Table 1, clearly show that a portfolio of even 60 stocks captures only 0.86 or 86% of the diversification of the market in question.

Ideal Number of Stocks
  1 15 30 60 Entire Market
Standard Deviation 45.00% 16.50% 15.40% 15.20% 14.50%
R2 0.00 0.76 0.86 0.86 1.00
Tracking Error 45.0 8.1 6.2 5.3 0.0

It is important to remember that even this concept of being 90% diversified with only 60 stocks is only relative to the specific market in question, i.e. U.S. large-capitalization companies. Therefore when you are building your portfolio, you must remember to diversify against the entire global market.

As we concentrate on decreasing risk in the portfolio, we must also remember to consider opportunity cost; specifically, the risk of missing out on the best performing stock markets. Figure 2 illustrates the historical performance among different areas of investments for the year 2010 broken down by style, sizes, and domestic or foreign.

Figure 2: Opportunistic tilt and diversification

To be properly diversified in order to adequately capture the market's returns and reduce risk, you must capture the entire global market and its known dimensions of size and style as listed.
1. Domestic Growth Small Companies
2. Domestic Value Small Companies
3. Domestic Growth Large Companies
4. Domestic Value Large Companies
5. Foreign Growth Small Companies
6. Foreign Value Small Companies
7. Foreign Growth Large Companies
8. Foreign Value Large Companies
9. Emerging Market Companies

Additionally, you must capture the entire industry diversification within each of the above markets.

1. Telecom Services
2. Utilities
3. Energy
4. Consumer Staples
5. Health Care
6. Materials
7. Information Technology
8. Financials
9. Consumer Discretionary
10. Industrials

Finally, you must be sure to own the next great overachievers. A study entitled The Capitalism Distribution, by Eric Crittenden and Cole Wilcox, of the Russell 3000 during 1983-2006 illustrates just how difficult that is. Below are some of the highlights of their study that present a visual representation of just how few of the individual stocks are actually going to be the winners you need to be picking.

Summary Findings by Crittenden and Wilcox

  • 39% of stocks were unprofitable
  • 18.5% of stocks lost at least 75% of their value
  • 64% of stocks underperformed the Russell 3000
  • 25% of stocks were responsible for all of the market's gains

Figure 3: Total returns of individual stock vs. Russell 3000 (1983-2006)

You must ask yourself how realistic is it that you or your stock manager can identify the top performers before they perform? How unrealistic is it to pick a few stocks and for one of them to be the next Dell (Nasdaq: DELL) or Microsoft (Nasdaq: MSFT) at the early stages of their run? How realistic is it that you end up with one of the almost 40% of stocks which lost money or one of the 18.5% that lost 75% of their value?

What are the chances today that you have the undiscovered overachievers in your account? The global stock universe is huge. Ask yourself, how many stocks do you really need to capture any specific area such as the energy sector or the financial sector? What if you only picked one and it was the one that went bankrupt? I doubt five per area would be enough, but for argument's sake, we'll say five stocks are adequate per area to feel confident.

The Minimum Needed

When you look at it like this, you need a minimum of five stocks in over 200 industries, which equals over 1,000 stocks!

Realistically I doubt even this number would be enough to capture the global equity portfolio. Some important things to consider before you start building a 1000 stock portfolio:

1. You would still have your or your manager's biases embedded into the portfolio.
2. Is your portfolio large enough to have a meaningful position size in each?
3. So many stocks to trade would increase the trading cost.
4. Administrative record-keeping and statements would be overwhelming.
5. Very difficult, time-consuming, and expensive to research and manage.
6. You still couldn't be 100% sure to capture every future super stock.
7. Performance dependent on your proprietary system or "stock picking guruness."

Why Do Some People Prefer Individual Stocks to Funds?

There are valid and rational concerns for not wanting to get into funds:

1. Cost
2. Fund Flows
3. Taxes

Fortunately, all of these concerns are easily overcome by only using low-cost, passive institutional funds or exchange-traded funds (ETFs). For example, Vanguard MSCI Emerging Market ETF (NYSE: VWO) can tax-efficiently capture emerging market segment well, while minimizing fund flow issues and for a relatively low cost annually, but the fees could change. DFA International Small Cap Value Fund is a mutual fund which attempts to capture the entire foreign value small company segment.

Though there are some valid concerns about funds, there is also a prevalence of invalid and irrational concerns:

  • Bad experience due to poor fund selection, application, and timing
  • Comfort in seeing familiar names such as General Electric (NYSE: GE), Procter & Gamble (NYSE: PG), Coke (NYSE: KO), etc.

Unfortunately, little can be done to overcome these concerns besides education and patience.

The Bottom Line

A properly diversified portfolio should include a meaningful allocation to multiple asset styles and classes. Not just industry diversification. Otherwise, you risk missing out on significant market opportunities. By using ETFs and institutional passive mutual funds, you can capture meaningful exposure to the entire global market portfolio with as few as 12 securities and a relatively low total portfolio cost. It's tax-efficient, easy to understand, monitor, manage and it makes good common sense.

Article Sources
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  1. Lawrence Fisher and James H. Lorie. "Some studies of variability of returns on investments in common stocks." The Journal of Business, Volume 43. Issue 2, 1970, Pages 99-134.

  2. Ronald J. Surz and Mitchell Price. "The truth about diversification by the numbers." The Journal of Investing, Volume 9, Issue 4, 2000, Pages 93-95.

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