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The Illusion of Diversification

By: Jason Whitby

By: Jason Whitby,MBA, CFA, CFP, AIFA

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 Jim their top 5 holdings and Jim would let them know if they were well diversified. Absolutely amazing and mostly refuted by the “stock picking” community which tend to believe the number of individual stocks needed to be diversified is actually closer to 30. While 30 is no doubt better than 5, it just isn’t good enough.

Where does the magical number 30 come from?

In 1965, Fisher and Lorie released a study on the ‘reduction of return scattering’ by 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 NYSE 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 evolved the statement 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 the something like Figure #1 to “prove” their claims.

Figure 1: Standard Deviation and Number of Stocks by Dresdner Kleinwort Macro Research.

Unfortunately neither point is really true.

The Reduction of Risk is not the same thing as Increasing Diversification.

The Fisher and Loire 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 Sur & Price addressed the short comings of the Fisher and Loire study by using proper diversification measurements. Specifically, they looked to R2 which measures diversification as the ‘percent of variance’ explained by the market as well as tracking error which measures the variance of portfolio returns versus it’s benchmark. The results of their study, Table 1, clearly shows that a portfolio of even 60 stocks captures only 0.86 or 86% of the diversification of the market in question.

Table 1: Risk and Diversification Measures for Portfolios of Various Sizes 1/96 – 6/99
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. US Large Capitalization Companies. Therefore when you are building your portfolio, you must remember to diversify against the entire global market. For reference, Figure 2 illustrates the global market that you need to capture and just how many “markets” there really are.

Figure 2: World Market Capitalization by Dimensional Fund Advisors.

Increasing Diversification means Reducing Risk and Capturing Returns.

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 3 illustrates the 2010 performance among different areas of investments broken down by style, sizes and domestic or foreign.

Figure 3: Representative Asset Class 2010 Performance.

To be properly diversified in order to adequately capture the market’s returns and reduce risk, you must capture the entire global market and it’s known dimensions of size & 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 recent study by Crittenden and Wilcox of the Russell 3000 during 1983-2006 illustrates just how difficult that is. Table 2 presents some of the highlights of their study and Figure 5 presents a visual representation of just how few of the individual stocks are actually going to be the winners you need to be picking.

Table 2: 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 4: Per Crittenden and Wilcox

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 or MSFT at the early stages of their run? How realistic is that you end up with the next WCOM, ENRON or TYCO instead? 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 one specific area such as the Large Company Energy Sector? What if you only picked 1 and it was BP? What if you picked 3 stocks to capture Large Company Finance Sector and they were Lehman, Freddie and AIG?

I doubt 5 per area would be enough but for arguments sake, well say 5 are adequate.

Minimum needed 5 stocks * 9 asset classes * 10 industries = 450

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 450 stock portfolio:

  1. You would still have your or your managers biases imbedded 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 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 “proprietary system” or “stock picking guruness”.

Why bother?

So why do some people still prefer individual stocks to funds?

  • Valid, Rational Concerns
  • Cost
  • Fund Flows
  • Taxes

Fortunately, all of these concerns are easily overcome by only using low cost, passive institutional funds or exchange traded funds. For example, Vanguard MSCI Emerging Market ETF (VWO) can tax efficiently capture the entire emerging market segment while minimizing fund flow issues and all for the low cost of 0.22% annually. DFA International Small Cap Value Fund (DISVX) does a fantastic job of capturing the entire foreign value small company segment for only 0.70% annually.

  • Invalid, Irrational Concerns
  • Bad experience due to poor fund selection, application and timing
  • Comfort in seeing familiar names such as GE, P&G, Coke, etc…

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

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 ETF and Institutional passive mutual funds, you can capture meaningful exposure to the entire global market portfolio with as few as 12 securities and a total portfolio cost of under 0.4%. Its tax efficient, easy to understand, monitor, manage and it makes good common sense. I have no idea why anyone would do it any other way.