How Much Diversification Is Enough?

Academics Have Sought to Achieve Ideal Diversification Levels for 50 Years

How Much Diversification Is Enough?
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Have you ever wondered, "How much diversification is enough?" It's a question that plagues new investors often, especially once they realize the powerful, mathematical advantages of diversification. It provides not only protection on the downside in case an individual business runs into trouble but, also, a bit of a lottery ticket on the upside as there is an increased chance one of your holdings will turn into a superstar performer like Amazon or Apple. Luckily for all of us, academics have looked at this very issue for generations and arrived at a fairly narrow range of total stocks that need to be held in an investment portfolio to maximize the benefits of diversification.

Let's take a look back at the history of the stock market diversification debate by looking at the four major studies you are likely to encounter on modern day college campuses.

10 Stocks May Be Enough

The first time any serious academic work in the modern world attempted to answer the question, "How much diversification is enough?" came in December of 1968 when John L. Evans and Stephen H. Archer published a study called Diversification and the Reduction of Dispersion: An Empirical Analysis in The Journal of Finance, Volume 23, Issue 5, pages 761-767.

Based on their work, Evans and Archer discovered that a fully-paid, debt-free portfolio (read: no margin borrowing) with as few as 10 randomly chosen stocks from a list of 470 companies that had complete financial data available for the prior decade (1958-1967) was capable of maintaining only one standard deviation, making it practically identical to the stock market as a whole. This approach of selecting random firms without any regard to the underlying security analysis, including income statement and balance sheet study, is known as "naive diversification" in the academic literature. An investor who engages in it exercises virtually zero human judgment. It makes no distinction between companies drowning in debt and those who don't owe anybody a penny and have tons of cash sitting around for extra safety, making it possible to weather even a Great Depression.

The core of their findings: As diversification is increased through adding additional positions to a stock portfolio, volatility (which they defined as risk) decreases. However, there comes a point at which adding an additional name to the investment roster provides very little utility but increases expenses, lowering return. The objective was to find this efficiency threshold.

Or, Maybe You Need 30-40 Stocks

Nearly twenty years later, Meir Statman published How Many Stocks Make a Diversified Portfolio? in the Journal of Financial and Quantitative Analysis, Volume 22, No. 3, September 1987, and insisted that Evans and Archer were wrong. He believed for a debt-free investor, the minimum number of stock positions to ensure adequate diversification was 30. For those who were using borrowed funds, 40 was enough.

Or 50 Stocks Are Required

In what is now a well-known study from the February 2001 issue of The Journal of Finance, Volume LVI, No. 1, John Y. Campbell, Martin Lettau, Burton G. Malkiel, and Yexia Xu, published a study called Have Individual Stocks Become More Volatile? An Empirical Exploration of Idiosyncratic Risk. It looked at the original Evans and Archer diversification study and attempted to re-run the results in the equity markets. It concluded that volatility had become sufficiently high that achieving the same relative diversification benefits required a portfolio of no fewer than 50 individual stocks.

Maybe 100 Stocks Aren't Enough

Finally published in November 2007 on pages 557-570 of Financial Review following completion a year earlier, a study that got a lot of attention called Diversification in Portfolios of Individual Stocks: 100 Stocks Are Not Enough, changed the definition of risk to a far more intelligent, real-world assessment. 

Their conclusion was thato to reduce the chances of failure to less than 1%, a randomly assembled portfolio had to include 164 firms.

If you went with a 10-stock portfolio, you had a 60% probability of success, meaning a 40% chance of failure.

If you went with a 20-stock portfolio, you had a 71% probability of success, meaning a 29% chance of failure.

If you went with a 30-stock portfolio, you had a 78% probability of success, meaning a 22% chance of failure.

If you went with a 50-stock portfolio, you had an 87% probability of success, meaning a 13% chance of failure.

If you went with the 100-stock portfolio mentioned in the study title, you had a 96% probability of success, meaning a 4% chance of failure. That may not sound like a lot, but when talking about your standard of living, that equates to 1-in-25 odds of living on Ramen. That is not, exactly, how you want to spend your golden years, especially if you planned on retiring rich.

Criticisms

One of the severe criticisms I have with the study published in 2007 is that it pulled from a riskier set of potential investments than the Archer and Evans 1968 study. Recall that Archer and Evans were far more selective in the preliminary screening process, sticking with larger companies and weeding out any firm that didn't have an established decade-long track record to avoid the propensity of Wall Street hyping promising new enterprises that can't deliver.

Those two factors alone mean that the pool from which Archer and Evans were constructing their naive diversification portfolios was vastly superior to the one used in the more recent study. It should surprise no one who did reasonably well in high school math that more diversification was necessary as the quality of potential candidates in the pool declined precipitously. It should have been a foregone conclusion to anyone with real-world experience. The probability of a small, little-known boat manufacturing going bankrupt is exponentially higher than a firm like Exxon Mobil or Johnson & Johnson going bust. The numbers are clear.

Look to Benjamin Graham

Where does that leave us? Like so many other areas of finance, it can be summed up as: Benjamin Graham was right. Graham, who wanted investors to own 15 to 30 stocks, insisted on seven defensive tests. Take the time to run the math and you find that his methodology effectively, and inexpensively, created the same bulwarks the major stock market indices enjoy, leading to drastically lower rates of failure with roughly comparable rates of concentration.

What were these seven tests? He expanded upon them but the summary version is:

  1. Adequate size of enterprise
  2. Sufficiently strong financial condition
  3. Earnings stability
  4. Established dividend record
  5. Established earnings growth
  6. Moderate price-to-earnings ratio
  7. Moderate ratio of price-to-assets

Graham favored established, rational metrics. Take, for example, the performance of airline stocks versus consumer staples stocks over the past half-century. The probability of declaring bankruptcy in the former group over any 50-year period, due to fixed costs and variable revenues with a total lack of pricing power, is radically higher. In contrast, the consumer staples enjoy much more variable cost structures, huge returns on capital, and real pricing power. If both are trading at 15x earnings, Graham might politely insist you were cognitively impaired to consider them equally attractive diversification candidates. Remove the airlines from the equation and, though you'll miss the occasional spectacular year like 2015 when energy prices declined causing stock prices to nearly double, it is the closest thing to a mathematical certainty you're going to get in the world of finance that your 25-50 year return rates increase.

Many professional investors know this. Unfortunately, their hands are bound because they're being judged by short-term clients who are obsessed with year-to-year, or even month-to-month benchmarks. If they were to attempt to behave in the most rational way, they'd be fired. Few would stay the course with them.

Obviously, you can always own 100 stocks if you like. It's a lot easier in a world of low-cost commissions. People do it all the time. A janitor in Vermont passed away last year and left an $8 million fortune spread across at least 95 companies. Alternatively, you can ignore all of this and buy an index fund as there are at least five reasons they are probably your best choice.