How Much Diversification Is Enough?

Academics Have Sought to Achieve Ideal Diversification Levels for 50 Years

How Much Diversification Is Enough?
Everyone knows you shouldn't put all of your money in a single investment but how much diversification is enough?. Katie Edwards / Ikon Images / Getty Images

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 Home Depot, Wal-Mart, or Microsoft, dragging the entire compound annual growth rate of your family's net worth upwards with it.

 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.

Evans and Archer Calculated 10 Stocks Were Enough Diversification In 1968

As every finance student probably knows (and nearly every finance textbook seeks to remind you), 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 and doesn't differentiate between a commodity-like business and a firm with high franchise value.  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.

Meir Statman Believed Evans and Archer Were Wrong, Arguing in 1987 That It Took 30-40 Stocks To Have Enough Diversification

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.

Campbell, Lettau, Malkiel, and Xu Published a Paper in 2001 Insisting Increased Stock Volatility Required an Update to Evan and Archer Because 50 Stocks Were Now 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.

Domian, Louton, and Racine Changed the Definition of Risk to a Better Real-World Metric and Concluded, in April of 2006, That Even 100 Stocks Weren'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.  Instead of considering how much a given portfolio fluctuated - a move I applaud as I have made absolutely clear my rather strong professional opinion that beta as a measurement of risk is complete bull except in a handful of situations - it sought to find out how many stocks were necessary were one to utilize naive diversification to build a portfolio that would not fall short of the risk-free Treasury rate over a holding period of two decades; in this case, 1985-2004.  The study built random portfolios of 1,000 large, publicly-traded companies in the United States.

The conclusion?  To reduce your chances of falling short by 99%, indicating a 1-in-100 risk of failure, 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 of the Diversification Studies Is Justified, Though They Are Still Somewhat Informative Under Limited Circumstances

One of the severe criticisms I have with the study published in 2007 is that it pulled from a far 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.  They stuck to significantly larger businesses (larger businesses, by definition, fail less frequently, have greater access to capital markets, are more likely to be capable of attracting the talent necessary to preserve themselves and prosper, and have more interested stakeholders who can step in and see the ship righted if things go poorly, resulting in lower catastrophic wipe-out rates than stocks with small market capitalization).  They then weeded 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.

While such a diversification study could be useful for firms such as Charles Schwab that are moving toward electronically assembled (Read: No human judgment) portfolios of securities, they are all but useless for a reasonably intelligent, disciplined investor.

Doubt it?  Consider the implications if the findings were correct.  Consider that as of this evening, the top 25 stocks represent the following concentration in the following stock market indices:

How, then, is the work of talented academics like Dr. Jeremy J. Siegel at Wharton possible when it shows over every 17 year period, equities have beat the inflation-adjusted returns of bonds?  Simple: The major indices have what amounts to quality modifications baked into their methodology.  Normal people do not take a dart and throw said dart at a list of names, building a portfolio that way.  (If they did, it would completely decouple p/e ratios from reality as money was evenly disbursed across enterprises with lower levels of share float.  Put more simply, if all investors put 1/500th of their assets into Apple with its $700+ billion market capitalization and 1/500th of their assets into United States Steel Corp., with its $3.6 billion market capitalization, the latter could not absorb the buy orders and the shares would get sent into orbit with zero justification.  The former, in contrast, would trade at a severe discount to its intrinsic value.)

The DJIA, which has beaten the S&P 500 over my lifetime by a not-insignificant 50 to 100 basis points per annum (that adds up to real money when you're talking about multiple decades) is hand-selected by the editors of The Wall Street Journal.  Only the largest, most profitable, representative companies in the world make it onto the list.  It is the blue chip stock hall of fame.

The NASDAQ and S&P 500 are market capitalization weighted indices, meaning the biggest (and almost always most profitable, unless we're in a stock market bubble), firms get shoved to the top and make up a disproportionate percentage of the owners' collective assets.

That's not all.  Siegel's work, in particular, shows that an equally weighted, across-the-board portfolio of the original S&P 500 in 1957 held with no subsequent modifications beat the actual S&P 500 for various reasons he's laid out in his extensive body of work, indicating the already demonstrated real-world safety of larger firms relative to their smaller counterparts.

In The End, If You Want to Know How Much Diversification Is Enough, 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 was not a believer in naive diversification.  He wanted 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 despite the methodology changes over the past few decades that are fundamentally altering the nature of the product.