Sunday, March 6, 2011

Optimal Diversification: Correlation and the Winner-Takes-All Phenomenon


I have always found the concept of diversification intriguing. What is the ideal level of portfolio diversification? What is that ideal range where return is maximized and volatility is minimized?  These are the kinds of questions I have sought to answer.

While it may seem incomprehensible, the fact is, the number of securities needed to gain most of the benefits of diversification (about 90%) is about 15.  Research from the field of Finance indicates that increasing a portfolio beyond 15 holdings contributes very little additional diversification to the portfolio.  Once a portfolio contains 10 to 15 securities, further volatility reduction reaches a point of diminishing returns.

The implications for investors seeking to minimize volatility are significant.  For instance, a portfolio of 20 securities spread out over diverse asset classes, industries and countries will have roughly the same amount of volatility as a portfolio of 2,000 securities invested likewise.


To understand the portfolio dynamics that lead to the above phenomenon let’s take a look at the concept of correlation.

A portfolio holding a single asset will have a standard deviation (a measure of volatility) identical to the standard deviation of the asset.  However, a portfolio of two assets does not have a standard deviation equal to the average of the assets’ standard deviations.  While portfolio returns are linear and represent a simple weighted average, portfolio risk in not linear.  In this case, portfolio volatility is a result of three factors: security A’s standard deviation, security B’s standard deviation and the correlation between security A and B. Correlation is the co-movement between investments or the degree to which they move together.

Correlation is at the heart of the concept of diversification.  Risk is reduced through low correlations because as one security’s price goes down the other may go up.  In general, portfolios of securities are less risky than the underlying individual securities themselves.  For instance, a portfolio with 80% in fixed income securities and 20% in equities will likely have a lower volatility than a portfolio with 100% in fixed income even though we might expect the equity component to increase overall volatility.  Risk is reduced because 80% of the portfolio in bonds has a higher correlation with more bonds than with 20% of the portfolio in equity.  The benefits of investing in another asset class out weigh the increased volatility of the equity component.

An important implication of correlation is that we must view diversification and its effect on risk on the basis of the portfolio as a whole instead of viewing the risk of the individual portfolio assets on their own.

We can gain an intuitive grasp of the benefits of limited diversification by looking at correlation.  It is this correlation factor that helps us achieve adequate diversification with as few as 10 to 15 securities.  The offsetting movements of securities held in a portfolio can be taken advantage of with 15 securities but with an increased number of holdings, there is very little corresponding decrease in risk.

Benefits to Broad Diversification

Practical considerations also play a role in portfolio development and some factors argue for broader diversification.

Owning a highly concentrated portfolio can put tremendous demands on one’s psyche.  Anyone who has owned a portfolio with one or two main holdings can attest to the dramatic swings that can occur—the emotional toll can be somewhat taxing.  When the number of holdings in the portfolio increases to, say, 5 and then to 10, volatility decreases dramatically and fluctuations begin to level out.  As the number of holdings increase the investor is less likely to form an emotional attachment to any one security—an attachment that could negatively affect the investor’s objectivity and judgment.  For instance, if an investor owns 200 securities, the relevance of any particular security is likely to be low.  It’s much easier to make decisions detached from emotion and preconception when analyzing a security whose impact on a portfolio is negligible.

A final benefit to broad diversification is the possible ancillary advantage of observing a wider range of businesses than a focused investor would.  While there’s no limit to the amount of research and number of prospects a focused investor can follow, an investor owning a portfolio of 30 to 50 stocks has an added incentive to monitor quite a few companies.  The best performing and worst performing stocks in the group can teach us the most.  By following large numbers of diverse portfolio holdings you are more likely to increase your knowledge base and investing experience as you are exposed to the operations of many companies.  This breadth has a way of enlarging our frame of reference—of expanding our business experience and broadening our insights into the nature of investing.  Even a broadly diversified portfolio that has quite a few weak performers can at least be of educational value.  Understanding fundamentally weak businesses is a first step in understanding truly great businesses.

Drawbacks to Broad Diversification

Economist John Maynard Keynes wrote the following in 1934:

“As time goes on, I get more and more convinced that the right method in investment is to put fairly large sums into enterprises which one thinks one knows something about and in the management of which one thoroughly believes. It is a mistake to think that one limits one's risk by spreading too much between enterprises about which one knows little and has no reason for special confidence... one's knowledge and experience are definitely limited and there are seldom more than two or three enterprises at any given time in which I personally feel myself entitled to put full confidence.”

Warren Buffett wrote a similar passage in Berkshire Hathaway’s 1993 letter to shareholders:
"We believe that a policy of portfolio concentration may well decrease risk if it raises, as it should, both the intensity with which an investor thinks about a business and the comfort level he must feel with its economic characteristics before buying into it."

I am inclined to agree with the above sentiments.  As the number of portfolio holdings gets smaller the investor’s research and due diligence becomes better because there is so much at stake.  Entrants into the portfolio must meet higher standards and pass tougher tests.  Conversely, as the number of holdings increases the standards for entry into the portfolio will inevitably decrease.  Why would an investor want to buy a stock that is his 50th choice when that investment could be invested in his or her top prospects?  At the extremes of diversification, a portfolio with a very high number of holdings will simply track the performance of the overall stock market and the investor’s presence becomes somewhat redundant.

General George S. Patton once said, “No decision is difficult to make if you will get all of the facts.” And as a practical matter, it is far easier to get all of the facts when you are dealing with a reasonable number of securities.  By limiting the number of securities in a portfolio, an investor has a much easier job of getting all the relevant facts and doing the appropriate due diligence during the research process.  However, as the number of holdings increases, the job of researching and monitoring holdings becomes more difficult.

Asymmetry in the Stock Market

A small set of leading companies often create almost all of the new shareholder value. Simultaneously, the value of their less successful competitors declines. As an example, Wal-Mart has built tremendous shareholder value over the years while K-mart has destroyed tremendous value.  Elite consulting company McKinsey has coined the term the “winner-takes-all economy” to describe this phenomenon.  According to McKinsey, 5 to 10 percent of the companies in a given industry can create all of the shareholder value.  This feature of the stock market affects choices with regard to the level of portfolio diversification, as you will see later on.

The concept of asymmetry addresses the distribution of stock returns from the worst performers to the best performers.  If we observe historical stock returns, we find that performance is not balanced or symmetrical—it is asymmetrical.  The distribution or returns is skewed because of a small number of companies that create most of the value.  Furthermore, the top 10 companies will have a performance record more pronounced than the worst 10 performers—that is, the leaders will affect the market more than the losers.  Assuming an investor does not dabble in options or sell stock short, the potential upside to buying stock long is unlimited while the worst downside is a negative 100% return.  This results in asymmetry of returns.  For example, the worst performing stock in the United States stock market over a given ten year period will, undoubtedly, have a return of -100%.  In a perfectly balanced symmetrical market, assuming an average annual return of 10% in the stock market, the best performer would have an annual return of 18%, and the 10-year return would be about 419%.  Averaging the two returns gives us a portfolio return of 159% over the ten years or 10% per year.  In this example, our portfolio of the best and worst stocks returns the market average of 10% per year.

However, in the real world, the market behaves quite differently.  Although the worst performer will go down 100%, the best performer will do far better than 419% over ten years.  Even during the worst decade for stocks in the 2nd half of the 20th century—the 1970s—the best performing stock easily outpaced the 419% benchmark.  Keystone International returned 2,400% during the 1970s.  Keystone was a leader in the manufacturing of valves and flow control products for the oil industry.  The company was purchased and merged with Tyco International in 1997.

In investing, it is quality that matters more than quantity.  As an analogy, the German composer and organist Johann Pachelbel is remembered for one composition that stands above all his other work—Canon in D Major.  While he was not as prolific as some of his contemporaries, he made his mark on history with that one creation.  All it takes is one company to make the difference in a portfolio.  If you had owned companies such as General Motors or Avon in the 1950s, IBM or Xerox in the 1960s, ChemFirst Inc. or Keystone International in the 1970s, Wal-Mart or Circuit City in the 1980s and Microsoft or Dell during the 1990s you would have experienced tremendous gains.

To give you an idea of what is possible when you pick a winner and everything goes right, let’s take a look at what Dell Computer Corporation did during the 1990’s.  Dell’s stock price increased a not-too-shabby 60,800% during the 1990’s.  An investment of $10,000 in 1990 would have grown to $6,090,000 by the end of 1999.  Great investment prospects are difficult to find but when you find that rare gem of an opportunity the rewards are well worth the effort.  It is a tribute to the genius of the free market economy that so few businesses earn exceptionally high returns.  On the rare occasions when a stock outperforms the average by a wide margin, we find companies in industries with high barriers to entry and potent management that knows how to exploit advantages.

In a focused portfolio with limited diversification a single stock can make all the difference.  Let’s say you had a portfolio of $100,000 in cash on January 1, 1990. If you invested $10,000 in Dell and the remainder in 9 other gems such as Waste Management, CUC International, Sunbeam, Rite Aid Corporation, Bre-X, YBM Magnex, Livent, Philip Services, Commodore Business Machines and Wang Laboratories (some of these companies may not have traded as early as 1990 but you will see in a moment that this really does not affect our analysis). We will make the conservative assumption that the value of the 9 companies excluding Dell on December 31, 1999 is $0.  The value of the Dell stake is $6,090,000 as determined by our earlier analysis.  Therefore our total ten-year return for the portfolio works out to 5,990%.  The average annual return for this portfolio in the 1990’s is 51% despite the fact that we are assuming the remainder of the portfolio went bankrupt.  Ninety percent of the holdings went to zero but the portfolio performance was salvaged because there was a big winner that had a significant percentage of the portfolio assets at the beginning of the period.

The key to strong portfolio performance is to be able to identify market leaders and make them core holdings in your portfolio. Asymmetry relates to diversification choices, because if you have a broadly diversified portfolio it is very difficult to take full advantage of the best investment opportunities.  Each security makes up only a small fraction of a broadly diversified portfolio.  A concentrated portfolio is required in order to invest substantial assets in the best prospects.  Furthermore, a highly diversified portfolio that does own a big winner will be forced to continually re-balance the portfolio by selling off this winner to reduce its weighting and maintain broad diversification.  In short, the benefits of owning a great growth stock are not fully realized in a highly diversified portfolio. The key is to recognize potential in a company, invest a significant portion of your portfolio in it and hold it for the long-term.


William O’Neil, publisher and founder of Investor’s Business Daily, said:  “Broad diversification is a hedge for lack of knowledge, or ignorance.”  And while broad diversification may be suitable for some investors, it offers very little hope of achieving better than average results. Warren Buffett is a focus investor with a relatively concentrated portfolio of stocks and his investment results bear witness to the potential of a focused approach.

Professional investors who are confident in their ability to find a small group of companies that have long-term competitive advantages and are reasonably priced may want to consider limiting portfolio diversification.

The average retail investor, however, may still want to stick with an index fund—a mutual fund or exchange traded fund that tracks the market average.

Any person considering an investment should seek independent advice from an investment advisor on the suitability of the particular investment.  Blog postings are for educational purposes only and do not constitute a recommendation for the purchase or sale of any security. The information is not intended to provide investment or financial advice to any individual or organization and should not be relied upon for that purpose.

No comments:

Post a Comment