Investment professionals are taught, and tell their clients, that their portfolios should be diversified (though “properly diversified”, or “well-diversified” are probably better descriptions).  Unfortunately, only a small percentage of these investment professionals, and a small percentage of investors in general, have any understanding what diversification truly is, and even fewer know how to achieve it or measure it.

It sickens the heart. After all, we're talking about your future.

Investopedia defines diversification as “a risk-management technique that mixes a wide variety of investments within a portfolio. The rationale behind this technique contends that a portfolio of different kinds of investments will, on average, yield higher returns and pose a lower risk than any individual investment found within the portfolio.”  It goes on to say that “Diversification strives to smooth out unsystematic risk events in a portfolio so that the positive performance of some investments will neutralize the negative performance of others. Therefore, the benefits of diversification will hold only if the securities in the portfolio are not perfectly correlated.”  While this definition and explanation covers the basics of diversification, it does not provide the proper emphasis.  (Investopedia’s article on diversification does a better job, but still misses the mark.)

If you look at random at a dozen Internet articles on portfolio diversification, you will likely find at least ten of them resorting to the phrase: “Don’t put all of your eggs in one basket.”  That’s fine as far as it goes, but it doesn’t go nearly far enough.  It is no great improvement to put your eggs in five or ten or fifty different baskets if all of those baskets are riding in a minivan that is driving off a cliff.  Most investors interpret this phrase to mean, “Invest in many different securities”, or “Invest in many different market sectors”, or “Invest in many different asset classes”, or “Invest in many different geographical locations”.  What they’re missing is that all of these interpretations are merely possible means to the end, not the end in themselves.

The first sentence in the Investopedia definition covers the single, most important characteristic of diversification: it is a technique for managing the risk in a portfolio.  This is the fundamental goal of diversification: reducing risk without reducing return.  Investing in a variety of securities is not the goal.  Investing in a variety of industries, or sectors, or asset classes, or geographical markets is not the goal.  Reducing risk (for a given expected return) is the goal.  It follows, therefore, that, to understand diversification, you have to understand risk.

Suppose that you have three investments that earn an average of 1% per month each, with monthly returns shown in Table 1 and Figure 1:

Clearly, most investors would judge that investment B is riskier than investment A, because the monthly returns of B vary more widely than those of A; investors would describe investment B as more volatile than investment A.  Similarly, C is more volatile than B.  This volatility is most commonly measured by the standard deviation of the returns: a statistical measure of how widely spread the returns are.  Table 2 gives the standard deviations of returns for investments A, B, and C. These statistics agree with our assessment of risk: A's standard deviation of returns is the lowest of the group, and C's is the highest.

Diversification, then, is the technique of combining several securities in a portfolio with two goals in mind: to achieve a particular average return, and to reduce the standard deviation of the returns: to reduce the risk.  To achieve this reduction of risk, the returns of the individual securities must demonstrate the behavior of investments A, B, and C in Figure 1: when one of the securities has a higher than average return, another has a lower than average return; in other words, the returns of the individual securities do not move up and down together.

The Investopedia explanation includes this characterization of a well-diversified portfolio: the positive performance of some investments will neutralize the negative performance of others. This goes too far: most investors would prefer having all of the securities in their portfolio showing positive performance, but Investopedia makes it sound as though this cannot happen in a well-diversified portfolio. In fact, it can. The key to diversification isn't that positive returns by some securities will neutralize negative returns of others, it's that above-average returns by some securities will neutralize below-average returns of others, even when the returns of all the securities are positive.

One measure of the degree to which the returns of two securities move up and down together is called the correlation of those returns.  Correlations range in value from -1.0 to +1.0.  A correlation of +1.0 means that the returns move up and down together, while a correlation of -1.0 means that when one is up the other is down; values between these extremes mean that sometimes the returns move in the same direction, sometimes in opposite directions.  The lower the correlations, the more risk reduction an investor can achieve; low (preferably negative) correlations are better than high correlations.

Correlations are generally written in table or matrix form.  Table 3 gives the correlations for investments A, B, and C.

Table 3 shows that the correlation of returns for A and B is -0.514, for A and C it is +0.294, and for B and C it is -0.869.  The fact that two of correlations are negative and all are less than +0.5 means that there is scope for considerable risk reduction in this portfolio. To reduce the risk, however, requires a proper mix of A, B, and C.

Table 4 describes two portfolios: the first has equal investments in A, B, and C, and the second has the mix that gives the lowest risk – the lowest standard deviation of returns. Because all three investments - A, B, and C - have average monthly returns of 1%, both of these portfolios will also have average monthly returns of 1%. Note that the standard deviation of returns for Portfolio 1 is actually greater than the standard deviation for Investment A. This illustrates an important point: the wrong mix of securities - even securities with low correlations of returns - may increase your risk over a single-security portfolio, without increasing your return.

Table 5 and Figure 2 show the monthly returns for two portfolios.

When an investor wants a diversified portfolio, he should look for securities whose returns are not strongly, positively correlated.  The most common method that investors use to do this is to invest in various asset classes – large cap value stocks, small cap growth stocks, international bonds, domestic real estate, commodities, and so on – relying on general historical correlations of returns between these classes.  For example, bond returns are typically negatively correlated with stock returns, so having both stocks and bonds in a portfolio is seen as risk-reducing measure.  Real estate and commodities have historically had very low correlations of returns with both stocks and bonds, so including these assets in a portfolio is also seen as reducing portfolio risk.  Similarly, many investors will choose securities in different market sectors – technology, health care, banking, construction, and so on – as a means to diversify their portfolios, presumably expecting that investments in different sectors will have lower correlations of returns than investments in the same or similar sectors.

Unfortunately, these strategies often do not produce the anticipated results.  Securities in very different asset classes, or very different sectors, or very different geographical locations may have very strong, positive correlations.  Conversely, securities in the same asset class, in the same sector, and in the same geographical location may exhibit very low – even negative – correlations.  An example of the former comes from an article in the Wall Street Journal on 12/2/06 that advocated including both the Vanguard Total Stock Market Index Fund (VTSMX) and the Vanguard Total International Stock Index Fund (VGTSX) - a domestic stock fund and an international stock fund - in a well-diversified retirement portfolio.  Over the 5 years from 10/01 to 10/06 their correlation of monthly returns was +0.85, and over the 5 years from 10/96 to 10/10 it was +0.82.  An example of the latter would be the stocks of NYSE Group, Inc. (NYX) and Goldman Sachs, Inc. (GS); though both are in the U.S. financial sector their correlation of returns over the last 2½ years is only +0.11.

None of this should come as a surprise, however.  It is unrealistic to believe that any individual security will behave with the same characteristics as a large, homogenized asset class.  Economic conditions, for example, can affect some companies in the same sector or asset class in very different ways, and can affect some companies in different sectors or asset classes in very similar ways.  What matters are the characteristics of the specific securities in a portfolio, not some mythical representative of some arbitrary asset class or market sector.

All of this means that investors cannot rely on the common shortcuts to achieve a well-diversified portfolio.  Instead of merely choosing representative securities from each of several asset classes or market sectors, he must analyze how the specific securities he is considering will work together in a portfolio.  Furthermore, he must have the analytical tools available to will allow him to determine the allocation that will give him the lowest-risk portfolio that is expected to achieve the desired level of return.

So, the next time you hear an investment professional start to discuss diversification, be sure to ask him if he really knows what diversification is.  If he doesn’t mention minimizing portfolio risk for a given return (or maximizing return for a given level of risk), if he only talks about asset classes or market sectors or stocks versus bonds, or if he says that diversification is easy to achieve, you might consider talking to someone else. After all, we're talking about your future.