How to think about diversification

(MoneyWatch) In terms of the number of stocks, the most diversified portfolio an investor in the U.S. stock market can have is to own a total stock market fund. The Wilshire 5000 Total Market Index was established by the Wilshire Associates in 1974, naming it for the approximate number of issues it included at the time. At various times the total number of stocks on the three exchanges (NYSE, AMEX and Nasdaq) exceeded that figure by a wide margin, and at times it has been smaller.

Today, an investor in the Vanguard Total Stock Market Index Fund (VTSMX) would now own a fund that holds approximately 3,300 stocks, not much different than the number of stocks in the iShares Russell 3000 ETF (IWV). An S&P 500 Index fund would still be well diversified owning 500 stocks, and it would capture about 75 percent of the total stock market.

What is important to understand about each of these broad market indices is that their holdings are based on market-cap weightings. For example, Apple (AAPL) is the largest stock in the S&P 500, with a weighting of almost 5 percent, and the top 10 holdings constitute more than 20 percent of the index.

Although a total stock market index or the Russell 3000 owns many more stocks, including hundreds of small stocks, they haven't performed differently than the S&P 500. The following table presents the annualized returns and the annual standard deviation of the three indexes from 1979 (inception date for the Russell 3000) through 2011.

While the other two indexes are more broadly diversified than the S&P 500, their performances have been virtually identical over the past 33 years. Thus, it seems that adding more stocks to an S&P 500 Index didn't improve diversification in any effective way. Let's now look at another way to think about diversification of risks.

The Three-Factor Model

Many investors think of diversification by the number of stocks or mutual funds they own. Unfortunately, diversification of stock market risk doesn't work by the numbers. Research into the sources of return of stock portfolios have found that the vast majority, over 90 percent, of the variation in returns of diversified portfolios is determined by their exposure to three factors:

• Beta -- or the exposure to stock-market risks
• Size -- or the risk of small-cap stocks
• Value -- or the risk of value stocks

These are often referred to as risk factors. The market factor is referred to as beta. The size factor is referred to as SmB (the return of small stocks minus the return of big stocks), and the value factor is referred to as HmL (the return of high book-to-market stocks minus the return of low book-to-market stocks). For the period 1927-2011, the annual average premium for taking the risk of stocks was 7.8 percent, for SmB it was 3.2 percent, and for HmL it was 4.7 percent.

Many investors include small-cap and value stocks in their portfolios because they have historically provided higher returns. They may also include them because they provide another often overlooked benefit -- they help to diversify your portfolio. The reason is that some of the risks of both small-cap and value stocks are risks that are unique to them. We can see that when we look at correlations of returns -- the degree to which their returns have a tendency to vary together. For the period 1927-2011, the annual correlation of the small-cap premium to the equity premium has been only about 0.4. The correlation of the value premium to the equity premium has only been about 0.1. And there has been virtually no correlation of the small-cap premium to the value premium. The low correlation shows that the small-cap premium and the value premium are independent risk factors. And that makes them good diversifiers of the risks of stocks in general. With this understanding, we now return to looking at our three market indexes.

For the period 1979-2011, the three major indexes (CRSP 1-10, Russell 3000 and the S&P 500) all had betas of about 1 and HmLs of 0. And both the Russell 3000 and the CRSP 1-10 had loadings on SmB of about 0. Some people are confused by the 0 loadings on size and value for the Russell 3000 and the CRSP 1-10 because they do hold small and value stocks. However, because the large stocks they own have negative exposure to SmB, and the growth stocks they own have negative exposure to HmL, their net exposure is 0. By definition, this must be true for any total market fund. It just happens to be that the S&P 500 has a 0 HmL loading. And, as you would expect, because of its large-cap nature, it has a negative loading on SmB of -0.2.

Now we will take a different tack in thinking about diversification.

Small-cap value stocks

The DFA Small Cap Value Portfolio (DFSVX) was the first passively managed small value fund, with an inception date of April 1993. So we will use it for discussion purposes. From inception through December 2011, its loadings on the three factors were about 1 for beta, but the SmB loading was 0.8, and the HmL loading was over 0.6. And the fund owns over 1,300 stocks.

So now let's take a look at the question of diversification. While a total market fund or a Russell 3000 fund own more stocks, in terms of diversifying the sources of risk, both of those indexes have exposure to only the market factor (beta). They have no exposure to the risk factors (or sources of returns) of SmB and HmL.

Relative to the S&P 500, which acts virtually identically to a total market fund, DFSVX has far more stocks (1,324 as of March 31, 2012), and its holdings are less concentrated. While the top 10 companies make up more than 20 percent of the S&P 500, the top 10 holdings of DFSVX make up less than 10 percent of the fund. In addition, DFSVX has high loadings on both SmB and HmL, while the S&P 500 has a negative loading on SmB and no loading on HmL. And both have about the same loading on market risk (about 1.0).

In terms of sources of risks, number of stocks and concentration, DFSVX is far more diversified than the S&P 500. Now this doesn't make DFSVX a better investment. However, no matter how we look at it, the fund is more diversified. So let's look at another metric.

Certainly, small-cap value stocks are much more volatile than the S&P 500. From 1927 through 2011, the annual standard deviation of the S&P 500 was about 20 percent, while it was more than 35 percent for small-cap value stocks (as represented by the Fama-French Small Value Index). Investors were at least compensated for the higher volatility, as small-cap value stocks returned 13.5 percent compared to the 9.8 percent return of the S&P 500.

Hopefully, you'll now think differently about your portfolio and how well diversified it is. You should consider how your holdings are diversified not just between stocks and bonds, and U.S., international and emerging market stocks, but also across the factors that explain returns.

Image from Flickr user Victor1558