A Primer on Correlation (The Measure of Portfolio Diversification)

The basic premise underlying diversification and portfolio asset allocation is summarized in a simple sentence by Harry Markowitz: "To reduce risk it is necessary to avoid a portfolio whose securities are all highly correlated with each other."¹ It is assumed that Markowitz was equating the term "risk" with volatility of returns. Additionally, William Bernstein observes that "the concept of correlation of assets is central to portfolio theory-the lower the correlation, the better."² Reducing the volatility of returns in a portfolio is achieved by combining assets that tend to have low correlation to each other.

There are many examples of the importance of low correlation among the components of a system. For example, a basketball team needs players with different attributes and talents – they need a diversified team. Building a basketball team with five point guards is not a great idea, as much as we value point guards. A center is needed, as well as several forwards. Because they have different attributes and talents, the correlation between point guards and power forwards is low, and low correlation is what we're after. Low correlation between the various parts of a system = diversification.

The maximum correlation between two parts of a system is +1.00 (or 100%) and the minimum correlation is –1.00 (or –100%). A correlation of +1.0 indicates that the behavior of the two parts is very similar (two twin brothers who both play point guard). A correlation of –1.00 indicates that the two parts behave very differently (a left-handed 6'1" point guard and a right-handed 7'4" center). A correlation of zero indicates that the behavior between the two parts is basically random/

As it pertains to investment portfolios, correlation between two assets within a portfolio is measured in the range of –1.0 to +1.0, where –1.0 indicates that the price movement of two assets is perfectly inversely related. When one goes up, the other goes down, and vice versa. A correlation coefficient of zero indicates no correlation between the assets, while a correlation of +1.0 indicates perfect positive correlation. When one goes up, the other goes up.

When building investment portfolios, we are trying to minimize the number of high correlations (above 0.70) between the various assets in the portfolio. A correlation of 0.70 between two portfolio assets indicates that 70% of their behavior is similar. A review of the 10-Year Correlations of Each Sub-Asset in 7Twelve^TM reveals that over 90% of the 66 correlations are below 0.70. Also impressive is the fact that 27 (or nearly 40%) of the correlations are zero or below.

The average correlation among all the assets in the 7Twelve portfolio is a remarkably low 0.14.

Here is another way to look at the 7Twelve portfolio. The correlation between the performance of the 7Twelve portfolio and the performance of the S&P 500 Index is about 50% (see 7Twelve^TM Accumulation Portfolio Performance). In other words, they are not highly correlated. The correlation between the performance of American Funds Capital Income Builder and the performance of the S&P 500 Index is also very low at 44%. Fidelity Global Balanced has a surprisingly high correlation with the S&P 500 at 94%. T. Rowe Price Personal Strategy Balanced and the S&P 500 Index have a 89% correlation, while the Vanguard Balanced fund has a 97% correlation with the S&P 500 Index. Of course, the correlation between the Vanguard 500 Index and the S&P 500 Index is 100%, representing perfect correlation. Perfect correlation with an index that is not broadly diversified is not the goal. The S&P 500 Index is not a broadly diversified index. Rather, it is an index of large US stocks only.

There is nothing inherently wrong with having a high correlation to the S&P 500. However, the S&P 500 does not represent a well-diversified portfolio   as evidenced by three consecutive years with negative returns (2000, 2001, and 2002). Well-diversified portfolios tend to avoid or minimize negative returns. With that in mind, having a portfolio and/or fund that is highly correlated to the S&P 500 Index means you are subject to the risks that accompany a less diversified investment.

When building a portfolio, it's also important to pay attention to cost. As shown in the 7Twelve^TM Accumulation Portfolio Performance, the equally weighted 7Twelve portfolio has an annual expense ratio of 0.69%, or 69 basis points (bps). American Funds Capital Income Builder has a 56 bps expense ratio but also has a 5.75% front-end commission when shares are purchased. (There are different share classes of Capital Income Builder, each with different loads and expense ratios.) Fidelity Global Balanced is a bit expensive at 1.18% or 118 basis points. The T. Rowe Price Personal Strategy Balanced fund has a 79 bps expense ratio, while the Vanguard funds have exceptionally low expense ratios of 20 bps and 18 bps respectively. Vanguard is well known for keeping the cost of their funds very low.

Keeping costs low is an important goal. But, it is a secondary goal. The primary goal is performance. Remember that the annual returns of all the portfolios in the 7Twelve^TM Accumulation Portfolio Performance report are "net" of expenses-meaning that the expense ratios have been fully accounted for in the performance figures.

The average annual expense ratio of "world allocation funds" (that is, funds that invest in a wide variety of asset classes) is about 1.29%. So, the annual cost of the 7Twelve portfolio is about one-half the cost of the average world allocation fund. The average expense ratio of all 3,354 funds that had a full 10-years of performance as of December 31, 2007 was 105 bps, or 1.05%.