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. As shown below, 79% of the 66 correlations are below 0.70. Over the 10-year period from 1/1/2000 to 12/31/2009, the average correlation among all the funds in the Passive 7Twelve portfolio was an impressively low 0.34.

Average Correlation Among the ETFs in the Passive 7Twelve Portfolio = 0.34.

	Mid US	Small US	Non-US Dev.	Non-US Emerg.	Global Real Estate	Natural Resources	Commod- ities	US Aggregate Bonds	Inflation-Protected Bonds	Non-US Bonds	Cash
Large US	0.90	0.83	0.87	0.81	0.59	0.65	0.29	–0.07	0.08	0.19	–0.12
Mid US		0.92	0.85	0.83	0.66	0.69	0.36	–0.08	0.10	0.16	–0.08
Small US			0.81	0.76	0.75	0.59	0.23	–0.03	0.08	0.20	–0.07
Non-US Dev.				0.88	0.63	0.72	0.41	0.06	0.20	0.47	–0.15
Non-US Emerg.					0.53	0.70	0.45	–0.03	0.13	0.32	–0.15
Global Real Estate						0.36	0.21	0.08	0.23	0.30	–0.08
Natural Resources							0.63	–0.02	0.21	0.29	–0.03
Commodities								–0.03	0.32	0.26	–0.02
US Aggregate Bonds									0.73	0.60	0.12
Inflation-Protected Bonds										0.59	0.03
Non-US Bonds											–0.13