Are Correlations Increasing? Craig L. Israelsen February 2012This article examines the patterns of correlation among the returns of 12 broad investment asset classesover the nine-year time frame from 1993-2011. The asset classes include large US stock, midcap USstock, small cap US stock, non-US stock developed, non-US stock emerging, real estate, naturalresources, commodities, US bonds, TIPS, non-US bonds, and US cash.For the purposes of this article, large cap US stock (S&P 500 Index) will be used as the baseline indexagainst which the correlations of the other 11 asset classes will be measured.Table 1. 12 Asset Classes and Representative Index Core Asset Classes Representative Index US Large Cap Stock S&P 500 Index US Mid Cap Stock S&P Midcap 400 Index US Small Cap Stock Russell 2000 Index Developed Non-US Stock MSCI EAFE Index Emerging Non-US Stock MSCI Emerging Markets Index Real Estate Dow Jones US Select REIT Index Natural Resources Goldman Sachs Natural Resources Index Commodities Deutsche Bank Liquid Commodity Index Total Return US Aggregate Bonds Barclays Capital Aggregate Bond Index Inflation Protected Bonds Barclays Capital US Treasury Inflation Note Index International Bonds Barclays Capital Global Treasury Ex-US Index Cash 3 Month Treasury BillFirst, a brief re-fresher on correlation. The basic premise underlying diversification and portfolio assetallocation is summarized in a simple sentence by Harry Markowitz, “To reduce risk it is necessary toavoid a portfolio whose securities are all highly correlated with each other1.” It is assumed thatMarkowitz was equating the term “risk” with volatility of returns. Additionally, William Bernsteinobserves that “the concept of correlation of assets is central to portfolio theory—the lower thecorrelation, the better2.” Reducing the volatility of returns in a portfolio is achieved by combining assetsthat tend to have low correlation to each other.There are many examples of the importance of low correlation among the components of a system. Forexample, a basketball team needs players with different attributes and talents—they need a diversifiedteam. Building a basketball team with five point guards is not a great idea, as much as we value point1 Markowitz, H., 1991, Portfolio Selection, Blackwell Publishing.2 Bernstein, W., 2001, The Intelligent Asset Allocator, McGraw Hill.
guards. A center is needed, as well as several forwards. Because they have different attributes andtalents, the correlation between point guards and power forwards is low—and low correlation is whatwe’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 minimumcorrelation is -1.00 (or -100%). A correlation of +1.0 indicates that the behavior of the two parts is verysimilar (two twin brothers who both play point guard). A correlation of -1.00 indicates that the two partsbehave very differently (a left-handed 6’1” point guard and a right-handed 7’4” center). A correlation ofzero 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 inthe range of -1.0 to +1.0, where -1.0 indicates that the price movement of two assets is perfectlyinversely related. When one goes up, the other goes down, and vice versa. A correlation coefficient ofzero indicates no correlation between the assets, while a correlation of +1.0 indicates perfect positivecorrelation. When one goes up, the other goes up.When building investment portfolios we are trying to minimize the number of high correlations (above0.70) between the various assets in the portfolio. A correlation of 0.70 between two portfolio assetsindicates that 70% of their behavior is similar.Myth: All Correlations Went to “1.0” in 2008As outlined below in Table 2, all correlations did not go to 1.00 in 2008 (as also shown by the red coloredbars in Figure 1). In fact, 9 asset classes had equal or higher correlations to the S&P 500 Index in 2011than in 2008 (noted by yellow highlighting). The figures in Table 2 represent the correlation coefficientsbetween the S&P 500 Index and other 11 indexes (using 12 monthly returns for calendar years 2005,2008, and 2011).It is correct to say that in 2008 the correlation between large US stock and the other 11 asset classeswere higher in all but one asset class (cash) compared to correlations in 2005. Furthermore, in 2011nine of the 12-month correlations with the S&P 500 Index were higher than in 2008 (the exceptionsbeing US Aggregate Bonds and TIPS).Using 2005 to 2008 and 2008 to 2011 as moments in time, we clearly observe that correlations amongvarious asset classes and the S&P 500 Index have, in most cases, increased. However, saying thatcorrelations “have gone to 1.0” is a different matter. The actual correlation data do not support thatstatement—particularly when examining the correlations between the S&P 500 and the four fixedincome assets (US Bonds, TIPS, non-US bonds, cash).Where correlation has noticeably increased is among the eight equity and equity-like asset classes: largeUS stock (the base asset against which other assets are correlated), midcap US stock, small cap US stock,non-US stock developed, non-US stock emerging, real estate, natural resources, and commodities. Evenso, the 0.80 correlation between large US stock and commodities as of 2011 is still lower than thecorrelation between large US stock/midcap US stock and large US stock/small cap US stock in any of thepast three periods under review (2005, 2008, 2011). The point is that despite the higher correlationbetween commodities and large US stock, commodities remain a superior diversifier for large US stockthan midcap US stock or small cap US stock.
Table 2. 12-Month Correlation to S&P 500 Index 2005 2008 2011 US Midcap Stock 0.96 0.98 0.98 US Small Cap Stock 0.93 0.96 0.98 Non US Developed Stock 0.60 0.90 0.94 Non US Emerging Stock 0.76 0.84 0.86 US REIT 0.66 0.81 0.93 Natural Resources 0.55 0.68 0.93 Commodities -0.01 0.52 0.80 US Aggregate Bonds -0.19 0.35 -0.35 TIPS -0.35 0.53 0.26 Non US Bonds -0.23 0.08 0.34 US Cash 0.25 0.07 0.18 Figure 1. Correlation of monthly returns with S&P 500 Index over 12-month periods 1.00 0.80 0.60 0.40 0.20 0.00 -0.20 -0.40 -0.60 2005 2008 2011Let’s now take a longer view of correlation using 36-month periods instead of 12-month periods. InTable 3 we see the correlation between large US stock and the other 11 asset classes over three 36-month periods (2003-2005, 2006-2008, and 2009-2011). The general pattern is clear: correlations have
increased in recent years in most cases. However, among the four fixed income asset classes the patternof correlation with large US stock is anything but consistent (shown also in Figure 2).Table 3. 36-month Correlations to S&P 500 Index 2003 - 2005 2006 - 2008 2009 - 2011 US Midcap Stock 0.91 0.95 0.96 US Small Cap Stock 0.88 0.91 0.95 Non US Developed Stock 0.84 0.90 0.93 Non US Emerging Stock 0.74 0.82 0.86 US REIT 0.44 0.76 0.84 Natural Resources 0.45 0.68 0.85 Commodities -0.19 0.44 0.70 US Aggregate Bonds -0.03 0.19 0.00 TIPS -0.01 0.33 0.13 Non US Bonds 0.21 -0.02 0.51 US Cash -0.12 0.49 0.10 Figure 2. Correlation of monthly returns with S&P 500 Index over 36-month periods 1.00 0.80 0.60 0.40 0.20 0.00 -0.20 -0.40 2003 - 2005 2006 - 2008 2009 - 2011
Finally, it is worthwhile to consider a much longer time frame as it pertains to the correlation betweencommodities and large US stock. In Figure 3 we observe the rolling 10-year (i.e., 120-month)correlations between large cap US stock and commodities (as represented by the S&P Goldman SachsCommodity Index) from 1970 to 2011.Form this viewpoint we clearly see that the pattern of correlation between US stock and commoditiescan fluctuate widely. We have experienced time periods in the past (1980’s) where commodities and USstock had relatively high correlation. We are again in such a period. The important observation is thathigh correlations do not necessarily persist.So, while it is true that correlation between the S&P 500 Index and many other major asset classes hasincreased in recent years, it is not necessarily the case that such correlations will stay high going forward. Figure 3. 10-Year Rolling Correlations: 1970-2011 Large US Stock to Commodities 1.00 0.80 0.60 0.40 0.20 0.00 -0.20 -0.40 -0.60 -0.80 -1.00 1990 2006 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2007 2008 2009 2010 2011------------------------------------------Craig L. Israelsen, Ph.D. is a professor at Brigham Young University. He is a principal at Target Date Analytics(www.OnTargetIndex.com) and the designer of the 7Twelve Portfolio (www.7TwelvePortfolio.com).