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Of Commodities And Correlations |

Of Commodities And Correlations

June 24, 2013


Proponents of commodity investing typically point to the overall low correlation between commodities and other asset classes as one of the three main benefits of commodity investing (the other two being equitylike returns and a positive correlation with inflation).1 Over the last 50 years, the stock-commodity and stock-bond correlations have been close to zero. However, these point estimates conceal wide degrees of variation. For instance, the annual correlation between stocks and commodities has ranged from -0.39 to 0.76.2

As has been widely noted, the recent stock-commodity correlation has been at the upper end of its historic range. Less widely discussed, the bond-commodity correlation has been at the lower end of its historic range. This situation has led some to wonder whether the relationship between stock and commodity returns has permanently changed, with some suggesting that increased investor interest has led to a higher correlation between stocks and commodities.

In this article, we explore the evolution of the stock-commodity and bond-commodity correlations. We also explore the evolution of the correlation of commodities to each other. In particular, we are interested in whether these correlations have changed over time and whether variation in the correlations is affected by underlying economic conditions.

We find that the stock-commodity correlation and the intra-commodity correlation have a business cycle component; i.e., these correlations increase during the periods of economic distress. However, the bond-commodity correlation does not display a similar relationship. All three correlations are highly persistent, meaning that shocks to these correlations last a long time, some longer than others. For instance, one-standard-deviation shocks to stock-commodity and bond-commodity correlations have half-lives of 9.3 and 6.9 months, respectively, while shocks to intra-commodity correlation have half-lives of 20.8 months.3

Data And Summary Statistics
The commodities we study are those contained in either the Dow Jones-UBS Commodity Index or the S&P GSCI (the former Goldman Sachs Commodity Index), omitting duplicates (e.g., we include WTI crude oil, but not Brent crude oil), and including tin, platinum and soybean meal, based on the subjective assessment that they are important economically, have liquid futures markets and are of interest to investors.4 We construct (excess) investment returns for futures by taking a long position at the end of each week in the nearest-to-expiry future that does not have its first notice date or expiration date in the next month. We construct an equal-weighted index, and from this, construct weekly returns.

For the stock-commodity correlation, we compute realized correlations between weekly stock5 and commodity returns. We use the same method for the bond-commodity correlation. Weekly bond returns are based on 10-year Treasury yields available from the Federal Reserve. Total returns are computed assuming the bond has 10 years to maturity, the coupon is equal to the initial yield and interest is compounded semiannually. For the average intra-commodity correlation, we take the average of the realized correlations of all the commodity pairs measured over annual horizons. For simplicity, we sometimes refer to this as the intra-commodity correlation.

Figure 1 displays summary statistics for correlations computed over annual windows (again, using weekly returns). Over the period 1962 to 2012, the average stock-commodity correlation is moderately positive: 0.13. The average bond-commodity correlation is a moderately negative -0.09, and the average correlation of commodities to each other is surprisingly low: 0.15 in our sample. The medians of these distributions are all reasonably close to their means.

Despite having average correlations not far from zero, all correlation pairs exhibit wide variation. The stock-commodity correlation ranges from -0.39 to 0.76, the bond-commodity correlation ranges from -0.53 to 0.36 and the average intra-commodity correlation ranges from 0.04 to 0.44.

Correlation To Other Asset Classes
Figure 2 displays the stock-commodity correlation (quarterly data with annual correlation window) from 1962 to 2012. The figure also displays recessions as identified by the NBER and the average default spread—a real-time indicator of economic strength—over the 12-month rolling period.6 Most salient, the two biggest spikes in the correlation between stocks and commodities correspond to the two deepest recessionary periods: the early 1980s and the late 2000s. In the fourth quarter of 1982, the rolling annual stock-commodity correlation reached 66 percent. Real GDP shrank 1.4 percent in 1982. Stock-commodity correlation spiked to 76 percent during and just after the seven-quarter recession that began in Q4 2007. Spikes in correlation also correspond to the recessions of the early 1970s and the early 2000s. However, the relation is far from perfect. The correlation reached its lowest levels during the recession of the early 1990s. Although the correlation reached its all-time highs during the recession of 2008, it was significantly negative during a portion of that recession. Additionally, the correlation rose in late 1963, a period of strong growth.

The stock-commodity correlation tracks the default spread. From the late 1970s through the early 1990s, the relation between the default spread and stock-commodity correlation is remarkably tight. These graphical results suggest a business cycle component to the stock-commodity correlation.

Figure 3 displays the bond-commodity correlation along with the default spread and recessions. Compared to the stock-commodity correlation, the bond-commodity correlation has more muted upside spikes and does not display the same pattern with regard to the business cycle. Although the bond-commodity correlation spikes to its historic highs of 36 percent in the early 1980s, it plunged during the 2008 recession. The stock-commodity correlation is currently close to its historic highs, but the bond commodity correlation is close to its historic lows.

In order to more deeply understand the relation between the stock-commodity correlation and the business cycle, we employ a regression analysis. The first three columns of Figure 4 display the results of regressing stock-commodity correlation on lagged stock-commodity correlation, real GDP growth and the contemporaneous default spread. The coefficient on lagged correlation is 0.41, with a t-statistic of 3.22. The correlation between stocks and commodities is persistent, implying a half-life of 9.3 months for a one-standard-deviation shock to the stock-commodity correlation. Regression (II) adds contemporaneous real GDP growth. The coefficient is negative, with a t-statistic slightly below standard significance levels. Regression (III) drops GDP and adds the default spread. The coefficient on the default spread is 0.166, with a statistically significant t-statistic of 2.48. These results broadly confirm the picture in Figure 2: When the economy is weak, especially as measured by the default spread, the correlation between stocks and commodities is high.

The last three columns of Figure 4 display the results for the same regression analysis using the bond-commodity correlation. The bond-commodity correlation is persistent, with a coefficient of 0.302 (a bit less than the stock-commodity correlation) and a t-statistic of 2.82. However, the coefficients on the business cycle variables are close to zero and statistically insignificant. The bond-commodity correlation does not seem to have a business cycle component.

Intra-Commodity Correlation
The correlation of commodities to one another is important to investors because lower intra-commodity correlation means that a portfolio of commodities will have more diversification and thus lower volatility. Conversely, high intra-commodity correlation means lower diversification and higher volatility. Erb and Harvey [2006] show that the historical correlation of commodities to each other is low (0.09). Tang and Xiong [2010] show that intra-commodity correlation varies over time, increasing from 2007 through the end of their sample in 2010, and that the correlation between oil and several other commodities has increased since the beginning of their sample in the mid-1980s.

Figure 5 displays the average intra-commodity correlation for the commodities in our data set.7 The business cycle pattern previously seen in the correlation between stocks and commodities is apparent in the intra-commodity correlation series. During periods of economic weakness, intra-commodity correlation is highest. Also, as with the correlation between stocks and commodities, the two highest peaks of intra-commodity correlation occur during the 2008 recession and the recessionary period of the early 1980s. The intra-commodity correlation also shows a pronounced spike during the recessionary period of the early 1970s—a pattern less pronounced in the stock-commodity correlation.

Figure 6 displays the regression results of the intra-commodity correlation. The pattern of results is very similar to those seen in the stock-commodity correlation regressions. The average intra-commodity correlation is highly persistent (coefficient: 0.671; t-statistic: 8.58) and is higher during periods of economic weakness. In regression (II), the coefficient on real GDP is -0.018, with a t-statistic of -1.68. In regression (III), the coefficient on the default spread is 0.067, with a t-statistic of 2.64.

Discussion And Interpretation Of Results
That stock-commodity and intra-commodity correlations are at historic highs has been widely noted. Conversely, bond-commodity correlations are at historic lows. However, these historic levels are not unprecedented. Both the stock-commodity and intra-commodity correlation spiked to similar levels in the early 1980s. Both these periods, the early 1980s and the late 2000s, contain the two deepest recessions of the last 50 years. Regression analysis further suggests that the stock-commodity and the intra-commodity correlations are inversely related to economic strength. This result is strong when economic strength is proxied by the default spread. Commodities are more correlated to stocks and each other, but not bonds, during bad economic times.

Why might the stock-commodity correlation have a business cycle component? There are at least two possible explanations: one based on firm behavior, one based on investor behavior. In bad times, firms will be quick to cut variable costs to avoid bankruptcy or in response to constrained credit conditions.8 Further, when times are bad, firms may take falling stock prices as a signal that things are getting worse (and vice versa), leading to an increase in the stock-commodity correlation. Firms quickly cutting variable costs during bad times can also motivate a business cycle effect on intra-commodity correlation. The argument is the same: In bad times, firms will cut variable costs more quickly than in good times to avoid bankruptcy, causing commodities—the variable inputs—to co-move more tightly. This explanation also explains why the bond-commodity correlation does not have a business cycle component: The future payoffs of Treasury bonds are not tied to economic strength or weakness; thus, companies will not interpret their movements as indicators of future economic states.

An alternative investor-based explanation of the time-varying correlation between stocks and commodities is that in bad times, investor risk aversion is high, and that in these periods, investors move in or out of risky assets as a group, leading all risky assets to move together. This notion is captured in the common statement that when bad things happen, “all correlations go to 1,” or that bad times are more subject to “risk-on/risk-off” scenarios.

Another motivation that also works through the channel of investors is the “financialization” of commodities hypothesis discussed by Masters [2008] and Tang and Xiong [2010], to name just a few studies. According to the financialization hypothesis, the correlation between stocks and commodities has permanently increased due to heightened investor involvement in commodity markets. However, the financialization hypothesis has difficulty explaining the spike in commodity correlations in the early 1980s, since investor interest in commodities was limited at that point in time.

How Well Does The Model Fit?
Figure 7 plots the stock-commodity correlation along with the fitted line from regression (III), in which the independent variables are lagged correlation and the default spread. The fitted line tracks observed stock-commodity correlation reasonably well over the entire sample. At Q3 2012, the final point in the sample, the model line is well over its average (34 percent compared with 13 percent) but does not reach the final observed value of 54 percent. Figure 8 displays the observed intra-commodity correlation and the fitted line from regression (III).9 The fit is quite good. The modeled and the actual correlation match exactly, 25 percent, at the most recent point in the sample, Q3 2012.


In recent years, the stock-commodity correlation and average intra-commodity correlation have hit historic highs, while the bond-commodity correlation has hit historic lows. Though extreme, current levels have been reached (or nearly so) in the past. In particular, the stock-commodity and the intra-commodity correlation spiked in the early 1980s, the period of the deepest recession in the sample prior to the recession of 2007-2009.

Bhardwaj, G. and A. Dunsby (2013), “The Business Cycle and the Correlation between Stocks and Commodities,” SummerHaven Investment Management, available at:

Bernanke B., M. Gertler and S. Gilchrist (1996), “The Financial Accelerator and Flight to Quality,” Review of Economics and Statistics, 78: 1-15.

Erb, C. and C. Harvey (2006), “The Strategic and Tactical Value of Commodity Futures,” Financial Analysts Journal 62(2): 69-97.

Gorton, G. and G. Rouwenhorst (2006), “Facts and Fantasies about Commodity Futures,” Financial Analysts Journal 62: 47-68.

Kiyotaki N. and J. Moore (1997), “Credit Cycles,” Journal of Political Economy, 105(2): 211-248.

Masters M. (2008), Testimony before the Committee on Homeland Security and Governmental Affairs, U.S. Senate, May 20.

Tang, K. and W. Xiong (2010), “Index Investment and Financialization of Commodities,” NBER Working Paper 16385.

1 See Gorton and Rouwenhorst (2006).
2 We use weekly asset returns to generate realized correlations over annual windows. For a detailed discussion of the methodology, see Bhardwaj and Dunsby (2012), available at
3 Estimates of half-life are based on the regression results reported below.
4 For a complete list of commodities and the period of data availability of individual commodities, see Bhardwaj and Dunsby (2012). In 1962, when this study starts, there are nine commodities in the sample. This number grows to 25 with the addition of the natural gas in May 1990.
5 For stocks, we use the percent change in the S&P 500 price index. Dividends are not included.
6 A 12-month period is identified as recessionary if it contains at least one recessionary month. This is why the entire period January 1980 through November 1982 is grayed, even though it contains two distinct recessions. Default spread is defined as the average of difference of Moody’s Seasoned Baa Corporate Bond Yield (BAA), and Moody’s Seasoned Aaa Corporate Bond Yield (AAA).
7 Figure 5 retains its same basic shape if only the nine commodities that exist for the entire sample are included, though the overall level of correlation is higher since most of the full sample commodities are agriculturals. GDP growth is measured over the same period as the dependent variable.
8 See the models of Bernanke et al. (1996), and Kiyotaki and Moore (1997).
9 We don’t include a similar analysis for the bond-commodity correlation since this series does not exhibit a business cycle component.


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