Futures Trading and the Excess Comovement of Commodity Prices

We empirically reinvestigate the issue of the excess co-movement of commodity prices initially raised in Pindyck and Rotemberg (1990). Excess co-movement appears when commodity prices remain correlated even after adjusting for the impact of fundamentals. We use recent developments in large approximate factor models to consider a richer information set and adequately model these fundamentals. We consider a set of eight unrelated commodities along with 184 real and nominal macroeconomic variables, from developed and emerging economies, from which nine factors are extracted over the 1993-2013 period. Our estimates provide evidence of time-varying excess co-movement which is only occasionally significant. We further show that speculative intensity is a driver of the estimated excess co-movement, as speculative trading is both correlated across the commodity futures markets and correlated with the futures prices. Our results can be taken as direct evidence of the significant impact of financialization on commodity-price cross-moments.


Introduction
Commodity markets have undergone major changes over the past two decades. The popularity of commodityrelated financial instruments, such as commodity indices, has led many observers to conclude that commodity markets are now more intimately connected to financial markets, and so may also co-move more significantly (Tang and Xiong (2012), Cheng and Xiong (2013), Hamilton and Wu (2015), Basak and Pavlova (2016)). While a greater number of participants in commodity markets may bring about improved risk sharing, the financialization process has been widely criticized as a potential source of excessive price volatility (Stoll and Whaley (2010)). This paper investigates whether the excess co-movement of commodity prices is related to the growing financial influence in commodity markets.
The excess co-movement of commodity prices deserves analysis for at least two reasons. First, residual correlation (or "co-movement") may mean that " [...] commodity demands and supplies are affected by unobserved forecasts of the economic variable." (Pindyck and Rotemberg -PR hereafter -(1990), p. 1174), thereby indicating that the standard demand-supply model may not be able to explain commodity returns adequately. This conclusion, which is at odds with standard economic theory, suggests that further research is needed to uncover the new relevant fundamentals, or change the way in which these fundamentals are measured. Second, from a portfolio-management perspective, the presence of co-movement limits the diversification of investors who manage a portfolio containing a number of commodity futures. 1 PR define excess co-movement as commodity prices remaining correlated even after adjusting for the impact of common macroeconomic variables. They select six variables: the U.S. index of industrial production, the consumer price index, the effective $US exchange rate 2 , the three-month Treasury bill interest rate (cf. Frankel and Rose (2010)), the M1 monetary measure (cf. Frankel (2006)) and the S&P 500 stock index, which are supposed to represent the fundamentals. Nevertheless, the authors recognize that: "[...] a major limitation of our approach is that we can never be sure we have included all relevant macroeconomic variables and latent variables." (p. 1185). 3 One major issue in filtering the returns from common factors is indeed the selection of the variables to be considered.
To deal with the issue of omitted variables, we suggest relying on a large approximate factor model, along the lines of Stock and Watson (2002a, b), which allows us to enlarge the information set significantly while 1 Investment in commodity markets from a portfolio perspective is discussed in Gorton and Rouwenhorst (2006), Erb and Harvey (2006), Rouwenhorst and Tang (2012) and Gorton et al. (2013), among many others. 2 The early contribution by Gilbert (1989) emphasizes the relevance of the exchange rate as an explanatory variable for commodity prices; see also the recent papers by Chen et al. (2010) and Ferraro et al. (2015). 3 The same variables are used in Deb et al. (1996). Leybourne et al. (1994) further discuss the issue of omitted variables. preserving a sufficiently low dimension for the econometric estimation. 4 We thus avoid the arbitrariness and computational difficulties of selecting relevant variables, in particular when the number of possible combinations is large. Borensztein and Reinhart (1994) underline the need to consider well-defined supply and demand variables in order to explain commodity prices. In particular, the authors advocate the inclusion of variables for Eastern Europe that are likely to be relevant for their sample period of 1970-1992. In the same spirit, we consider a set of economic variables from developed and emerging countries (China, India and Brazil, among others) that should allow us to filter out commodity returns more accurately, as these countries have played a central role in shaping commodity prices over recent years. While commodity prices are the product of transactions in one particular part of the world, they also reflect a great deal of information which has been generated throughout the world. For instance, the price of crude oil, say U.S.
West Texas Intermediate (WTI), is widely accepted as a world price, while being mainly traded in the U.S.
The factors extracted from our world data set are quite successful in explaining monthly commodity returns. Following the idea of Ludvigson and Ng (2009) of grouping explanatory variables into meaningful categories, we uncover the sets of variables that best explain commodity returns. Our estimates show that monthly commodity returns over the last two decades are mainly correlated with the real aggregate variables in emerging countries, highlighting the important role played by these countries in shaping commodity prices over this period. We then show that there is only sporadic empirical evidence of excess co-movement between commodity returns over the 1993-2013 period. 5 As such we extend PR's analysis in two directions. First, we investigate the time-varying behavior of the phenomenon, thereby providing further insights into the analysis of excess co-movement. Second, we look at a recent period that includes both a pronounced increase in commodity prices around 2008 and the recent financial crisis. Last, we take heteroscedasticity into account as this can play a critical role in measures of correlation. 6 Highlighting these stylized facts regarding excess co-movements in commodity prices in recent years is our first contribution.
The main novelty in our paper, which constitutes our second contribution, is that we establish an empiri-4 Recent economic research on the determination of commodity prices occasionally makes use of factor models. Examples of this growing literature are Byrne et al. (2013), Gospodinov and Ng (2013), West and Wong (2014) and Christoffersen et al. (2014). While these papers investigate more or less directly the issue of the co-movement of commodity prices, they all extract principal components from a set of commodity prices to explain the evolution of commodity prices, only considering a few additional macroeconomic variables -such as interest rates, exchange rates and inflation -to analyze the link between these variables and their estimated factors. As such, their approach is very different from ours. 5 As will be made clear in the empirical sections, we adopt a measure of excess co-movement that is similar to that used in Kallberg and Pasquariello (2008), in that we consider the average of the squared residual correlations between all pairs of commodities. We hence allow both positive and negative correlations to contribute to the excess co-movement estimate. 6 As shown by Forbes and Rigobon (2002), the usual sample correlation is a biased measure of the true correlation when volatility is time-varying, which is a well-known stylized fact regarding financial series. As most of our commodity returns are characterized by time-varying volatility, we use the correlation coefficient corrected for heteroscedasticity of Forbes and Rigobon (2002). cal relationship between the notion of excess co-movement and speculative activity in commodity futures markets. Surprisingly, academic research has not yet investigated the potential determinants of excess comovement in commodity prices. We suggest an explanation for this phenomenon following the intuition developed in Barberis and Shleifer (2003) that "investors categorize risky assets into different styles and move funds among these styles depending on their relative performance." (p. 161). As such, if most commodities are classified into a "commodity style", seemingly unrelated commodities are likely to co-move more than would be expected based on fundamental analysis. 7 This is precisely what we demonstrate in our present work. Our results are also in line with the recent work by Basak and Pavlova (2016), who go beyond the behavioral approach in Barberis and Shleifer (2003) and develop a multi-asset, multi-good general equilibrium model with heterogenous investors, some of whom are institutional investors, considering characteristics that are specific to commodities such as the presence of inventories. The model, in the tradition of Lucas-tree models, is solved in closed-form and provides a rich set of implications, among which an increase in the correlation between commodities following institutional positioning, and more so for commodities that are included in an index. Our results provide strong support for the outcome in Basak and Pavlova (2016), and may then be seen as an empirical validation of their model.
Our empirical work makes use of data from the U.S. Commodity Futures Trading Commission (CFTC) to estimate speculative intensity. While the categories in the publicly-available data from the CFTC do not distinguish perfectly between the various categories of traders, as discussed previously in Bessembinder (1992) and Stoll and Whaley (2010) among many others, we here show that they are informative for the explanation of excess co-movement. Our measure of speculative activity in futures markets follows the recent work by Han (2008) on sentiments in financial markets but is reminiscent of the so-called Working's T measure. Our empirical strategy provides direct evidence of the explanatory power of speculative intensity for excess co-movement: we show that speculative activity is correlated across commodity futures markets and, at the same time, that speculative activity is correlated with futures prices. This last result is obtained from an instrumental-variable analysis to avoid endogeneity issues between returns and positions in futures markets.
The empirical work closest to ours is Tang and Xiong (2012), which also considers the financialization of commodities as a potential source of the recent increase in co-movements between commodity returns.
Their "analysis focuses on connecting the large inflow of commodity index investment to the large increase of commodity price co-movements in recent years by examining the difference in these co-movements be-7 Interestingly, Barberis and Shleifer (2003) (2012), we adopt a very different empirical approach. In particular, we specifically consider fundamentals that are critical in the analysis of co-movements.
The plan for the rest of the paper is as follows. In the next section, we present the data used for the empirical analysis. In Section 3, we very briefly review the factor-model methodology and calculate the factors used to filter the commodity returns. The excess co-movement is then estimated in Section 4, while Section 5 is dedicated to the analysis of the relationship between excess co-movement and speculation. Finally, Section 6 concludes by discussing some limits to and possible future extensions of our work.

Data
We consider a set of eight commodity prices: wheat, copper, silver, soybeans, raw sugar, cotton, crude oil and live cattle. These are representative of the main commodity classes and are assumed to be unrelated as defined in PR, in the sense that their supply or demand cross-elasticities are almost zero. All prices are cash prices except for crude oil, where the front-month contract price is taken as a proxy for the cash price, to avoid the distorting impact of delivery issues for this particular commodity. All prices are in nominal $US.
Due to data limitations, in particular for macroeconomic variables from emerging countries, we consider monthly observations from February 1993 to November 2013. Data are from Datastream.
The prices are displayed in Figure 1.  Barberis, Shleifer and Wurgler (2005), who theoretically and empirically analyze the behavior of newly-included stocks in a stock index. It is shown that the price co-movement between the stock and the index significantly increases after this inclusion.
2009 but rise steeply in 2010; they stabilize or fell in 2012. Returns are log difference of prices. 9 The descriptive statistics in Table 1 reveal evidence of skewness -negative in six cases out of eight -and excess kurtosis. The Jarque-Bera test consequently rejects the hypothesis of a Gaussian distribution for all returns.
The presence of heteroscedasticity, which is a standard feature in financial price series, may lie behind this non-normality.  Stock and Watson (2002b) and Ng (2007, 2009) are thus not well-suited for our current purpose.
We have the same classes of data for both developed and emerging countries. We include measures of the country's aggregate activity level such as the industrial production index and manufacturing orders and capacity utilization. Other real variables are related to household expenditure: household consumption, housing starts and car sales. We add variables related to the labor market (wages and unemployment) and international trade (exports, imports and terms of trade). These real variables are assumed to be correlated with the world demand for commodities. The main categories of nominal variables that we include are monetary aggregates, stock indices, interest rates, exchange rates with the dollar, and producer and con-9 Part of the existing literature (Palaskas and Varangis (1991), Leybourne et al. (1994)) considers excess co-movement of nominal or real price rather than return, and relies on a co-integration analysis. We think that return is more appealing when dealing with risk management issues, and thus consider the excess co-movement of returns as in the seminal work of PR. Returns rather than prices have also been considered more recently in Ai et al. (2006) and Malliaris and Urritia (1996) for the main agricultural commodities. 10 Each variable is rendered stationary in an appropriate manner: the chosen transformation appears in the penultimate column of the sumer price indices. These nominal variables help us to model the relationship between commodity returns and interest rate or the inflation rate. Finally, we add the Real Activity Index to the above, as developed in Kilian (2009). This is "based on dry cargo single voyage ocean freight rates and is explicitly designed to capture shifts in the demand for industrial commodities in global business markets" (p. 1055), following a long tradition of economists who have noted the correlation between economic activity and ocean-freight rates.
3 Filtering commodity returns using large approximate factors models In this Section, we first briefly review the large approximate factors method. Recent techniques to establish the optimal number of factors are presented in Appendix B; additional developments can be found in the survey by Bai and Ng (2008) of large approximate factors models. The remainder of the Section is dedicated to the projection of commodity returns on the estimated factors.

Static factors calculation
We use the static factor model of Stock and Watson (2002a). We do not consider the dynamic version of Forni et al. (2005), as recent work (Boivin and Ng (2005)) has shown that the dynamic and static factor models perform equally well, especially when the factors have unknown dynamics, which is often the case in empirical work. In addition, the dynamic factor model is best suited to forecasting, which is not the purpose of our work.
We have a sample {x it } of i = 1, ..., N cross-section units and t = 1, ..., T time-series observations. Each x it is split into a component depending on a set of r << N common factors F t = (f 1t , f 2t , ..., f rt ) ′ and an idiosyncratic component e it : where λ i is the (r × 1) factor loading.
If we define the (N ×1) vectors of observations and idiosyncratic components at date t as X t = (x 1t , ..., x N t ) ′ , e t = (e 1t , ..., e N t ) ′ and Λ = (λ 1 , ..., λ N ) ′ the (N × r) matrix of factor loadings, the factor decomposition is written as In classical factor analysis, F t and e t are assumed to be serially and cross-sectionally uncorrelated, and the number of units of observation N is fixed. Stock and Watson's (2002a,b) "large dimensional approximate factor models" differ from the classical model in two ways: the idiosyncratic errors are allowed to be "weakly correlated" across i and t 11 and the sample size tends to infinity in both directions.
We assume k factors and use the principal components method to estimate the (T × k) factor matrix F k and the corresponding (N × T ) loading matrix Λ k . The estimates come from the solution to the following optimization problem: This classical principal component problem is solved by settingΛ k equal to the eigenvectors of the largest The consistency and asymptotic normal distribution of the principal component estimator as N, T → ∞ have been respectively demonstrated by Stock and Watson (2002a), Bai and Ng (2002) and Bai (2003).
The next step is to determine the optimal number of factors. The literature on this issue has not come to a clear consensus on how to select relevant factors and, as shown in Table B.1 in Appendix B, different methods lead to very different outcomes. 14 We follow traditional practice in principal component analysis and choose the first nine factors, as the incremental explanatory power beyond these nine factors is only small. The nine factors explain 37% of the variability of the 184 macroeconomic variables.

Modelling commodity returns
Our measure of excess co-movement makes use of commodity returns which have been filtered for common components. As such, once we have calculated the static factors, the second step of the empirical analysis, consists in filtering the returns using these estimated factors. The first step is the linear regression of returns 11 Although Stock and Watson (2002a) use different sets of assumptions to characterize "weak correlations", the main idea is that the cross-correlations and serial correlations have an upper bound. 12 As the factors Ft and the loading matrix Λ are not separately identifiable (see Bai and Ng (2008) for more details), constraints are imposed to obtain a unique estimate 13 When N > T , a computationally simpler approach is to use the T × T matrix XX ′ . 14 Methods based upon information criteria and Kapetanios (2010) are described in Appendix B. on the first three factors: where r it represents the i th commodity return at date t, α i is the constant, β i the vector of factor coefficients for the i th commodity, andF t = ( F 1,t , F 2,t , F 3,t ) ′ the vector of the first three factors at date t. The results from seemingly-unrelated-regressions (SUR) appear in Table 3. The R 2 varies from 1.07% for soybeans to 28.58% for crude oil. The factors F 2 and F 1 are significant in most regressions. While the explanatory power figures for agricultural commodity returns are not substantially higher than those in PR, we do obtain a much higher R 2 for metals and energy commodities. 15 The ARCH-LM test shows that six out of the eight series of residuals have time-varying variance.
In a second approach, as in Stock and Watson (2002b) and Ludvigson and Ng (2009), we consider all possible combinations of the first nine estimated factors and, for each commodity, select the regression which minimizes the BIC criterion. Once each set of regressors has been selected, we jointly estimate the eight regressions via SUR. Our aim here is to identify the best model from a set of common regressors for each commodity. This approach aims to eliminate as much residual correlation as possible, and so strengthen our evidence for any excess co-movement. The SUR estimates appear in Table 4, and show a significant increase in explanatory power for crude oil, while this figure remains low for the other commodities. Again, the F 1 and F 2 factors are significant for most of the eight commodities and the ARCH-LM test rejects the null hypothesis of constant variance for three series of residuals.
While the factors cannot be identified econometrically, it is very useful to identify the macroeconomic variables behind the factors affecting commodity returns. To interpret the factors, we follow Ludvigson and Ng (2009) and divide our 184 series into developed and emerging countries, and then real and nominal vari-15 To further improve the explanatory power, we also considered potential nonlinearities with quadratic or cubic factors. We choose the specification with the highest adjustedR 2 . The set of factors is nowF nl ) and the regressions become: The best-specifications results are not shown here (but are available upon request) We do not find any notable increase in the R 2 for any commodity. We therefore retain linear factors in the returns equation.
ables. 16 Each of the 184 original variables is then regressed on one factor with the resulting R 2 appearing on the horizontal axis. We can thus see which macroeconomic variables obtain the highest R 2 . The factor in question can then be thought to represent this set of variables. Figure 2 shows the R 2 for the F 1 and F 2 factors. The F 1 factor can be seen to reflect more the real variables in emerging economies. The correlation of F 1 with crude oil and copper returns underlines the growing role of emerging economies in determining these commodity prices. 17 This finding is in line with previous work showing that oil (e.g. Hamilton (2009) or Kilian and Hicks (2013)) and agricultural prices (e.g. Hamilton and Wu (2015)) are mainly driven by demand from emerging countries rather than speculative activity.
The interpretation of factor F 2 is less obvious. This is highly correlated with a small number of real variables but its explanatory power with respect to interest rates, producer and consumer price indices and monetary aggregates in both developed and emerging countries is greater than that of F 1 . We thus interpret F 2 as representing these latter variables. The relation between interest rates and commodity prices is discussed in a number of recent contributions (Barsky and Kilian (2002), Frankel and Rose (2010)) although the empirical evidence is fairly weak. Our estimates provide some evidence of a relationship between nominal variables and commodity prices. The price indices and monetary aggregates may pick up the effect of inflation on commodity prices.
The activity index from Kilian (2009) brings no additional information as it attracts only an insignificant estimated coefficient -except for copper, at the 10% threshold only -indicating that F 1 does a better job of modelling commodity returns. This conclusion is of interest as this real-activity index is considered to be as a proxy for economic activity. We believe that this result confirms the ability of statistical factors to aggregate information from a large number of variables and capture high-frequency growth rates. To better understand the insignificance of Kilian's index, Table 5 shows the estimates from univariate regressions of the nine empirical factors on Kilian's index. The estimates are very significant but with little explanatory power. This is likely due to the low-frequency nature of the Kilian Index, and further demonstrates the benefit from using statistical factors in modeling monthly commodity returns.
Finally, the omission of inventory data in our analysis is worthy of mention. It is commonly thought that stock levels may help us to better model commodity returns, following Working's Theory of Storage. For instance, Pindyck (2001) uses weekly inventory data from the U.S. Department of Energy to model the convenience yield in the WTI crude oil market. Geman and Nguyen (2005) rely on a number of worldwide 16 The classification in Ludvigson and Ng (2009) is finer but is applied to U.S. variables only. Their classification is likely not applicable when a number of economies are considered for reasons of interpretability. 17 China imports 30% of all the copper traded in the world. sources to construct their own inventory series for soybeans which they use to model this commodity's forward curve. Baumeister and Kilian (2012) consider a number of oil-specific inventory series to forecast real-time monthly oil prices. We do not include inventory information in our empirical analysis as we wish to filter returns using fundamentals that are, at least partly, common to all commodities. By doing so, data related to commodity demands that we proxy via our factors are relevant as they represent common fundamentals. Conversely, data such as inventories are very particular to each commodity and so less likely to explain any correlation in commodity returns. As such, even if we recognize that inventories matter in particular cases such as, for instance, forecasting commodity prices (see Kilian (2012, 2014) for the case of oil), they do not do so here, where it is rather common factors that are our primary concern.
4 Testing for the excess co-movement of commodity returns

Testing for residual correlation
The residuals from the regressions above reflect commodity returns after controlling for fundamentals. We first evaluate the correlation in residuals, as in PR. Tables 6 and 7 show the sample correlations (in the upper triangular part) and their p-values 18 (in the lower triangular part) for the residuals from the three-factor and BIC linear filters.
The results from both sets of regressions confirm the hypothesis of excess co-movement. We find 16 and 18 significant sample correlations at the 1% and 5% significance levels, respectively, for the three-factor regressions; the analogous numbers for the BIC-minimizing regressions are 9 and 10. Unsurprisingly, the Breusch-Pagan LM test rejects the null hypothesis of no residual correlation in both cases. In the BICminimizing regressions, five sample correlations are no longer significant, mostly related to crude oil. 19 Filtering commodity returns therefore somewhat reduces the number of significant correlations. However, as the significant correlations range from 0.4711 (wheat and soybeans) to 0.1066 (copper and crude oil) the level of residual correlation remains quite substantial. 18 The p-value is calculated by transforming the correlationρ to create a t-statistic with T − 2 degrees of freedom, where T is the number of observations. 19 One possible explanation is that the oil-return filtering is more successful than that for other commodities.
4.2 A global, unbiased and time-varying measure of excess co-movement One major limit of the use of sample correlation to gauge excess co-movement is the bias in the former when volatility is time-varying. 20 This argument has been put forward in the contagion literature 21 by Forbes and Rigobon (2002), among others. 22 When there is a simultaneous rise in the respective volatility of two variables, the typical sample correlation measure overestimates the true correlation. Forbes and Rigobon (2002) propose an unbiased correlation estimator: as our residuals very often have time-varying volatility, this is the estimator we use to evaluate excess co-movement.
We follow Kallberg and Pasquariello (2008), who apply the Forbes and Rigobon estimator on a movingwindow basis to yield a more precise estimator of the true correlation. We end up with a global measure, as we treat all residual correlations equally, without focusing on the correlation of one particular commodity with another. We calculate a time-varying measure of excess co-movement which will show us whether excess co-movement is a permanent feature of commodity markets or if it is only occasional. Our global measure of excess co-movement is the average of all the squared unbiased correlations. We use squared correlation measures as some of the estimated correlations are negative. Our estimate is nonparametric and avoids the mean-reversion problem inherent in the parametric approach, such as in the dynamic conditional correlation model (DCC, Engle (2002)). As noted in Kallberg and Pasquariello (2008), the financial literature has offered a number of examples where rolling filters perform very well as compared to more sophisticated parametric specifications. In the following, we present the bias-corrected correlation estimator and the aggregation process to obtain our overall excess co-movement measure.
For all pairs of non-redundant returns i ̸ = j, we calculate the residual correlation: whereû i,t is the residual from the i th commodity-return equation. As the sample correlationρ ij,t is biased in the case of heteroscedasticity, this is called the "conditional correlation".
The Forbes and Rigobon (2002) bias-corrected correlation estimator iŝ var(û i,t ) LT − 1 corrects the conditional correlationρ ij,t for the change between the i ith return's short-term var(û i,t ) and long-term var(û i,t ) LT volatilities. 23ρ * ij,t is called the unconditional correlation. As we do not make any ex ante assumption regarding the direction of the propagation of shocks from one commodity to another, we alternately assume that the source of these shocks is asset i (inρ * ij,t ) or asset j (inρ * ji,t ). We therefore have two unconditional and possibly different correlations,ρ * ij,t andρ * ji,t . Our global excess co-movement measure is based on these unconditional correlations.
As suggested in King et al. (1994) and Kallberg and Pasquariello (2008), we compute the arithmetic mean of the pairwise squared unbiased correlations for each commodity i. A non-null unconditional correlation ρ * ij,t ̸ = 0 andρ * ji,t ̸ = 0, whatever its sign, is taken as evidence of excess co-movement between commodities i and j. A measure of excess co-movement between commodity i and the others is defined as: for all commodity returns i = 1, ..., K, where K = 8 is the number of commodities.
Our global and time-varying measure of excess co-movement is then the mean of the excess squared unconditional correlations over all commodities: We treat the covariance matrix of return residuals as observable, and construct a time series of rolling realized excess squared correlations for each commodity i.δ i,t andρ * i,t are estimated over short-and longterm intervals of fixed length N [t − N + 1, t] and gN (with g > 1) [t − gN + 1, t], respectively. We use a rolling window of N= 30 monthly observations for short-term volatility and gN = 60 monthly observations for long-term volatility.

Estimation results
We compute three averages of squared correlations, all of which appear in Figure 1, to evaluate the importance of filtering returns and illustrate the time-variation in volatility. The first (dashed line) is the average of the squared unconditional correlations in returns:ρ * ret,t = 1 where the unbiased correlations are calculated for non-filtered returns. The second (dashed-dotted line) is the average of the squared conditional correlations between residuals:ρ t = 1 We here use residual correlations that are not corrected for changes in volatility. The last solid line is the average of the unconditional squared correlationsρ * t as defined in the previous section, which is our estimate of excess co-movement. returns using some measures of fundamentals, and shows that the rise in commodity-returns correlation is partly due to common factors. Juvenal and Petrella (2015) find that the co-movements between the prices of oil and other commodities reflect global demand shocks. We are partially in line with them in that, once factors related to demand are taken into account, the residual correlation is lower, with this effect being stronger in recent years when demand shocks were larger.
Second, looking at bothρ * t andρ t , taking time-variation in volatility into consideration only moderately affects the estimated correlation: the two lines are almost identical except in periods of high volatility, where there is a difference (although only small) between the two measures.
Third, and most importantly, our measure of excess co-movement is significant at the 5% level only half of the time in the period under consideration. 24 We thus conclude that the excess co-movement in commodity prices cannot be viewed as a general feature of commodity markets but is rather sample-dependent. As PR do not investigate time-variation in their excess co-movement measure, our results cannot be compared to theirs. There is a possibility, however, that the estimated excess co-movement over the 1960-1985 period that PR find is insignificant over some sub-samples, thereby questioning the determinants of this phenomenon. In the same vein as the correlation plot in Tang and Xiong (2012), the chart of average squared correlations in Figure 1 provides a finer description of the estimated excess co-movement. This latter is mostly significant during periods of financial crisis: from mid-2000 to early 2003, and from 2008 onwards. 24 The significance threshold is 0.1669 and is plotted as a horizontal dotted line in Figure 1.
In their 'convective risk flows' model, Cheng et al. (2015) show that financial traders cut their net long positions in response to market distress. A coordinated drop in the long positions of financial traders may help explain excess co-movement. Alternatively, excess co-movement may also reflect a 'flight-to-quality' phenomenon, where investors decide to partly leave the stock market and invest heavily in commodities to diversify their positions. Moreover, the period starting in 2000 also corresponds to the growing financialization of commodity futures markets, as excellently surveyed in Cheng and Xiong (2014a). As such, excess co-movement might be related to speculative activity in commodity futures markets. Whether excess co-movement comes the changing nature of trading in commodity markets is a central question that we answer in the next section.

Explaining excess co-movement
The  (2012), Hamilton and Wu (2015) and Lehecka (2015)). Surprisingly, there is no work dealing with the impact of financialization on cross-market return linkages except for that in Tang and Xiong (2012). 25 The latter attempt to explain the recent rise in the co-movement of a number of commodity prices via five hypotheses: (i) the financialization of commodities, (ii) the rapid growth of emerging economies, (iii) the recent world financial crisis, (iv) inflation and (v) the adoption of biofuels. Our research question is linked to the arguments in Tang and Xiong (2012), in that we arguably jointly test their first and third hypotheses, and consider the second and fourth in Section 3 when we filter returns using common factors. In particular, we have shown that growth in emerging economies leads commodity prices (hypothesis (ii)), and that commodity returns are correlated with a 'nominal variables' factor (hypothesis (iv)). Both of these effects likely contribute to excess co-movement and are expressly taken into account in our work.
This section aims to show that speculation in commodity futures markets is a significant determinant of our estimated excess co-movement. The issue is new and challenging, as no significant evidence has been put forward in the literature to date. Our empirical approach is as follows. In a first step, we show that speculative activity and filtered futures returns are correlated for most of the commodities in our sample.
Then, in a second step, we show that measures of speculative activity are correlated across commodities.
Taken together, these results provide direct evidence of speculation as a driver of excess co-movement. 26

Measure of speculative intensity
Our measure of speculative intensity builds on the work in Han (2008), where a new speculative index is developed following the literature on investor sentiment (see Baker and Wurgler (2007)). 27  ulators. The usefulness of these CFTC data has previously been discussed in Bessembinder (1992) and Cheng and Xiong (2014b), as many traders carry out activities which cover both hedging and speculation.
In particular, Cheng and Xiong (2014b) show that hedgers may react to changes in commodity futures prices in a number of U.S. Agricultural markets, which is undoubtedly a form of speculation. In what follows, we show that CFTC data are informative for our purpose despite the potential bias in the definition of categories of traders.
We also experiment with alternative measures of trading activity. The first of these is the Working's T speculative index, as recently used in Büyüksahin and Robe (2014). A second measure of trading activity is hedging pressure, as defined in de Roon et al. (2000), who showed that futures risk premia depend on both own-market and cross-market hedging pressure. Their measure of hedging pressure is calculated as the difference between the number of short and long hedge positions, divided by the total number of hedge 26 We wish to thank a referee for suggesting this methodological approach. 27 The analysis in Han (2008) deals with S&P 500 futures contracts. The author also relies on a proxy based on the Investors Intelligence's weekly that is not relevant for commodity markets. 28 Since 2006, the CFTC has also released a weekly Disaggregated Commitments of Traders (DCOT) report each Friday. This complements the COT report by providing more detailed categories of traders such as Index Traders who have played a significant role in recent years. We do not use the DCOT data here, as it would considerably restrict the analysis sample period.
positions. This measure focuses on the positions of traders who are hedgers, i.e. who have a cash business for the commodity. It is different from the Han index, where the denominator is the total open interest and not the total number of speculative positions, but the idea is roughly similar as hedging pressure also picks up the difference between long and short positions. 29 Results from using either Working's T or hedging pressure are very similar to those presented here, and are not reported to save space (but available upon request).

Empirical results
To deal with the potential correlation of Han's indices and the business cycle, we regress our speculative indices on the same set of factors ( F 1t , F 2t , F 3t , F 6t , F 8t ) as was used to filter commodity returns. Then, to gauge the explanatory power of Han's indices, we include them in univariate regressions of the form: where Res i,t is the i th commodity return residual at time t and H j,t is Han's index for the j th commodity at time t adjusted for the factors. Our choice to use contemporaneous variables in the regressions is motivated by the monthly frequency and the efficient-market hypothesis stating that any impact of index funds should be instantaneously reflected in prices (see Gilbert and Pfuderer (2014) for further developments on this issue). We also choose to consider all the Han indices in each univariate regression following existing research on cross-commodity trading and its potential impact on prices (e.g. de Roon et al. (2000)). 30 The estimated coefficients appear in Table 9. We observe that, with the exception of oil, copper and silver, commodity returns are correlated with their own Han's index. The R 2 mostly ranges between 1% and 2%, but reaches 12.29% for raw sugar. We find a positive and significant impact of the Han index on its corresponding commodity for wheat, raw sugar, soybeans and live cattle. For these commodities, speculative trading and returns move in the same direction. We also observe some cross-effects: the raw sugar and copper Han indices have an impact on wheat returns, and the cotton Han index has an effect on crude oil returns. In these cases, the estimated coefficient is negative but only weakly significant. The interpretation of these cross-effects is quite challenging as there is no link, such as substitutability or complementarity, between the commodities concerned.
One may rightly suspect that these OLS estimates are plagued by endogeneity. To assess the presence of 29 The sample correlation between Han's index and hedging pressure ranges from -0.78 for live cattle to -0.98 for cotton. 30 Singleton (2014) implicitly considers the role of cross-positions, as his measure of index funds in oil markets in derived from index funds positions in grain markets. endogeneity, we estimate all previous regressions via GMM and use one-period and two-period lagged Han indices as instruments. 31 The results in Table 10 show that the test for exogeneity based on the difference in the J-test does not reject the exogeneity of the Han index for cotton, crude oil and live cattle. We therefore consider the previous OLS estimates as valid: the Han index has a positive effect on its own commodity for cotton and live cattle while that for cotton has a negative impact on oil. We reject the exogeneity of the Han index in the wheat, raw sugar and soybeans regressions. Hansen's (1982) J-test for overidentifying restrictions validates our set of instruments. We also check that the instruments are not weak. With the exception of soybeans, the GMM estimates are in line with the previous OLS regressions for these three commodities. Wheat returns are still negatively and significantly impacted by the Han index for raw sugar, although the indices for wheat and copper are no longer significant. The raw sugar Han index still has a positive impact on its return.
Our approach through instrumental variables unambiguously shows that there is a significant impact of changes in the speculative index on contemporaneous returns, even after controlling for endogeneity for most commodities. This impact is positive when the Han index and the return pertain to the same commodity.
We now focus on sample cross-correlations between speculative intensities in commodity futures markets.
As expected from the "style investing" hypothesis developed in Barberis and Shleifer (2003) or the more general increase in non-commercial positions in commodity-futures markets in the last decades (see Cheng and Xiong (2014a)), the cross-correlations between speculative indices are mostly positive and significant as shown in Table 11. There are respectively 10, 15 and 19 significant cross correlations at the 1%, 5% and 10% significance levels. The cross-correlations are significantly negative in only three cases (silver and raw sugar, silver and soybeans, wheat and live cattle). We therefore have evidence that speculative indices move together, even for commodities of different classes such as, for instance, wheat and copper, cotton and crude oil, or raw sugar and live cattle.
Overall, our empirical results demonstrate that speculative activity is a significant driver of excess comovement. We thus confirm the implications in Basak and Pavlova (2016) that institutional investors do play a role in linking commodity futures prices. Our results are also in line with those in Tang and Xiong (2012), but provide stronger evidence of the impact of speculation on co-movements as we on purpose control for the impact of real variables on commodity prices. More generally, our results demonstrate the 31 Our methodology resembles the approach in Raman et al. (2016), who gauge the effect of the participation of financial traders in oil futures post-electronification using two-stage least squares, or the method in Gilbert and Pfuderer (2014), who investigate the causal role of index trading on grain markets using instrumental variables. As changes in futures positions and futures returns are simultaneously determined, these methods are naturally relevant when analyzing financialization. critical role of trading for price determination, and the overall importance of the "financialization of the commodity markets", a concept that has attracted growing interest in academic and political spheres over recent years.

Concluding remarks
The aim of this paper was to reconsider the question of the excess co-movement of commodity prices and to provide an explanation of this phenomenon, if it was found to be present in the data.
We believe that our paper offers new perspectives for the analysis of co-movement in commodity returns.
First, as discussed above, we use the large approximate factor model method to uncover the relevant factors that allow us to explain commodity returns. To the best of our knowledge, this is the first time that this method has been used to filter out returns before looking for excess co-movement. The main advantage of factors is that they allow us to deal with a large number of variables, while retaining econometric tractability, thereby including a richer set of fundamentals. We thus avoid any artificial limit on the information set, which has been a major constraint in previous work.
Our second contribution is to provide an explanation of the excess co-movement in commodity returns.
Previous work has emphasized the methodological aspects of the assessment of the hypothesis of excess co-movements. Surprisingly, however, the issue of which variables are related to this phenomenon has not been analyzed to date. Our indicator of speculative activity, calculated using traders' positions available from CFTC, is both correlated across commodities and with futures prices, thereby providing evidence of speculation as a driver of excess co-movement.
The limits of our analysis are good topics for future research. First, we consider, as in most factor-models in the literature, the factors as if they were data rather than being estimated. Even if this may have only a small effect on our results, it would be useful to investigate the small-sample case using simulation techniques as in Ng (2007, 2009).
Second, MIDAS regressions may be used to include more information at different frequencies. Tang and Xiong (2012) consider daily and monthly regressions, and MIDAS may help to combine the two data sources, with daily market indices and monthly or quarterly macroeconomic variables. This is the setting in Karali and Power (2013), who mix high-and low-frequency variables to explain the volatility of commodity returns. Such a setting may allow us to consider volatility spillovers, as in the penultimate section in Tang and Xiong (2012). The analysis of commodity volatility co-movement may have interesting implications for financial risk management.
Third, alternative measures of trading activity, such as liquidity measures, may help better explain excess co-movement. In this respect, the recent contributions of Marshall et al. (2012Marshall et al. ( , 2013 may aid in the selection of appropriate liquidity measures for commodities and the evaluation of the explanatory power of their common liquidity factor. These measures may additionally be calculated on a daily basis, thereby permitting the high-frequency analysis of the common evolution of commodity prices. Notes: (i) Monthly returns are computed as price log differences. (ii) Commodity prices are cash prices except crude oil where the current month contract price is taken as a proxy for the cash price. (iii) ***, ** and * respectively denotes rejection of the null hypothesis of a Gaussian distribution at 1%, 5 % and 10 % levels.  (ii) t-statistics are reported in parenthesis under the estimates. ***, **, and * respectively denotes rejection of the null hypothesis of no significance at the 1%, 5% and 10% levels. (iii) For the ARCH LM, ***, **, and * respectively denotes rejection of the null hypothesis of no ARCH effect at the 1%, 5% and 10% levels. (ii) t-statistics are reported in parenthesis under the estimates. ***, **, and * respectively denotes rejection of the null hypothesis of no significance at the 1%, 5% and 10% levels. (iii) For the ARCH LM, ***, **, and * respectively denotes rejection of the null hypothesis of no ARCH effect at the 1%, 5% and 10% levels.

Table 5
Regression of the Kilian real activity index on each of the 9 factors. Notes: Coefficient reports the estimated coefficient of each factor and t-stat its Student statistic. ***, **, and * respectively denotes rejection of the null hypothesis of no significance at the 1%, 5% and 10% levels. The real activity index is taken from Lutz Kilian's homepage. See Kilian (2009) for a definition of this index. Note: The upper triangular matrix reports correlation while the lower reports the p-values. The p-value is computed by transforming the correlationρ to create a t-statistic having T − 2 degrees of freedom, where T is the number of observations. ***, ** and * respectively denotes significance at 1%, 5 % and 10 %. Note: The upper triangular matrix reports correlation while the lower reports the p-values. The p-value is computed by transforming the correlationρ to create a t-statistic having T − 2 degrees of freedom, where T is the number of observations. ***, ** and * respectively denotes significance at 1%, 5 % and 10 %. (ii) F ρ * 2 is the mean percentage of average squared unconditional correlation significant at the 5 % level using the t-squared ratio testt 2 N − 2). (iii) ***. ** and * respectively denotes significance at 1%. 5 % and 10 %. (iv) Cρ is the correlation betweenρ * ret.t andρ * t .     Notes: (i) "av sq unc corr raw ret" is the average squared unconditional correlation of raw returns: ρ * ret.t . (ii) "av sq unc corr res fund " is the average squared conditional of factors regression residual: ρ * t . (iii) "av sq unc corr res all " is the average squared conditional of factors and trading indices regression residual. (iv) The confidence band the minimal value above which squared correlation is significant at 5 % level. It is computed from the t-squared ratio testt 2 and is equal to 1.6990.  Appendix B: Estimating the number of factors Bai and Ng (2002) propose two kinds of information criteria to select the number of common factors. If where g(N.T ) is a penalty function 32 andσ 2 equals S(k max ) for a pre-specified value of k max . The estimated number of factorsk minimises the aforementioned information criteria.
We also apply the sequential test of Kapetanios (2010) to determine the number of factors. This test is based on the property that if the true number of factors is k 0 . then. under some regularity conditions. the first k 0 eigenvalues of the population covariance matrix Σ will increase at rate N while the others will remain bounded. If we denote byλ k .k = 1.....N . the N eigenvalues of the sample covariance matrix X ′ X. the differenceλ k −λ k max +1 will tend to infinity for k = 1.....k 0 but remain bounded for k = k 0 + 1.....k max where k max is some finite number such that k 0 < k max . The null hypothesis that the true number of factors k 0 equals k (H 0.k : k 0 = k) against the alternative hypothesis (H 1.k : k 0 > k) is then tested via the test statisticsλ k −λ k max +1 . If there is no factor structure. thenλ k −λ k max +1 appropriately normalized by a sequence of constant τ N.T should converge to a law limit. In the presence of factors. it should tend to infinity. The law limit as the rate of convergence τ N.T → ∞ has to be estimated by resampling techniques.
The test is sequential. In a first step. we test (H 0.k : k 0 = k = 0) against (H 1.k : k 0 > 0). If we reject the null hypothesis. then we consider the null (H 0.k : k 0 = k + 1 = 1). We stop once we cannot reject the null hypothesis. Kapetanios (2010) called this algorithm the MED (maximal eigenvalue distribution) algorithm.
The estimated 33 numbers of factors are shown in Table B.1. There is clearly no agreement on the optimal number of factors. This result is similar to that in previous empirical work. in which there is considerable variance in estimates of the correct number of factors. 34 According to the information criteria of Bai and Ng (2002), the optimal number of factors runs from two to nine. The sequential test of Kapetanios the estimated factors F t appears in Table B.2. The first three factors explain only 20% of the variance in the 184 time series. with a figure of 36% for nine factors. We hence choose the first nine factors as potential regressors. The factor autocorrelations (up to three lags) in Table B.2 show that most factors are persistent.  Note: For i = 1....9.F it is estimated by the method of principal components using a panel of data with 184 indicators of economic activity from 1993:03 to 2010:03 (205 time series observations). The data are transformed (taking logs and differenced where appropriate) and standardized prior to estimation. ρ i denotes the i th autocorrelation. The 95% confidence bounds are ±0.1397. The relative importance of the common component.R 2 i . is calculated as the fraction of total variance in the data explained by factors 1 to i.