2. Data

2.1. CIT Positions

The Supplemental Commitment of Traders (SCOT) report published by the CFTC provides weekly CIT positions for CBOT corn, wheat, soybeans, and KCBOT wheat. Released every Friday at 3:30 p.m. Eastern time, the SCOT report contains the number of long and short contracts held by index traders as of the previous Tuesday’s market settlement. The SCOT reports are publicly available starting from January 2006. Previous studies argue that using only post-2006 data may lead to biased results because the build-up of CIT positions in grain markets was concentrated in the previous 2 years (Irwin and Sanders, Reference Irwin and Sanders2011; Sanders and Irwin, Reference Sanders and Irwin2011). The CFTC collected additional data for selected grain futures markets over 2004–2005 at the request of the U.S. Senate Permanent Subcommittee on Investigations (USS/PSI, 2009), and the additional data are used for this study. Specifically, weekly CIT positions for the four grain futures markets are available from January 6, 2004, to December 31, 2019, for a total of 853 weekly observations for each market.

One potential issue with the SCOT CIT data is the internal netting of positions by swap dealers that offer index products to investors. In some markets, short swap positions for certain commodity products tend to offset long swap positions associated with commodity index investments. Fortunately, previous research shows that netting of swap activity is minimal in agricultural markets and that the SCOT report provides accurate measures of aggregate CIT positions (Irwin and Sanders, Reference Irwin and Sanders2012a; Sanders and Irwin, Reference Sanders and Irwin2013). In Appendix Figure A1, we plot the net long positions in the four markets using the CFTC Index Investment Data (IID). Compared to the SCOT, IID represents the most accurate measure of index investment as it summarizes positions before the internal netting of swap activity (Irwin and Sanders, Reference Irwin and Sanders2012a). However, the IID data are only available quarterly from December 2007 to March 2010 and monthly from March 2010 to October 2015. As can be seen, the net long positions computed from the SCOT report behaved very similarly to that from the IID report during the period when both data sets were available. This suggests that the netting effect from swap dealers is likely minimal and remains so in the latter part of the sample. Overall, the CIT positions from the SCOT data should provide a reasonable approximation of investment trading activities.

Following previous studies, we compute the net long CIT position for a given market as:

(1) $$CIT\;Net\;Lon{g_t} = CIT{L_t} - CIT{S_t},$$

where CITL_t and CITS_t are the numbers of long and short contracts held by CITs at week t, respectively. In general, CITs hold relatively small short positions in grain futures markets, so the difference between long and net long positions is not large. Descriptive statistics for net long positions are presented in Table 1. For all four commodities, the net long positions are left-skewed, each with positive kurtosis, indicating heavy-tailed distributions. The Jarque-Bera (JB) test suggests that none of the series are normally distributed. The Augmented Dickey-Fuller (ADF) test shows that CIT net long positions are non-stationary.

Table 1. Summary statistics for weekly commodity index traders (CIT) positions and nearby futures prices in four grain futures markets, January 6, 2004, to December 31, 2019

Notes: Skewness measures the symmetry of a series’ distribution; when it is negative (positive), it indicates the distribution is skewed to the left (right). Kurtosis measures the tail shape of the distribution; when it is negative (positive), it indicates a thin (heavy)-tailed distribution. Jarque-Bera (JB) test is a “goodness of fit” test with the null hypothesis that a series follows a normal distribution. The null of the Augmented Dickey-Fuller (ADF) test is that a series has a unit root.

** indicates statistical significance at 5%, and *** indicates statistical significance at 1%.

We consider two stationary measures that directly reflect the “pressure” of index positions. The first is the change in CIT net positions for a given market:

(2) $$\Delta CIT\;Net\;Lon{g_t} = (CIT{L_t} - CIT{S_t}) - (CIT{L_{t - 1}} - CIT{S_{t - 1}}).$$

The second measure is the weekly percentage growth of CIT net long positions, defined as,

(3) $$\% CIT\;Net\;Lon{g_t} = {{(CIT{L_t} - CIT{S_t}) - (CIT{L_{t - 1}} - CIT{S_{t - 1}})} \over {(CIT{L_{t - 1}} - CIT{S_{t - 1}})}}$$

As can be seen in Table 1, the two index position measures both have heavy tails, highlighting the importance of considering different parts of distributions when analyzing CITs’ price impacts.

2.3. Sample Break

As noted above, our data cover index trader positions and nearby futures prices from the beginning of 2004 to the end of 2019. Figure 1 plots the total notional value of CIT positions summed across the four markets. Notional value for a given week in a given market is computed as CIT position × corresponding nearby futures price × futures contract size (5,000 bushels for all four commodities). We split the full sample into two sub-periods following the stages of “financialization” recently proposed by Irwin, Sanders, and Yan (Reference Irwin, Sanders and Yan2022). The first is the growth stage from 2004 to 2011, during which there was a rapid increase in commodity index investment. Two spikes in the CIT notional value were evident, one in 2007–2008 and the other in 2010–2011, with values ranging between $35 and $40 billion. The second stage is the post-financialization period from 2012 to 2019, where CIT notional value decreased steadily to around $15 billion in the last 3 years of the sample. If price pressure from CITs exists, it would make the most sense for it to be evident in the growth stage. In the statistical analysis that follows, we report results for the full sample and the two subsamples: the growth stage of financialization (2004–2011) and the post-financialization period (2012–2019). This accounts for the very different structural dynamics of index investment before and after 2011.

Figure 1. Notional value and equivalent net long positions of commodity index investment in four grain futures markets. Notes: The notional value of commodity index investment is calculated using the index positions retrieved from the SCOT report and corresponding nearby futures prices during the sample period. The growth and post-financialization stages are defined following Irwin, Sanders, and Yan (Reference Irwin, Sanders and Yan2022).

3. Linear Tests

Figure 2 plots CIT positions and futures prices for the four commodities. As can be seen, there is no contemporaneous increase in futures prices during the large build-up of index traders’ positions during 2004–05. Thereafter, if anything, there appears to be a negative relationship between CIT positions and futures prices. Of course, graphical evidence like this is only suggestive. It is important to test for direct statistical links between CIT positions and prices. We begin with the standard linear Granger causality test that has been used in numerous previous studies on the price impact of CIT. While these tests have been conducted repeatedly in the past, we include them here to provide a benchmark using the same data for the later CQ tests.

Figure 2. Weekly commodity index trader net long positions and nearby futures prices of CBOT corn, soybean, wheat, and KCBOT wheat, January 2004 to December 2019.

3.1. Linear Granger Causality Tests

In the widely used linear causality framework (Granger, Reference Granger1980), a time series regression is used to determine if one series is useful in forecasting another, or simply, “Granger causing.” The specification of the test for returns and CIT pressure is shown below for a given market:

(4) $${\rm Retur}{\rm n}_{t}=\alpha _{t}+\sum _{i=1}^{m}\gamma _{i}{\rm Retur}{\rm n}_{t-i}+\sum _{j=1}^{n}\beta _{j}\Delta {\rm Position}_{t-j}+\epsilon _{t}$$

where Return _t is the log difference in nearby weekly futures prices for a given market at time t, and ΔPosition _t is the measure of CIT pressure in the same market. Price returns and changes in positions are used because the level data (prices and CIT positions) are mostly non-stationary (see Table 1). The null hypothesis is that all β _j ′s are jointly zero, suggesting that CIT position changes do not Granger-cause returns. Alternatively, if CIT pressure indeed drives up futures prices, then β _j will be greater than zero. The optimal lag order based on Akaike Information Criterion (AIC) is one for both returns and position changes (m = 1, n = 1) for each of the four markets.

The results of the linear Granger causality test for the full sample and the two subsample periods are presented in Table 2 Panel A.Footnote ² For the full sample (2004–2019), in only one out of the four cases the null hypothesis of no Granger causality is rejected at the 5% significance level. The case is in the CBOT wheat market. Note that the direction of the estimated relationship is negative, suggesting that lagged CIT position changes negatively correlate with price changes, just the opposite of that implied by the Masters price pressure hypothesis. In the first subsample (2004–2011) or the growth stage of financialization, we fail to reject no Granger causality from positions to returns in all eight cases. In the second subsample from 2012 to 2019 (the post-financialization stage), we again found negative predictability from positions to returns for CBOT wheat and no predictability in other markets.

Table 2. Summary of three linear Granger causality test results for weekly commodity index traders (CIT) positions/position changes and prices/returns in four grain futures markets, January 6, 2004, to December 31, 2019

Notes: 1. Standard Granger causality test results are presented in Panel A. ** indicates statistical significance at 5%. F-test statistics are reported in the table, with the corresponding p-values in the parenthesis below. The null hypothesis is that no Granger causality exists from CIT position changes to futures returns. The estimated coefficients associated with the position variable are negative for cases with significant test statistics.

2. Augmented Granger causality test results are presented in Panel B. ** indicates statistical significance at 5%. Wald test statistics are reported in the table, with the corresponding p-values in the parenthesis below. The null hypothesis is that no Granger causality exists from CIT positions to futures prices.

3. Long-horizon regression test results are presented in Panel C. ** indicates statistical significance at 5%. Critical values for the rescaled t-statistics shown in the table (−0.672, 0.727) are available in Valkanov (Reference Valkanov2003, Table 4) for case 2, c = 0, δ = 0, T = 750. The null hypothesis is that no Granger causality exists from CIT position changes to futures returns.

4. The full sample period consists of 835 weekly observations. For the growth stage of financialization, there are 417 weekly observations from January 3 to December 27, 2011. The post-financialization period runs from January 3, 2012, to December 31, 2019, resulting in 418 weekly observations.

3.2. Augmented Granger Causality Tests

The second set of tests in the linear Granger causality framework is the augmented test of Toda and Yamamoto (Reference Toda and Yamamoto1995). When two time series are cointegrated or are not strictly stationary, the traditional Granger causality test may detect a spurious relationship that invalidates the results. To avoid such inconsistency, Toda and Yamamoto (Reference Toda and Yamamoto1995) suggest testing for Granger causality in a VAR model that accounts for cointegration and stationarity. Important to note is that the test specifies variables in levels, regardless of their orders of integration. Specifically, we estimate the following:

(5) $$\left[ {\matrix{ {Pric{e_t}} \cr {Positio{n_t}} \cr } } \right] = \mathop \sum \limits_{i = 1}^{p + {d_{max}}} \left[ {\matrix{ {{\gamma _{1,i}}} & {{\gamma _{2,i}}} \cr {{\gamma _{3,i}}} & {{\gamma _{4,i}}} \cr } } \right]\left[ {\matrix{ {Pric{e_{t - i}}} \cr {Positio{n_{t - i}}} \cr } } \right] + \left[ {\matrix{ {{\alpha _1}} \cr {{\alpha _2}} \cr } } \right] + t\left[ {\matrix{ {{\beta _1}} \cr {{\beta _2}} \cr } } \right] + \left[ {\matrix{ {{\varepsilon _{1,t}}} \cr {{\varepsilon _{2,t}}} \cr } } \right]$$

where ${\rm Price}_{t}$ is the nearby futures price and ${\rm Positio}n_{t}$ is the net long CIT position. We conduct the augmented Granger Causality test in the following steps: (1) each series is tested for the order of integration using the ADF test; (2) determine the value d _max, which is the maximum order of integration of two series; (3) set up the VAR model and use the AIC to determine the optimal lags p for the system; (4) use the augmented lag p + d _max to estimate the VAR system; and (5) apply the Wald test to determine if the position coefficients differ significantly from zero.

Testing results are presented in Table 2 Panel B. Note that only one set of results is presented since the augmented Granger causality test is based on the level of net long CIT positions instead of the change or percent growth in positions. We set d _max = 1 based on the ADF test. We then use AIC to find the appropriate lags with a maximum lag order of 20 lags and select two lags for the bivariate VAR model. As shown in Table 2 Panel B, we fail to reject the null of no causality from CIT positions to futures prices in any of the markets in either the full or the two subsamples when utilizing the augmented Granger causality test. Results provide strong evidence against the Masters Hypothesis that CIT activities increased futures prices.

3.3. Long-Horizon Regression Tests

Both the standard and augmented Granger causality tests are designed to detect relationships between weekly CIT positions/position changes and prices/returns. Such tests may have low power when detecting relationships over longer horizons (e.g., Summers, Reference Summers1986). Index trader positions may flow in “waves” that build up slowly, eventually pushing up prices, and then fade slowly as the process is reversed (Sanders and Irwin, Reference Sanders and Irwin2011). In this situation, horizons longer than a week may be needed to fully capture the relationship between CIT position pressure and futures returns. We follow Sanders and Irwin (Reference Sanders and Irwin2014, Reference Sanders and Irwin2016) and implement the long-horizon framework developed by Valkanov (Reference Valkanov2003). The model is defined for a given market as:

(6) $$\sum _{i=0}^{k-1}{\rm Retur}{\rm n}_{t+i}=\alpha +\beta \sum _{i=0}^{k-1}\Delta {\rm Position}_{t+i-1}+\epsilon _{t}$$

where all variables are the same as before. The dependent variable is the sum of futures returns from t to $t + k - 1,$ , and the independent variable is the sum of growth/change in CIT positions from t − 1 to t + k, with k being the horizon. In essence, equation (6) is an OLS regression of a k-period moving sum of the dependent variable at time t against a k-period moving sum of the independent variable in the previous period (t − 1). If the estimated β is positive, this indicates a fads-style model where prices tend to increase slowly over a relatively long period after widespread index fund buying. Following previous studies (Hamilton and Wu, Reference Hamilton and Wu2015; Sanders and Irwin, Reference Sanders and Irwin2014, Reference Sanders and Irwin2016; Singleton, Reference Singleton2014), we choose k = 4 and k = 12 to represent monthly and quarterly time horizons using the weekly data described in the data section.

Valkanov (Reference Valkanov2003) demonstrates that the OLS slope estimator in (6) is consistent and converges rapidly as the sample size increases. However, this specification creates an overlapping horizon problem for testing. Valkanov shows that Newey-West t-statistics do not converge to well-defined distributions and suggests using the rescaled t-statistic, $t/\sqrt{T}$ , along with simulated critical values for inference. Valkanov also demonstrates that the rescaled t-statistic generally is the most powerful among several alternative long-horizon test statistics.

We report the estimated OLS slope coefficients and the rescaled t-statistics for the Valkanov test at the monthly and quarterly horizons in Table 2 Panel C.Footnote ³ When we compare the test statistics with provided critical values, all rescaled t-statistics are within the range of the critical values, that is, non-statistically significant. Once again, estimation results from this linear test suggest no evidence that CIT positions pushed grain futures prices upward.

4. CQ Tests

In the previous section, we conducted three linear causality tests to provide a baseline result for the relationship between CIT activities and futures price movements. Consistent with most prior studies that use similar linear tests (e.g., Hamilton and Wu, Reference Hamilton and Wu2015; Lehecka, Reference Lehecka2015; Sanders and Irwin, Reference Sanders and Irwin2011; Stoll and Whaley, Reference Stoll and Whaley2010), we fail to reject the null of no causality in most cases.

As noted earlier, a concern with these findings is that the relationship between CIT positions and returns may be more subtle and difficult to detect than is possible with linear tests. In particular, linear tests may fail to detect a causal relationship hidden in the tails of the distribution (Lee and Yang, Reference Lee and Yang2012). To address this limitation, we apply the recently developed CQ test to investigate the directional predictability from the change in CIT net long positions to futures returns in the four grain futures markets. We also apply the CQ test to examine the directional impact of futures returns on CIT net long position changes.

Linton and Whang (Reference Linton and Whang2007) introduced the quantilogram, which measures the directional predictability of a stationary time series based on different parts of the distribution of a time series variable. The quantilogram method provides estimates of sample lead-lag correlation of quantiles and a Box-Pierce-type statistic that aggregates the individual correlations across lags. Based on the concept of the quantilogram for a single series, Han et al. (Reference Han, Linton, Oka and Whang2016) developed the CQ to measure the directional predictability of a pair of stationary times-series in all parts of the distributions and a Box-Ljung version of a portmanteau test for overall directional predictability. According to Han et al. (Reference Han, Linton, Oka and Whang2016), the CQ method has several advantages, as it (1) captures the directional lead-lag relationships across all parts of distributions; (2) does not require moment conditions of series; (3) only requires the time series to be stationary; and (4) includes long lags in the model specification to avoid concerns about degrees-of-freedom.

Specifically, for two strictly stationary time series variables, x _{1, t} and x _{2, t} , we define their cumulative distribution as ${F_i}\;\left( \cdot \right)$ , and their density function as ${F_i}\;\left( \cdot \right)$ . Next, we define the quantile function of each series as ${q_i}\;\left( {{\alpha _i}} \right) = \inf \left( {v:{F_i}\left( v \right) \ge {\alpha _i}} \right),\;\forall {\alpha _i} \in \left( {0,1} \right)$ for $\alpha \equiv {\left( {{\alpha _1},\;{\alpha _2}} \right)^T}$ . This quantile function returns the minimum quantile of x _i for the probability at α _i . The CQ for quantile α and lag k is specified as:

(7) $${\rho _\alpha }\left( k \right) = {{E[{\psi _{{\alpha _1}}}\left( {{x_{1,t}} - {q_{1,t}}\left( {{\alpha _1}} \right)} \right){\psi _{{\alpha _2}}}\left( {{x_{2,t - k}} - {q_{2,t - k}}\left( {{\alpha _2}} \right)} \right)} \over {\sqrt {E\left[ {\psi _{{\alpha _1}}^2\left( {{x_{1,t}} - {q_{1,t}}\left( {{\alpha _1}} \right)} \right)} \right]} \sqrt {E\left[ {\psi _{{\alpha _2}}^2\left( {{x_{2,t - k}} - {q_{2,t - k}}\left( {{\alpha _2}} \right)} \right)} \right]} }}$$

where ${\psi _{{\alpha _i}}}\left( u \right) \equiv 1\left( {u \lt 0} \right) - {\alpha _i}$ is a check function that captures the direction of deviation for a given quantile; $k = 0,\; \pm 1,\; \pm 2$ , …. Inside the check function, $\left\{ {1\left[ {\left[ {{x_{i,t}} \le {q_{i,t}}\left( \cdot \right)} \right]} \right]} \right\}$ is an indicator function, also known as the quantile-hit or quantile-exceedance process in the literature, that takes on a value of one when $\left[ {{x_{i,t}} \le {q_{i,t}}\left( \cdot \right)} \right]$ and zero otherwise. The ${\psi _{{\alpha _i}}}\left( \cdot \right)$ function transforms the indicator observations into a sorted sequence for a given quantile level. When an observation is smaller or equal to a given quantile, ${\psi _{{\alpha _i}}}\left( \cdot \right)$ returns $1 - {\alpha _i}$ ; whereas when an observation is greater than a given quantile, ${\psi _{{\alpha _i}}}\left( \cdot \right)$ returns − α _i . In essence, the CQ is the cross-correlation of two quantile-hit processes (Han et al., Reference Han, Linton, Oka and Whang2016).

Empirically, we have two stationary series of interests—the change in CIT net long positions and returns.Footnote ⁴ We denote these two time series as $\left\{ {{x_{1,t}},{x_{2,t}}} \right\}_{t = 1}^T$ , respectively. First, we estimate the unconditional quantile functions $\widehat{q_{i}}(\cdot )$ for each series by solving for the following minimization functions:

(8) $$\widehat{q_{i}}\left(\alpha _{i}\right)= {\rm argmin}_{{v_{i}\in \mathbb{R}}} \sum\limits _{t=1}^{T}\pi _{ {\alpha _{i}}}(x_{i,t}-v_{i})$$

where ${\pi _{\;{\alpha _i}}}\left( u \right) \equiv u\left( {{\alpha _i} - 1\left[ {u \lt 0} \right]} \right),\;i = 1,\;2$ . For a set of quantiles of two series $\{ {\hat q_{1,t}}({\alpha _1}),{\hat q_{2,t - k}}({\alpha _2})\} $ , the sample CQ is defined as:

(9) $$\hat{\rho }_{\alpha }\left(k\right)={\sum _{t=k+1}^{T}\psi _{{\alpha _{1}}}(x_{1,t}-\hat{q}_{1,t}\left(\alpha _{1}\right))\psi _{{\alpha _{2}}}(x_{2,t-k}-\hat{q}_{2,t-k}\left(\alpha _{2}\right)) \over \sqrt{\sum _{t=k+1}^{T}\psi _{\alpha _{1}}^{2}(x_{1,t}-\hat{q}_{1,t}\left(\alpha _{1}\right))}\sqrt{\sum _{t=k+1}^{T}\psi _{\alpha _{2}}^{2}(x_{2,t-k}-\hat{q}_{2,t-k}\left(\alpha _{2}\right))}}$$

where $k = 0,\; \pm 1,\; \pm 2, \ldots $ The CQ estimates, ${\hat \rho _\alpha }\left( k \right)$ , capture the directional predictability between two series at a given quantile set $\left\{ {{\alpha _1},\;{\alpha _2}} \right\}$ . Further, ${\hat \rho _\alpha }\left( k \right) \in \left[ { - 1,1} \right]$ . For example, when ${\hat \rho _\alpha }\left( 1 \right) = 0$ , this indicates that when the change in CIT net long positions at time t is above or below the quantile ${\hat q_{2,t - 1}}({\alpha _2})$ there is no correlation with returns at time t + 1 being above or below the quantile ${\hat q_{1,t}}({\alpha _1})$ . When ${\hat \rho _\alpha }\left( 1 \right) \gt 0$ , it suggests there is directional predictability between the change in CIT net long positions at time t and returns at time t + 1, given the two series hit in the quantiles of α ₁ and α ₂.

An example of corn over the full sample period is presented in Figure 3 to help illustrate how CQ statistics are computed. This plot shows an example of a pair of observations that both hit the quantile with α ₁ = α ₂ = 0.1. On September 27, 2011, the corn CIT position change is −15,920 contracts and hits in the 0.1 quantile for position changes. One week later on October 4, 2011, we observe a corn return of −10.41%, and it hit the 0.1 quantile for returns as well. The arrow shows that when changes in CIT net long positions are below the 0.1 quantile, it is followed by a return one week later that is also below its 0.1 quantile. This type of comparison is repeated for all observations to compute a CQ statistic for α ₁ = α ₂ = 0.1.

Figure 3. Illustration of the lead-lag dependence from CIT net long position changes at t − 1 to futures returns at t when both are in the low quantile of 0.1, full sample period in the corn market. Notes: On September 27, 2011, the change in corn CIT net long positions was −15,920 contracts and hits in the 0.1 quantile for position changes. One week later on October 4, 2011, we observe a corn return of −10.41% and it hit the 0.1 quantile for returns as well. The arrow shows that when changes in CIT net long positions are below the 0.1 quantile, it is followed by a return one week later that is also below its 0.1 quantile. This type of comparison is repeated for all observations to compute a CQ statistic for α ₁ = α ₂ = 0.1.

To test for the directional predictability of two series in different quantiles up to k lags, we follow the quantile version of the portmanteau statistical test proposed by Han et al. (Reference Han, Linton, Oka and Whang2016). To test if there is overall directional predictability from ${x_{2,t - k}}$ to ${x_{1,t}}$ , for $k \in \left\{ {1,2, \ldots ,p} \right\}$ , the null hypothesis is ${H_0}:\;{\rho _\alpha }\left( 1 \right) = {\rho _\alpha }\left( 2 \right) = \ldots = {\rho _\alpha }\left( p \right) = 0$ , against the alternative hypothesis ${H_a}:\;{\rho _\alpha }\left( k \right) \ne 0$ . The test statistic is:

(10) $$\hat{Q}_{a}^{\left(p\right)}={T(T+2)\sum _{k=1}^{p}\hat{\rho }_{\alpha }^{2}(k) \over T-k}$$

where $\hat Q_a^{\left( p \right)}$ is the portmanteau test statistic for overall directional predictability. The corresponding critical values for the portmanteau test (Han et al., Reference Han, Linton, Oka and Whang2016) are derived from the stationary bootstrap of Politis and Romano (Reference Politis and Romano1994). The stationary bootstrap is a block bootstrap procedure, and the length of each block is randomly determined. The strength of the block bootstrap is that it can reach a high convergence rate using nonparametric estimation to find critical values regardless of the distribution (Han et al., Reference Han, Linton, Oka and Whang2016).

The CQs for the full sample period are presented in Figures 4 through 7 for CBOT corn, soybeans, wheat, and KCBOT wheat, respectively.Footnote ⁵ We consider four quantiles for both returns and CIT positions: 0.10, 0.25, 0.75, and 0.90, resulting in 16 pairs of CQ results for each commodity. These four quantiles represent extreme large decreases, large decreases, large increases, and extreme large increases for the two series. Within each figure, there are 16 subplots that visualize how returns in these quantiles respond to the dynamics of lagged extreme changes in CIT net long quantiles. These plots are organized into four panels where each panel presents the estimated CQ estimates from one of the four quantiles of position changes to all four extreme levels of returns.

Figure 4. Cross-quantilogram from changes in CIT net long positions to returns in the CBOT corn futures market, 2004–2019. (a) Position change at quantile level 0.1. (b) Position change at quantile level 0.25. (c) Position change at quantile level 0.75. (d) Position change at quantile level 0.9.

Consider Figure 4(a) as an example. Here, the four CQ estimates for the lagged changes in CIT net long positions at the extreme low quantile (α ₂ = 0.1) and returns at the extreme low (α ₁ = 0.10), low (α ₁ = 0.25), high (α ₁ = 0.75), and extreme high (α ₁ = 0.90) quantiles for corn over the full sample period are presented. The black bar is the estimated sample CQ statistic at lag k, that is, ${\hat \rho _\alpha }\left( k \right)$ . The null hypothesis is that at lag k there is no predictability from the large negative movements in CIT position changes to large movements in futures returns. The red-dashed lines represent the 95% bootstrapped confidence intervals for no directional predictability with 1,000 bootstrapped replicates. We include 13 lags as this is approximately the same quarterly horizon we used in the long-horizon linear tests in the previous section. In total, there are 218 CQ test statistics for each commodity across various combinations of lags and quantiles.

Caution is needed when interpreting the sign of the CQ estimates. For CIT position changes in the two low quantiles (α ₂ = 0.1 or 0.25) and returns in two low quantiles (α ₁ = 0.1 or 0.25), which corresponds to the top row of plots in Figures 4–7, a positive CQ estimate suggests that a large drop in CIT net long positions (i.e., extreme low quantile for CIT position changes) is likely to predict large decreases in futures prices (i.e., extreme low quantile for returns); on the other hand, when the sign is negative, a large drop in CIT net positions is less likely to predict a subsequent large decrease in futures prices. Meanwhile, for CIT position changes in the two low quantiles and returns in the two high quantiles (α ₁ = 0.75 or 0.9), a positive CQ estimate (as plotted in the second row of Figures 4–7) suggests when a large drop in CIT net positions occurs, the likelihood of predicting a large increase in futures prices is low; whereas when CQ estimate is negative, the likelihood of predicting a large price increase (i.e., extreme high quantile for returns) is high.

Figure 5. Cross-quantilogram from changes in CIT net long positions to returns in the CBOT soybean futures market, 2004–2019. (a) Position change at quantile level 0.1. (b) Position change at quantile level 0.25. (c) Position change at quantile level 0.75. (d) Position change at quantile level 0.9.

Figure 6. Cross-quantilogram from changes in CIT net long positions to returns in the CBOT wheat futures market, 2004–2019. (a) Position change at quantile level 0.1. (b) Position change at quantile level 0.25. (c) Position change at quantile level 0.75. (d) Position change at quantile level 0.9.

The CQ test statistic is mostly non-significant in panels (a) and (b) of Figures 4–7. This suggests that over a 13-week horizon, whether CIT position changes are smaller or greater than the 0.1 or 0.25 quantiles cannot predict returns in either the left (quantiles 0.1 and 0.25) or right tails (quantiles 0.75 and 0.9) of the distribution for the four markets. For the few cases where the CQ estimates are significant, empirical evidence for different commodity markets is mixed. For example, during the full sample period in the soybean market, we observe that large decreases in CIT net long positions positively predict large decreases in returns. Meanwhile, in CBOT wheat we observe that large CIT net position decreases are followed by large increases in returns.

Panels (c) and (d) in Figures 4–7 plot the CQ estimates when the lagged CIT positions are in the two high quantiles (0.75 and 0.9). For returns located in the two low quantiles, that is, α ₁ = 0.1 or 0.25, a positive CQ estimate suggests that a large increase in CIT net positions is less likely to predict a large drop in futures prices, whereas a negative estimate suggests that a large increase in CIT net long positions is more likely to be followed by large decreases in futures returns. For returns in two high quantiles (α ₁ = 0.75, α ₁ = 0.9), when CQ estimates are positive, it indicates that when CIT net long position changes exceed high quantiles, they are likely to predict returns in high quantiles. Meanwhile, a negative CQ estimate suggests that a large increase in CIT net long positions is less likely to predict returns with a large increase. For most cases when CIT positions experience a substantial increase, there is no significant directional predictability from the change in CIT net long positions to returns.

Overall, across all combinations of quantiles and lags, the ratio of statistically significant CQ test statistics is low for all four commodities, ranging from around 4% for KCBOT wheat to around 10% for CBOT wheat. For those significant cases, there is no clear pattern of the estimated predictability from position changes to returns. Taken together, Figures 4–7 suggest that there are no systematic lead-lag relationships from CIT positions to futures prices when both series are in their extreme quantiles.

The portmanteau test statistics for directional predictability from changes in CIT net long positions to returns are presented in Figure 8. As noted earlier, the portmanteau test is an omnibus test that aggregates the CQ test statistics from 1 to 13 lags for each pair of quantiles of the two series. In the plot, the four quantiles of the position change and returns are on the x-axis and y-axis, respectively. Each cell represents the portmanteau test statistics of each quantile combination, with a darker color indicating a larger test value. Boarders around the cell indicate statistical significance at the 5% level. A solid border suggests that for lags from 1 to 13, the underlying CQ estimates have a positive dominant sign, whereas a dashed border indicates a negative dominant sign. Dominance is defined as the sign that appeared more frequently for the 13 estimates. We do this to aid in interpreting these few cases with overall significance.

Figure 7. Cross-quantilogram from changes in CIT net long positions to returns in the KCBOT wheat futures market, 2004–2019. (a) Position change at quantile level 0.1. (b) Position change at quantile level 0.25. (c) Position change at quantile level 0.75. (d) Position change at quantile level 0.9.

Figure 8. Cross-quantilogram portmanteau test results for weekly commodity index traders (CIT) positions and nearby futures returns in four grain futures markets, positions leading returns, January 6, 2004, to December 31, 2019. Notes: Darker color indicates large portmanteau test statistics. Boarders around a cell suggest the test statistic is significant at 5%. A solid border indicates the dominant sign of the underlying CQ estimates for the Box-Ljung test is positive, whereas a dashed border indicates a negative dominant sign.

Figure 8 shows that significant predictability from positions to returns only exists in one out of 64 cases for the full sample period. For the first and second subsamples, six and two cases, respectively, out of 64 fail to reject the null hypothesis of no directional predictability. In total, there are only 9 cases out of 192 (or 4.7%) with a significant portmanteau statistic, slightly less than the number of significant test statistics one would expect at random for a 5% significance level.

We further investigate the dominant sign for the cases with a significant portmanteau statistic in Figure 8. Out of the nine significant cases, in only one instance there is evidence supporting the Masters Hypothesis, that is, that a large increase in the CIT net longs has directional predictability to a large increase in futures returns. This occurred for CBOT corn in subperiod 1 for α ₁ = 0.75 and α ₂ = 0.9, where the portmanteau test statistic is significant, and the dominant sign is positive. In all the remaining significant cases the evidence does not support the Masters Hypothesis. For example, during the post-financialization period (Panel C) and $\alpha _{1}=0.75, \alpha _{2}=0.25$ in CBOT wheat market, the dominant sign is negative, implying that large decreases in CIT positions tend to directionally predict large increases in wheat returns. Compared to other markets, CBOT wheat has overall more significant cases, 6 out of 48 in the three sample periods combined. However, none of these six significant cases support the Masters Hypothesis that increased index trading led to higher commodity prices. Overall, we note that the number of significant cases (9 out of 192), regardless of the dominant sign, is basically what one would expect based on random chance and that there is even less evidence supporting the Masters Hypothesis (1 out of 192).

As the final part of the analysis, we examine the direction of predictability of futures returns to CIT positions. There is a documented tendency for large non-commercial speculators in agricultural futures markets to be trend followers (Sanders, Irwin, and Merrin, Reference Sanders, Irwin and Merrin2009). That is, the positions of large speculators in agricultural futures markets tend to increase after futures prices increase, and vice versa. The available evidence for CITs is not as strong. For instance, Aulerich, Irwin, and Garcia (Reference Aulerich, Irwin, Garcia, Aulerich, Irwin and Garcia2014) find a significant but small impact of past returns on daily CIT positions in 12 agricultural markets, but this disappears when the analysis is limited to roll windows. Lehecka (Reference Lehecka2015) analyzes weekly CIT positions in the same 12 agricultural futures markets and reports that past returns do not significantly impact CIT positions.

The portmanteau test statistics for directional predictability from returns to CIT net position changes are presented in Figure 9 for the full and two subsamples,Footnote ⁶ where returns are on the x-axis and position changes are on the y-axis. During the full sample period, significant causality exists from positions to returns in only 2 out of 64 cases. For the first and second subsamples, 5 and 3 cases, respectively, out of 64 we reject the null hypothesis of no directional predictability. In total, there are only 10 cases out of 192 with a significant portmanteau statistic. Mirroring the results for causality from positions to returns, this is only 5.2% of the total cases, slightly greater than the number of significant test statistics one would expect at random for a 5% significance level. Furthermore, in the 10 significant cases, only 5 show evidence that CIT net long positions significantly decrease following a drop in futures prices. Overall, these results provide scant support for the idea that extreme CIT position changes have a trend-following component.

Figure 9. Cross-quantilogram portmanteau test results for weekly commodity index traders (CIT) positions and nearby futures returns in four grain futures markets, returns leading positions, January 6, 2004, to December 31, 2019. Notes: Darker color indicates large portmanteau test statistics. Boarders around a cell suggest the test statistic is significant at 5%. A solid border indicates the dominant sign of the underlying CQ estimates for the Box-Ljung test is positive, whereas a dashed border indicates a negative dominant sign.

Our results are consistent with the notion that financial index investment is motivated by long-term investment objectives rather than short-term trading (e.g., Robe and Roberts, Reference Robe and Roberts2019; Stoll and Whaley, Reference Stoll and Whaley2010). Robe and Roberts (Reference Robe and Roberts2019) used non-public data from 2015 to 2018, including all trader-level futures positions reported to CFTC, to investigate the nature of market participants, the maturity structure of the positions held by different types of traders, and via the main business lines of these traders, their corresponding aggregate position patterns. Similar to our findings, their results show that the main goal of CITs is to have long-term and passive investments for portfolio diversification.

Given the mostly passive nature of index investment, the increasing participation of CITs may have a limited impact on the risk-sharing and information discovery function of futures markets, and further, futures price movements. The longstanding hedging pressure theory suggests speculators take over risks from hedgers and, in return, are compensated for a risk premium. The likelihood that CITs have changed the risk-sharing between hedgers and speculators is low if they do not actively trade commodities for their own needs. Meanwhile, since trading rules for index replication are well-defined and the specific allocation for commodities is also pre-determined (Stoll and Whaley, Reference Stoll and Whaley2010), the presence of index trading may have a limited impact on the price discovery function of futures trading.