2.1 Data source

The purpose of this paper is to examine the cross-market supply-chain predictability in China's financial market, which is the world's largest commodity futures market and the world's second-largest equity market. Based on the 2018 world ranking of commodity derivative trading volumes reported by the Futures Industry Association (FIA), Shanghai Futures Exchange (SHFE), Dalian Commodity Exchange (DCE) and Zhengzhou Commodity Exchange (ZCE) in mainland China occupy three of the top four positions. Not surprisingly, the pricing content contained in the commodity futures should be quite informative because of the huge trading volumes.

We collect the historical prices of the commodity futures and stocks in Mainland China from the CSMAR, covering the period from January 4, 2005 to December 31, 2019. To identify suppliers and customers in the stock market for each commodity, we use a novel data set from the Wind company, which provides this cross-market supply-chain linkage.

We select the commodity futures based on the following steps. First, we collect 60 commodity futures traded in China's future market during the period from year 2005 to 2019. Second, to have enough observations for the in-sample and out-of-sample tests, we delete 11 recently listed commodity futures whose numbers of trading days are less than 500 (soda ash, styrene, stainless steel, japonica rice RR, No. 20 rubber, urea, nonbleached kraft pulp, jujube, glycol, crude oil, and apple). Third, we continue to delete three commodities (ferrosilicon, mung bean, and late indica rice) because these commodities do not simultaneously link with both supplier-side and customer-side firms. Finally, we delete 10 commodities (blockboard, fiberboard, wire rod, fuel oil, rapeseed, wheat PM, wheat WT, japonica rice JR, early indica rice, and cotton yarn) which have very low trading volumes and produce discontinuous futures returns. In this way, we have 36 commodity futures for our analysis, belonging to four categories, that is, metals, industrials, energy, and agriculture. Specifically, the commodity futures traded on the SHFE, DCE, and ZCE are categorized into the following groups: (a) metals: silver, aluminum, gold, copper, iron ore, nickel, lead, steel rebar, silicon manganese, tin, and zinc; (b) industrials: glass, hot rolled coil, linear low-density polyethylene (LLDPE), methanol, polypropylene (PP), natural rubber, pure terephthalic acid (PTA), and polyvinyl chloride (PVC) (c) energy: bitumen, coke, coking coal, and thermal coal; and (d) agriculture: No. 1 soybeans, No. 2 soybeans, corn, cotton, corn starch, eggs, soybean meal, rapeseed oil, palm oil, rapeseed meal, white sugar, wheat WH, and soybean oil.

2.2 Summary statistics

Based on the supply-chain linkage information from the Wind data set, we build the supplier-side and customer-side stock portfolios for each commodity in China's financial market. We calculate the value-weighted equity returns at the daily horizon, excluding the newly listed stocks within 1 month.

To construct the continuous series of commodity futures returns, the common methodology is to use the nearest-to-maturity contracts (Booth et al., 1999) or on-the-run contracts (Fricke & Menkhoff, 2011), which are the futures contracts that have the largest trading volume during the specific trading period. In this paper, we obtain the time-series on-the-run contracts for each commodity at the daily horizon because this selection avoids the low liquidity problem of nearest-to-maturity contracts in China's commodity futures market. We obtain on-the-run futures returns for each commodity as follows. First, we select the future contract with the largest trading volume at trading day t. Next, we obtain the close prices for the future contract at day t and t − 1, and then calculate the daily return at day t using these close prices. We repeat this process for each trading day and obtain the time-series returns of on-the-run future.

We first present the overview of each commodity future and the numbers of supplier-side and customer-side listed firms in Table 1. The futures category, futures name, futures code, number of trading days, average daily trading volume, on-the-run contract observations, and average maturities are reported for each commodity futures. The number of trading days for the commodity futures varies from 1,165 to 3,648 during the full sample period as some of them are not listed at the beginning. Additionally, the detailed lists of the supplier-side and customer-side equities for each commodity, which are omitted for brevity, are available in the Wind data set.

Table 2 reports the summary statistics of the futures returns and the related supplier-side and customer-side equity portfolio returns. For each commodity futures, we present the mean, standard deviation and first-order autocorrelation of the time-series returns. The first-order autocorrelation coefficients of the supplier-side (or customer-side) stock returns are always positive, indicating positive momentum at the daily horizon in China's stock market. In the last three columns of Table 2, the correlation among the three returns series are also presented. We find that all the correlation coefficients between commodity futures returns and supplier-side (customer-side) stock returns are positive with an average value of 0.21 (0.18), indicating that there exists cross-market return comovement along the supply chain.

3.1 Univariate regression results

The null hypothesis is that the commodity futures returns ${R\mathrm{\_}\mathit{com}}_{i,t}$ have no predictive ability for supplier-side (customer-side) equity portfolio returns. The existing empirical evidence for stock markets (e.g., C. Li et al., 2020; Menzly & Ozbas, 2010; Shahrur et al., 2010) suggests positive signs of the ${\beta }_i$s for both the supplier side and customer side, which is consistent with the underreaction hypothesis. From the macroeconomic perspective, increases in commodity prices indicate a strengthened expectation of the future economy, and most of the macropredictors can positively predict the equity risk premium (Goyal & Welch, 2008). Following the theoretical and empirical evidence, we implement one-sided tests for H0 : ${\beta }_i\le 0$ against the alternative HA: ${\beta }_i>0$ using the Newey and West (1987) heteroskedasticity-consistent t-statistic.

Table 3 presents the estimation results of the in-sample univariate predictive regression, and the significance levels are accessed based on one-sided test statistics. When predicting the supplier-side equity returns, we find that 9 of the 11 metal futures (silver, aluminum, copper, iron ore, nickel, lead, steel rebar, tin, and zinc), 7 of the 8 industrial futures (glass, hot rolled coil, LLDPE, methanol, PP, natural rubber, and PTA), all the energy futures (bitumen, coke, coking coal, and thermal coal) and 7 of the 13 agriculture futures (No. 1 soybeans, corn, cotton, rapeseed meal, white sugar, wheat WH, and soybean oil) exhibit significantly positive estimates for $\beta$. Moreover, 35 of 36 commodity futures exhibit positive estimates for $\beta$ on the supplier-side, which is consistent with economic theory. The adjusted $R^2$ shown in the fifth column of Table 3 is relatively small, with an average of 0.24% for the significant predictors. Campbell and Thompson (2008) document that an $R^2$ less than 1% can be economically significant since a substantially unpredictable component is contained within the stock returns. If a high $R^2$ is easily obtained, this will lead investors to suspect that highly outstanding predictive regressions are spurious as such a case would be too profitable to believe. Therefore, the magnitude of $R^2$ in our result is reasonable and consistent with previous studies.

The predictability of commodity futures returns for customer-side stock returns is less significant than that for the supplier-side. As presented in Tables 3 and 5 metal futures (silver, iron ore, nickel, steel rebar, and tin), three industrial futures (glass, methanol, and natural rubber), all the energy futures (bitumen, coke, coking coal, and thermal coal) and four agriculture futures (corn, corn starch, wheat WH, and soybean oil) exhibit significantly positive estimates for $\beta$ while 30 out of 36 futures exhibit positive estimates $\beta$. In summary, our result indicates that commodity futures exhibit predictive power for stock returns along the supply chain, especially on the supplier side.

The positive estimates for $\beta$ of most commodity futures are consistent with the underreaction hypothesis and the positive correlation between commodity prices and macroeconomic conditions. Ferson et al. (2003) document that the statistical inference of running an in-sample predictive regression is disturbed when the predictor is highly persistent and correlated with the excess market return. To address this bias, we follow Neely et al. (2014) and run 5,000 simulations to calculate the wild bootstrapped p value for each regression. The results of the wild bootstrapped p values are similar with those tabulated in Table 3, and thus, our use of the t-statistic is considered substantially robust in the in-sample univariate regression.

3.2 Multivariate regression results after controlling common pricing factors

Table 4 reports the in-sample multivariate regression results after controlling these common pricing factors. For the supplier-side equity return predictability, the estimated $\beta$ loses its significance for five commodities including nickel, glass, bitumen, coking coal, and rapeseed meal while 3 of 36 futures exhibit insignificant negative estimates for $\beta$ after controlling common pricing factors. The remaining 22 significant estimates for $\beta$ in both univariate and multivariate regressions indicate that the commodity futures can predict the supplier-side equity portfolio returns, even after controlling common sources of return variation. On the customer side, eight commodity futures (silver, steel rebar, glass, natural rubber, bitumen, coke, coking coal, and corn starch) lose their statistical significance after controlling these three pricing factors. It is further noted that the in-sample predictive significance of energy futures is substantially subsumed by common factors in the multivariate regressions for both the supplier side and customer side. This may indicate that energy commodity information has a higher correlation with the classical risk factor of the stock market.

3.3 Regression results considering overall macroeconomic risk

The results in Table 5 and 6 represent the bivariate in-sample regressions for supplier-side and customer-side, respectively. We find that 26 of the supplier-side ${\hat{\beta }}_{\mathit{PC}}$s and 20 of the customer-side ${\hat{\beta }}_{\mathit{PC}}s$ exhibit significant estimates, meaning that the overall macroeconomic risk represented by the aggregate commodity demand is an important source of the cross-market supply-chain predictability. While in many cases, the idiosyncratic effect measured by ${\hat{\beta }}_{i,\mathit{supplier}}$ or ${\hat{\beta }}_{i,\mathit{customer}}$ loses its statistical significance, we find that seven commodities (i.e., tin, zinc, glass, natural rubber, bitumen, corn, and wheat WH) still obtain significant ${\hat{\beta }}_{i,\mathit{suppli}\mathit{er}}$, and seven commodities (i.e., tin, glass, LLDPE, natural rubber, bitumen, corn, and wheat WH) obtain significant ${\hat{\beta }}_{i,\mathit{customer}}$.

3.4 Pooled regression results

We replicate the regressions that include individual and time fixed effects, and the regression results are tabulated in columns 2–7 of Table 7. This result confirms the average effects across all the commodities as evidenced by the statistically significant estimates of β at the 1% level. Similarly, the coefficient of supplier-side is larger than that of customer-side in the pooled regression with or without including fixed effects.

The asymmetric predictability of commodity futures between supplier-side and customer-side equity portfolios may be due to the different responses of the expected cash flow to the commodity price shocks. Since commodities act as the output products for supplier-side firms, increases in commodity prices benefit the prospective revenue or cash flows of these firms and thus positively contribute to the stock prices. However, for customer-side firms, increases in commodity prices will improve the expected expenditures for these firms and weaken the positive equity return predictability when using the commodity-related predictor. Therefore, we obtain stronger cross-market return predictability for the supplier-side firms than the customer-side firms.

Another potential explanation for this predictability asymmetry may be that suppliers are often more concentrated on and thus exposed to one or few selected commodities, whereas for many customers, commodities are only a fraction of their costs.2 As a result, the supplier-side stock prices are more sensitive to the shock of commodity prices than the consumer-side stock prices.

Actually, we can see from Table 1, the supplier-side firms are less than customer-side firms for 27 out of 36 commodities. To test the above hypothesis, we define the concentration of supplier-side firms (${C\mathit{onc}}_{i,\mathit{supplier},t}$) as the ratio of commodity i's customer-side firm number to supplier-side firm number at time t, and a relatively smaller number of suppliers refers to a higher ${C\mathit{onc}}_{i,\mathit{supplier},t}$. Similarly, ${\mathit{Conc}}_{i,\mathit{customer},t}$ is the defined as ${1/C\mathit{onc}}_{i,\mathit{supplier},t}$. We sort all the observations by ${\mathit{Conc}}_{i,\mathit{supplier},t}\left({\mathit{or}\mathit{Conc}}_{i,\mathit{customer},t}\right)$ into three groups: low 30%, medium 40% and high 30%. If the level of ${\mathit{Conc}}_{i,\mathit{supplier},t}\left({\text{or}\mathit{Conc}}_{i,\mathit{customer},t}\right)$ for commodity i at time t places the observation in one of the three groups, we define its concentration dummy variable (i.e., ${\mathit{Conc}}_{i,\mathit{low},t},{\mathit{Conc}}_{i,\mathit{med},t},\mathit{and}{\mathit{Conc}}_{i,\mathit{high},t}$) as one and zero otherwise.

The estimation results in the last two columns of Table 7 show that observations with more concentrated firms, on either side, can acquire more significant estimate of $\beta$. This result indicates that the prices of more concentrated firms are more influenced by the commodity prices. Moreover, for the same interaction term, the supplier-side estimate for $\beta$ is more significant and larger than that of customer-side, which further indicates that more concentrated supplier-side firms exhibit more significant return predictability.

4.1 Preliminary evidence of forecasting results

By regressing ${\left\{f_{i,t}\right\}}_{t+1}^T$ on a constant, we can get the t-statistic of the constant, which is called the CW (Clark & West, 2007) statistic. This statistic is used to test the null hypothesis that the MSFE of the benchmark model is less than or equal to the MSFE of our selected forecasting model against the one-sided alternative hypothesis that the former term is larger than the latter term. This is consistent with assessing H0 : $R_{i,\mathit{OS}}^2\le 0$ against the alternative HA : $R_{i,\mathit{OS}}^2>0$.

Table 8 presents the out-the-sample results of this unrestricted OLS predictor. For both the supplier-side and customer-side equities, the MSFEs of the benchmark model and our model, the $R_{\mathit{OS}}^2$s and the CW statistics are reported. It is well known that the in-sample return predictability cannot guarantee outstanding out-of-sample performance. Compared with the in-sample estimation result, the number of commodity futures with significant out-of-sample performance is reduced since the historical average is a stringent benchmark in the equity market. The average $R_{\mathit{OS}}^2$ is −0.062% for supplier-side forecasts and −0.216% for customer-side forecasts. Therefore, the cross-market supply-chain forecasting model using this naïve strategy cannot easily beat the benchmark model for most commodities. Importantly, we find that the out-of-sample performance varies for different commodities. When forecasting the supplier-side equities, we find that five metal futures (silver, iron ore, nickel, steel rebar, and zinc), four industrial futures (glass, LLDPE, methanol, and natural rubber), two energy futures (coking coal and thermal coal), and two agriculture futures (corn and wheat WH) obtain significantly positive $R_{\mathit{OS}}^2$s with an average of 0.249%. For the customer-side equities, the predictability is significant for five commodity futures (iron ore, glass, methanol, coking coal, and corn) with an average $R_{\mathit{OS}}^2$ of 0.194%. In particular, the commodity futures of iron ore, glass, methanol, coking coal, and corn have significant out-of-sample predictive power for both supplier-side and customer-side equity returns and these commodity futures also obtain significant estimates of $\beta$ at the 1% level in the univariate regressions. Therefore, the out-of-sample tests further indicate that a number of commodity futures exhibit statistically significant equity return predictability along the supply chain, especially on the supplier side.

4.2 Economic benefits

Panel A of Table 9 tabulates the results of the economic gains for the allocated portfolio consisting of supplier-side equities and the risk-free asset. We briefly report the economic gains for those commodities with statistically significant and positive out-of-sample $R_{\mathit{OS}}^2$s. For all 13 commodity futures reported in Panel A, all the Sharpe ratio gains take positive values. Except for the commodity futures with relatively low $R_{\mathit{OS}}^2$s including corn, zinc, and wheat WH, all the reported commodity futures exhibit positive CER gains for the supplier-side allocated portfolios.

Similarly, Panel B of Table 9 reports the results for the allocated portfolio including customer-side equities and the risk-free asset. For all five commodity futures with significantly positive $R_{\mathit{OS}}^2$s, the Sharpe ratio gains are all positive while only glass and iron ore, which have the highest $R_{\mathit{OS}}^2$s, obtain positive CER gains. Moreover, most other commodity futures with insignificant out-of-sample $R_{\mathit{OS}}^2$s exhibit even worse Sharpe ratio gains and CER gains.

Based on our portfolio allocation exercise, we find that the magnitude of $R_{\mathit{OS}}^2$ should, at a minimum, exceed approximately 0.10% to obtain economic significance. We confirm that commodity futures with strong in-sample and out-of-sample predictive significance can obtain economic gains from the perspective of the Sharpe ratio and CER. Additionally, the statistical and economic significance of the out-of-sample forecasting tests among several typical commodities continue to suggest that commodity futures returns substantially and positively affect the supplier-side equity returns and customer-side equity returns on the next trading day.

5.1 Predictability over business cycle

In Table 10, we report the out-of-sample forecasting results over the business cycle. On the supplier side, of the 36 commodity futures, the $R_{\mathit{OS},i,\mathit{REC}}^2$s for 27 futures are higher during the recession period than there are during the expansion period. We also find that 16 commodity futures during the recession period exhibit significantly positive $R_{\mathit{OS},i,\mathit{REC}}^2$ values that exceed the number during the full sample period. Further, the respective magnitudes of $R_{\mathit{OS},i,\mathit{REC}}^2$ for iron ore, glass and coking coal are 1.451%, 1.209%, and 1.117% during the recession period and this indicates that relatively substantial economic significance is obtained for the three commodities. The average $R_{\mathit{OS},i}^2$ also increases from −0.062% during the full sample period to 0.056% during the recession period. On the customer side, as presented in the last four columns of Table 10, a similar result for the predictability over business cycle is obtained. The results above are consistent with the previously confirmed hypothesis that economic recessions would increase the investors' risk aversion and thus enhance their demands for higher risk premiums, which drive stronger return predictability in the stock market.