Return and Volatility Co-Movement in Commodity Futures Markets: the Effects of Liquidity Risk

Quantitative Finance

ISSN: 1469-7688 (Print) 1469-7696 (Online) Journal homepage: http://www.tandfonline.com/loi/rquf20

Return and volatility co-movement in commodity futures markets: the effects of liquidity risk

Yongmin Zhang & Shusheng Ding

To cite this article: Yongmin Zhang & Shusheng Ding (2018) Return and volatility co-movement in commodity futures markets: the effects of liquidity risk, Quantitative Finance, 18:9, 1471-1486, DOI: 10.1080/14697688.2018.1444562 To link to this article: https://doi.org/10.1080/14697688.2018.1444562

Published online: 23 Apr 2018.

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Return and volatility co-movement in commodity futures markets: the effects of liquidity risk

YONGMIN ZHANG*†‡ and SHUSHENG DING‡

†School of Business, Ningbo University, 818 Fenghua Road, Ningbo, 315000, China ‡Nottingham University Business School China, Centre for Global Finance, University of Nottingham Ningbo China, 199 Taikang East Road, Ningbo, 315100, China

(Received 16 January 2017; accepted 7 October 2017; published online 23 April 2018)

Commodity markets are a widely researched topic in the field of finance. In this paper, we investigate the co-movement of return and volatility measures in different commodity futures markets and how these measures are affected by liquidity risk. First, we find that commodity returns display co- movement and that liquidity risk plays a key role in shaping asset return patterns. Moreover, we show that the volatilities of commodity returns co-move, and we demonstrate the role of liquidity risk in this joint pattern. We also find that the commodity markets we investigated share a common volatility factor that determines their joint volatility co-movement. Because liquidity risk affects both commodity returns and volatility shocks, it might be interpreted as the common causal factor driving both measures simultaneously. Therefore, we affirm the view that liquidity shocks are firmly related to two residual risks originating from both market return and market volatility. Finally, we also show that liquidity spillovers can significantly drive cross-sectional correlation dynamics.

Keywords: Commodity futures markets; Price co-movement; Liquidity effects; Volatility co-movement JEL Classiﬁcation: E30, F00

Introduction and Sanders 2011). Most new investors entering this market were of an institutional nature, which led to an extraordi- Commodity futures prices, such as those related to gold and nary growth and size of commodity market trading volumes oil, have been at the centre of financial and economic news (Domanski and Heath 2007). Consequently, commodity for much of the last decade. The oil price, for instance, markets have attracted much attention and have become a peaked at over US$140 per barrel in 2008, only to fall back much investigated topic of academic interest (see Narayan to less than US$30 per barrel at the beginning of 2016. et al. 2013, Bunn et al. 2015, Sockin and Xiong 2015). Such substantial swings in the price of oil render this mar- Commodity futures prices are crucial for economic analy- ket particularly volatile. This volatility pattern is similar to sis, and the literature documents the integral relationships the evolution of prices of many other assets traded in finan- between commodity prices and the state of economic devel- cial markets. For example, the simultaneous sudden decline opment. Cody and Mills (1991) illustrate a close relationship observed in both commodity and stock prices interacted between commodity prices and economic indicators such as with each other to exacerbate the synchronized downturn in the consumer price index (CPI). Clarida et al.(1998) demon- both markets. Choi and Hammoudeh (2010) identified the strate that commodity prices are firmly linked to inflation, stronger degree of synchronicity between commodity interest rates and output. Stock and Watson (2003) argue that futures markets and stock markets after the financial crisis. commodity prices can serve as a predictor of inflation and Other scholars also documented the various types of inter- output growth. Chinn and Coibion (2014) also note that actions between the stock markets and the commodity mar- understanding the movement and changes of commodity kets (see Vivian and Wohar 2012, Creti et al. 2013). More prices could be helpful in short-term policy deliberations. importantly, the inflow of capital into commodity futures Furthermore, the correlation between asset volatility and markets has soared to new heights in the last decade (Irwin asset return has been substantially researched in the financial area (see French et al. 1987, Hamao et al. 1990, *Corresponding author. Email: [email protected] LeBaron 1992). The relationship between trading volume

© 2018 Informa UK Limited, trading as Taylor & Francis Group 1472 Y. Zhang and S. Ding and asset volatility has also been investigated in the litera- two previous models. The increase of cross-sectional vari- ture. In futures markets, trading volume can serve as ables does not significantly add explanatory power to the a proxy for market liquidity. Bessembinder and Seguin model, which suggests that most of the explanatory power in (1993) show how trading volume strongly affects price the previous two models overlaps. The variation part that volatility, particularly when there is a volume shock. In fact, cross-sectional volatilities can explain is similar to the part trading activities and investor behaviour in the futures mar- that cross-sectional liquidities can explain. Consequently, it ket play important roles in affecting futures prices and price makes sense to hypothesize that liquidity is an important volatility (Chatrath et al. 1996). Trading activities were transmission channel driving the volatility spillover. An demonstrated to be closely related to market liquidity in the increased level of volatility observed in one commodity mar- stock market (Chordia et al. 2001). Consequently, it can be ket and an ensuing decline in liquidity can result in a similar argued that in the futures markets, liquidity can also play decline in liquidity in other markets, which in turn can also an important role in determine the path of the volatility. render those markets more volatile. More importantly, we Because commodity price volatility constitutes a measure also confirm the positive relationship between liquidity of the dispersion of price changes, policy-makers are there- shocks and volatility shocks. The contemporaneous co-move- fore concerned not only about commodity prices per se but ment of both commodity volatilities and liquidities might also about their volatilities given their potential to add to strengthen the linkage and spillover effects among different inflation pressures (Creti et al. 2013). Volatility of commod- commodity markets. Because the cross-sectional analysis ity prices is therefore a central issue for the global econ- cannot fully explain the volatility co-movement, we illustrate omy. Excessive fluctuations of commodity prices were a that there is a common market volatility factor affecting all widely discussed topic of concern during the 2009 G20 commodity markets and that this factor generates the volatil- meeting. Commodity price volatility is also a measurement ity co-movement of individual commodity markets. of risk, and one of the most important functions of the com- Because liquidity risk affects both commodity return and modity futures market is to transfer price risk (Garbade and volatility shocks, it might serve as a mediator between com- Silber 1983). Thus, volatility plays a key role in hedging modity return and commodity volatility, particularly for the possibilities and in allocating assets in the commodity returns and volatility shocks. When there is a volatility futures markets. Consequently, understanding the origin and shock, the liquidity shock might occur contemporaneously. evolution of price volatility can help investors, particularly Conversely, the liquidity shock is influential in affecting institutional investors, to construct better hedging strategies commodity returns. Consequently, volatility shocks can play and to make better asset allocation decisions. an important role in determining commodity returns via the Because volatility is of pivotal importance in financial liquidity risk effect. Moreover, liquidity shocks are firmly markets, the co-movement of volatility in different commod- related to the residual risks from both asset return and asset ity markets will also be scrutinized. Volatility co-movement volatility after controlling for market return and macroeco- significantly affects risk management, portfolio selection nomic variables. Liquidity shocks are negatively correlated and, more importantly, derivative pricing. Studying the co- with the residual risks from asset return regressions and movement of various volatility indicators can also aid in the positively correlated with the residual risks from asset understanding of financial market issues such as the trans- volatility regressions. mission of shocks throughout the financial system (see Lin Finally, we also show that the level of liquidity plays a et al. 1994, Edwards and Susmel 2003, Calvet and Fisher vital role in time-varying correlations between commodity 2004). Because volatility is a key factor in determining markets. The commodity market correlations might also be of derivative pricing, it is essential to explore how various importance for the transmission of shocks and episodes of volatility measures in different derivative markets co-move instability spreading from market to market (Saghaian 2010, with one another. Consequently, this paper investigates return Du and McPhail 2012, Ji and Fan 2012). More importantly, and volatility co-movements in different commodity futures time-varying correlations are also influential in hedging markets. First, we find that commodity returns exhibit co- strategies with futures (Lien and Yang 2006). Consequently, movement and that liquidity risk plays a key role in shaping we investigate the explanatory power of liquidity levels origi- asset return patterns. By controlling for the market return and nating from the two correlated markets. We conduct a test to other macroeconomic variables in the regression analysis, we investigate the extent to which liquidity level can explain any find that the residual part of the asset return is firmly corre- correlation of returns between markets. Our findings indicate lated with the liquidity risk, which indicates that liquidity liquidity levels play an important role in commodity futures can serve as a risk factor in pricing commodity futures. markets by affecting both volatility and return correlations. A common volatility trend observed in commodity Based on these results, we hope to inform both research- returns is an indication of liquidity acting as a key factor in ers and practitioners on the volatility and liquidity proper- transmitting volatility spillovers. We initially confirm the ties of futures market and how these can affect derivative existence of an interaction between the volatilities of differ- pricing and the general behaviours of commodity prices. ent commodity returns via cross-sectional regression. Then, The paper is organized as follows. In section 2, we describe we identify the cross-sectional liquidity effects on volatility. the data with volatility and liquidity measures for commod- We finally embed all cross-sectional volatility and liquidity ity markets. In section 3, we demonstrate the return measures into one common estimation framework and co-movement in the five commodity futures markets. We record the adjusted-R2. The increase of adjusted-R2 in the also show that liquidity risk plays a key role in the asset final regression model is quite marginal compared with the return pattern. In section 4, we demonstrate that the Return and volatility co-movement in commodity futures markets 1473 liquidity shocks are closely related to the volatility shocks proxy has the maximal correction ratio among all proxies, and show the effects of market volatility. More importantly, and they strongly recommend that researchers use this we show that liquidity might serve as a transmission chan- proxy when modelling commodity liquidity. Consequently, nel for volatility spillover from other markets. In section 5, we will use the proxy mentioned in Amihud (2002), which we illustrate that liquidity levels from the two correlated takes the following form: markets can explain the time-dependent correlations. Section 6 concludes the paper. jjRt LtðAMÞ ¼ Amihudt ¼ Volt

where Rt is the asset return at time t and Volt is the asset Data and methodology trading volume at time t. Intuitively, when trading volume is high, the amount of According to the NASDAQ commodity family report liquidity measure is small, and the asset is considered more fi (2013), there are ve families of commodities, namely liquid. The Amihud measure clearly extracts the information energy (such as crude oil (oil hereafter)), agricultural (such from the trading volume. as corn), livestock (such as live cattle), precious metals For the empirical analysis, we use the realized returns of (such as gold) and industrial metals (such as copper). We fi commodity futures, denoted as rt, which is de ned as select one commodity from each sector (as indicated in the Pt rt ¼ ln . Then, we normalize the commodity prices by brackets) to construct a cross-sectional commodity portfolio. Pt1 The representative commodities are the most actively traded taking the natural log of all commodity prices. For liquidity commodities in their corresponding sectors. The trading measures, the statistical summary table for liquidity mea- volumes of crude oil, corn, copper, live cattle and gold are sures in the five commodity futures markets is presented in the highest in their corresponding families. The selected table 1. commodity prices are futures prices with the nearest maturi- According to table 1, it could also be argued that there ties of the particular commodity, and they are the most could be size bias effects among different futures markets actively traded types. because the means and standard deviations of liquidity mea- For the data description, the superscript ‘ca’ represents sures are widely divergent across different commodity live cattle commodity futures, ‘cop’ represents copper com- futures markets. To eliminate the size bias effects, we nor- modity futures, ‘cor’ represents corn commodity futures, ‘g’ malize our liquidity measures. The normalized liquidity represents gold commodity futures, ‘o’ represents oil com- measure is defined as follows: ‘ ’ i i modity futures, and MLt represents market liquidity indi- Lt = (Liquidity Amihud measure (LtðAMÞ) -mean of the cator. ‘L’ stands for the Amihud measure of liquidity, ‘σ’ liquidity Amihud measure)/standard deviation of the liquid- stands for the volatility and ‘r’ stands for the realized ity Amihud measure. returns of commodity futures. The data provider is Thom- Table 2 shows the normalized liquidity levels in the five son Datastream, and the data period is from 1 January 2005 futures markets. It is plausible that size bias effects are to 31 December 2013, which is the maximal available data effectively eliminated. All regression results in this paper for the common period, and all data are collected on a daily are based on normalized liquidity measures. Moreover, basis. because the daily Amihud measure is extremely noisy, to In addition, we adopt the CRB (Commodity Research smooth the time series process of liquidity measures, we Bureau) Index as the proxy for the commodity futures mar- adopt a rolling over strategy to calculate the liquidity mea- ket price index. The CRB Index currently comprises 19 sures based on the normalized data. In other words, we commodities, including energy, agriculture and metal, which obtain the moving-average daily Amihud measure, which should be a solid representation of overall commodity indicates that one particular day’s liquidity measure is effec- prices. tively the average of the previous month’s (the past For a commodity liquidity measure, Marshall et al. 21 days) liquidity measures. Our liquidity data frequency is (2012) tested a large number of liquidity proxies in com- thereby on a daily basis. Let t be the rolling average of modity markets. They found that the Amihud liquidity liquidities from the past 21 trading days, i.e.

Table 1. Statistical summary table for liquidity measures in the ﬁve representative commodity futures markets (Amihud measure). This table provides a detailed statistical summary of the original ﬁve representative Amihud liquidity measures, showing that there might be a large size effect across different commodity futures markets.

Obs Mean Std. Dev. Min Max

ca LtðAMÞ 2261 2.07E-9 4.74E-9 0 1.99E-7 cor L ð Þ 2261 3.08E-10 5.23E-10 0 1.39E-8 copt AM LtðAMÞ 2261 2.89E-7 4.74E-7 0 6.76E-6 o L ð Þ 2261 5.72E-10 9.33E-10 0 1.77E-8 gt AM LtðAMÞ 2261 1.12E-10 1.96E-10 0 5.1E-9 1474 Y. Zhang and S. Ding

X20 We initially test the co-movement among futures returns 1 L ¼ L t 21 t i themselves. From the return correlation matrix, all of the i¼0 commodity returns appear to be positively correlated with where Lt-i is the liquidity measure at day t-i. one another (see table 3). More importantly, the p-values of The realized returns, the volatility of realized returns and return correlations also indicate that all of the correlation the monthly moving-average of normalized Amihud mea- coefficients are statistically significant. sures are three key variables for the empirical analysis in Then, we investigate the co-movement between liquidity the paper. Moreover, we include three control variables in innovations and excess commodity futures returns. We try our return regression analysis, which are S&P 500 return, to determine empirically whether the liquidity risk can dollar index return and short-term interest rate, and the con- abundantly explain the residual part that the market risk or trol variables are all at a daily frequency (Tang and Xiong other macroeconomic variables cannot explain. If the liquid- 2012). ity risk relates to the residual part isolated from the commodity market risk, exchange risk, interest risk and stock market risk, it most likely constitutes most of the noise information in the market. It is also consistent with our Liquidity risk effect on commodity futures returns findings that after controlling the liquidity variable from the co-integration tests, the residual part becomes stationary. In this section, we test the co-movement between excess We adopt the CRB index return as the proxy for the commodity futures returns and liquidity innovations using commodity market returns. We initially run the regression the Amihud measure. We define the excess commodity of the returns of the five commodity families with the futures returns as the residuals of commodity futures returns returns of the CRB Index, the stock market return, the dol- that are not explained by the market returns and macroeco- lar index return and interest rate and take the residuals. nomic control variables, and we define the liquidity risk as For the regression equations, the liquidity innovations. This approach is consistent with the literature because the liquidity risk is measured as the ri ¼ ai þ ai rCRB þ ai SP þ ai DI þ ai IR þ ki (1) volatility of the liquidity shocks (Pástor and Stambaugh t 1 2 t 3 t 4 t 5 t t 2003, Sadka 2006). Furthermore, the co-movement relation- i ship between liquidity risk and asset returns has been where i = ca, cor, cop, o and g, respectively, kt is the resid- demonstrated by Pástor and Stambaugh (2003) in the stock uals that are not explained by the market risk, and SP, DI markets. We extend their findings to commodity futures and IR are control variables that stand for the S&P 500 markets, and we test the co-movement between liquidity return, dollar index return and short-term interest rate, innovations and excess commodity futures returns. respectively.

Table 2. Statistical summary table for normalized Amihud liquidity measures.

Obs Mean Std. Dev. Min Max

ca − Lt 2261 0.0002 1.00 0.45 41.45 cor − Lt 2261 0.0002 1.00 0.59 26.07 cop − Lt 2261 0.0002 1.00 0.61 13.66 o − Lt 2261 0.0002 1.00 0.61 18.39 g − Lt 2261 0.0002 1.00 0.57 25.44

Note: This table provides a detailed statistical summary for ﬁve representative normalized Amihud liquidity measures, showing that the size effect across different commodity futures markets has been effectively eliminated.

Table 3. Commodity returns correlation matrix with p-value.

ca cor cop o g rt rt rt rt rt

ca rt 1 cor rt 0.1567 1 (0.00) cop rt 0.158 0.2254 1 (0.02) (0.00) o rt 0.1585 0.2999 0.4507 1 (0.00) (0.00) (0.00) g rt 0.1162 0.3553 0.2267 0.2275 1 (0.00) (0.00) (0.00) (0.00)

Note: This table presents the correlations among the five commodity returns. All five commodity returns are highly correlated and positively affect one another. The correlation coefficients are proved statistically significant. Return and volatility co-movement in commodity futures markets 1475

i Then, we try to measure the liquidity innovations in the dt is the residuals that are not explained by the liquidity commodity futures markets. A more recent paper by Feng autoregression, which can be noted as the liquidity shocks et al. (2014) has valued the options with liquidity risk. The (innovations), where i = ca, cor, cop, o and g, respectively. following two stochastic equations are identified in Feng For the return regression equation, we save the residual et al. (2014) for asset prices and asset liquidity, respec- parts of each commodity family, denoting the residuals as i tively: kt (in equation (1)). Then, we run the autoregression in qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi equation (2) and take the residuals as the liquidity risks, denoted as di (in equation (2). Then, we construct the corre- = ¼ þ 2 þð 2Þ 2 2 S þ L t dSt St udt r 1 q b Lt dWt qbLtdWt i i lation matrix between kt and dt. We illustrate that the liq- ¼ ð Þ þ L fi dLt a h Lt dt ndWt uidity risk is rmly correlated with the residuals that are not explained by the market risk after controlling the exoge- where σ is individual asset price volatility, ρ is correlation nous variables, and the results are presented in table 4. All between individual asset return and market liquidity, β is of the commodity liquidity risks are significantly related to sensitivity of asset price variance to market liquidity, α is the market residuals that are not explained by the market i the mean reversion speed of market liquidity, θ is the long- index return. Then, we reveal a relationship between dt and i term mean of market liquidity and ξ is the volatility of mar- individual commodity return rt by controlling the market ket liquidity. index return and three exogenous variables. The regression From those two equations, we can see that the volatility results are shown in table 5. All commodity futures returns part has been decomposed into two parts. One is related to are significantly correlated with the market index return and s di the market risk dWt , and the other is related to the liquidity the liquidity risks (the t) after controlling S&P 500 return, L risk, dWt . The variance of commodity futures prices that dollar index return and short-term interest rate. The liquidity are not explained by the market risk could relate to the liq- risk can be an explanatory factor for commodity futures uidity risk. In this section, we will test whether the residuals returns after controlling the market index return and the not explained by the market risk can be explained by the exogenous variables. The liquidity risk can explain the liquidity risk. Because the liquidity risk part is measured by commodity futures returns’ variances that market index the residual of the liquidity stochastic equation, which is return and other exogenous macroeconomic variables fail to L ¼ ð Þ di fi ndWt dLt a h Lt dt, we can empirically approximate explain. Moreover, the t appears to have a signi cantly the liquidity risk through the following regressions: negative relationship with all commodity futures returns, which implies the negative effect of liquidity risks measured by the Amihud method on the commodity futures returns. Li Li ¼ ai þ ai Li þ di (2) t t1 1 2 t1 t

ri ¼ ai þ ai rCRB þ ai di þ ai SP þ ai DI þ ai IR þ ei (3) t 1 2 t 3 t 4 t 5 t 6 t t

Table 4. Liquidity risk and asset return residual correlation matrix with p-value. ρ ca ca ρ cor cor ρ cop cop ρ o o ρ g g (kt , dt ) (kt , dt ) (kt , dt ) (kt , dt ) (kt , dt ) Correlation −0.05 −0.06 −0.07 −0.15 −0.07 (0.02) (0.02) (0.00) (0.00) (0.00)

Table 5. Regression results for commodity futures returns and liquidity risk (Amihud measure).

ca cor cop o g rt rt rt rt rt

crb rt 0.15 0.93 1.18 1.50 0.37 (0.00) (0.00) (0.00) (0.00) (0.00) i − − − − − dt 0.005 0.002 0.003 0.004 0.001 (0.02) (0.01) (0.01) (0.00) (0.00) SPt 0.0027 −0.005 0.016 −0.001 −0.015 (0.48) (0.53) (0.09) (0.88) (0.00) DIt 0.021 −0.003 0.014 −0.001 −0.039 (0.02) (0.87) (0.35) (0.96) (0.00) IRt −0.001 0.0002 0.001 −0.0001 0.0002 (0.00) (0.01) (0.45) (0.01) (0.00)

Note: This table reports the regression results for commodity returns and the liquidity shocks by controlling the market return. As shown, all commodity liquidity shocks signiﬁcantly negatively affect commodity futures returns after controlling S&P 500 return, dollar index return and short-term interest rate. 1476 Y. Zhang and S. Ding

Table 6. Correlation matrix of liquidity innovations.

ca cor cop o g dt dt dt dt dt ca dt 1 cor dt 0.51 1 (0.00) cop dt 0.002 0.08 1 (0.83) (0.00) o dt 0.072 0.034 0.17 1 (0.00) (0.16) (0.00) g dt 0.032 0.061 0.09 0.058 1 (0.17) (0.79) (0.00) (0.01)

Note: This table presents the correlations among the five commodity liquidity innovations (i.e. liquidity shocks). Some of the liquidity shocks are significant correlated, whereas the rest of the shocks are not firmly correlated. where i = ca, cor, cop, o and g, respectively. For robustness, we also adopt another liquidity measure, Then, we construct a correlation matrix for liquidity inno- namely the Roll measure, for the empirical analysis; the Roll vations from different futures markets. We found that all measure is not associated with trading volumes. We use the correlations exhibit positive relationships and that over one- effective spread estimator developed by Roll (1984). The half of the correlations are statistically significant (see table measure is also broadly used in a number of financial papers 6). When there is a liquidity shock in one futures market, such as Goyenko et al. (2009) and Corwin and Schultz the shock can spread to other markets; all futures markets (2012). The proxy utilizes the covariance of the price can be affected. Consequently, the positive correlations changes as an effective measure of the bid–ask spread. among liquidity innovations can be an influential factor for Roll (1984) assumes that the stocks have fundamental return co-movement, as shown in table 3. values, denoted as Vt at time t. Vt follows equation (4): The crucial role of liquidity futures returns relates to liquidity measures. The liquidity measure we use is primarily based on the trading volume in the commodity markets. Vt ¼ Vt1 þ et (4) Research on trading volume in the literature notes that trad- fi ing volume plays an informative role in the nancial mar- Next, he denotes Pt as the last observed trade price on day t ket. For example, Blume et al. (1994) test the potential and presumes that Pt follows equation (5): usefulness of trading volume in the financial market. They assert that trading volume can offer investors additional 1 information that the market price cannot offer. In addition, Pt ¼ Vt þ EQt (5) 2 Lee and Swaminathan (2000) claim that trading volume will be helpful in predicting cross-sectional stock returns and where E is the effective spread and Qt is a buy/sell indicator momentum closely related to price. for the last trade that equals +1 for a buy and −1 for a sell. Trading volume associates with asset price in three He further assumes that Qt is equally likely to be +1 or −1 dimensions. First, trading volume is positively correlated and that Qt is serially uncorrelated and independent of εt. with price change (see Karpoff 1987). One reason for the Then, he takes the first difference of equation (5) and phenomenon might be the disposition effect, which causes inserts the result from equation (4), which yields investors who hold a security to be less willing to sell after a price decline than after a price rise. Odean (1998) shows that stocks with gains are sold by individual investors at 1 DP ¼ EDQ þ e (6) twice the rate stocks with losses are sold. Second, trading t 2 t t volume is correlated with transaction costs. Similarly, Kar- poff (1987) notes that trading volume will increase with the ðD ; D Þ¼1 2 Consequently, Cov Pt Pt1 4 E or, equivalently, growing number of active traders. When the trading volume pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi is higher, the Amihud measure is lower, and the market is spread ¼ 2 covðDP ; DP Þ more active. Because sellers are more likely to sell the t t 1 asset, the cost for trading the asset would be reduced, which because when the covariance is positive, the formula is illustrates that the trading cost will diminish with the trad- undefined. We therefore use a modified version of the Roll ing volume. Admati and Pfleiderer (1988) develop a model estimator (Goyenko et al. 2009): that states the negative relationship between trading volume and transaction cost. The trading volume and asset volatility have been fully documented in the literature. In the next pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ðD ; D Þ; ðD ; D Þ section, we try to unfold the relationship between asset liq- ¼ 2 cov Pt Pt1 cov Pt Pt1 0 spread ; ðD ; D Þ [ uidity and asset volatility in the commodity futures markets, 0 cov Pt Pt1 0 in which the asset liquidity measurement is volume-based. (7) Return and volatility co-movement in commodity futures markets 1477

Tables 7 and 8 summarize the data for the Roll measure of three exogenous variables. The regression results are similar to commodity liquidity. We also use the monthly moving-aver- the previous results, shown in table 10. Other than the corn age method to smooth the Roll measure. Using the Roll futures, the commodity futures returns are significantly influ- measure, we run the regression equations (1), (2) and (3) enced by their commodity liquidities. It is arguable that for the robustness check. because the Roll measure of liquidity, which is based on the In table 9, we also demonstrate that most of the residuals covariance of the price changes, is relatively small for corn that are not explained by the market risk and the liquidity risk futures, the Roll measure of liquidity might not significantly are firmly connected, except for corn futures, using the Roll affect corn futures returns. However, it might lead to the weak measure for robustness. Then, we also use the Roll measure to market liquidity effects of those markets. Section 4 shows that i prove the relationship between dt and individual commodity the non-agricultural (energy and industrial metal) futures mar- i return rt by controlling the market index return and the other ket liquidity effects are much stronger than are the agricultural

Table 7. Statistical summary table for liquidity measures in the ﬁve representative commodity futures markets (Roll measure). This table provides a detailed statistical summary of the original ﬁve representative Roll liquidity measures.

Obs Mean Std. Dev. Min Max

ca LtðRollÞ 2325 0.004 0.006 0 0.24 cor L ð Þ 2325 0.008 0.01 0 0.13 copt Roll LtðRollÞ 2325 0.01 0.01 0 0.11 o L ð Þ 2325 0.81 0.98 0 8.11 gt Roll LtðRollÞ 2325 0.005 0.006 0 0.02

Table 8. Statistical summary table for normalized Roll liquidity measures.

Obs Mean Std. Dev. Min Max

Lca 2325 0.0001 1.00 −0.59 37.37 tðRollNÞ Lcor 2325 0.0001 1.00 −0.79 12.68 tðRollNÞ Lcop 2325 0.0001 1.00 −0.96 9.14 tðRollNÞ Lo 2325 0.0001 1.00 −0.82 7.44 tðRollNÞ Lg 2325 −0.0001 1.00 −0.89 3.56 tðRollNÞ Note: This table provides a detailed statistical summary for the normalized ﬁve representative Roll liquidity measures.

Table 9. Liquidity risk and asset return residual correlation matrix with p-value (Roll measure). ρ ca ca ρ cor cor ρ cop cop ρ o o ρ g g (kt , dt ) (kt , dt ) (kt , dt ) (kt , dt ) (kt , dt ) Correlation 0.04 0.02 −0.03 −0.06 −0.04 (0.06) (0.48) (0.10) (0.01) (0.08)

Table 10. Regression results for commodity futures returns and liquidity risk (Roll measure).

ca cor cop o g rt rt rt rt rt

crb rt 0.16 0.92 1.20 1.53 0.38 (0.00) (0.00) (0.00) (0.00) (0.00) i − − − dtðRollÞ 0.005 0.004 0.002 0.003 0.001 (0.06) (0.49) (0.09) (0.02) (0.09) SPt 0.002 −0.034 0.016 −0.001 0.006 (0.00) (0.19) (0.01) (0.91) (0.10) DIt 0.02 0.002 0.016 0.005 −0.019 (0.30) (0.74) (0.29) (0.64) (0.15) IRt −0.002 0.0002 0.00002 −0.0001 0.0001 (0.65) (0.00) (0.50) (0.01) (0.00)

Note: This table reports the regression results for commodity returns and the liquidity shocks by controlling the market return. As shown, most commodity liquidity shocks significantly negatively affect commodity futures returns after controlling S&P 500 return, dollar index return and short-term interest rate. However, the liquidity shocks of agricultural futures such as cattle futures have a positive effect on the return, whereas the corn futures exhibit insignificant results. 1478 Y. Zhang and S. Ding futures markets. Therefore, it could be robustly argued that the Because the liquidity and volatility in all five commodity liquidity risk can be an explanatory factor for commodity markets are firmly correlated, we are also interested in test- futures returns after controlling the market index return and the ing whether there is a relationship between shocks of exogenous variables. Furthermore, the liquidity risk can volatility and shocks of liquidity. We initially run the explain the commodity futures returns’ variances, which the autoregression of liquidity in equation (2) and take the i market index return fails to explain; other than cattle and corn residuals as the liquidity shocks, denoted as dt. Then, we futures, the liquidity shocks exhibit a negative effect on com- run the autoregression of volatility in equation (8) and take i modity futures returns. the residuals as the volatility shocks, denoted as gt. We then construct a correlation matrix of shocks of volatility and shocks of liquidity. The liquidity and volatility shocks in all five commodity markets clearly are positively correlated Liquidity effect on commodity futures volatility spillover and exhibit statistical significance (see table 16). Therefore, and co-movement the contemporaneous shocks of volatility and liquidity will have a considerable effect on the commodity futures Liquidity effect on volatility co-movement returns. From previous results, it appears that liquidity plays an important role in affecting commodity return co-movement. i i i i i i r r ¼ u þ u r þ g (8) More importantly, all five commodity returns co-move in the t t 1 1 2 t 1 t same direction under the effect of liquidity shocks (see figure 1). Consequently, it is reasonable to presume that liquidity where i = ca, cor, cop, o and g, respectively. levels can influence the volatilities of the five commodity futures markets, and the volatilities of the five commodity futures markets can have common trends. Figure 2 shows Single liquidity effect on volatility that the volatilities of different commodity markets all had high magnitudes during 2008. It is thereby arguable that the Because liquidity and volatility have a close relationship, volatilities of the five commodity futures markets might have we try to determine whether the liquidity can explain the a common trend. We thus construct a correlation matrix volatility for its own market. Then, we construct the regres- between volatilities in the five markets. It is observable that sion models to test whether liquidity plays an important role all volatilities are positively correlated, and the p-value of the in shaping the volatility terms in commodity futures mar- strong cross-sectional positive relationship between com- kets. The regression results presented in table 17 show that modity volatilities is found statistically significant. The the liquidity term explains a large proportion of the volatil- cross-sectional correlations might intimate that all five com- ity term in the copper and crude oil markets, but not for the modity markets tend to have similar high volatility and low agriculture and gold markets from the adjusted R2 term (see volatility periods. More importantly, volatilities have positive table 17). Comparing tables 15 and 17 shows that high cor- effects on each other (see table 11). Consequently, the five relations between volatilities and liquidities in copper and commodity futures markets tend to be more volatile during oil also lead to high R2 terms in regression equations. Con- similar periods. The commodity futures liquidities also pre- versely, the adj-R2 is relatively low for gold futures and sent a common trend. The correlation matrix for the five corn futures because the effect of its own market liquidity commodity liquidities is presented in table 12 for the Ami- on volatility is small, and they receive the effects of liquid- hud measure, which shows that all of the commodity liquidi- ity from other commodity markets. For example, the adj-R2 ties are positively correlated and all of the coefficients are for explaining gold futures volatility is much higher in the statistically significant. It is thereby arguable that the com- cross-sectional liquidity regression results (see table 18). modity liquidities also have a common trend, which would i ¼ þ i þ i; be consistent with the previous return co-movement; volatil- rt ai biLt et ity and liquidity in different commodity futures markets also show co-movement (tables 11 and 12). We are interested in determining whether liquidity can where i = ca, cor, cop, o and g, respectively. influence the volatility in the commodity futures markets. First, we test whether the liquidity time series and the volatility time series in the commodity markets are station- Cross-sectional liquidity spillover and volatility spillover ary processes. Tables 13 and 14 clearly show that the liquidity and volatility processes in the commodity markets We then construct similar regression models by adding the are all stationary processes at the 10% significance level. liquidities from other markets to see whether the R2 term Next, we establish a correlation matrix for the liquidity and increases. If so, it is arguable that the additional explana- volatility in the commodity markets. Table 15 shows that tion power might come from the liquidity of other com- the liquidity and volatility in all five commodity markets modity futures markets. The regression model results have are positively correlated and exhibit statistical significance. been represented in table 18. For the cattle futures market, The synthetic effects in liquidity and volatility might shape the R2 term has increased by approximately 16%, which the return pattern in the commodity futures markets. indicates that the variance of the cattle markets largely Return and volatility co-movement in commodity futures markets 1479

Figure 1. Daily returns for ﬁve commodity markets. depends upon the liquidities of other commodity markets. has increased to 30% from 13%, which also shows its Similarly, the adjusted-R2 term of corn futures results is strong dependence upon cross-sectional liquidity effects. near zero for its own liquidity measure, but the adjusted- The increases of the R2 term for the copper, crude oil and R2 term has increased to 10%, which implies that the vari- gold markets are approximately 10%, and their own ance of the corn markets also relies on the liquidities of liquidities already dominate the market volatility explana- other commodity markets. The adjusted-R2 for gold results tions. 1480 Y. Zhang and S. Ding

Figure 2. Daily volatility for ﬁve commodity markets.

Therefore, it can be concluded that the non-agricultural regression model can explain 58% of copper volatility and (energy and industrial metal) futures market liquidity effects 70% of crude oil volatility. It is thereby arguable that most are much stronger than those of liquidities in the agricul- of the volatility variations in both futures markets come tural futures markets. The non-agricultural futures market from the liquidity variations. Furthermore, we have shown liquidity effects are reﬂected not only in their own market that the liquidities from energy and industrial metal have volatilities but also in other agricultural futures market spillover effects on volatilities of agricultural commodities. volatilities. In other words, agricultural futures markets are We next build a cross-sectional model to test the volatil- weaker; therefore, their volatility terms have been shaped ity spillover effects in the commodity futures markets. We by other futures market liquidities. More importantly, the try to show that the volatility of one commodity market can Return and volatility co-movement in commodity futures markets 1481

Table 11. Correlation matrix of return volatilities with p-value.

ca cor cop o g rt rt rt rt rt

ca rt 1 cor rt 0.22 1 (0.00) cop rt 0.39 0.35 1 (0.00) (0.00) o rt 0.45 0.38 0.69 1 (0.00) (0.00) (0.00) g rt 0.29 0.31 0.65 0.53 1 (0.09) (0.00) (0.00) (0.00)

Note: This table presents the correlations of volatilities of the five commodity markets. All volatilities are highly correlated and positively affect one another. The correlation coefficients are proved statistically significant.

Table 12. Commodity liquidity correlation matrix with p-value.

ca cor cop o g t t t t t

ca t 1 cor t 0.4959 1 (0.00) cop t 0.5297 0.4138 1 (0.00) (0.00) o t 0.5235 0.2540 0.8566 1 (0.00) (0.00) (0.00) g t 0.4466 0.4502 0.5806 0.5061 1 (0.00) (0.00) (0.00) (0.00)

Note: This table presents the correlations among the five commodity liquidities. All five commodity liquidities are highly correlated and positively affect one another. The correlation coefficients are proved statistically significant.

Table 13. Augmented Dicky–Fuller test for ﬁve commodity futures market liquidity time series.

ca cop cop o g t t t t t DF −14.97 −21.17 −19.78 −29.92 −12.98 (0.00) (0.00) (0.00) (0.00) (0.00)

Table 14. Augmented Dicky–Fuller test for ﬁve commodity futures market volatility time series.

σca,t σcor,t σcop,t σo,t σg,t

DF −5.97 −5.79 −2.73 −3.47 −4.48 (0.00) (0.07) (0.00) (0.01) (0.00)

Table 15. Correlations between liquidity and volatility for the ﬁve commodity futures markets.

ρ ca ca ρ cor cor ρ cop cop ρ o o ρ g g (rt , ͞ t ) (rt , ͞ t ) (rt , ͞ t ) (rt , ͞ rt ) (rt , ͞ t ) Correlation 0.42 0.12 0.69 0.74 0.36 (0.00) (0.00) (0.00) (0.00) (0.00)

be inﬂuenced by the volatilities of other commodity mar- agricultural commodities, namely cattle futures and corn kets. The results presented in table 19 apparently deliver futures, have weak connections with other commodity mar- the idea of spillover effects. For instance, the volatilities of kets. The volatilities from other markets can explain 1482 Y. Zhang and S. Ding

Table 16. Correlations between liquidity shock and volatility shock for the ﬁve commodity futures markets with p-values.

ρ ca ca ρ cor cor ρ cop cop ρ o o ρ g g (dt , gt ) (dt , gt ) (dt , gt ) (dt , gt ) (dt , gt ) Correlation 0.33 0.37 0.42 0.53 0.27 (0.00) (0.00) (0.00) (0.00) (0.00)

Table 17. Regression results for commodity return variance and liquidity level.

ca cor cop o g I rt rt rt rt rt

i t 0.004 0.001 0.009 0.012 0.002 (0.00) (0.00) (0.00) (0.00) (0.00) Constant (αi) 0.009 0.02 0.018 0.02 0.0012 (0.00) (0.00) (0.00) (0.00) (0.00) Adj-R2 0.16 0.01 0.47 0.53 0.04

Note: This table presents the regression results for the liquidity levels on the volatilities of the different commodity futures markets. All liquidity levels have signiﬁcant effects on their own market volatility.

Table 18. Regression results for commodity return volatility and cross-sectional liquidity level.

ca cor cop o g I rt rt rt rt rt ca − t 0.005 0.003 0.005 0.003 0.005 (0.00) (0.00) (0.00) (0.00) (0.21) cor − − − − − t 0.002 0.004 0.004 0.004 0.004 (0.00) (0.23) (0.00) (0.00) (0.00) cop t 0.003 0.006 0.02 0.01 0.007 (0.00) (0.00) (0.00) (0.00) (0.00) o − − − − t 0.002 0.003 0.008 0.005 0.004 (0.00) (0.00) (0.00) (0.00) (0.00) g − − − − t 0.001 0.003 0.001 0.007 0.001 (0.02) (0.00) (0.00) (0.00) (0.05) Adj-R2 0.32 0.10 0.58 0.70 0.31

Note: This table presents the regression results for the liquidity levels on the volatility of the different commodity futures markets on a cross-sectional basis. All liquidity levels have signiﬁcant effects on their own market volatility, and most liquidity levels have signiﬁcant effects on other markets’ volatilities.

Table 19. Regression results for testing the cross-sectional volatility spillover effect.

ca cor cop o g I rt rt rt rt rt ca − rt N/A 0.41 0.23 0.69 0.002 (0.02) (0.00) (0.00) (0.95) cor rt 0.019 N/A 0.05 0.64 0.31 (0.02) (0.00) (0.00) (0.00) cop rt 0.056 0.08 N/A 0.20 0.055 (0.00) (0.00) (0.00) (0.00) o rt 0.09 0.15 0.33 N/A 0.063 (0.00) (0.00) (0.00) (0.00) g − rt 0.008 0.16 0.63 0.24 N/A (0.95) (0.00) (0.00) (0.00) Adj-R2 0.21 0.17 0.59 0.54 0.44

Note: This table presents the regression results for the effects of market volatilities across different commodity markets. All market volatilities have signiﬁcant effects on other markets’ volatilities, and the adjusted-R2 is relatively high. Return and volatility co-movement in commodity futures markets 1483 approximately 20% of the volatility variation. Conversely, Overlap of two spillover effects the volatilities of non-agricultural commodities are substan- Additionally, we consolidate the two regression models to tially affected by other markets, particularly copper volatil- examine an increase of the adjusted-R2. Table 20 shows that ity; nearly 60% of the volatility variation comes from other the increases of adjusted-R2 are quite marginal compared markets. with the previous two models. The increase of adjusted-R2 for cattle commodities compared with the cross-sectional X5 i ¼ þ j þ i; volatility regression model is approximately 13%, whereas rt ai bjLt et j¼1 the increase is only 2% compared with the cross-sectional liquidity regression model. In contrast, the increase of adjusted-R2 for the corn commodity compared with the where i = ca, cor, cop, o and g, respectively. cross-sectional volatility regression model is approximately 5%, but the increase is 12% compared with the cross-sec- X5 tional liquidity regression model. The increases of adjusted- i ¼ þ j þ i; 2 ﬁ rt ai bjrt et R are summarized in table 21 for all ve markets. In gen- j¼1;j6¼i eral, the increases are marginal. Consequently, the explanatory powers of volatility and liquidity share a large where i = ca, cor, cop, o and g, respectively. proportion of commonly explained variation. Liquidity can be seen as an intermediary to transmit the volatility spillover effects from other markets.

Table 20. Regression results for cross-sectional volatilities and liquidities.

ca cor cop o g I rt rt rt rt rt ca − t 0.004 0.0013 0.003 0.0004 0.0023 (0.00) (0.04) (0.00) (0.34) (0.00) cor − − − − t 0.0016 0.0016 0.0016 0.0004 0.0016 (0.00) (0.00) (0.00) (0.11) (0.00) cop t 0.0013 0.0003 0.009 0.027 0.000 (0.00) (0.56) (0.00) (0.00) (0.99) o − − − − t 0.018 0.003 0.006 0.01 0.003 (0.00) (0.00) (0.00) (0.00) (0.00) g − − t 0.0003 0.001 0.00003 0.007 0.003 (0.00) (0.00) (0.89) (0.00) (0.00) ca − rt N/A 0.096 0.014 0.37 0.008 (0.08) (0.97) (0.00) (0.78) cor rt 0.014 N/A 0.03 0.15 0.05 (0.08) (0.05) (0.00) (0.00) cop rt 0.004 0.06 N/A 0.25 0.26 (0.97) (0.05) (0.00) (0.00) o rt 0.096 0.27 0.22 N/A 0.22 (0.00) (0.00) (0.00) (0.00) g − rt 0.004 0.16 0.48 0.45 N/A (0.78) (0.00) (0.00) (0.00) Adj-R2 0.34 0.22 0.71 0.81 0.55

Note: This table presents the regression results for the effects of both market liquidity levels and market volatilities across different commodity markets. Most market liquidity levels and market volatilities have signiﬁcant effects on other markets’ volatilities, and the adjusted-R2 is quite high.

Table 21. Increases of adjusted-R2 of the consolidated model compared with the two cross- sectional models.

ca cor cop o g rt rt rt rt rt (%) (%) (%) (%) (%)

Liquidity 2 12 13 11 24 Volatility 13 5 12 27 11

Note: This table compares the adjusted-R2 from table 20 with the adjusted-R2 from table 18 (the liquidity cross-sectional model, denoted as Liquidity) and with the adjusted-R2 from table 19 (the volatility cross- sectional model, denoted as Volatility). 1484 Y. Zhang and S. Ding

Table 22. Regression results for the market volatility model.

ca ccor cop o g rt rt rt rt rt

crb rt 1.60 2.71 6.61 1.41 2.38 (0.00) (0.00) (0.00) (0.00) (0.00)

Note: This table presents the regression of individual volatilities on the volatility of the CRB index. All individual volatilities are positively affected by the market volatility.

Table 23. Correlations between liquidity shocks (δit) and volatility residuals (μit) for the ﬁve commodity futures markets.

ρ ca ca ρ cor cor ρ cop cop ρ o o ρ g g (dt , lt ) (dt , lt ) (dt , lt ) (dt , lt ) (dt , lt ) Correlation 0.11 0.01 0.09 0.09 0.05 (0.00) (0.00) (0.66) (0.00) (0.08)

X5 X5 co-movement in the commodity futures markets. On the i ¼ þ j þ k þ i; rt ai bjLt ckrt et other hand, liquidity also affects volatility and volatility co- j¼1 k¼1;k6¼i movement. Specifically, the liquidity shocks are positively correlated with volatility shocks, which are defined as the residual risks from market volatility. More importantly, liq- where i = ca, cor, cop, o and g, respectively uidity can be viewed as an intermediary to transmit the volatility spillover effect from other markets. Therefore, liquidity shocks have effects on both residual risks from the market return and the market volatility, in which they are Positive effect of liquidity shocks on volatility residuals negatively correlated with the residual risks from the market Because the cross-sectional volatilities and liquidities cannot return and positively correlated with the residual risks from fully explain the volatility co-movement in the commodity the market volatility. markets, we further build a model of market volatility to explain the volatility co-movement in the commodity markets. Table 22 clearly shows that all individual volatilities Liquidity spillover effects on cross-sectional return are positively correlated with the market volatility, which is correlation dynamics measured by the volatility of the CRB index. Similar to the results presented in table 5, we argue that there is a market In the previous sections, we show that returns have positive volatility effect just as there is a market return effect. The cross-sectional correlations as shown in table 3, in which market volatility effect can result in the co-movement of all such correlations are static. In this section, we will present individual volatilities in commodity futures markets because cross-sectional correlations that are time-dependent; in other it has positive effects on all individual volatilities. Further- words, the strength or degree of positively correlated move- more, we are interested in the residual part, which cannot ments of returns from cross-sectional commodity futures be explored by the market volatility. Contrary to the results will vary over time. Then, we demonstrate that the liquidity presented in table 4, in which all residual risks from the level can have a significant effect on the degree of market return are all negatively correlated with the liquidity cross-sectional correlation. Table 24 shows that most time- shocks, in table 23, there is a positive effect of liquidity dependent correlations can be explained by their individual shock towards the residual risk from the market volatility liquidity levels. In other words, the correlations between except for the corn futures. Therefore, liquidity shocks can two commodity markets will be significantly influenced by act as an additional factor to the market factor for commod- their liquidity levels. If the market becomes illiquid and the ity futures volatility. correlations between the two markets are higher, then different markets could have a downside co-movement. There- ri ¼ ai þ ai rCRB þ li; t 1 2 t t fore, liquidity level plays an important role in the commodity futures markets. It is not only transmitting the cross-sectional market volatilities but also affecting the where i = ca, cor, cop, o and g, respectively. correlations between markets. Hence, the liquidity effects are twofold in the commodity futures markets concerning futures returns and futures r ¼ r þ ri þ r j þ r q ; ; a ; b L b Lt e ; volatilities. On the one hand, they induce price and return i j t i j i t j i j Return and volatility co-movement in commodity futures markets 1485

Table 24. Regressions of time-dependent cross-sectional returns correlations on liquidity levels.

r r r r r I qca;cor;t qca;cop;t qca;o;t qca;g;t qcor;cop;t

i; t −0.04 −0.008 −0.037 −0.006 −0.14 (0.05) (0.70) (0.08) (0.00) (0.00) j; t −0.09 0.036 0.019 0.04 0.13 (0.00) (0.00) (0.01) (0.00) (0.00) r r r r r qcor;o;t qcor;g;t qcop;o;t qcop;g;t qo;g;t

i; t −0.016 0.021 0.049 −0.07 −0.07 (0.09) (0.04) (0.00) (0.00) (0.00) i; t 0.09 0.032 −0.10 0.08 0.04 (0.00) (0.00) (0.00) (0.00) (0.00)

Note: This table presents the regression results for the effects of individual liquidity levels on correlations between returns from two commodity markets. Most liquidity levels signiﬁcantly affect the time-dependent cross-sectional return correlations between two commodity markets.

r where qi;j;t represents the time-dependent return correlations a volatility shock will most likely occur. The contemporane- between commodity i and commodity j,andi = ca, cor, ous co-movements of both commodity volatilities and liq- cop, o and g, respectively. uidities might strengthen the linkage and spillover effects among different commodity markets. Finally, because the liquidity risk affects both commodity return residuals and volatility shocks, it might serve as an Conclusions intermediary between commodity return and commodity volatility. When there is a volatility shock, the liquidity shock In summary, we scrutinize in this study return and volatility might occur contemporaneously. Conversely, the liquidity co-movements in different commodity futures markets. We shock is influential in affecting commodity returns and their also study how the co-movements are affected by liquidity fi correlations. Consequently, the volatility shock might have a risk. First, we nd that various measures of commodity significant effect on the commodity return through the liquid- returns exhibit co-movement and that liquidity risk plays an ity risk effect. Therefore, hedging strategies and derivative important role in shaping asset return patterns. By control- pricing models will also consider the liquidity risk effects. In ling for a measure of aggregate market return and a number fi a further step, we also show that the return correlations of additional exogenous variables, we nd that the residuals between different commodity markets are also affected by the from the regression equations for commodity returns are market liquidity levels. Therefore, when there is a sharp rise firmly correlated with the liquidity innovations, which indi- fl or decline in market liquidity, the cross-sectional return corre- cates that uctuations in liquidity can serve as a proxy for lations might be significantly influenced. Consequently, hedg- latent risk factor, which is relevant in pricing commodity ing strategies might need to be adjusted accordingly. futures. The robustness checks for our results are performed for both Amihud and Roll measures for liquidity. Moreover, we show that various volatility measures of Disclosure statement commodity returns share a common trend, which can be interpreted as a common market volatility factor. We per- No potential conflict of interest was reported by the authors. form regressions of individual commodity volatility measures on either cross-sectional volatilities or liquidities, or 2 on both, and compare the adjusted-R metrics. The Funding increases of adjusted-R2 in the final regression model are quite marginal compared with the models with only cross- This work is supported by Natural Science Foundation of Ningbo sectional liquidities or cross-sectional volatilities as explana- Research [grant number 2017A610135] and Ningbo-CASS collab- tion variables. The increase of cross-sectional variables can- orative fund [grant number NZKT201701]. not significantly add explanatory power to the model, which might suggest that most of the explanatory power in the pure liquidity or pure volatility models overlaps. The References variation part that cross-sectional volatilities can explain is similar to the part that cross-sectional liquidities can Admati, A.R. and Pfleiderer, P., A theory of intraday patterns: Vol- explain. Consequently, it makes sense to hypothesize that ume and price variability. Rev. Financ. Stud., 1988, 1(1), 3–40. the liquidity is an important transmission channel driving Amihud, Y., Illiquidity and stock returns: Cross-section and time- – the volatility spillover. More importantly, we also confirm a series effects. J. Financ. Mark., 2002, 5(1), 31 56. Bessembinder, H. and Seguin, P.J., Price volatility, trading volume, positive relationship between liquidity shock and volatility and market depth: Evidence from futures markets. J. Financ. shock. It is conceivable that when there is a liquidity shock, Quant. Anal., 1993, 28(1), 21–39. 1486 Y. Zhang and S. Ding

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