Economic spillovers between related derivatives markets: The case of commodity and freight markets

Transportation Research Part E 68 (2014) 79–102

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Transportation Research Part E journal homepage: www.elsevier.com/locate/tre

Economic spillovers between related derivatives markets: The case of commodity and freight markets Manolis G. Kavussanos a,1, Ilias D. Visvikis b,⇑, Dimitris N. Dimitrakopoulos a a b

Athens University of Economics and Business, Department of Accounting and Finance, 76 Patission St, TK 104 34 Athens, Greece World Maritime University, PO Box 500, SE-201 24 Malmö, Sweden

a r t i c l e

i n f o

Article history: Received 3 November 2013 Received in revised form 1 April 2014 Accepted 5 May 2014

Keywords: Shipping Commodity markets Futures/forward markets Causality Price discovery Volatility spillovers

a b s t r a c t Extant literature investigates volatility spillovers between spot markets of the same asset class or between derivatives and their underlying spot markets. This paper investigates economic spillovers between the freight and commodity derivatives markets. The economic relationship tested links the derivative price of the commodity transported with the derivative price on the freight rate. High frequency data on commodities are synchronised with freight data and freight rates of different vessels are matched with portfolios (baskets) of commodities that these vessels carry. The investigation of various types of commodities transported under different types of freight contracts reveal that in most cases new information appears first in the returns and volatilities of the commodities futures markets, before it is spilled over into the freight derivatives markets. Thus, agricultural commodity futures informationally lead the freight markets. The results can help improve the understanding of the information transmission mechanisms between freight and commodity markets. Ó 2014 Elsevier Ltd. All rights reserved.

1. Introduction Cross-market information transmission is a research area that has received a lot of attention from both academia and practitioners alike (see Nazlioglu et al., 2013; Wu and Li, 2013; Jung and Maderitsch, 2014; and Reboredo, 2014, among others). Economic shocks in one market can impact other markets with various degrees of severity. In perfectly efficient markets, new information is simultaneously incorporated into the prices of the markets, in such a way that prices adjust to new equilibrium levels without any time delay (Chan et al., 1991). However, transactions costs, information asymmetries, supply-demand imbalances and other market microstructure issues may create information spillover relationships between markets (see Wahab and Lashgari, 1993; and Fleming et al., 1996, among others). The importance of modelling such relationships is linked with the nature of trading dynamics between markets. Cross-market linkages and spillover effects broadly fall into three categories. The first constitutes a linkage between spot markets that are fundamentally linked through supply and demand functions (see Yu et al., 2007 on spot grain commodities and freight prices; and Haigh and Bryant, 2001 on barge, ocean freight prices and soybeans prices, among others). The second refers to information flows between derivatives markets and their underlying spot markets (see Coppola, 2008 on futures and spot commodity markets; and Kavussanos and Visvikis, 2004 on forward and spot freight markets, among others), and the third one, which, surprisingly enough, has received the least attention, concerns return and volatility spillovers ⇑ Corresponding author. Address: World Maritime University, Citadellsvägen 29, Malmö, PO Box 500, SE-201 24 Malmö, Sweden. Tel.: +46 (0) 40 35 63 72; fax: +46 (0) 40 12 84 42. E-mail addresses: [email protected] (M.G. Kavussanos), [email protected] (I.D. Visvikis), [email protected] (D.N. Dimitrakopoulos). 1 Tel.: +30 210 8203167. http://dx.doi.org/10.1016/j.tre.2014.05.003 1366-5545/Ó 2014 Elsevier Ltd. All rights reserved.

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between different derivatives markets (see Chng, 2009 on natural gas, palladium and gasoline Japanese futures markets; Chulia and Torro, 2008 on DJ Euro Stoxx 50 index futures and Euro Bund futures markets; Fung et al., 2010 on US and Chinese aluminium and copper futures markets; Kavussanos et al., 2010 on freight forwards and commodity futures markets; Ding and Pu, 2012 on US stock, bond and credit derivatives markets; Trujillo-Barrera et al., 2012 on US crude oil, ethanol, and corn futures markets; Beckmann and Czudaj, 2014 on US corn, cotton, and wheat futures markets; and Liu et al., 2014 on Chinese copper, aluminium, natural rubber and soybean futures, amongst others). This study investigates the information (spillovers) relationships between freight derivatives markets of the dry bulk sectors of ocean going vessels and the available derivatives of the commodities carried by these vessels, and analyses the magnitude and direction of these spillovers.2 More than 90% of the world’s commodity trade is transported by ocean going vessels (George, 2013). The international market for freight services possesses some special features that set it apart from other commodity markets, due to its high volatility, cyclical nature, the seasonal influences of the commodities transported, and its non-storable nature, amongst others (see Kavussanos and Visvikis, 2011). The latter characteristic alone differentiates the freight market from all other storable commodities, as the theory of storage and the cost-of-carry no-arbitrage relationships cannot be applied for the pricing of freight derivatives contracts (see Kavussanos and Visvikis, 2004). As such, there is an increasing need for more sources of information that may be utilised by economic agents participating in these markets for the pricing and trading of such commodity contracts.3 Furthermore, according to Skiadopoulos (2013), commodity futures markets have attracted a lot of attention during the last decade from practitioners, regulators and academics due to: (i) an increase of investments in commodities; (ii) the perception that they are an alternative investment asset class; (iii) the commodity boom, between 2004 and 2008; and (iv) the Dodd-Frank Wall Street Reform and Consumer Protection Act in 2010, for the regulation of margins in commodity futures markets. The implications of the economic linkages uncovered in this study are important as returns and volatilities are related to the rate of information flow to a market, and changes in them reflect the appearance of new information. Investigating the extent to which (and the magnitude of) commodity derivatives’ (return and volatility) shocks are spilled over to freight derivatives markets and vice versa, are important. The design of investment portfolios, asset pricing and risk management, are some of the important areas of application of the findings (see for example, Reboredo, 2014). Thus, international investors, in order to guarantee sufficiently diversified freight portfolios, have to observe and monitor continuously the changes in market linkages (between commodity futures and freight derivatives) and assess if these changes are transitory or have a more permanent nature (Jung and Maderitsch, 2014). Traders may utilise the revealed linkages to construct profitable trading strategies; that is, take trading positions on the freight derivatives markets according to the direction of the commodity derivatives forward curves or take trading positions on the freight options markets to gain from volatility changes spilled from the commodity derivatives markets. Additionally, hedgers can monitor the freight and commodity derivatives markets to implement risk management through hedging in a more effective manner. The investigation of the topic is also related to seaborne transportation, as commercial decisions in maritime transportation (e.g. chartering of vessels) can be supported by information that may come, ahead from the decision, from the commodity futures markets. This, may in turn, lead to more informed decision-making and to an increase in the efficiency of the freight market (see Goulas and Skiadopoulos, 2012). Furthermore, agricultural commodities are regarded as financial assets, and as such, globalisation and increased world market integration have accelerated the ‘‘financialization of commodities’’ (Nazlioglu et al., 2013). Due to the cross-border trade of commodities around the world, commodity markets are linked with operations in seaborne transportation markets. Therefore, policy makers and regulators analyse the dynamics of return and volatility transmissions between commodities and shipping markets in order to guide them into better decisions. In terms of policy implications, as significant spillover effects have been found to exist between market channels, policy changes in commodity markets should have an impact on shipping markets (see also, Jung and Maderitsch, 2014). Sound policy measures then should be based on a clear comprehension of the transmission mechanisms between commodity and shipping markets. This paper contributes to the literature in a number of ways: First, it investigates how the derivatives market of the commodity transported is linked to the freight derivatives market of the vessel transporting it. Following that, and since it has been found in the literature that the derivatives markets under investigation informationally lead their corresponding underlying spot (physical) markets, the main findings here should apply in the spot (physical) freight and commodity markets as well.4 This economic link further contributes to the pricing of freight derivatives, which are not so precisely priced

2 The major ones are dry bulk, wet (liquid) bulk, general cargo, and liquid gas. Cargo carrying/ocean shipping has distinct segments (see Kavussanos 2010, among others). This study in its analysis concentrates in the dry bulk segment. Specifically, it focuses on the Capesize, Panamax and Supramax sectors, as they are the major and most prominent sub-sectors of dry bulk, and most importantly, for the freight rates of which and the commodities carried, freight and commodity derivatives prices are available. 3 For instance, Prokopczuk (2011) employs alternative affine continuous-time models of the spot price dynamics in order to derive closed-form valuations for freight futures contracts. 4 Kavussanos and Visvikis (2004), show that freight derivatives markets are broadly unbiased and that the freight derivatives market informationally leads the underlying (physical) spot market for freight rates. As such, freight derivatives can be utilised as price discovery vehicles for spot freight markets. Participants can have a better assessment of risk management, chartering and budget planning decisions by utilising the information available in the freight derivatives market as a price discovery vehicle. Wheat, corn, soybean and coal futures, which correspond to the underlying commodities transported in the shipping routes of the dry bulk freight derivatives contracts, for which data are available, are also shown in the literature to fulfill their price discovery role in relation to their underlying spot markets; see for instance, McKenzie and Holt (2002) for US corn futures and Yang and Leatham (1999) for US wheat commodity futures markets, among others.

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given the non-storable nature of their underlying ‘‘commodity’’; namely the freight service (see Kavussanos and Visvikis, 2004).5 To the best of our knowledge, this is the first study to empirically examine cross-market return and volatility information spillovers between the major segments of dry bulk freight derivatives and the corresponding derivatives markets for the products that are carried by the vessels operating in these segments. Thus, all major sub-segments of the dry bulk sector (Capesize, Panamax and Supramax vessels) for which there are freight derivatives prices are investigated. This facilitates comparisons of the results between the segments. Additionally, since different types of freight contracts (route-specific and time-charter contracts – see Section 3 for more details) are involved it enables comparisons between the different freight contracts.6 The empirical investigation of various types of commodities transported under different types of freight contracts reveal that in most cases new information appears first in the returns and volatilities of the commodities futures markets, before it is spilled over into the freight derivatives markets. Thus, commodity futures informationally lead the freight derivatives markets. Consideration of the different commodities and their link with corresponding freight derivatives enables the comparison of effects between commodities. Second, by utilising a data set large enough to include the global financial crisis, the paper investigates the possibility of significant structural changes on the spillover patterns between the examined variables, which may arise under such adverse market conditions. Investigating and incorporating the influence of such structural breaks in an information spillover framework is important to investors and traders engaging in these derivatives markets, as derivatives contracts can serve the role of ‘‘break discovery’’ to the underlying spot markets. Lien and Yang (2010) argue that the breaks in futures markets always take place before those in the physical markets. Therefore, locating structural breaks in derivatives markets can serve as an indication that such breaks will occur later in the spot markets. Third, due to different time zones some markets may be more liquid than others, and as such, are able to incorporate global information faster than other markets. Since the US commodity futures markets open at a different time than the time of the announcement of freight derivatives prices in the UK, it is possible that non-synchronicity may influence the results.7 Most of the studies in the literature (especially the sectoral ones), do not emphasise enough this market microstructure effect, and as such, do not utilise ‘‘time-matched’’ data. In order to ensure that the spillover inferences are not biased due to non-synchronous trading among the markets, a ‘‘time-matched’’ high frequency data set is created, in which the prices of all commodity futures contracts are retrieved in the US, on a daily basis, at the exact publication time of the freight derivatives prices in London, and thus, overcoming the possibility of non-synchronicity in the data. Furthermore, to account for the different commodities transported by the vessels of the underlying freight derivatives baskets and routes, synthetic equally weighted commodity futures baskets are also constructed. Having secured that the results are free from non-synchronicity issues, they can be used from researchers to make further efficient econometric inferences. Fourth, this paper investigates and reveals that commodity and freight derivatives markets are interrelated, standing in a long-run equilibrium (cointegration) relationship between them, even after allowing for structural breaks. The existence of a cointegrating relationship, therefore, binding the two derivatives markets together, can help improve the understanding of the information transmission mechanisms between freight and commodity derivatives markets (and consequently between their underlying spot markets) and assist market participants into more effective trading, investment and hedging decisions. The remainder of this paper is structured as follows. The next section presents the economic framework and methodology used. Section 3 analyses the data and outlines some preliminary results. Section 4 presents the return and volatility spillover results. Section 5 measures the economic significance of the main spillover results. The sixth section provides a critical discussion of the results. Finally, Section 7 concludes the paper. 2. Methodology and methods 2.1. Economic framework and implications of spillovers Forward Freight Agreements (FFAs) are Over-The-Counter (OTC) forward contracts between a buyer and a seller, to settle a freight rate, for a specified quantity of cargo (in a voyage chartering agreement) or number of days (in a time-charter agreement), for a specific type of vessel, for one or a combination of the major trade routes of the dry bulk, tanker and containership sectors of the shipping industry. Charterers that wish to fix a vessel in a future time period to cover cargo transportation requirements protect themselves against freight rate increases by buying FFAs. Shipowners wishing to hire their vessels in a future time period can hedge themselves against freight rate decreases by selling FFAs. The trading routes, which serve as the underlying assets of dry bulk FFA contracts, are based on the Baltic Capesize Index (BCI), the Baltic 5 Goss and Avsar (1999) argue that a major difference between non-storable and storable commodities (when both spot and derivatives markets exist) is that the magnitude of the forward premium (contango) in the case of storable commodities is limited by the ‘‘marginal net cost of storage’’, whereas for non-storable commodities no restriction exists. Keynes (1930) mentions that in the case of backwardation, no such restriction exists, both for storable and non-storable commodities. Tomek and Gray (1970) argue that futures prices of storable commodities provide more reliable forecasts (and thus can assimilate more information) than those for non-storable commodities, as the futures prices for non-storable commodities serve as a source of price stability, while the futures prices for storable commodities serve as a measure of inventory allocation. 6 The only exception is the study by Kavussanos et al. (2010), which investigates the Panamax market only. 7 On any given day, the Baltic Exchange freight derivatives prices are announced at 17:30 London time, while Chicago Mercantile Exchange (CME) closing futures prices are published at 19:15 London time (13:15 in Chicago).

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Panamax Index (BPI), the Baltic Supramax Index (BSI) and the Baltic Handysize Index (BHSI).8 For tanker and container FFAs are the Baltic Dirty Tanker Index (BDTI), Baltic Clean Tanker Index (BCTI) and Shanghai Containerised Freight Index (SCFI), World Container Index (WCI), respectively. The Baltic Exchange indices comprise the most important routes in each segment of the industry and are designed to reflect freight rates across spot voyage and time-charter routes. OTC trades can be cleared in a clearing-house eliminating credit risk between contract counterparts. Freight derivatives are cleared in NOS Clearing ASA (since 2001), in Chicago Mercantile Exchange (CME) ClearPort (since 2005), in London Clearing House LCH. Clearnet (since 2005), in Singapore Exchange (SGX) AsiaClear (since 2006) and in Shanghai Clearing House (SHCH) in China (since 2012). Kavussanos et al. (2004a) investigate the impact of FFA trading on spot freight market price volatility and argue that FFA trading has reduced the spot price volatility of all investigated routes, has a decreasing impact on the asymmetry of volatility (market dynamics) and has substantially improved the quality and speed of information flow. Similarly, commodity futures contracts are agreements to buy or sell a certain amount of a commodity, of certain specifications in a future time period. Commodity futures contracts reflect the future price of the commodities transported by vessels in routes that are the underlying assets of the FFA contracts. Additionally, commodity futures constitute the main hedging instruments for shippers who are involved in seaborne transportation. The type of vessel carrying each commodity depends on the economics of the industry that creates the demand for the commodity and the regions where the industries using the raw materials are established, relative to the raw material producing countries. For instance, Capesize vessels typically carry commodity parcel sizes of approximately 150,000–170,000 metric tons of iron ore because these are the typical commodity sizes of iron ore required by the steel mills using iron-ore as raw material in the production of steel. A typical route that such vessels operate is between the iron-ore producing Brazil and Northern Europe, where the steel mills are established. The size of the vessel used of course requires that the ports are deep enough, with enough storage facilities and sufficient handling gear to accommodate these vessels. Economic theory and intuition suggests that bi-directional linkages between freight derivatives (FFA) markets and commodity futures markets for commodities carried by ships may exist. On one hand, the final CIF (Cost, Insurance and Freight) prices of commodities transported by sea should reflect the global demand and supply conditions for these commodities. The CIF prices incorporate the FOB (Free on Board) prices, insurance and freight. As a consequence, freight rates and the information incorporated in freight markets affect the final demand for the commodity through the pricing channel, the degree of the impact depending on the contribution of freight to the CIF prices and on the elasticity of demand with respect to freight rates. It is also known that FFA prices are related to the underlying freight rates. On the other hand, what happens in commodity markets affects the demand for freight services, as the latter depends directly on the former. Moreover, commodity futures prices are linked to the underlying commodity price. Commodity and freight rate markets then should be linked. The nature of this economic relationship between the two derivatives markets is addressed in this study and is consistent with the presented empirical findings.9 Given that derivatives contracts exist on these two sets of markets, the information available in the commodity derivatives market is expected to also reveal itself in the freight derivatives market and vice versa. Moreover, due to the forward looking behaviour of derivatives markets, possible spillover effects between spot markets make themselves evident first in the corresponding derivatives markets. Market participants, active in the freight (commodity) derivatives markets, can benefit by the existence of such spillover effects, as they can exploit the information incorporated in the commodity (freight) derivatives prices for investment and hedging purposes. 2.2. Cost of carry relationships The final CIF price of commodities transported by sea, which incorporate the FOB price, insurance and freight, reflects the global demand and supply conditions for these commodities. Consider the demand for a commodity carried by bulk carrier ships, say for wheat. This demand depends on the CIF spot price of the commodity at time t, SCIF,t, as this is the price that the final consumer pays. One could decompose this SCIF,t price into the FOB price of the commodity that has been negotiated during the last period in the market (SFOB,t1), the current freight rate (SFR,t) and the insurance required for the transportation of the commodity (INS). Mathematically:

SCIF;t ¼ SFOB;t1 þ SFR;t þ INS

ð1Þ

The insurance part in the above equation is relatively steady over time. However, both SFOB,t1 and SFR,t are quite volatile and depend on the demand and supply conditions of the commodity and freight markets, respectively. For instance, the spot freight rate for the transportation of the relevant commodity depends on the demand and supply conditions of the freight market for this commodity; that is, on the number of cargoes of the commodity being available for transportation at any point in time (but also on other types of cargo, such as wheat, corn and coal that are transported by similar types of vessels), as well as on the number of vessels available to transport the commodity at that point in time. As shown by Kavussanos et al. 8

More details on the various freight market indices, their construction process, and the use of FFAs can be found in Kavussanos and Visvikis (2006, 2011). As pointed out by a reviewer, it should be noted here that the described economic relationship should hold for commodities that are exported by ocean going vessels, and not for commodities that are domestically consumed by the use of other modes of transportation (say barges, tracks and pipelines, among others). 9

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(2004b), the unbiasedness hypothesis holds in the freight market, and as such, the FFA price (FFR,t) can substitute the spot freight rate, SFR,t, yielding:

SCIF;t ¼ SFOB;t1 þ F FR;t þ INS

ð2Þ

Similarly, the spot price of the commodity (SCIF,t) is determined by the demand and supply of cargoes for this commodity. The commodity futures (CIF) price, FCIF,t, in turn, is determined through the following cost of carry relationship:

F CIF;t ¼ SCIF;t þ C

ð3Þ

where, C refers to the cost of carrying the commodity forward in time and incorporates the rather steady over time storage, insurance and financial costs and the time-varying convenience yield, partly because of the inability of investors and speculators to short the underlying commodity. Substituting Eq. (3) into (2) yields:

F CIF;t ¼ SFOB;t1 þ F FR;t þ INS þ C

ð4Þ

From Eq. (4), it is evident that the derivatives market of the commodity transported is linked to that of the freight market; that is, the futures price for a commodity today (FCIF,t) is related to the one-period lag of the spot price of the physical commodity (SFOB,t1), the current price of the freight derivatives market (FFR,t), the insurance to transport the commodity (INS) and the cost of carry components (C). As previously mentioned, due to the fact that the freight rate service is a non-storable commodity, the usual cost-of-carry no arbitrage arguments to price these forward contracts do not hold. Thus, there is a lack of a precise pricing model for FFA prices. If significant spillover effects are found linking the two derivatives markets together, Eq. (4), when solved for the FFA price, can serve as an indirect pricing model for FFA contracts. It is expected that agricultural commodity futures play a leading role in the international information discovery process. If so, then brokers, market makers, and other market participants should use them as a benchmark when pricing FFA contracts. Following the above, this paper empirically investigates the dynamic interrelationship between the commodity and the related freight derivatives markets, for a number of commodities carried by sea. 2.3. Stationarity and cointegration To determine the order of integration of each price series the standard unit root tests of Dickey and Fuller (ADF, 1981), Phillips and Perron (PP, 1988) and Kwiatkowski et al. (KPSS, 1992) and the later test of Lee and Strazicich (2003, 2004) (LS henceforth) that accounts for structural breaks are used.10 A drawback of the standard unit root tests (like the ADF and PP) is that structural breaks may affect their outcome, as economic variables may be better described as stationary processes around a breaking level, rather than integrated of order one. Thus, standard unit root testing procedures may erroneously fail to reject the null hypothesis that a series is integrated of higher order. In order to identify and account for structural breaks in the unit root testing of economic variables, during a highly volatile environment that includes a financial crisis, the LS unit root test is also employed. This test allows for two endogenous structural breaks in the levels of the series.11 The LS test is superior to other similar tests in that it offsets the loss of power of tests that search for one structural break by including structural breaks both under the null and the alternative hypotheses (with the rejection of the null to indicate trend stationarity).12. Suppose that the Data Generating Process (DGP) of a time-series yt is described as:

yt ¼ d0 Z t þ nt ;

nt ¼ kt1 þ pt

ð5Þ

where, Zt is a vector of exogenous variables and pt  iidNð0; rp Þ. The LS test allows for two shifts in the level of the series, while the null and alternative hypotheses are given by the following equations, respectively13: 2

H0 :

yt ¼ l0 þ d1 B1t þ d2 B2t þ yt1 þ x1t

ð6aÞ

H1 :

yt ¼ l1 þ ct þ d1 D1t þ d2 D2t þ x2t

ð6bÞ

where, Zt = [1, t, D1t, D2t]0 , Djt = 1 for t P Tbj + 1 (j = 1, 2) and zero otherwise, Bjt = 1 for t = Tbj + 1 (j = 1, 2) and zero otherwise, Tb indicates the time period when a break occurs, and x1t and x2t are stationary error-terms. The B1t and B2t break dummies are required to avoid the dependence of the test’s statistics on the break’s size d1 and d2. The LM unit root test statistic then is estimated as:

~ t1 þ Dyt ¼ d0 Z t þ uv

k X ~ t1 þ ht Dv

ð7Þ

i¼1

10 The KPSS test addresses the lack of power of the ADF and PP tests, in rejecting the null hypothesis of a unit root when it is false, by having stationarity as the null hypothesis. 11 Mehl (2000) argues that by adding more than two breaks the time-series are closer to becoming a random-walk process, and therefore, unit root tests with multiple structural breaks are less relevant. 12 The assumption of no breaks under the null hypothesis may lead to size distortions in the presence of a unit root with breaks (see Lee and Strazicich, 2003) 13 There is another version of the LS test, which allows for two shifts in the level and trend of the series, but it is not used here, as the sample size is not large enough to justify the existence of trends in the investigated series.

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~v  ^ ~ v is given by yt  dZt, y1 and Z1 ~ t ¼ yt  w where, v dZ t ðt ¼ 2; . . . ; TÞ; ^ d are coefficients in the regression of Dyt on DZt, w ~ t1 (i = 1, . . . , k) are included to account for serial correlation. represent the first observations of yt and Zt, respectively, and Dv ~ t1 terms we start from a maximum of k = 10 terms and use Following LS, in order to determine the lag length (k) of the Dv the 10% asymptotic critical value to determine the significance of the t-statistic of the last lag. We continue eliminating insig~) tests the unit root null nificant lags until the last term is statistically significant otherwise k is set to zero. The t-statistic (s hypothesis (u = 0). The minimum Lagrange Multiplier (LM) test determines the time location of the two endogenous breaks, ~ðki Þ. Following LS, the structural breaks are determined endogenously from each kj = Tbj/T, using a grid search as LMs ¼ ln fki s economic variable at the location where the t-test statistic is minimised over the trimming region [0.15T, 0.85T], where T denotes sample size. Critical values for the one- and two-break cases are tabulated in Lee and Strazicich (2003, 2004), respectively. Given a set of two non-stationary series, Johansen (1988) tests are used next to determine whether the series stand in a long-run relationship between them; that is, that they are cointegrated. The following Vector Error Correction Model (VECM) is estimated:

DX t ¼

p1 X

Ci DX ti þ

Y

X t1 þ et ;

et jXt1  distrð0; Ht Þ

ð8Þ

i¼1

where, Xt is the 2  1 vector (FFAt, FUTt)’ of log-FFA and log-commodity futures prices, respectively, D denotes the first difference operator, et is a 2  1 vector of residuals (eS,t, eF,t)’ that follow an as-yet-unspecified conditional distribution with mean zero and time-varying covariance matrix, Ht. The coefficient matrix P contains the essential information about the relationship between FFAt and FUTt. Specifically, the VECM specification contains information on both the short- and long-run adjustment to changes in Xt, via the estimated parameters Ci and P, respectively. If P has a reduced rank, that is rank(P) = 1, then there is a single cointegrating relationship between FFAt and FUTt, which is given by any row of matrix P and the expression PXt1 is the error-correction term. In this case, P can be factored into two separate matrices a and b, both of dimensions 2  1, where 1 represents the rank of P, such as P = ab’, where b’ represents the vector of cointegrating parameters and a is the vector of error-correction coefficients measuring the speed of convergence to the long-run equilibrium.14 As global economic and financial shocks may cause shifts in the cointegration relationship between economic variables, it is also important to account for the existence of structural breaks in integrated systems of variables. A shortfall of Johansen’s (1988) standard cointegration test is that it is prone to Type II error when breaks exist in the cointegrating system (i.e. it fails to reject the null of no cointegration when in fact there is cointegration with breaks; see Villanueva, 2007). This in turn, may lead to misspecification of the long-run properties of a dynamic system, inadequate estimation and incorrect inferences. In that respect, the residual-based cointegration test of Gregory and Hansen (1996a,b) is used, under two models that allow, respectively, the alternative hypothesis for one endogenous intercept shift (‘‘level shift’’ or Model C as Gregory and Hansen name the model) and a shift in both intercept and slope (‘‘regime shift’’ or Model C/S) of the cointegration vector at some unknown date:

yt ¼ a1 þ a2 Dt þ b1 xt þ et

ð9aÞ

yt ¼ a1 þ a2 Dt þ b1 xt þ b2 Dt xt þ et

ð9bÞ

where, the break dummy Dt = 1 for t = t⁄ + 1, . . . , T and Dt = 0 for t = 1, . . . , t⁄, t⁄ is an endogenously determined break date of a sample of size T, a1 and (a1 + a2) are the intercepts before and after the break at t⁄, and b1 and (b1 + b2) are the cointegrating slope coefficients before and after the break. Then the Phillips–Perron Zt statistic, which is an ADF-type test that uses a corrected covariance matrix is estimated for the residuals of the equations.15 The process is repeated until the minimum value of the statistic (Z t ) is found, which corresponds to the break date. The critical values are provided by Gregory and Hansen (1996a,b). However, it should be noted that if the standard cointegration models (without breaks) reject the null of no-cointegration then there is no need to test for cointegration with breaks. In contrast, if the standard cointegration models cannot reject the null, then the Gregory and Hansen test is used, which tests for a shift in the cointegration vector at some point in time (see Gregory and Hansen, 1996a). Finally, since this test does not provide consistent standard-errors for parameter hypothesis testing, the Fully-Modified OLS (FM-OLS) estimator, proposed by Phillips and Hansen (1990) is used. The latter estimates a heteroskedasticity and autocorrelation consistent covariance matrix in order to extract the parameters of the cointegration Error-Correction Terms (ECTs). 14 Since rank(P) equals the number of characteristic roots (or eigenvalues) which are different from zero, the number of distinct cointegrating vectors can be obtained by the ktrace and kmax statistics of Johansen (1988). 15 Monte Carlo experiments indicate that from the three recursive tests of Gregory and Hansen (ADF and the Phillips–Perron Zt and Za) the Zt test performs better than the ADF and Za tests (see Gregory and Hansenm 1996a,b) and therefore, only the Zt results are reported in the ensuing analysis.

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2.4. Return and volatility spillovers To investigate for return spillovers between the various derivatives markets, pairs of FFA and commodity futures, corresponding to the major commodities transported by the specific vessels, are constructed. The following VECM is estimated in each case:

DFFAt ¼

p1 p1 X X aFFA;i DFFAti þ bFFA;i DFUTti þ qFFA zt1 þ e1;t i1

DFUTt ¼

ei;t jXt1  distrð0; Ht Þ

p1 p1 X X aFUT;i DFFAti þ bFUT;i DFUTti þ qFUT zt1 þ e2;t i1

ð10aÞ

i1

ð10bÞ

i1

where, DFFAti and DFUTti are the logarithmic first-differences of FFA and commodity futures prices, respectively, zt1 (=FFAt1  FUTt1) is the lagged ECT, which represents the long-run relationship between the two derivatives markets, ei,t are stochastic error-terms that follow an as-yet-unspecified conditional distribution, with mean zero and time-varying covariance matrix Ht and aFFA,i, bFFA,i, aFUT,i and bFUT are short-run coefficients. If some non-zero bFFA,i (aFUT,i) coefficients, i = 1, 2, . . ., p  1, are statistically significant in Eq. (10a) (10b) then a unidirectional causality exists from commodity futures (FFA) to FFA (commodity futures), and it is argued that FUTt (FFAt) Granger causes FFAt (FUTt). A two-way feedback relationship, between FFAt and FUTt prices, exists if both bFFA,i and aFUT,i coefficients are significant. These hypotheses are tested by employing a Wald test on the joint significance of the lagged estimated coefficients of DFFAti or DFUTti. When heteroskedasticity is evident in the residuals of the error-correction equations, the t-statistics are adjusted by White’s (1980) heteroskedasticity correction. Finally, when no cointegration is established between FFA and commodity futures price series, a bivariate Vector Autoregressive (VAR) model is estimated instead of a VECM, excluding the zt1 term from Eqs. (10a) and (10b). Impulse response functions are further estimated to provide a more detailed insight on the spillover relationships, by measuring the reaction of FFA and commodity futures prices in response to one standard error shocks in the equations of the VAR and VECM models, estimated as Seemingly Unrelated Regressions (SUR) systems. Generalised Impulse Responses (GIR) are estimated to overcome the issues induced by the orthogonalization of the underlying shocks through the Cholesky decomposition of the covariance matrix of Eq. (8). The conditional second moments of FFA and commodity futures prices are estimated using the following bivariate Generalised Autoregressive Conditional Heteroskedasticity (GARCH) model with the Baba et al. (1990) augmented positive definite parameterisation in order to capture higher moment dependencies (volatility spillovers):

Ht ¼ A0 A þ B0 Ht1 B þ C 0 et1 e0t1 C þ S10 u1;t1 u01;t1 S1 þ S20 u2;t1 u02;t1 S2 þ E0 ðzt1 Þ2 E

ð11Þ

where, A is a (2  2) lower triangular matrix of coefficients, B and C are (2  2) diagonal coefficient matrices, S1 and S2 are the matrices of the spillover effect parameters, u1,t1 and u2,t1 are matrices of lagged square error-terms and E is a diagonal matrix containing the coefficients of the squared error-correction term, ec11, ec22. In this setting, u1,t1 is the volatility spillover effect from the FFA market to the commodity futures market and u2,t1 is the volatility spillover effect from the commodity futures market to the FFA market. The element of S1 (S2), s121 (s212), measures the spillovers of the FFA (commodity futures) volatility equation to the volatility of the commodity futures (FFA) equation. By incorporating the lagged squared ECT in the conditional variances and covariance, the model is capable to highlight the potential relationship between disequilibrium (measured by the ECT) and risk (measured by the conditional variance). Once again, when no cointegration is discovered between FFA and commodity futures price series, a BEKK VAR-GARCH model is estimated, as in Eq. (11), but without including the lagged squared ECT, (zt1)2. The following bivariate Exponential-GARCH (EGARCH) model of Nelson (1991) is used, when asymmetries are observed in the conditional variances; that is, positive returns are followed by higher volatility than negative returns:

Ht ¼ exp½A0 A þ B0 Ht1 B þ C 0 et1 e0t1 C þ D0 et1 e0t1 D þ S10 u1;t1 u01;t1 S1 þ S20 u2;t1 u02;t1 S2

ð12Þ

where, the coefficients are as previously defined and the diagonal (2  2) D matrix measures the asymmetry effects of shocks on volatility (dii):

  dii ðeii;t1 Þ ¼ di jeii;t1 jE ðjeii;t1 jÞ þ deii;t1

ð13Þ

When the EGARCH model fails to eliminate the asymmetries in the data, the asymmetric GJR-GARCH model of Glosten et al. (1993) is used instead that allows positive and negative innovations to returns to have different impact on the conditional variance. In a bivariate BEKK-VECM setting, the conditional variance according to the GJR model is defined as:

Ht ¼ A0 A þ B0 Ht1 B þ C 0 et1 e0t1 C þ D0 ft1 f0t1 D þ S10 u1;t1 u01;t1 S1 þ S20 u2;t1 u02;t1 S2

ð14Þ

where, D is a 2  2 diagonal matrix of the coefficients of asymmetry, ft1 = et1Gt1, and Gt1 is a 2  1 vector of indicator variables which take the value of 1 if et1 < 0 and zero otherwise. If the coefficient of the indicator variable (Gt1) is positive

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and significant, this indicates that lagged negative innovations have a larger effect on returns than positive ones, and thus, nonlinear dependencies in the volatility of the returns exist. The conditional Student-t distribution is used as the density (likelihood) function of the error-term et and the number of degrees of freedom v is treated as another parameter to be estimated. Baillie and Bollerslev (1995) show that for v < 4, the Student-t distribution has an undefined or infinite kurtosis. In such cases the Quasi-Maximum Likelihood Estimation (QMLE) of Bollerslev and Wooldridge (1992), which estimates robust standard errors and yields an asymptotically consistent normal covariance matrix, is used. The most parsimonious specification for each model is estimated by excluding insignificant terms. Finally, the Broyden, Fletcher, Goldfab, Shanno (BFGS) algorithm is used, which maximises the log-likelihood function, in order to estimate the parameters of the GARCH models. 3. Data and preliminary statistics The dataset used in the paper consists of daily Baltic Forward Assessments (BFAs) and commodity futures price series obtained from Reuters, Bloomberg, Datastream International and Tick Data. The period investigated extends from May 2006 to October 2009, yielding a total of 868 daily observations. Since in the literature it is argued that the spillover relationship between prices changes depend significantly on the data frequency used (see Nazlioglu et al., 2013), high frequency data are used in this study: (i) to time-match the non-synchronous trading intervals between the different commodity and freight derivatives markets; (ii) to capture as much information embedded into derivatives returns as possible. Taking into consideration the specific liquidity of the freight derivatives we wish to avoid missing valuable information by the use of lower-frequency (e.g. monthly) data; (iii) as the information flow within a market system typically reflects the investors’ expectations, and since freight rates are based on future expectations in shipping that can change rapidly from one day to the next; and (iv) to be consistent with several studies in the literature on price discovery and spillover relationships (see for example, Kavussanos and Visvikis, 2004; Ding and Pu, 2012; Nazlioglu et al., 2013; Jung and Maderitsch, 2014, amongst others). Again, following the literature, BFAs and commodity futures prices are always those of the nearby (prompt) month contract (same maturity contract) because it is the most liquid and active contract (see Bessembinder and Chan, 1992; Daskalaki et al., 2014, among others). When futures contracts approach their settlement delivery day (beginning of the delivery period), the trading volume decreases sharply. Therefore, in order to avoid thin markets and expiration effects, we rollover to the next nearest-to-maturity contract one week before the nearby contract expires. This way, we do not estimate returns by using prices of contracts with different delivery dates. There is sufficient liquidity in the nearby contract up to a few days before its maturity date to justify such a rollover policy. When a market is not open on a given day, for a national holiday or any other event, the corresponding returns in all other markets are removed from the sample. BFAs are forward OTC mid bid and offer FFA prices (based on what the current bid and ask quotes are) provided by a panel of FFA brokers appointed by the Baltic Exchange. The Baltic panellists every business day assess and report their professional judgment of mid FFA market prices on each Baltic index publication day, for the routes defined by the Baltic Exchange. Then the BFAs are reported in the market by 17:30 London time. BFAs are regarded as the most representative FFA data, as they include information from the most active FFA brokers. If no actual FFA trade has been conducted in a specific day for a specified maturity, then the panellists should take into account all market information available before quoting the BFA price. The panellists are FFA brokers and must be members of the Baltic Exchange and of the FFA Brokers Association (FFABA). As with the panellists of the various underlying indices of the Baltic Exchange, they must follow the rules and regulations for the production of the BFAs. According to the trading volume data of the Baltic Exchange, an increase in the number of traded dry bulk FFA contracts took place between 2002 and 2008, arriving at the highest of 2.3 million lots in 2007 (see Alizadeh, 2013). According to market sources, in 2011, the physical seaborne trades were about 3.1 billion metric tonnes, while the estimated FFA market was about 1.1 billion metric tonnes of seaborne trade. The used BFA (henceforth FFA) data consists of freight derivatives contracts on C4 (Richards Bay in South Africa to Rotterdam) and C7 (Bolivar in Columbia to Rotterdam) routes of the Capesize index, on P2A (Skaw-Gibraltar range to a trip in the Far East) route of the Panamax index, and on time-charter baskets. The choice of routes for which FFA prices are taken is determined by the availability of corresponding futures prices on commodities carried on the particular route. The baskets of time-charter rates are constructed by the Baltic Exchange’s dry bulk time-charter Capesize, Panamax, Supramax and Handysize routes. The standard vessel size and the composition of each FFA time-charter basket as it stood for the period of the analysis of the data is detailed in Table 1. The weights reported next to the route of each vessel size illustrate the most dominant cargoes transported in each case. According to Clarksons, iron ore and coal account each for 30% of the total dry bulk business, grains (corn, wheat and soybeans) account for 10%, and finally, minor bulk commodities account for the remaining 30% of the total dry bulk seaborne trades. As can be seen, iron ore and coal are the major commodities transported in the routes of the Capesize basket. The Panamax basket includes a wider range of commodities transported (for example, grains, coal, iron ore, bauxite and sulphur). Finally, the Supramax basket includes an even more diverse list of commodities transported (grains, fertilizers, steel, petcock and scrap). Four commodity futures contracts (coal, corn, wheat and soybeans) are employed in the paper. These commodities reflect the major commodities transported in the underlying routes of the aforementioned FFA contracts. Corn, wheat and soybeans grain futures contracts trade at the Chicago Mercantile Exchange (CME) and are regarded as the underlying commodities of

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M.G. Kavussanos et al. / Transportation Research Part E 68 (2014) 79–102 Table 1 Dry bulk time-charter baskets. Source: Baltic Exchange. Route weights (%)

Typical cargoes carried

Panel A: Capesize time-charter BFA basket (172,000 dwt vessels) C8_03 Gibraltar/Hamburg Trans-Atlantic round voyage C9_03 Continent/Mediterranean trip Far East C10_03 North Pacific round voyage C11_03 China/Japan trip Mediterranean/Continent

Route description

10 5 20 15

Iron ore, coal Iron ore Iron ore, coal Coal

Panel B: Panamax time-charter BFA basket (74,000 dwt vessels) P1A_03 Trans-Atlantic round voyage P2A_03 Skaw-Gibraltar/Far East P3A_03 Japan-S. Korea North Pacific round voyage P4A_03 Far East via North Pacific/Skaw-Passero

25 25 25 25

Grains, Grains, Grains, Grains,

Panel C: Supramax time-charter BFA basket (52,000 dwt vessels) S1A Antwerp–Skaw (Denmark) trip to Far East S1B Canakkale (Turkey) trip to Far East S2 Japan–South Korea/North Pacific or Australia round voyage S3 Japan–South Korea trip from Gibraltar–Skaw (Denmark) range S4A US Gulf–Skaw-Passero S4B Skaw-Passero–US Gulf

12.5 12.5 25 25 12.5 12.5

Grains, fertilizers Steel, fertilizers Fertilizers Steel Grains, Petcoke, Scrap Steel

coal, iron ore, bauxite iron ore coal, sulphure coal, sulphure

This table contains three panels whose base are the Baltic Exchange indices. Each panel comprises the routes of the index, which are used by the Baltic Exchange to create and report baskets of freight rates. These baskets of freight rates are then used as underlying commodities upon which Freight Forward Agreements (FFA) are written. The Baltic Exchange also reports average (over brokers) FFA prices, namely Baltic Forward Assessments (BFA) prices. Grains include wheat, corn and soybeans. The four time-charter routes of the Capesize basket correspond to 50% of the route weighting of the Baltic Capesize Index (BCI). The remaining 50% weight is allocated to the five voyage routes of the index – for more details see the Baltic Exchange.

the Panamax and Supramax trades. Coal futures refers to the Richards Bay All Publication Index-4 (API4) coal futures, which trade in the European Energy Exchange (EEX), and is regarded as one of the major underlying commodities of the Capesize trades. Iron ore represents the other major commodity of Capesize trades, and therefore, OTC Iron Ore Swaps (IOS) promptmonth contracts are also employed. IOS contracts are cash settled agreements between a buyer and a seller of iron ore for a specific amount of time and at a fixed price. The IOS contracts (quoted US$/mt) used are cash settled against The Steel Index (TSI) 62% Fe Fines benchmark, use as a settlement price the arithmetic average of all TSI reference prices in the expiring month, and are cleared in SGX AsiaClear and CME ClearPort. Daily prices for IOS prompt-month contracts are from their inception in 30 April 2009 to 21 March 2014, obtained from Marex Spectron Commodity Research Group.16 All commodity derivatives are quoted on free on board prices. The inclusion criteria of the aforementioned commodity derivatives in the ensuing analysis are data availability, trading activity (liquidity) and the importance (weight) of each commodity in the cargoes of each FFA basket constituent routes. Consequently, sulphur and minor commodity derivatives contracts (salt, clinker, and pet coke) do not trade in an organised exchange, and thus, were not included in the analysis. Due to the different commodities transported by the vessels corresponding to the investigated markets, the use of single commodity futures may not proxy sufficiently the actual composition of the cargoes transported in some cases. To account for the different commodities transported by the vessels of the underlying BFA baskets and routes, synthetic equally weighted commodity futures baskets are also constructed. The synthetic futures baskets comprise the major commodities transported by each vessel type. Specifically, the synthetic basket 1 consisting of wheat, corn, soybean and API4 coal futures is used as a proxy for the cargoes of the Panamax trades. The synthetic basket 2 proxy the cargo of the Supramax trade and includes wheat, corn, soybean futures. Moreover, the non-synchronous trading times between the investigated markets may induce serial correlation (predictability) in the residuals of the used models. In any given day, the European Energy Exchange – EEX closing futures prices are published at 15:30 London time (16:30 in Leipzig, Germany), the BFA prices are announced at 17:30 London time, while CME closing futures prices are published at 19:15 London time (13:15 in Chicago). Thus, the Baltic Exchange market on day t, by announcing the prices of the day before the CME market on day t, CME commodity futures prices may be able to assimilate more information than BFA forward prices, and thus, may exhibit an informational lead (predictability element) in comparison with BFA prices. Instead of using daily close-to-close prices, past literature has: (i) separated daily open-to-close prices from daily close-to-open prices; (ii) has lead the market data by one day ahead for the market that closes before the other markets; (iii) has used overlapping (rolling) multiday returns; and (iv) has reverted to lower-frequency data sets. However, all the above solutions are not suitable when returns are autocorrelated or when testing for information spillovers (predictability), and as such they are not directly comparable. Thus, in order to ensure that the spillover inferences are not biased by

16 The use of OTC swap contracts for iron ore is dictated by the fact that organised iron ore futures markets are only recently established, and as such, render any empirical investigation not feasible due to insufficient data. For example, iron ore futures were launched by the Indian Commodity Exchange (ICEX) in January 2011, by the Singapore Mercantile Exchange (SMX) in March 2012, by the CME in May 2013, and by the Dalian Commodity Exchange (DCE) in October 2013. As their data sample differs with the rest of the analysis, only the spillover results are discussed in Section 4. Their preliminary statistics tests are available from the authors upon request.

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Table 2 Descriptive statistics of daily logarithmic first-differences of FFA and commodity futures prices (05/2006–10/2009). T Panel A: FFA price series CTC 868 C4

868

C7

868

PTC

868

P2A

868

STC

868

Mean

Std

Skew

Kurt

J–B

Q(12)

Q2(12)

ARCH(5)

0.00022 [0.917] 0.00004 [0.971] 0.00023 [0.824] 0.00027 [0.872] 0.00069 [0.510] 0.00002 [0.988]

0.0620

2.644 [0.000] 0.021 [0.797] 0.763 [0.000] 1.714 [0.000] 1.152 [0.000] 5.310 [0.000]

101.445 [0.000] 16.467 [0.000] 17.664 [0.000] 88.410 [0.000] 20.288 [0.000] 151.226 [0.000]

372,776.7 [0.000] 9,795.3 [0.000] 11,355.3 [0.000] 282,792.1 [0.000] 15,060.5 [0.000] 830,228.1 [0.000]

74.221 [0.000] 231.307 [0.000] 245.594 [0.000] 33.458 [0.001] 389.584 [0.000] 46.098 [0.000]

0.521 [1.000] 23.604 [0.023] 54.311 [0.000] 0.772 [1.000] 26.597 [0.009] 0.142 [1.000]

0.049 [1.000] 17.743 [0.003] 44.362 [0.000] 0.525 [0.991] 10.760 [0.056] 0.057 [1.000]

0.611 [0.000] 0.090 [0.282] 0.114 [0.172] 0.573 [0.000] 0.269 [0.001] 0.248 [0.003]

3.959 [0.000] 1.446 [0.000] 1.232 [0.000] 2.773 [0.000] 2.277 [0.000] 2.234 [0.000]

620.08 [0.000] 76.717 [0.000] 56.661 [0.000] 325.098 [0.000] 197.735 [0.000] 189.189 [0.000]

14.381 [0.277] 12.801 [0.384] 9.959 [0.620] 13.635 [0.325] 22.129 [0.036] 22.812 [0.029]

383.779 [0.000] 40.294 [0.000] 92.899 [0.000] 145.800 [0.000] 129.028 [0.000] 122.458 [0.000]

113.643 [0.000] 16.196 [0.006] 51.562 [0.000] 53.037 [0.000] 66.895 [0.000] 64.206 [0.000]

Panel B: Commodity futures price series Coal 868 0.00029 [0.711] Corn 868 0.00043 [0.579] Wheat 868 0.00026 [0.579] Soybean 868 0.00046 [0.760] Synthetic basket 1 868 0.00039 [0.530] Synthetic basket 2 868 0.00040 [0.536]

0.0302 0.0299 0.0497 0.0308 0.0399

0.0233 0.0233 0.0252 0.0196 0.0185 0.0190

Data series are daily prices, measured in logarithmic first-differences. CTC is the Capesize BFA four time-charter average basket; C4 is the BFA for the Capesize C4 route (Richards Bay to Rotterdam); C7 is the BFA for the Capesize C7 route (Bolivar to Rotterdam); PTC is the Panamax BFA four time-charter average basket; P2A is the BFA for the Panamax P2A route (Skaw-Gibraltar range to Far East); STC is the Supramax BFA six time-charter average basket; coal is the API4 coal futures contract, traded in the European Energy Exchange (EEX); corn, soybeans and wheat are futures contracts traded in the Chicago Board of Trade (CME); synthetic basket 1 is an equally weighted index, consisting of grain (corn wheat and soybean) futures, traded in CME and API4 coal futures, traded in EEX; and synthetic basket 2 is an equally weighted index, consisting of the same grain futures as in synthetic basket 1. Figures in square brackets [.] indicate exact significance levels. T is the number of observations. Mean is the sample mean of the series. Std is the estimated standard pffiffiffi deviation. Skew ^3  Nð0; 6Þ and and under the null are T a p ffiffiffi Kurt are the estimated centralized third and fourth moments of the data; their asymptotic distributions ^4  3Þ  Nð0; 24Þ. J–B is the Jarque and Bera (1980) test for normality; the statistic is distributed as v2(2). Q(12) and Q2(12) are the Ljung–Box (1978) QT ða statistics on the first 12 lags of the sample autocorrelation function of the raw series and of the squared series, respectively; these statistics are distributed as v2(12). ARCH(5) is the Engle (1982) test for ARCH effects; the statistic is distributed as v2(5).

a non-synchronous trading problem among the markets a ‘‘time-matched’’ data set is created by intra-day data purchased from Tick Data,17 in which the prices of all commodity futures contracts at CME are retrieved on a daily basis at 17:30 (London time) to match the exact publication time of the BFA prices in London.18 Table 2 provides summary statistics of the logarithmic first-differences of FFA and commodity futures price series. Sample means are statistically zero in all cases. The most volatile series, based on the standard deviation values, are the FFA baskets, which exhibit higher (approximately double) values, compared to the standard deviations of the commodity futures series. The standard deviation of the FFA routes range somewhere between the standard deviations of FFA baskets and commodity futures series. Skewness values indicate that all series, besides route C4 and the corn and wheat futures, exhibit statistically significant (positive or negative) skewness. All series have significant excess kurtosis, with FFA excess kurtosis values being substantially higher than that of commodity futures prices. In turn, Jarque and Bera (1980) tests indicate departures from normality for all price series examined. The discrepancy between the standard deviation and kurtosis values among the FFAs and commodity futures series highlight the difference in terms of the distributional attributes of these markets. The Ljung–Box Q-statistic (Ljung and Box, 1978) based on up to 12 lags of the sample autocorrelation function indicates strong serial dependence in all FFA price series, but no serial correlation in the commodity futures series. The Ljung–Box Q-statistic, applied on the squared series, and the ARCH test (Engle, 1982) indicate existence of heteroscedasticity and ARCH effects, respectively in all commodity futures series and only in route-specific FFA series. No ARCH effects are evidenced in the case of FFA baskets, where their variances appear to be homoskedastic.

17 Tick Data offers inter-day (tick-by-tick) historical data for equity, options, futures, cash index, and market indicators. They collect data directly from official exchange archives after the close. Several data validation processes are applied to filter any data inconsistencies. Futures data start from 1974 and include minutes and seconds time stamps data. Tick Data offers 13 currency futures, 44 equity index futures, 29 interest rate futures, 10 metal futures, 14 energy futures, 6 food and fibre futures, 11 grain futures, 4 meat futures, and 1 commodity index futures. For more details see: www.tickdata.com. 18 Unfortunately, this procedure cannot be applied to EEX coal data as they are reported before the BFA prices on any given day and thus the closing prices of each day are used in the ensuing analysis.

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Table 3 reports unit root tests for the FFA and commodity futures price series. The Augmented Dickey–Fuller (ADF, 1981) and Phillips and Perron (PP, 1988) conventional tests, applied on the log-levels and log-first differences of all price series, reveal that all variables are log-first difference stationary, all having a unit root on the log-levels representation. The Kwiatkowski et al. (KPSS, 1992) test also provides support for the log-first difference stationary assumption. Regarding the unit root testing in the presence of breaks, Lee and Strazicich (2003, 2004) test results indicate that the hypothesis of a unit root with break(s) cannot be rejected for all of the employed logarithmic price series. Thus, all series considered are non-stationary on the log-level representation.19 As different markets have different speeds of adjustment and reaction to breaks induced by shocks into the economic system, and since the break points are estimated endogenously in the two Lee and Strazicich models, it is expected that the break points may differ across the markets. However, it seems that in the freight derivatives market a break, in most of the series, occurs unanimously between the two models around May-June 2008, when the freight markets collapsed. The P2A route is the only FFA series that exhibits two structural breaks (the B1t and B2t dummy variables are significant at 10% and 5% significance levels, respectively). The first break occurs nearby the end of 2007 (together with the statistical significant breaks in the CTC and STC baskets), when the sub-prime crisis was initiated in the US. The second break occurs in the middle of 2008 (together with a significant break in route C4), when freight prices had reached an all-time high record level, due to market expectations for a buoyant future demand for seaborne transportation services and subsequently fell to times their previous values in the space of just a few months. In contrast, all commodity futures series (including the two synthetically constructed baskets), besides the coal series, exhibit two significant break points, the first occurring between the end of 2007 to early 2008, when the sub-prime crisis showed in its full extent, and the second occurring between the end of 2008 to early 2009, when commodity market prices started to pick up. The commodity boom is expected to have enhanced the strengths of the economic relationships between the investigated variables, making structural breaks easier to be exposed. For a review of the commodities futures literature see Skiadopoulos (2013). Johansen’s cointegration tests, reported in Table 4, show that in three out of the fifteen FFA and commodity futures pairs a cointegrating (long-run equilibrium) relationship exists. These are the Capesize (CTC basket, C4 and C7 routes) series with the coal futures (API4) series. The Schwartz Bayesian Information Criterion (SBIC), used to determine the lag length of the VAR models, indicates two lags in all cases. As mentioned earlier, the Johansen’s test can be misleading in the presence of structural breaks, as it may incorrectly accept the null of no cointegration, when in fact cointegration with a structural break exists. For this purpose the Gregory and Hansen (1996) test for cointegration is employed in the cases where cointegration with the Johansen test is not found. The former tests the null of no cointegration against the alternative of cointegration with a possible break. The test reveals that cointegration, in the presence of structural change, exists in five additional pairs of FFA with commodity futures series. These are the PTC basket, the STC basket and route P2A with soybean futures, the PTC basket with the synthetic 1 futures basket and the STC basket with the synthetic 2 basket. In all cases, the time of the break is situated around December 2007, which coincides with the start of the global financial crisis. Moreover, the coefficients of the cointegrating vector are statistically significant in all cases according to the t-statistics. On the other hand, none of the wheat and corn commodity futures markets are cointegrated with the freight derivatives markets by either the Johansen (1988) or the Gregory and Hansen (1996) tests. A possible explanation for this could be the existence of excessive speculation in one contract market but not in the other, driving the long-run relationship away from its equilibrium (cointegrated) level. Overall, cointegration results seem to be related with the type and importance of commodity cargoes transported by each type of vessel.20 For instance, all FFA prices are cointegrated with coal and soybean futures, which constitute major commodities in the Capesize and Panamax/Supramax trades, respectively. The same holds between the time-charter FFA baskets and the synthetic commodity baskets, being aggregate ‘‘indices’’ of major time-charter freight rates and commodity prices, respectively. On the other hand, after examining the structural stability of the systems, it can be robustly stated that there is no evidence of cointegration between wheat and corn futures and their respective FFAs. This result can be due to the lesser importance of these commodities in the relevant physical trades. The extant literature on whether cointegration between interrelated futures markets exists is contentious. Among the studies that find cointegration between futures markets is that of Liu (2005) on (corn, hog and soybean) commodity futures, while studies that report no evidence of cointegration between futures markets include those of Low et al. (1999) on commodity futures and Chulia and Torro (2008) on stock and bond futures markets, among others. The next section examines the informational spillovers between the investigated FFA and commodity futures markets. 4. Spillover empirical results 4.1. Spillovers under cointegrated relationships Table 5 presents the return and volatility spillover results for the pairs of FFA and commodity futures prices that stand in a long-run (cointegrating) relationship. For the Capesize trades (CTC–Coal, C4–Coal, and C7–Coal) and the STC–Soybean pair 19 It has to be noted that comparison of prices, instead of returns, of the investigated variables in the ensuing analysis may yield more indicative results in relation to the economic theory described. However, the non-stationary behaviour of the price series (see Section 3) would render the results questionable, due to spurious regressions. 20 It should be noted that for the cases that a cointegrating relationship is not found, economic shocks in the market could lead commodity futures (FFA) prices to follow an opposite direction than FFA (commodity futures) prices.

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Table 3 Unit root tests of FFA and commodity futures prices (05/2006–10/2009). ADF Levels CTC

C4

C7

PTC

P2A

STC

Coal

Corn

Wheat

Soybean

Synthetic basket 1

Synthetic basket 2

PP 1st Levels Differences

1.276 22.284 (1) (0)

1.172 21.331 (1) (0)

1.330 14.845 (2) (1)

1.006 23.506 (1) (0)

1.301 14.529 (2) (1)

0.828 24.239 (1) (0)

1.132 28.296 (0) (9)

1.634 27.598 (0) (0)

1.602 28.878 (0) (0)

1.518 28.943 (0) (0)

1.493 29.531 (0) (0)

1.535 29.780 (0) (0)

1.280 (9)

1.306 (12)

1.470 (16)

1.168 (14)

1.361 (15)

1.005 (14)

1.261 (0)

1.758 (10)

1.580 (6)

1.573 (9)

1.537 (10)

1.566 (10)

KPSS 1st Levels Differences 22.297 (4)

21.720 (7)

23.005 (13)

24.583 (12)

20.619 (12)

25.628 (13)

28.497 (8)

27.742 (9)

28.884 (7)

28.985 (8)

29.577 (10)

29.797 (10)

0.713 (23)

0.771 (23)

0.654 (23)

0.848 (23)

0.723 (23)

0.918 (23)

1.080 (23)

1.037 (23)

0.939 (23)

1.857 (23)

1.418 (23)

1.419 (23)

LS two breaks in intercept

LS one break in intercept

TB1{k1} TB2{k2} B1t

B2t

LM test statistic

417 {0.5} 24/12/ 07 379 {0.4} 31/10/ 07 379 {0.4} 31/10/ 07 425 {0.5} 08/01/ 08 392 {0.5} 19/11/ 07 417 {0.5} 24/12/ 07

545 {0.6} 30/06/ 08 540 {0.6} 23/06/ 08 524 {0.6} 30/05/ 08 609 {0.7} 29/09/ 08 524 {0.6} 30/05/ 08 545 {0.6} 30/06/ 08

2461.7

7364.6*

1.659 (8)

(0.722)

(2.201)

395 {0.5} 22/11/ 07 544 {0.6} 27/06/ 08 323 {0.4} 13/08/ 07 477 {0.5} 20/03/ 08 477 {0.5} 20/03/ 08 477 {0.5} 20/03/ 08

563 {0.6} 24/07/ 08 680 {0.8} 09/01/ 09 589 {0.7} 01/09/ 08 620 {0.7} 14/10/ 08 636 {0.7} 05/11/ 08 680 {0.8} 09/01/ 09

*

0.533

3.947

(0.778)

(5.494)

0.858

1.097

(1.270)

(1.576)

1511.5

5034.7*

(1.360)

(4.238)

***

*

1888.1

5149.6

(1.676)

(4.330)

1959.6*

860.06

(2.309)

(1.020)

4.604***

3.310

(2.001)

(1.392)

27.780* 31.864*

545 {0.6} 30/06/ 08 1.892 (9) 540 {0.6} 23/06/ 08 1.894 (9) 533 {0.6} 12/06/ 08 1.366 (10) 568 {0.7} 01/08/ 08 1.559 (4) 524 {0.6} 30/05/ 08 1.133 (5) 545 {0.6} 30/06/ 08

1819.6

1.480 (5)

6.455*

1.731 (4)

(2.827) (3.299) 42.005

*

(2.270)

*

48.831

(4.764) *

1.523 (0)

(2.638)

102.095* 57.721*

1.739 (6)

(2.723) ***

54.407

21.689

(5.040)

(2.040)

72.280*

50.172*

(5.125)

(3.665)

TB1{k1} B1t

1.514 (6)

1.580 (6)

599 {0.7} 15/09/ 08 589 {0.7} 01/09/ 08 589 {0.7} 01/09/ 08 599 {0.7} 15/09/ 08 571 {0.7} 05/08/ 08 599 {0.7} 15/09/ 08

LM test statistic 1.545 (8)

(0.534) 3.930*

1.829 (9)

(5.474) 0.038

1.840 (9)

(0.055) 1016.4 1.152 (5) (0.853) 5001.4*

1.465 (4)

(4.210) 944.69 1.070 (5) (1.119) 1.416 (5)

(2.773) 34.608* 1.659 (4) (3.561) 48.907* 1.452 (0) (2.636) 77.823* 1.660 (6) (3.663) 32.648* 1.422 (8) (3.056) 44.834* 1.446 (6) (3.227)

ADF is the Augmented Dickey Fuller (1981) test. The ADF regressions include an intercept term; the lag-length of the ADF test (in parentheses) is determined by minimising the SBIC (1978). PP is the Phillips and Perron (1988) test; the truncation lag for the test is in parentheses. Levels and 1st Differences correspond to price series in log-levels and log-first differences, respectively. The 95% critical value for the ADF and PP tests is 2.86. KPSS is the Kwiatkowski et al. (1992) unit root test; the critical values are 0.463 and 0.347 for the 5% and 10% levels, respectively. LS is the Lee and Strazicich (2003) test for one and two structural breaks in the intercept. TBi is the number of the observation that the structural break i occurs and figures in curly brackets {} indicate the percentage of the data that the break occurs (i.e. ki = TBi/T, where T is the total number of observations in the sample). Under the TBi, the date of the break is also displayed. Bit is the dummy variable for the ith structural break in the intercept, which is standard normally distributed. Figures in parentheses are t-statistics. The lag-length of the LS test (in parentheses) is determined by the ‘‘general-to-specific’’ method of Lee and Strazicich (2003). The 5% and 10% critical values for the LS test with one structural break are 3.566 and 3.211, while those for two structural breaks are 3.842 and 3.504, respectively. * Significance at the 5% significance levels. *** Significance at the 10% significance levels.

an asymmetric VECM-EGARCH process is found to provide a better fit to the data, while for the PTC–Soybean pair a VECMGJR-GARCH process best fits the data, all eliminating any asymmetries, as shown by the Engle and Ng (1993) test statistics (sign bias, negative size bias, positive size bias and the joint test of sign and size bias) presented in panel C of the same table.

Table 4 Cointegration Tests between FFA and Commodity Futures Prices. Price Series

Lags

Johansen kmax

2

C4–Coal

2

C7–Coal

2

PTC–Corn

2 [4, 4]

PTC–Wheat

2 [1, 1]

PTC–Soybean

2 [0, 0]

PTC–Synthetic 1

2 [0, 0]

P2A–Corn

2 [6, 6]

P2A–Wheat

2 [1, 1]

P2A–Soybean

2 [6, 6]

P2A–Synthetic 1

2 [4, 4]

STC–Corn

2 [3, 3]

STC–Wheat

2 [1, 0]

STC–Soybean

2 [0, 0]

STC–Synthetic 2

2 [0, 0]

Estimated cointegrating vector

Johansen (J): b0 = [1, b1, b2]

H0

H1

H0

H1

Zt⁄{k}

Zt⁄{k}

r=0 r61

r=1 r=2

r=0 r61

rP1 r=2

C

C/S

–

–

[1,

–

–

[1,

–

–

[1,

2.69 {0.50} 3.36 {0.46} 4.98* {0.48} 4.67* {0.48} 2.84 {0.51} 3.27 {0.68} 4.67* {0.48} 4.21 {0.49} 2.68 {0.50} 3.39 {0.47} 4.78* {0.48} 4.61* {0.48}

2.65 {0.50} 3.38 {0.47} 5.01* {0.48} 4.79*** {0.48} 2.85 {0.70} 3.50 {0.70} 4.67 {0.48} 4.21 {0.47} 2.63 {0.50} 3.47 {0.70} 4.77*** {0.48} 4.60 {0.48}

25.80 8.82 26.25 7.29 25.77 7.14 10.65 2.30 7.02 1.07 7.13 2.11 9.19 2.27 10.33 2.39 8.07 1.52 6.28 2.28 9.03 2.13 13.23 2.66 8.72 1.01 8.48 2.33 10.34 2.31

34.62 8.82 33.53 7.29 32.91 7.14 12.94 2.30 8.09 1.07 9.24 2.11 11.46 2.27 12.72 2.39 9.59 1.52 8.57 2.28 11.16 2.13 15.89 2.66 9.73 1.01 10.81 2.33 12.65 2.31

b1,

b2

1,491.2 (5.20) 0.37 (5.33) 0.40 (5.58)

34,783.2] (1.44) 5.16] (0.88) 6.18] (1.03)

Gregory–Hansen (C): [1, a1, a2, b1]

a1

a2

b1

41,082.3 (21.26) 37,127.2 (22.18)

53,075.8 (41.03) 41,959.6 (40.50)

113.39] (47.39) 191.68] (52.58)

[1,

50,171.7 (22.38)

51,729.1 (34.45)

129.14] (46.50)

[1,

26,919.7 (17.67) 25,336.5 (19.54)

41,468.9 (40.72) 32,981.4 (41.72)

86.38] (45.85) 116.00] (52.82)

[1, [1,

[1,

Gregory–Hansen (C/S): [1, a1, a2, b1,b2]

[1, [1,

[1,

a1

a2

b1

b2

44,544.2 (14.44) 43,753.1 (15.84)

46,584.1 (10.03) 30,883.4 (8.00)

117.93 (29.70) 207.18 (32.91)

7.18] (1.45) 22.97] (2.99)

– 

– 

– 

– 

25,722.8 (10.62) – –

43,639.8 (11.91) – –

84.79 (27.24) – –

2.44] (0.63) – –

M.G. Kavussanos et al. / Transportation Research Part E 68 (2014) 79–102

CTC–Coal

Gregory–Hansen ktrace

Lags is the lag length of the Vector Autoregressive (VAR) models used for the Johansen’s (1981) test, while figures in squared brackets [] indicate the lag length of the C and C/S Gregory and Hansen (1996) tests, respectively; the lag length for the Johansen test is determined by minimising the SBIC (1978), while for the Gregory and Hansen tests it is determined by setting a maximum lag length of six and following a downward t-test for the significance of additional terms. r represents the number of cointegrating vectors. ^ ki , in the kmax and ktrace cointegration tests, are the estimated eigenvalues of the P matrix in Eq. (8). Estimates of the coefficients in the cointegrating vector are normalised with respect to the coefficient of the FFA price. Figures in parentheses () indicate t-statistics of the cointegrating vector’s coefficients. Critical values for the kmax and ktrace statistics are 20.26 (17.98) and 15.89 (13.91) for the null hypothesis and 9.16 (7.56) for the alternative hypothesis at the 5% (10%) significance levels. C, C/S stand for the level shift, and the regime shift models, respectively, of the Gregory and Hansen (1996) cointegration test. Curly brackets indicate the percentage of the data that the break occurs; critical values for the Zt⁄ are 4.61 (4.34), 4.95 (4.68) at the 5% (10%) significance level for the C and C/S models, respectively. The coefficients a1, a2, b1, b2 are the cointegrating coefficients of the intercept, the intercept dummy, the commodity futures variable and the regime shift dummy, respectively. See notes in Table 2 for the notation of the price series. * Significance at the 5% significance level. *** Significance at the 10% significance level.

91

Ht ¼ A0 A þ B0 Ht1 B þ C 0 et1 e0t1 C þ S10 u1;t1 u01;t1 S1 þ S20 u2;t1 u02;t1 S2 þ E0 ðzt1 Þ2 E

92

Table 5 Maximum-likelihood estimates of restricted BEKK VECM-GARCH models. P Pp1 DFFAt ¼ p1 a DFFAti þ i1 bFFA;i DFUTti þ qFFA zt1 þ e1;t ð10aÞ i1 FFA;i Pp1 P DFUTt ¼ i1 aFUT;i DFFAti þ p1 b D FUT þ q z þ e ð10bÞ 2;t ti FUT t1 i1 FUT;i ð11Þ

Ht ¼ exp½A0 A þ B0 Ht1 B þ C 0 et1 e0t1 C þ D0 et1 e0t1 D þ S10 u1;t1 u01;t1 S1 þ S20 u2;t1 u02;t1 S2 þ EC0 ðzt1 Þ2 EC 0

0

Ht ¼ A A þ B Ht1 B þ C

0

e

0 t1 t1 C

e

0

þD

ft1 f0t1 D

þ S1

0

u1;t1 u01;t1 S1

VECM-EGARCH(1, 1) CTC

aj,i, j = FFA, FUT i = 1, 2

bj,i, j = FFA, FUT i = 1, 2 Wald Test

u2;t1 u02;t1 S2

ðin CTC; C4; C7 with coalÞ

ðin PTC with soybeanÞ

VECM-EGARCH(1, 1)

ð12Þ

ð14Þ VECM-EGARCH(1, 1)

VECM-GJR-GARCH(1, 1)

Coal

C4

Coal

C7

Coal

PTC

Soybean

7.371E08*

1.299E04

2.979E04*

1.367E04***

3.081E04*

4.318E07*

1.921E07* (2.757)

(4.644)

(1.614)

(4.559)

(1.714)

(4.770)

(2.482)

(1.921) 0.161*

0.009

0.281*

0.040

0.213*

0.046***

0.123*

0.015

(4.704) 

(0.676) 

(6.294) 0.173* (5.087) 0.050 (1.204)

(1.691) 0.024 (0.872) 0.055 (1.622)

(1.100) 

0.049 (1.454)

(1.448) 0.036 (1.312) 0.054 (1.597)

(3.616) 

0.027 (0.299)

(8.220) 0.117* (3.428) 0.042 (0.997)

0.218* (2.536)

0.028 (0.825)

0.014 [0.907]

0.025 [0.875]

1.002 [0.317]

0.089 [0.765]

1.169 [0.280]

0.462 [0.497]

8.365 [0.004]

0.445 [0.505]

0.970* (31.78) 0.053 (1.075) 0.1819 (1.470) 0.0001 (1.154) 1.655*** (1.788) 

0.4332* (5.371) 0.0534*** (1.864) 0.4452* (3.849) 0.936* (82.37) 0.151* (2.510) 0.0051 (0.172) 0.002 (1.403) 0.293 (1.361) 

0.942* (63.64) 0.150* (3.258) 0.1750* (3.668) 0.003* (3.194) 0.710* (2.235) 

0.0683 (1.301) 0.0565 (1.312) 0.2140* (2.839) 0.986* (131.8) 0.166* (2.996) 0.0699* (4.337) 0.001 (1.469) 0.004 (0.031) 

0.0524*** (1.913) 0.0557 (1.385) 0.2072 (0.819) 0.989* (44.287) 0.034* (3.353) 0.0545 (0.911) 

0.973* (30.83) 0.026* (2.787) 0.008 (0.815) 





Panel B: Conditional variance parameters 1.1150* (2.472) 0.0255 (0.959) 0.2291 (0.992) bkk, k = 1, 2 0.826* (11.560) ckk, k = 1, 2 0.021 (0.689) si, i = 1, 2 0.0175 (0.978) eci, i = 1, 2 0.0001* (2.222) dii, i = 1, 2 2.053 (1.265)  gii, i = 1, 2

x11 x21 x22

Panel C: Diagnostic tests on standardised residuals Log-Likelihood 3707 Skewness 1.245 [0.000] 0.020 [0.809] Kurtosis 26.252 [0.000] 2.742 [0.000] J–B 25,061.6 [0.000] 271.05 [0.000] Q(12) 13.861 [0.241] 9.296 [0.595] Q2(12) 0.801 [1.000] 18.684 [0.067] ARCH(12) 0.041 [0.839] 0.066 [0.797] SBIC 7271 Sign bias 0.232 [0.817] 1.620 [0.106]

4109 0.815 [0.000] 14.595 [0.000] 7772.6 [0.000] 26.597 [0.005] 4.096 [0.967] 0.032 [0.859] 8075 0.873 [0.383]

0.155 [0.063] 3.005 [0.000] 328.97 [0.000] 10.009 [0.530] 4.913 [0.935] 0.098 [0.755] 1.806 [0.071]

4229 0.081 [0.331] 11.566 [0.000] 4822.1 [0.000] 28.038 [0.003] 5.463 [0.907] 1.093 [0.296] 8317 1.489 [0.137]

0.970* (101.3) 0.124* (3.201) 0.1265* (2.903) 0.002* (3.317) 0.709* (2.332) 

0.118 [0.156] 2.874 [0.000] 299.69 [0.000] 11.881 [0.373] 5.556 [0.901] 1.221 [0.269] 1.892 [0.059]

*

3.909 (4.849) 4035 0.588 [0.000] 24.737 [0.000] 22,069 [0.000] 11.981 [0.365] 4.205 [0.963] 0.324 [0.985] 7929 0.161 [0.872]

0.257*** (1.647)

0.267 [0.001] 1.419 [0.000] 82.765 [0.000] 13.769 [0.246] 13.256 [0.277] 1.159 [0.308] 0.328 [0.743]

M.G. Kavussanos et al. / Transportation Research Part E 68 (2014) 79–102

Panel A: Conditional mean parameters qj, j = FFA, FUT 8.118E08***

þ S2

0

Negative size bias Positive size bias Joint bias test

0.792 [0.429] 0.689 [0.491] 0.351 [0.789]

0.581 [0.561] 1.004 [0.316] 2.086 [0.101]

1.248 [0.213] 0.073 [0.942] 1.524 [0.207]

Synthetic 1 1.908E07*

VECM-GARCH(1, 2) PTC Panel A: Conditional mean parameters qj, j = FFA, FUT 3.245E07***

0.245 [0.807] 0.343 [0.731] 1.693 [0.167]

0.356 [0.722] 1.179 [0.239] 1.277 [0.281]

0.385 [0.700] 0.582 [0.561] 1.614 [0.185]

0.115 [0.885] 0.933 [0351] 0.313 [0.815]

P2A

Soybean

STC

Soybean

STC

Synthetic 2

2.513E07*

1.480E07* (2.436)

3.751E07* (2.117)

2.670E07* (3.031)

3.659E07*** (1.815)

2.719E07* (2.814)

VECM-GARCH(1, 1)

VECM-EGARCH(1, 1)

0.943 [0.346] 1.428 [0.154] 1.123 [0.339]

VECM-GARCH(1, 1)

(2.635) (3.009) aj,i, j = FFA, FUT i = 1, 2

0.015 (1.212)

0.386* (11.357)

0.047*** (1.883)

0.119*

0.018

0.126*

0.023

  0.247* (2.708)

  1.740E03 (0.051)

0.075* (2.069) 0.086* (2.535) 0.128* (2.711)

0.012 (0.461) 0.041*** (1.668) 0.028 (0.809)

(3.519)   0.184* (2.672)

(1.052)   0.027 (0.773)

(3.693)   0.223* (3.119)

(1.407)   0.012 (0.344)

6.278 [0.012]

0.228 [0.633]

13.315 [0.001]

0.211 [0.899]

12.816 [0.001]

0.001 [0.974]

10.771 [0.001]

0.077 [0.782]

0.0092* (5.426) 0.0018* (3.429) 0.0004 (0.432) 0.028 (1.268) 2.235* (6.711)  8.271E04 (0.008) 1.548E05* (2.695)

0.975* (171.63) 0.189* (7.984)  0.2498* (2.797) 2.070E06* (3.331)

Panel B: Conditional variance parameters x11 0.0121* (4.030) x21 0.0024* (2.769) x22 0.0005 (0.582) bkk, k = 1, 2 0.0031 (0.050) ckk, k = 1, 2 0.593* (3.446) 0.025 (0.657) si, i = 1, 2 0.0159 (0.886) eci, i = 1, 2 0.0270E04*

0.960* (77.66) 0.053 (0.890) 0.229* (5.847) 1.2214* (2.484) 0.010E05

(2.866) dii, i = 1, 2



(0.961) 

Panel C: Diagnostic tests on standardised residuals Log-Likelihood 3815 Skewness 1.578 [0.000] 0.085 [0.307] Kurtosis 47.496 [0.000] 1.242 [0.000] J–B 81,664 [0.000] 56.611 [0.000] Q(12) 7.268 [0.777] 14.150 [0.205] Q2 (12) 0.889 [0.999] 9.693 [0.558] ARCH(12) 0.079 [0.999] 0.772 [0.679] SBIC 7,488 8,353 Sign bias 1.959 [0.051] 0.170 [0.865] Negative size bias 0.301 [0.764] 0.110 [0.912] Positive size bias 0.725 [0.469] 1.267 [0.206] Joint bias test 1.339 [0.260] 0.743 [0.527]

1.653E05 (0.211) 1.674E04 (1.036) 1.694E03* (3.490) 0.992* (387.94) 0.967* (192.99) 0.087* (2.295) 0.223* (9.212)   0.0710* (3.022) 2.86E05 (4.5E05) 2.244E07* 6.933E08*** (1.738) (5.940)

0.0491* (1.411) 0.0521 (1.682) 0.0025 (0.0683) 0.994* (299.03) 0.042* (2.229)  0.2113* (4.728) 2.357E06* (2.454)

0.996* (202.63) 0.097* (3.202)  0.0884* (3.862) 1.125E06 (1.634)





0.766* (4.858)

0.064 (0.525)

4254 0.758 [0.000] 17.305 [0.000] 10,851 [0.000] 14.845 [0.190] 4.875 [0.937] 0.375 [0.972] 8,448 0.205 [0.837] 1.139 [0.255] 0.431 [0.667] 0.609 [0.609]

0.341 [0.000] 2.117 [0.000] 177.87 [0.000] 12.345 [0.338] 9.749 [0.553] 0.811 [0.639] 8,142 0.176 [0.860] 0.852 [0.394] 1.249 [0.212] 0.981 [0.401]

4295 0.130 [0.112] 17.646 [0.000] 11,211 [0.000] 19.539 [0.052] 9.001 [0.622] 0.789 [0.662]

0.056 [0.501] 1.824 [0.000] 120.18 [0.000] 11.891 [0.372] 10.472 [0.489] 0.852 [0.596]

4142 1.147 [0.000] 36.535 [0.000] 48,242 [0.000] 27.569 [0.004] 1.358 [0.999] 0.122 [0.999]

0.118 [0.157] 1.254 [0.000] 58.609 [0.000] 19.365 [0.0648] 11.237 [0.424] 0.913 [0.533]

0.207 [0.836] 0.418 [0.676] 0.855 [0.393] 0.348 [0.790]

0.565 [0.573] 1.484 [0.138] 1.286 [0.199] 1.272 [0.283]

0.365 [0.715] 0.059 [0.953] 0.386 [0.699] 0.080 [0.971]

0.263 [0.792] 0.057 [0.954] 1.602 [0.109] 1.167 [0.321]

93

All variables are in natural logarithms. Figures in parentheses () and in squared brackets [] indicate t-statistics and exact significance levels, respectively. In all FFA and commodity futures pairs, the GARCH models are estimated utilising the QMLE, while the Broyden et al. (BFGS) algorithm is used. qt1 represents the lagged ECT (qt1 = b0 Xt1). Wald Test is the causality test, distributed as v2(n), where n is the number of lags in the VECM specification. dii and gii are the asymmetry coefficients of the EGARCH and GJR models, respectively. J–B is the Jarque and Bera (1980) normality test. Q(12) and Q2(12) are the Ljung–Box (1978) tests for 12th order serial correlation in the standardised residuals and heteroskedasticity in the standardised squared residuals, respectively. ARCH(12) is Engle’s (1982) F-test for ARCH effects. SBIC is the Schwartz Bayesian Information Criterion (1978). The Bias test statistics for the Engle and Ng (1993) tests are the t-ratio of b in the regressions:   þ u2t ¼ a0 þ bY t1 þ xt (sign bias test); u2t ¼ a0 þ bY t1 þ et1 þ xt (negative size bias test); u2t ¼ a0 þ bY t1 þ et1 þ xt (positive size bias test), where u2t are the squared standardised residuals (e2t =ht ). Y  t1 is a   þ dummy variable taking the value of one when et1 is negative and zero otherwise, and Y þ ¼ 1  Y . The joint bias test is based on the regression u2t ¼ a0 þ b1 Y  t1 t1 t1 þ b2 Y t1 et1 þ b3 Y t1 et1 þ xt . The joint test H0: b1 = b2 = b3 = 0, is an F-test with 95% critical value of 2.60. See notes in Table 2 for the notation of the price series. * Significance at the 5% significance levels. *** Significance at the 10% significance levels.

M.G. Kavussanos et al. / Transportation Research Part E 68 (2014) 79–102

bj,i, j = FFA, FUT i = 1, 2 Wald Test

(1.687) 0.130* (3.862)

0

0

Ht ¼ A A þ B Ht1 B þ C

0

0 t1 t1 C

e

e

þ S1

0

u1;t1 u01;t1 S1

þ S2

0

u2;t1 u02;t1 S2

0

Ht ¼ A A þ B Ht1 B þ C

0

0 t1 t1 C

e

e

þD

0

ft1 f0t1 D

0

þ S1

u1;t1 u01;t1 S1

VAR(1)-GJR-GARCH(1, 1) PTC

bj,i, j = FFA, FUT i = 1, 2 Wald Test

0.182⁄ (2.482) 6.375 [0.011]

Panel B: Conditional variance parameters a11 0.0252⁄ (5.162) a21 0.0009 (0.911) a22 0.0049⁄ (3.796) bkk, k = 1, 2 0.013 (0.108) ckk,1, k = 1, 2 0.496⁄ (2.417)  si, i = 1, 2 dii, i = 1, 2 gii, i = 1, 2

ð10bÞ

0

þ S2

u2;t1 u02;t1 S2

ð11Þ

ðin P2A with cornÞ

ðin PTC with cornÞ

ð12Þ

ð14Þ

VAR(1)-GARCH(1, 2)

VAR(2)-EGARCH(1, 1)

VAR(2)-GARCH(1, 2)

Corn

PTC

Wheat

P2A

Corn

P2A

Wheat

0.021 (1.351) 

0.133⁄ (3.957) 

0.015 (0.851) 

0.035 (0.1.03) 1.836 [0.175]

0.165⁄ (2.481) 6.329 [0.011]

0.019 (0.568) 0.729 [0.393]

0.404⁄ (11.968) 0.107⁄ (3.148) 0.057 (1.409) 2.915 [0.232]

0.071⁄ (2.496) 0.035 (1.241) 0.038 (1.104) 6.279 [0.043]

0.406⁄ (11.970) 0.105⁄ (3.114) 0.064⁄⁄⁄ (1.748) 2.815 [0.093]

0.046 (1.455) 1.492 (0.136) 0.019 (0.557) 0.857 [0.355]

0.0195⁄ (6.507) 0.0009 (1.066) 0.0044⁄ (2.899) 0.222 (0.682) 0.403⁄ (3.397) 0.306 (1.111) 0.0643⁄ (2.513) 

0.947⁄ (44.627) 0.139 (1.034) 0.216⁄⁄⁄ (1.759) 0.5567⁄ (1.975) 





0.956⁄ (54.173) 0.093 (0.979) 

1.204E05 (1.497E04) 

1.364⁄ (3.136) 

2.442 (3.627)

0.251 (3.256)

Panel C: Diagnostic tests on standardised residuals Log-Likelihood 3532 Skewness 2.034 [0.000] 0.124 [0.138] Kurtosis 57.492 [0.000] 1.339 [0.000] J–B 11,972 [0.000] 66.881 [0.000] Q(12) 10.409 [0.494] 10.222 [0.510] 2 Q (12) 0.504 [0.999] 3.550 [0.981] ARCH(12) 0.045 [1.000] 0.272 [0.993] SBIC 6,963 6,775 Sign bias 0.017 [0.986] 0.751 [0.453] Negative size bias 0.121 [0.904] 0.909 [0.363]

0.0253⁄ (2.299) 0.0009 (0.967) 0.0047⁄ (2.122) 0.0001 (0.011) 1.818 (1.023) 0.008 (0.208) 0.0265 (1.312) 

0.946⁄ (28.777) 0.008 (0.096) 0.260⁄ (4.317) 1.0158⁄ (3.494) 





3438 2.937 [0.000] 75.525 [0.000] 20,682 [0.000] 8.724 [0.404] 0.512 [0.999] 0.046 [1.000] 8,019 1.204 [0.229] 0.208 [0.835]

0.234 [0.154] 0.703 [0.000] 25.683 [0.000] 7.469 [0.759] 15.709 [0.152] 1.311 [0.206] 7,631 1.088 [0.277] 1.145 [0.253]

0.0100 (0.563) 0.0018 (0.056) 0.2961⁄ (2.052) 0.997⁄ (461.97) 0.038⁄ (2.089) 

0.959⁄ (50.509) 0.006 (0.183) 

0.0016 (0.202) 1.358 (1.244) 

0.0352 (1.585) 9.030 (0.210) 

4073 1.024 [0.000] 13.653 [0.000] 6,862 [0.000] 14.508 [0.206] 4.199 [0.964] 0.342 [0.981]

0.049 [0.550] 1.380 [0.000] 68.919 [0.000] 8.324 [0.684] 8.965 [0.625] 0.668 [0.783]

3879 0.837 [0.000] 27.362 [0.000] 27,053 [0.000] 14.534 [0.205] 2.795 [0.993] 0.221 [0.997]

0.237 [0.005] 0.661 [0.000] 23.813 [0.000] 7.845 [0.727] 16.925 [0.110] 1.369 [0.175]

0.939 [0.348] 0.777 [0.438]

1.001 [0.317] 0.957 [0.339]

0.919 [0.358] 0.392 [0.695]

0.585 [0.559] 1.371 [0.171]

M.G. Kavussanos et al. / Transportation Research Part E 68 (2014) 79–102

Panel A: Conditional mean parameters aj,i, j = FFA, FUT 0.129⁄ i = 1, 2 (3.855) 

ð10aÞ

ðwithout an squared ECT termÞ

Ht ¼ exp½A0 A þ B0 Ht1 B þ C 0 et1 e0t1 C þ D0 et1 e0t1 D þ S10 u1;t1 u01;t1 S1 þ S20 u2;t1 u02;t1 S2 0

94

Table 6 Vector Autoregressive (VAR) restricted BEKK-GARCH parameter estimates. P P DFFAt ¼ p1 a DFFAti þ p1 b DFUTti þ qFFA zt1 þ e1;t ðwithout an ECT termÞ i1 FFA;i i1 FFA;i P Pp1 DFUTt ¼ p1 a D FFA þ b DFUTti þ qFUT zt1 þ e2;t ðwithout an ECT termÞ ti i1 FUT;i i1 FUT;i

Positive size bias Joint bias test

0.209 [0.835] 0.022 [0.996]

1.269 [0.205] 0.643 [0.587]

0.577 [0.564] 0.512 [0.674]

0.720 [0.472] 0.509 [0.677]

1.339 [0.181] 1.244 [0.292]

1.310 [0.191] 0.643 [0.587]

VAR(1)-GJR-GARCH(1, 1)

VAR(1)-GARCH(1, 2)

P2A

Synthetic 1

STC

Corn

STC

Wheat

Panel A: Conditional mean parameters aj,i, j = FFA, FUT 0.392⁄ (11.516) i = 1, 2 0.078⁄ (2.121) 0.084⁄ (2.486) bj,i, j = FFA, FUT 0.129⁄ (2.586) i = 1, 2 0.064 (1.128) 0.065⁄⁄⁄ (1.651) Wald Test 8.995 [0.011]

0.049⁄ (2.129) 0.013 (0.541) 0.035 (1.495) 0.011 (0.317) 0.052 (1.513) 0.058⁄⁄⁄ (1.698) 3.952 [0.139]

0.123⁄ (3.666) 

0.026 (1.326) 

0.129⁄ (3.825) 

0.126⁄ (3.754) 

0.167⁄ (2.845)   8.154 [0.004]

0.035 (1.013)   1.759 [0.185]

0.088⁄⁄⁄ (1.658)   10.629 [0.005]

0.161⁄ (3.013)   3.188 [0.203]

Panel B: Conditional variance parameters a11 0.0176⁄ (2.911) a21 0.0004 (0.938) a22 0.0028⁄ (3.961) bkk, k = 1, 2 0.584⁄⁄⁄ (1.834) ckk,1, k = 1, 2 0.383⁄ (2.321)  si, i = 1, 2 0.0721⁄ (2.723) gii, i = 1, 2 0.066 (0.221)

0.0183⁄ (4.304) 0.0008 (1.259) 0.0041⁄ (3.949) 0.959⁄ (95.229) 0.172⁄ (3.599)  0.468⁄ (1.891) 0.179 (2.471)

0.0055⁄ (2.428) 0.0017 (0.798) 0.0040 (1.024) 0.007 (0.316) 2.156 (1.640)  3.502E04 (0.005) 3.095 (1.537)

0.967⁄ (79.885) 0.109 (1.375)  9.563E04 (0.006) 0.207⁄ (3.074)

0.003 (0.034) 3.224⁄ (2.563) 0.006 (0.055) 0.032 (1.124) 

0.955⁄ (32.139) 0.040 (0.292) 0.236⁄ (2.445) 0.8025⁄ (2.835) 

0.115 [0.169] 1.381 [0.000] 70.668 [0.000] 9.849 [0.544] 3.186 [0.988] 0.247 [0.996]

4460.722 4.955 (0.000) 89.869 (0.000) 294,627 (0.000) 3.398 (0.984) 0.532 (0.999) 0.0447 (1.000)

0.209 (0.012) 0.728 (0.000) 25.383 (0.000) 16.061 (0.139) 16.318 (0.130) 1.363 (0.178)

0.887 [0.375] 1.067 [0.286] 1.476 [0.140] 0.870 [0.456]

0.838 (0.402) 0.134 (0.893) 0.694 (0.488) 0.298 (0.826)

0.341 (0.734) 0.957 (0.339) 0.975 (0.327) 0.666 (0.573)

Panel C: Diagnostic tests on standardised residuals Log-Likelihood 4179 Skewness 0.542 [0.000] 0.128 [0.126] Kurtosis 27.329 [0.000] 1.362 [0.000] J–B 26,898 [0.000] 69.052 [0.000] Q(12) 12.583 [0.321] 13.886 [0.239] Q2(12) 2.584 [0.995] 9.786 [0.549] ARCH(12) 0.203 [0.998] 0.833 [0.615] SBIC 8203 7243 Sign Bias 0.192 [0.848] 0.079 [0.937] Negative size bias 0.222 [0.825] 0.648 [0.517] Positive size bias 0.246 [0.806] 1.552 [0.121] Joint bias test 0.098 [0.961] 1.516 [0.209] See notes in Table 5.

3666 0.460 [0.000] 72.409 [0.000] 189,001 [0.000] 12.147 [0.353] 0.776 [0.999] 0.070 [0.999] 8827 0.209 [0.834] 0.124 [0.901] .0425 [0.671] 0.076 [0.973]

0.384 [0.701] 0.675 [0.567]

M.G. Kavussanos et al. / Transportation Research Part E 68 (2014) 79–102

VAR(3)-GJR-GARCH(1, 1)

0.247 [0.805] 0.294 [0.830]

95

96

M.G. Kavussanos et al. / Transportation Research Part E 68 (2014) 79–102

In contrast, for the remaining Panamax (PTC–Synthetic 1 and P2A–Soybean) and Supramax (STC–Synthetic 2) trades symmetric VECM-GARCH models are estimated, as there is no evidence of asymmetries in the conditional variance. The diagnostic tests reported in panel C indicate that the standardised residuals of the employed models are in all cases free from serial correlation (with the exception of the C4, C7 and STC equations, where the Newey–West autocorrelation correction is used) and heteroskedasticity. Furthermore, the Engle’s (1982) heteroskedasticity test also indicates no ARCH effects. Panels A and B, of the same table, present the maximum-likelihood mean (return) and variance (volatility) parameters estimates of the estimated models, respectively. More specifically, in panel A, in all cases, the ECT coefficients (qj) are statistically significant. In all Panamax and Supramax pairs, ECT coefficients attain opposite signs; that is, the negative FFA coefficients and the positive commodity futures coefficients are in accordance with convergence towards a long-run equilibrium. Thus, in response to a positive forecast error, the FFA prices will decrease, while the commodity futures prices will increase in values in order to restore the long-run equilibrium. In contrast, in the three Capesize pairs, the ECT coefficients are positive (and significant in most cases) in both FFA and commodity futures equations. This finding may be partially explained by the existence of a structural break in the cointegrating system, following the Gregory and Hansen (1996b) earlier results. According to the short-run dynamics of the models, as shown by the statistically significant bFFA,1 coefficient in the FFA equations and the statistically insignificant aFUT,1 and aFUT,2 coefficients in (most of) the commodity futures equations, it seems that commodity futures returns have a unidirectional positive impact on FFA returns in all investigated Panamax and Supramax cases. This result is also in accordance with the statistical significance of the causality Wald tests. Thus, market information is discovered first in commodity futures markets (soybeans and the two synthetic commodity baskets) and then it appears in the FFA markets. This is expected, as the demand for freight is created in commodity markets, resulting in freight markets lagging behind commodity markets in their reaction to news in these markets. These results can also be partially justified by the fact that commodity futures markets are more liquid with lower transactions costs compared to FFA markets. Fleming et al. (1996) argue that the market with the lowest overall trading costs (and higher liquidity) will react more quickly to new information and thus, provide the price discovery function. In contrast to a priori expectations, in Capesize markets there is no spillover relationship in either direction; that is, neither coal futures nor Capesize FFAs, on the time-charter basket (CTC) or on individual routes (C4 and C7), are capable of transmitting any new information to the other market and in that way act as price discovery vehicles. This may be due to the fact that transportation costs for coal represent a higher percentage of the final price of the commodity in comparison to grain commodities, as in some instances they may account for 70% of the CIF price of coal (as per the World Coal Institute).21 This in turn, may erode the signalling power of coal futures markets for the respective FFA markets, as the latter seem to have a dominant role in the formation of the coal futures price. Moreover, it may be due to the fact that there is no one-to-one equivalence between the freight routes and the commodities carried, and as such, a geographical difference in the price dynamics may emerge, due to short-term local imbalances. Commodities that match better the Capesize coal trades are the Colombian and Rotterdam coal. However, derivatives contracts for these commodities do not currently exist. On the other hand, and according to the empirical results, Capesize FFA markets do not spill information to coal futures markets as well. This finding is in accordance with the results in all other FFA markets, where FFAs lag behind commodity futures in terms of information assimilation. Panel B presents the parameter estimates of the conditional variance of the models, where the lagged disequilibrium squared error-term is also included as explanatory variable in the conditional variances of the model. The statistical significance of the lagged error-terms (ckk) and lagged variance-terms (bkk) of the variance equations indicate that volatility is time-varying in all cases. Besides the PTC–Soybean pair, in all other cases the coefficients of the squared lagged ECTs (eci) are statistically significant and negative in most FFA and commodity futures equations. Thus, the ECT of the previous period has important predictive power for the conditional variances of cointegrated series and should be included in the volatility models. Finally, out of the eight examined pairs, in three pairs (C4–Coal, PTC–Synthetic 1 and STC–Synthetic 2) there is a unidirectional volatility spillover from the commodity futures to the FFA markets and in two pairs (C7–Coal and STC–Soybean) there is a bi-directional causal relationship. The magnitude of the si coefficient shows that this bi-directional causal relationship runs stronger from the commodity futures to the FFAs. Finally, only in two FFA basket cases (CTC–Coal and PTC–Soybean) there seems to be no volatility spillover between the markets and in one case (P2A–Soybean) FFAs seem to spillover volatility to the commodity futures. Overall, in most cases, commodity futures informationally lead the freight derivatives market in both returns and volatilities.

4.2. Spillovers under non-cointegrated relationships The return and volatility spillover results for the pairs of FFA and commodity futures prices that do not stand in a cointegrating relationship are shown in Table 6. Results indicate that for the PTC–Corn, P2A–Synthetic 1 and STC–Corn cases a VAR-GJR-GARCH process effectively captures the asymmetries present in the data, while for the P2A–Corn pair a VAR-EGARCH process best fits the data. These results can be seen by the Engle and Ng (1993) tests, which are presented 21 Grain transportation costs typically account for a much smaller percentage of the CIF price of grains. For instance, as of June 2011, the transportation cost of corn and soybeans from US to Japan accounts for 19% and 7% of the CIF price of corn and soybeans, respectively.

M.G. Kavussanos et al. / Transportation Research Part E 68 (2014) 79–102

97

in panel C of the same table. On the other hand, for the remaining three pairs, a symmetric VAR-GARCH is fitted to the data successfully. Results of the Ljung–Box (1978) statistics for 12th-order serial correlation of levels and squared levels of standardised residuals and Engle’s (1982) test, presented in panel C, indicate absence of any serial correlation and heteroskedasticity, respectively. Panel A of Table 6 presents the maximum-likelihood mean parameter estimates of the estimated models. As can be seen, in six out of the seven pairs, where cointegration is not found even after accounting for the possibility of a structural break in cointegrated systems, a unidirectional positive spillover effect exists from the commodity futures returns to the FFA returns. This is documented by the positive and statistically significant bFFA,1 and bFFA,2 coefficients in the FFA equations and the statistically insignificant aFUT,1 and aFUT,2 coefficients in the commodity futures equations, as well as by the statistical significance of the causality Wald tests. These spillover findings in the returns are in accordance with earlier results coming from cointegrated markets, where market information is discovered first in commodity futures markets and then it appears in FFA markets. Thus, so far it seems that regardless of the existence of a long-run cointegrating relationship, commodity futures informationally lead FFA returns. In contrast, in the case of the P2A–Corn pair an inverse unidirectional relationship is found; that is, there is a statistically significant spillover relationship from the P2A FFA market to the corn commodity futures market, which is in contrast to the original expectations. It seems that FFA trades discover prices prior to corn futures trades, as new information is revealed and incorporated first in the FFA returns, before it is spilled over to corn returns. These results can be partially explained by the fact that corn physical trades affect to a larger extent the demand of smaller vessel types (e.g. Supramax vessels) which are used for their transportation than larger ones (e.g. Panamax vessels) that carry mostly iron ore and wheat cargoes. It follows that any price discovery function between the relevant freight and commodity derivatives markets is more clearly evidenced in the smaller Supramax vessels than in the larger Panamax ones. Panel B of Table 6 presents the parameter estimates of the conditional variance models. The statistical significance of the lagged error-terms (ckk) and lagged variance-terms (bkk) of the variance equations indicates once again that volatility is timevarying in all cases. In three out of the seven pairs examined (PTC–Corn, PTC–Wheat and STC–Wheat), there is a unidirectional volatility spillover from the commodity futures to the FFA markets. A bi-directional causal relationship is found in two pairs (P2A–Wheat and P2A–Synthetic 1), which according to the magnitude of the si coefficient, runs stronger from the commodity futures to the FFAs. It seems that time-charter baskets of freight rates and the individual P2A route of the Panamax trades are able to receive successfully new information from commodity futures markets. Overall, in most cases, commodity futures informationally lead the freight derivatives market in both returns and volatilities. In only two cases (P2A–Corn and STC–Corn), there is no evidence of volatility spillovers in either direction. Finally, results for prompt-month FFA Capesize basket (CTC) and iron ore swap (IOS) contracts, from well-specified and free from any linear or non-linear dependencies VAR-GARCH models, indicate that there are significant spillover effects from the FFA market to the IOS market, both in terms of returns and volatilities. These significant effects may be attributed to the fact that the FFA market is better developed and more liquid than the IOS market, which started only back in April 2009.22 According to IOS trading volumes (in mt), 6,987,000mt of iron ore were hedged in 2009, 41,938,000mt were hedged in 2011, and 263,805,400mt were hedged in 2013. This compares with an estimated level of 540,325,000 tonnes (=540,325 lots  1000 tonnes per contract) of total (cleared and OCT) Capesize voyage based ocean transportation hedged in 2009, 509,344,000 tonnes hedged in 2011, and 591,755,000 tonnes in 2013.

4.3. Impulse response analysis By analysing the Generalised Impulse Responses (GIR) functions of a SUR-VAR (when cointegration is not found) or of a SUR-VECM (when cointegration is found) an insight into the dynamics of the causal relationship between FFA and commodity futures markets can be obtained. Impulse responses measure the reaction of FFA and commodity futures prices in response to one-unit standard error shocks in the equations of the models. Fig. 1 presents the time paths of the FFA and commodity futures price innovations for a 10 days-ahead horizon, first in the FFA returns (upper graphs) and second in the commodity futures returns (lower graphs). Only the responses of the FFA Capesize time-charter basket with coal futures (CTC-API4), of the FFA Panamax time-charter basket with the Synthetic 1 basket (PTC-SYN1), and of the FFA Supramax timecharter basket with soybeans futures (STC-SOY) are shown in order to conserve space.23 In the FFA Capesize basket (CTC) with the API4 coal futures it can be seen that the adjustment time varies between the two price series, taking approximately 4–5 days to revert back to the original state after the shock for the FFA CTC prices (solid line in the upper graph). Adjustment in commodity futures prices (dashed line in the lower graph) takes place in half the period, as it takes around 3 days for the FFA CTC prices to adjust. An overshooting is observed in the FFA CTC prices, while coal futures prices exhibit a lower impact. The most important finding, however, is that when the FFA CTC prices are affected by a shock (in the upper graph), coal futures prices remain almost unaffected. The same also holds true when the coal futures prices are affected by one standard error shock (in the lower graph) with FFA CTC prices not responding. These findings are in accordance with earlier results of no spillover relationships from either market. 22 23

For the sake of brevity, results are not presented here but are available from the authors upon request. The responses for the remaining markets are available from the authors upon request.

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M.G. Kavussanos et al. / Transportation Research Part E 68 (2014) 79–102 Response of PTC to Generalized One S.D. Innovations

Response of CTC to Generalized One S.D. Innovations .07 .06

Response of STC to Generalized One S.D. Innovations

.05

.04

.04

.03

.03

.02

.02

.01

.01

.00

.05 .04 .03 .02 .01 .00

.00 1

2

3

4

5

6

CTC

7

8

9

-.01 1

10

2

3

4

API4

5

6

7

8

9

10

1

.024 .020

3

4

5 STC

Response of SYN1 to Generalized One S.D. Innovations

Response of API4 to Generalized One S.D. Innovations

2

SYN1

PTC

6

7

8

9

10

SOYBEANS

Response of SOYBEANS to Generalized One S.D. Innovations

.020

.020

.015

.015

.010

.010

.005

.005

.000

.000

.016 .012 .008 .004 .000 1

2

3

4

5 CTC

6

7

8

9

-.005 10 1

API4

2

3

4

5 PTC

6

7 SYN1

8

9

-.005 10 1

2

3

4

5 STC

6

7

8

9

10

SOYBEANS

Fig. 1. Generalised impulse responses in the FFA and commodity futures markets CTC, PTC and STC are the Capesize, Panamax and Supramax BFA four timecharter average baskets; API4 and soybeans are the coal and soybean commodities futures contracts; SYN1 is the synthetic 1 basket, which consists of wheat, corn, soybean and API4 coal commodity futures.

Consider next the case of the FFA Panamax basket (PTC) with the commodity futures synthetic basket (SYN1). When the FFA PTC prices are subjected to a shock (in the upper graph), the commodity futures prices react to the new ‘‘news’’ in the market that originate from the shock and respond accordingly in order to incorporate the news into prices. When the commodity futures prices are subjected to a shock (in the lower graph) the FFA PTC prices do not seem to have the information assimilation capacity to respond to the shock. The same findings also hold in the case of the FFA Supramax (STC) basket with the soybeans commodity futures. These findings are in accordance with earlier causality Wald test results. Overall, it seems that commodity futures returns respond to new information coming from the FFA market and arrive at a long-run equilibrium level more rapidly than their corresponding FFA prices, but not the other way around. Thus, it seems that investors, which collect and analyse new market information on a daily basis, are not indifferent about transacting in these derivatives markets, and as such, new information is revealed first in the commodity futures market, before it is spilled over in the FFA market.

5. Economic significance of spillover results Wu (2001) argues that a ‘‘volatility feedback effect’’ (time-varying risk premium) is a result from an expected increase in volatility, which will increase the required rate of return, and consequently, will lead to an asset price decrease (negative returns) to allow for higher future returns. Following the volatility spillovers found in the previous analysis, it is of interest to further investigate their economic significance; that is, whether these spillovers can lead to a profitable trading strategy, after accounting for transactions costs. The economic significance of the revealed spillover relationships are examined from the perspective of an investor interested in utilising these findings in order to profit from investing in the commodity futures and the FFA markets. However, it is worth noting that the implications emerging from this paper are not limited to trading and may involve several aspects related to derivatives markets such as the function of price discovery, hedging effectiveness and derivatives markets design, amongst others. The methodology followed to test for the economic significance of the findings is based on Wu (2001). Specifically, two crossed trading strategies are employed depending on the market that originates the piece of news; that is, a crossed strategy involves taking a short (long) position in the i market when an increasing (decreasing) spillover is predicted in asset j.24 24 Braun et al. (1995) and Pardo and Torro (2007) distinguish further between bad news (good news) expressed as an negative (positive) unexpected return shock, followed by an expected decrease (increase) in conditional volatility and very bad news (very good news) expressed as an unexpected price decrease (increase) followed by an expected increase (decrease) in conditional volatility.

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M.G. Kavussanos et al. / Transportation Research Part E 68 (2014) 79–102 Table 7 Profitability of trading strategies from economic cross-market spillovers. Description of trading strategy

Bad news (%)

Good news (%)

Panel A: Cointegrated pairs of FFA and commodity futures Crossed strategy on coal market (taking signals from the CTC market) Crossed strategy on C4 market (taking signals from coal market) Crossed strategy on Synthetic 1 (taking signals from PTC market) Crossed strategy on PTC market (taking signals from Synthetic 1) Crossed strategy on synthetic 2 (taking signals from STC market) Crossed strategy on STC market (taking signals from synthetic 2) Average return (from cointegrated pairs)

0.03 1.47 0.93 1.62 1.65 1.35 0.73

0.12 1.34 0.63 0.42 0.59 0.26 0.47

Panel B: Non-cointegrated pairs of FFA and commodity futures Crossed strategy on wheat market (taking signals from STC market) Crossed strategy on STC market (taking signals from wheat market) Crossed strategy on corn market (taking signals from PTC market) Crossed strategy on PTC market (taking signals from corn market) Crossed strategy on wheat market (taking signals from PTC market) Crossed strategy on PTC market (taking signals from wheat market) Average return (from non-cointegrated pairs)

0.63 0.32 1.67 0.66 0.03 1.53 0.80

0.31 0.72 0.02 0.72 0.35 0.64 0.46

The table reports the returns (net of transaction costs) realised from implementing a crossed trading strategy between FFA and commodity futures markets. The crossed trading strategy involves taking short or long positions on one market based on signals obtained from the other market. Specifically, volatility spillovers documented in Tables 5 and 6 are used as signals to setup the trading strategies. Transaction costs include exchange, clearing and brokerage fees. Transaction costs for grain commodity futures are approximately $1.51 per contract, for the API4 coal futures are approximately $8 per contract and for the FFA contracts 0.015% brokerage and exchange fees plus $7 clearing fee per lot for all FFA time-charter baskets and $5 per lot for FFA C4.

Volatility spillovers between commodity futures and FFA markets documented in Tables 5 and 6 are used as signals to setup the trading strategies highlighted above. These trading strategies are based on the ‘‘volatility feedback effect’’ to distinguish between bad news and good news as follows: In the case of bad news an increasing volatility spillover in asset i should lead investors to take a short position on asset j. The opposite happens in the case of good news that involves a decreasing volatility spillover suggesting taking a long position on asset j. The two trading strategies are implemented only in the case of derivatives product pairs where evidence of significant volatility spillovers is found. Therefore, the cointegrated pairs are C4-API4, the PTC-Synthetic 1 and the STC-Synthetic 2. The non-cointegrated pairs are the STC-Wheat, PTC-Corn, and PTC-Wheat. In order to evaluate the trading strategies an in-sample and an out-of-sample period is used. The in-sample period used for the estimation of the VECM and VAR-GARCH models spans the period May 2006 through September 2008, and the out-of-sample period used for evaluating the trading strategies spans the period September 2008 through October 2009. For the cointegrated pairs we utilise the concept of time-varying cointegration of Bierens and Martins (2010) to apply the four trading strategies. According to time-varying cointegration, a time-varying VECM in conjunction with the diagonal BEKK GARCH of Eq. (9) is estimated recursively throughout the out-of-sample period. The time-varying VECM is estimated according to Eq. (8). However, according to time-varying cointegration, the coefficient matrix P of Eq. (8) is time varying with P ¼ ab0t , where b0t are time-varying matrices. According to findings,25 time-varying cointegration is found for all cointegrated pairs. In the case of the non-cointegrated pairs we utilise the VAR-BEKK GARCH model to test the trading strategies. A trading strategy is profitable when yielding a positive return after taking into consideration transactions costs for the derivatives contracts.26 Table 7 displays the outcome of the crossed trading strategies, by estimating the model each time a return is known and by then forecasting volatility for the next period. The results of Table 7 indicate that in the case of non-cointegrated FFA and commodity futures pairs, crossed strategies based on bad news and good news when taking the signal from commodity markets (and investing in FFA markets) yield consistently positive returns. The best strategy both for the non-cointegrated and cointegrated pairs is the one based on bad news, which yields an average daily profit of 0.80% and 0.73% across all markets, respectively. Overall, findings indicate that investors may utilise the spillover relationships and take into advantage the informational superiority of commodity futures market vis-à-vis the FFA markets to devise profitable investment strategies.

6. Discussion Overall, results indicate that commodity futures, in general, lead FFAs both in returns and volatilities. As far as returns are concerned, this is confirmed for the Panamax and Supramax markets, where only unidirectional spillovers from commodity futures returns to freight FFA returns are found. In contrast, there seems to be no relationship in returns between Capesize and coal derivatives markets. Regarding volatility spillovers, in most cases, there is a unidirectional relationship from 25 26

For the sake of brevity we dot provide here the results for the test of time-varying cointegration, but are available from the authors upon request. When open outcry transactions costs are used for commodity futures contracts, results are qualitatively the same.

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commodity futures to the time-charter baskets FFAs and a bi-directional relationship between commodity futures and single-route FFAs, with the latter relationship running stronger from the commodity futures to the FFA market. The above empirical findings can be explained as follows: First, commodity futures, which trade in well-organised markets, are more liquid than FFAs, with their average daily contract trading volume being roughly triple that of FFA contracts. As a consequence, commodity futures are regarded as more efficient markets, subjected to less market frictions and mispricing. Blasco et al. (2009), report that, in line with the transactions cost theory, the futures market with its higher liquidity and lower transactions costs, leads the price discovery process. McMillan and Ülkü (2009) argue that as the volume of trades increases in futures markets, the price discovery function is strengthened, as the futures markets become more informationally efficient. Chordia et al. (2008) argue that higher liquidity attracts arbitrage trading, leading to diminishing return predictability and eventually higher market efficiency. Chung and Hrazdil (2010) also report that increased liquidity enhances market efficiency, after controlling for the effects of market capitalisation, trading volume and trading frequency. Goulas and Skiadopoulos (2012) report that the IMAREX freight futures market is not informationally efficient for very short (daily) horizons and that the existence of a daily positive risk-premium implies that the unbiasedness hypothesis does not hold for the IMAREX market. Following these results, the finding that commodity futures unidirectionally lead freight derivatives, both in returns and volatilities, may be due to a predictability of the freight derivatives market. Finally, Alizadeh (2013) argues that freight derivatives (FFA) price changes Granger-cause trading volume, while there is no evidence of causality from volume to price changes; that is, ‘‘a momentum effect drives the FFA market and trading activities, as price increases tend to lead to more transactions and trading activities’’. Second, less trading costs result in higher trading and in more efficiently functioning markets (see Chordia et al., 2011). The examined commodity futures have less transactions costs in comparison to FFA trades. There is a flat rate per contract of approximately 0.10% or lower of the contract value, while for FFAs trades the brokerage fee is typically 0.25% of the contract value on top of the fees of the clearing-house in case the trade is cleared. Third, as FFA contracts are risk management instruments for exposures reciprocating from operations only in the maritime industry, and since they represent an ‘‘unconventional’’ family of commodity derivatives markets, they do not attract as much trading interest from institutional investors as the mainstream commodity futures markets examined in the paper.27 Fourth, as the FFA market is an emerging market, established back in 1992, it is expected to informationally lag the wellestablished and liquid commodity markets, where corn and wheat futures trade from 1877 and soybean futures from 1936. McMillan and Ülkü (2009) argue that as a market matures, more informed investors arrive overpowering the impact of disposition trading on prices. Bohl et al. (2011) argue that if unsophisticated investors trade in a market, the quality of the price signal may be reduced, and thus, the market’s price discovery function may be diminished. This is also verified by Chordia et al. (2011) as more institutional trading has increased information-based trading, decreased volatility and increased the efficiency of the prices. Fifth, commodity futures prices are more ‘‘visible’’ than FFA markets. This is due to the fact that commodity futures prices are determined by the interaction of supply and demand in an organised exchange, while FFA prices are determined by the interaction of supply and demand in OTC markets, with less transparency of information regarding volume, actual bids and offers, number of trades, etc. The aforementioned market characteristics seem to provide reasons behind the empirical findings and explain the information superiority of commodity futures markets in comparison to FFA markets. The implications of the economic linkages uncovered here are important on a practical perspective, for design of portfolios, asset pricing and risk management, as they determine the benefits of diversification, the development of accurate asset pricing models, optimal time-varying hedge ratios and VaR measures (Reboredo, 2014). Traders may utilise the revealed linkages to construct profitable trading strategies, while hedgers can monitor the commodity futures markets to implement freight risk management through hedging in a more effective manner. Policy makers and regulators need to analyse the dynamics of return and volatility transmissions between commodities and shipping markets and sound policy measures should be based on a clear comprehension of the transmission mechanisms between commodity and shipping markets.

7. Conclusion This paper examines return and volatility spillover effects between different but related ocean freight and commodity futures markets. Such effects are economically important for all participants active in the examined markets. The economic relationship tested empirically links the derivative price of the commodity transported with the derivative on the freight rate (FFA) of the vessel transporting it. Various types of commodities transported under different types of freight contracts investigated reveal that in most cases new information appears first in the returns and volatilities of the commodities futures markets, before it is spilled over into the FFA markets. Thus, wheat, corn and soybeans are important commodity futures markets to monitor in order to understand what may occur in the dry bulk FFA market, which subsequently can provide lead information on the underlying freight markets. The results can help improve the understanding of the information transmission mechanisms between freight and commodity derivatives, and consequently spot, markets. They can further assist for the more precise pricing of the non-storable freight derivatives contracts, where the theory of storage does not hold. These 27 For example, on January 2012, according to the Baltic Exchange and ICAP Shipping International Ltd., the nominal value of dry bulk FFAs was US$ 689 million, whereas the values of wheat, corn, and soybeans futures were US$313 mil, $790 mil and $600 mil, respectively, summing up to a total of $1703 mil.

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results are of great value to market participants in the international shipping and commodity markets, as they can be used to enter into more effective trading, investment, chartering and hedging decisions. Acknowledgements The authors would like to thank for their comments, the editor and four anonymous reviewers, as well as the participants of the following conferences, where earlier versions of this paper were presented: International Association of Maritime Economists (IAME) Conference, Taipei, Taiwan, 6–8 September 2012; and 3rd International Symposium on Ship Operations, Management and Economics, The Greek Section of the Society of Naval Architects and Marine Engineers (SNAME), Athens, Greece, 7–8 October 2010. Also, the authors would like to thank Georgi Slavov of Marex Spectron Commodity Research Group, for providing the iron ore swap data. Any remaining errors are the authors’ responsibility. References Alizadeh, A.H., 2013. Trading volume and volatility in the shipping forward freight market. Transport. Res. – Part E, Logist. Transport. Rev. 49, 250–265. Baba, Y., Engle, R.F., Kraft, D.F., Kroner, K.F., 1990. Multivariate Simultaneous Generalised ARCH. Mimeo. Department of Economics, University of California, San Diego. Baillie, R.T., Bollerslev, T., 1995. On the interdependence of international asset markets. In: Aggarwal, R., Schrim, D. (Eds.), Global Portfolio Diversification: Risk Management, Market Microstructure and Implementation Issues. Academic Press, New York, pp. 19–29. Beckmann, J., Czudaj, R., 2014. Volatility transmission in agricultural futures markets. Econ. Model. 36, 541–546. Bessembinder, H., Chan, K., 1992. Time varying risk premia and forecastable returns in futures markets. J. Financ. Econ. 32, 169–193. Bierens, H.J., Martins, L.F., 2010. Time varying cointegration. Econometr. Theory 26, 1453–1490. Blasco, N., Corredor, P., Santamaría, R., 2009. Information spillovers between derivative markets with differences in transaction costs and liquidity. Appl. Econ. Lett. 16, 1039–1047. Bohl, M.T., Salm, C.A., Schuppli, M., 2011. Price discovery and investor structure in stock index futures. J. Fut. Market 31, 282–306. Bollerslev, T., Wooldridge, J.M., 1992. Quasi-maximum likelihood estimation of dynamic models with time-varying covariances. Econometr. Rev. 11, 143– 172. Braun, P.A., Nelson, D.B., Sunier, A.M., 1995. Good news, bad news, volatility and betas. J. Financ. 5, 1575–1603. Chan, K., Chan, K.C., Karolyi, G.A., 1991. Intraday volatility in the stock index and stock index futures markets. Rev. Financ. Stud. 4, 657–684. Chng, M.T., 2009. Economic linkages across commodity futures: hedging and trading implications. J. Bank. Financ. 33, 958–970. Chordia, T., Roll, R., Subrahmanyam, A., 2008. Liquidity and market efficiency. J. Financ. Econ. 87, 249–268. Chordia, T., Roll, R., Subrahmanyam, A., 2011. Recent trends in trading activity and market quality. J. Financ. Econ. 101, 243–263. Chulia, H., Torro, H., 2008. The economic value of volatility transmission between the stock and bond markets. J. Fut. Market 28, 1066–1094. Chung, D., Hrazdil, K., 2010. Liquidity and market efficiency: a large sample study. J. Bank. Financ. 34, 2346–2357. Coppola, A., 2008. Forecasting oil price movements: exploiting the information in the futures market. J. Fut. Market 28, 34–56. Daskalaki, C., Kostakis, A., Skiadopoulos, G., 2014. Are there common factors in individual commodity futures returns? J. Bank. Financ. 40, 346–363. Dickey, D.A., Fuller, W.A., 1981. Likelihood ratios statistics for autoregressive time series with a unit root. Econometrica 49, 1057–1072. Ding, L., Pu, X., 2012. Market linkage and information spillover: evidence from pre-crisis, crisis, and recovery periods. J. Econ. Business 64, 145–159. Engle, R.F., 1982. Autoregressive conditional heteroskedasticity with estimates of the variance of United Kingdom inflation. Econometrica 50, 987–1007. Engle, R.F., Ng, V., 1993. Measuring and testing the impact of news on volatility. J. Financ. 48, 1749–1777. Fleming, J., Ostdiek, B., Whaley, R.E., 1996. Trading costs and the relative rates of price discovery in stock, futures and options markets. J. Fut. Market 16, 353–387. Fung, H.G., Liu, Q., Tse, Y., 2010. The information flow and market efficiency between the U.S. and Chinese aluminum and copper futures markets. J. Fut. Market 30, 1192–1209. George, R., 2013. Ninety percent of everything: inside shipping, the invisible industry that puts clothes on your back, gas in your car, and food on your plate. Metropolitan Books, August. Glosten, L.R., Jagannathan, R., Runkle, D.E., 1993. On the relationship between the expected value and the volatility of the nominal excess returns on stocks. J. Financ. 48, 1779–1801. Goss, B.A., Avsar, S.G., 1999. Non-storables, simultaneity and price determination: The Australian (finished) live cattle market. Aust. Econ. Pap. 38, 461–480. Goulas, L., Skiadopoulos, G., 2012. Are freight futures markets efficient? Evidence from IMAREX. Int. J. Forecast. 28, 644–659. Gregory, A.W., Hansen, B.E., 1996a. Residual-based tests for cointegration in models with regime shifts. J. Econometr. 70, 99–126. Gregory, A.W., Hansen, B.E., 1996b. Tests for cointegration in models with regime and trend shifts. Oxford Bull. Econ. Stat. 58, 555–560. Haigh, M., Bryant, H.L., 2001. The effect of barge and ocean freight price volatility in international grain markets. Agricult. Econ. 25, 41–58. Jarque, C.M., Bera, A., 1980. Efficient tests for normality, homoscedasticity and serial independence of regression residuals. Econ. Lett. 6, 255–259. Johansen, S., 1988. Statistical analysis of cointegration vectors. J. Econ. Dyn. Contr. 12, 231–254. Jung, R., Maderitsch, R., 2014. Structural breaks in volatility spillovers between international financial markets: contagion or mere interdependence? J. Bank. Financ., in press. Available from: . Kavussanos, M.G., 2010. Business risk measurement and management in the cargo carrying sector of the shipping industry – an update. In: The Handbook of Maritime Economics and Business. Lloyds of London Press, London, pp. 709–743 (Chapter 25). Kavussanos, M.G., Visvikis, I.D., 2004. Market interactions in returns and volatilities between spot and forward shipping markets. J. Bank. Financ. 28, 2015– 2049. Kavussanos, M.G., Visvikis, I.D., 2006. Derivatives and Risk Management in Shipping. Witherbys Publishing and Seamanship International, UK. Kavussanos, M.G., Visvikis, I.D., 2011. Theory and Practice of Shipping Freight Derivatives. Risk Books, UK. Kavussanos, M.G., Visvikis, I.D., Batchelor, R., 2004a. Over-the-counter forward contracts and spot price volatility in shipping. Transport. Res. – Part E, Logist. Transport. Rev. 40, 273–296. Kavussanos, M.G., Visvikis, I.D., Dimitrakopoulos, D.N., 2010. Information linkages between Panamax freight derivatives and commodity derivatives markets. Maritime Econ. Logist. 12, 91–110. Kavussanos, M.G., Visvikis, I.D., Menachof, D., 2004b. The unbiasedness hypothesis in the freight forward market: evidence from cointegration tests. Rev. Deriv. Res. 7, 241–266. Keynes, J.M., 1930. A Treatise on Money, vol. II. Macmillan, London. Kwiatkowski, D., Phillips, P.C., Schmidt, P., Shin, Y., 1992. Testing the null of stationarity against the alternative of a unit root: how sure are we that economic time series have a unit root? J. Econometr. 54, 159–178. Lee, J., Strazicich, M.C., 2003. Minimum Lagrange multiplier unit root tests with two structural breaks. Rev. Econ. Stat. 85, 1082–1089. Lee, J., Strazicich, M.C., 2004. Minimum LM unit root test with one structural break. Working Papers 04-17, Department of Economics, Appalachian State University.

102

M.G. Kavussanos et al. / Transportation Research Part E 68 (2014) 79–102

Lien, D., Yang, L., 2010. The effects of structural breaks and long memory on currency hedging. J. Fut. Market 30, 607–632. Liu, Q., Wong, I., An, Y., Zhang, J., 2014. Asymmetric information and volatility forecasting in commodity futures markets. Pacific-Basin Financ. J. 26, 79–97. Liu, Q.W., 2005. Price relations among hog, corn, and soybean meal futures. J. Fut. Market 25, 491–514. Ljung, M., Box, G., 1978. On a measure of lack of fit in time series models. Biometrica 65, 297–303. Low, A.H.W., Muthuswamy, J., Webb, R.I., 1999. Arbitrage, cointegration, and the joint dynamics of prices across discrete commodity futures auctions. J. Fut. Market 19, 799–815. McKenzie, A., Holt, M., 2002. Market efficiency in agricultural futures markets. Appl. Econ. 34, 1519–1532. McMillan, D., Ülkü, N., 2009. Persistent mispricing in a recently opened emerging index futures market: arbitrageurs invited. J. Fut. Market 29, 218–243. Mehl, A., 2000. Unit root tests with double trend breaks and the 1990s recession in Japan. Jpn. World Econ. 12, 363–379. Nazlioglu, S., Erdem, C., Soytas, U., 2013. Volatility spillover between oil and agricultural commodity markets. Energy Econ. 36, 658–665. Nelson, D.B., 1991. Conditional heteroskedasticity in asset returns: a new approach. Econometrica 59, 347–370. Pardo, A., Torro, H., 2007. Trading with asymmetric volatility spillovers. J. Business Financ. Acc. 34, 1548–1568. Phillips, P.C.B., Hansen, B.E., 1990. Statistical inference in instrumental variable regression with I(1) processes. Rev. Econ. Stud. 57, 99–125. Phillips, P.C.B., Perron, P., 1988. Testing for a unit root in time series regression. Biometrica 75, 335–346. Prokopczuk, M., 2011. Pricing and hedging in the freight futures market. J. Fut. Market 13, 440–464. Reboredo, J.C., 2014. Volatility spillovers between the oil market and the European Union carbon emission market. Econ. Model. 36, 229–234. Skiadopoulos, G., 2013. Advances in the commodity futures literature: a review. J. Derivat. 20, 85–96. Tomek, W.G., Gray, R.W., 1970. Temporal relationships among prices of commodity futures markets: their allocative and stabilizing roles. Am. J. Agric. Econ. 52, 372–380. Trujillo-Barrera, A., Mallory, M., Garcia, P., 2012. Volatility spillovers in US crude oil, ethanol, and corn futures markets. J. Agric. Resour. Econ. 37, 247–262. Villanueva, O.M., 2007. Spot-forward cointegration, structural breaks and FX market unbiasedness. J. Int. Financ. Market Inst. Money 17, 58–78. Wahab, M., Lashgari, M., 1993. Price dynamics and error correction in stock index and stock index futures markets: a cointegration approach. J. Fut. Market 7, 711–742. White, H., 1980. A heteroskedastic-consistent covariance matrix estimator and a direct test for heteroskedasticity. Econometrica 48, 817–838. Wu, G., 2001. The determinants of asymmetric volatility. Rev. Financ. Stud. 14, 837–859. Wu, H., Li, S., 2013. Volatility spillovers in China’s crude oil, corn and fuel ethanol markets. Energy Policy 62, 878–886. Yang, J., Leatham, D., 1999. Price discovery in wheat futures markets. J. Agric. Appl. Econ. 31, 359–370. Yu, T.H., Bessler, D.A., Fuller, S., 2007. Price dynamics in US grain and freight markets. Can. J. Agric. Econ. 55, 381–397.