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ECONOMIC SPILLOVERS BETWEEN RELATED DERIVATIVES MARKETS:

THE CASE OF COMMODITY AND FREIGHT MARKETS

MANOLIS G. KAVUSSANOS*

Athens University of Economics and Business Department of Accounting and Finance

Athens, Greece, Email: mkavus@aueb.gr

ILIAS D. VISVIKIS ALBA Graduate Business School

Athens, Greece, Email: ivisviki@alba.edu.gr  

DIMITRIS N. DIMITRAKOPOULOS Athens University of Economics and Business

Department of Accounting and Finance Athens, Greece, Email: jim@aueb.gr

DECEMBER 2011

ABSTRACT Extant studies in the literature investigate volatility spillover effects between spot markets of the same asset class or between derivatives and their underlying spot markets. This paper considers, for the first time, economic spillovers between two different and important for the world economy derivatives markets; namely, the freight forward market and the commodity futures markets of commodities transported by ocean-going vessels. An economic relationship linking the two markets is proposed and tested empirically. Moreover, the difficulty of derivatives pricing of the non-storable freight service may be overcome by considering the link with the derivatives of the commodity transported proposed in this paper. Return and volatility spillover effects of high significance are uncovered, for the first time, between the two distinct but interrelated derivatives markets. Keywords: Futures and Forward Markets, Causality, Price Discovery, Volatility Spillovers, Shipping and Commodity Markets. JEL Classification: G13, G14, C32

Corresponding Author: Manolis G. Kavussanos, Athens University of Economics and Business, 76 Patission Str., 10434, Athens, Greece, Tel: +30 210 8203167, Fax: +30 210 8203196, Email: mkavus@aueb.gr.

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1. INTRODUCTION

Cross-market information transmission is a research area that has received a lot of attention from

both academia and practitioners alike. Following Working (1970), economic shocks in one market

can impact with various degrees of severity other markets. In perfectly efficient markets, new

information is simultaneously incorporated into the prices of the markets, in such a way so that

prices adjust to new equilibrium levels without any time delay (see Chan et al., 1991). However,

transactions costs, information asymmetries, supply-demand imbalances and other market

microstructure issues may create information spillover (lead-lag) relationships between markets

(see Wahab and Lashgari, 1993; Fleming, et al., 1996, among others). The importance of

modelling such relationships is linked with the nature of trading dynamics between markets.

Investors and fund managers can utilize such information spillovers to create investment strategies

and portfolios, respectively. Regulators and policy decision-makers are interested in these

relationships in order to better monitor and supervise the markets. Economic agents participating

in these markets can utilize these relationships in investment and hedging decisions, as the

difference in reaction times between markets can be exploited in derivatives trades.

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

functions1. The second refers to information flows between derivatives markets and their

underlying spot markets2, and the third one, which, surprisingly enough, has received the least

attention, concerns return and volatility spillovers between different derivatives markets3. This

paper investigates the information (spillovers) relationships between freight and commodity (grain

and oil) derivatives markets and analyses the magnitude and direction of these spillovers.

More than 95% of the world’s commodity trade is transported by ocean-going vessels. The

international market for freight services possesses some special features that set it apart from other

commodity markets, due to its high level of volatility, cyclical nature, the seasonality influences of

the commodities transported, and its non-storable nature, amongst others. The latter characteristic

alone differentiates the freight market from all other storable commodity markets, as the theory of

storage and the cost-of-carry no-arbitrage relationships cannot be applied for the pricing of                                                             1 See Kao and Wan (2009) on energy markets; 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. 2 See Coppola (2008) on futures and spot commodity markets; Kavussanos and Visvikis (2004) on forward and spot freight markets, among others. 3 See Chng (2009) on natural gas, palladium and gasoline Japanese futures markets; Chulia and Torro (2008) on stock (the DJ Euro Stoxx 50 index futures) and bond (the Euro Bund futures) derivatives markets; Fung, et al. (2010) on US and Chinese aluminum and copper futures markets; and Kavussanos et al. (2010) on freight forwards and commodity futures markets, among others. 

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derivatives contracts for freight. As such, there is an increasing need for more sources of

information, that may be utilized by economic agents participating in these markets for the pricing

and trading of such commodity contracts4, 5.

Economic theory and intuition suggests that bi-directional linkages between freight derivatives

markets – Forward Freight Agreements (FFA) – 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 somehow and market

participants monitor both markets when taking investment decisions. The nature of this economic

relationship between the two derivatives markets is addressed in this paper and is consistent with

the presented empirical findings.

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 behavior of derivatives markets, possible

spillover effects between spot markets may 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.

                                                            4 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. 5 Prokopczuk (2011) employs alternative affine continuous-time models of the spot price dynamics in order to derive closed-form valuations for freight futures contracts.

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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 Panamax Index (BPI), the Baltic Supramax Index (BSI)

and the Baltic Handysize Index (BHSI)6. 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.

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.

This paper contributes to the literature in a number of ways: First, it puts forward an economic

framework, where the derivative market of the commodity transported is linked to that of the

freight market of the vessel transporting it, which shows that commodity futures informationally

lead the freight derivatives markets. Following that and since it has been found in the literature

that the derivatives markets under investigation informationally lead their corresponding

                                                            6 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).

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underlying spot (physical) markets, the main findings here should apply in the spot freight and

commodity markets as well7. This economic framework further contributes to the pricing of FFAs,

which are not so precisely priced given the non-storable nature of their underlying “commodity”;

namely the freight service (see Kavussanos and Visvikis, 2004)8.

Second, by utilizing a data set large enough to include a global financial crisis, the paper

investigates the statistical properties of the variables of interest, as well as, their long-run

interrelationships during crises periods. Structural breaks that may arise in either case in such

adverse market conditions may have a significant effect on the spillover patterns between the

examined variables. 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 (see Lien et al. 2003). 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 of such breaks taking place in

the spot markets.

Third, since the US commodity futures markets close at a different time interval than the time of

the announcement of FFA prices in the UK, it is possible that non-synchronicity may influence the

results9. In order to ensure that the spillover inferences are not biased by a non-synchronous

trading problem among the markets, a “time-matched” 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.

                                                            7 Kavussanos and Visvikis (2004), show that FFA markets are broadly unbiased and that the FFA market informationally leads the underlying (physical) spot market for freight rates. As such, FFAs can be utilized as price discovery vehicles for spot freight markets. Wheat, corn, soybean and coal futures, which correspond to the underlying commodities transported in the shipping routes of the dry-bulk FFA contracts, 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. 8 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. 9 In any given day, the Baltic Exchange FFA 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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Fourth, to the best of our knowledge, with the exception of Kavussanos et al. (2010), this is the

first paper to empirically examine cross-market return and volatility information spillovers

between freight and commodity derivatives markets. Moreover, it extends the Kavussanos et al.

(2010) study by combining the sub-segments of dry-bulk vessels (Capesize, Panamax and

Supramax), which carry various types of commodities under different types of freight contracts

(route-specific and time-charter contracts – see section 3 for more details), allowing comparisons

between the various dry-bulk shipping sectors and the different freight contracts, respectively.

Fifth, this paper investigates and reveals that commodity and freight derivatives markets are

interrelated, standing in a long-run equilibrium (cointegration) relationship between them. Finally,

results 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, linking freight and commodity derivatives markets, and the methodology used.

Section three analyses the data and outlines some preliminary results. Section four presents the

return and volatility spillover results. The fifth section provides a critical discussion of the results.

Finally, section six concludes the paper.

2. METHODOLOGY

2.1. Economic Framework

The final CIF price of commodities transported by sea, which incorporate the FOB price,

insurance and freight, should reflect 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,t-1), the current

freight rate (SFR,t) and the insurance required for the transportation of the commodity (INS).

Mathematically:

SCIF,t = SFOB,t-1 + SFR,t + INS (1)

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The insurance part in the above equation is relatively steady over time. However, both SFOB,t-1 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 on a particular route (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. (2004), 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 = SFOB,t-1 + FFR,t + INS (2)

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:

FCIF,t = SCIF,t + C (3)

where, C refers to the relatively steady over time cost of carrying the commodity forward in time

and incorporates storage, insurance and financial costs. Substituting Equation (3) into (2) yields:

FCIF,t = SFOB,t-1 + FFR,t + INS + C (4)

From equation (4), it is evident that the derivative 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,t-1), the current price of the

freight derivatives market (FFR,t), the insurance to transport the commodity (INS) and the cost of

carry components (C). This economic relationship can be used to assist the pricing of the non-

storable derivatives contracts for freight. 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.

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2.2. 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

used10. 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 ones (see Perron 1997). 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 series11. 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. Critical

values for the one- and two-break cases are tabulated in Lee and Strazicich (2004) and (2003),

respectively13.

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:

ΔXt =

1p

1i

ΓiΔXt-i + ΠXt-1 + εt ; εt | t-1 ~ distr(0, Ht) (5)

where Xt is the 2x1 vector (FFAt, FUTt)’ of log-FFA and log-commodity futures prices,

respectively, Δ denotes the first difference operator, εt is a 2x1 vector of residuals (εS,t, εF,t)’ that

follow an as-yet-unspecified conditional distribution with mean zero and time-varying covariance

matrix, Ht. Johansen and Juselius (1990) show that the coefficient matrix Π 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                                                             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 due to sample size considerations.

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estimated parameters Γi and Π, respectively. If Π has a reduced rank, that is rank(Π) = 1, then

there is a single cointegrating relationship between FFAt and FUTt, which is given by any row of

matrix Π and the expression ΠXt-1 is the error-correction term. In this case, Π can be factored into

two separate matrices α and β, both of dimensions 2x1, where 1 represents the rank of Π, such as

Π = αβ’, where β’ represents the vector of cointegrating parameters and α is the vector of error-

correction coefficients measuring the speed of convergence to the long-run equilibrium14.

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 = α1 + a2Dt + β1xt + εt (6a)

yt = α1 + a2Dt + β1xt + β2Dt xt + εt (6b)

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, α1 and (α1 + a2) are the intercepts before and after the

break at t*, and β1 and (β1 + β2) 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 equations15. The process is repeated until the minimum

value of the statistic (Z∗) 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                                                             14 Since rank(Π) equals the number of characteristic roots (or eigenvalues) which are different from zero, the number of distinct cointegrating vectors can be obtained by the λtrace and λmax statistics of Johansen (1988). Critical values are provided by Osterwald-Lenum (1992). 15 Monte Carlo experiments indicate that from the three recursive tests of GH (ADF and the Phillips-Perron Zt and Za) the Zt test performs better than the ADF and Za tests (see Gregory and Hansen, 1996a, b) and therefore, only the Zt results are reported in the ensuing analysis. 

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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 Philips 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).

2.3. 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:

FFAt =

1

1

p

i

aFFA,iFFAt-i +

1

1

p

i

bFFA,iFUTt-i + qFFAzt-1 + ε1,t (7a)

εi,t | t-1 ~ distr(0, Ht)

FUTt =

1

1

p

i

aFUT,iFFAt-i +

1

1

p

i

bFUT,iFUTt-i + qFUTzt-1 + ε2,t (7b)

where, FFAt-i and FUTt-i are the logarithmic first-differences of FFA and commodity futures

prices, respectively, zt-1 (= FFAt-1 – FUTt-1) is the lagged ECT, which represents the long-run

relationship between the two derivatives markets, εi,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

Equation 7a (7b) 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 exist if both bFFA,i and aFUT,i coefficients are

significant. These hypotheses are tested by employing a Granger (1988) Wald test on the joint

significance of the lagged estimated coefficients of ΔFFAt-i or ΔFUTt-i. 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

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and commodity futures price series, a bivariate Vector Autoregressive (VAR) model is estimated

instead of a VECM, excluding the zt-1 term from Equations (7a) and (7b).

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 Equation (5) (see Pesaran and

Shin, 1998).

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. (1987) augmented positive definite parameterisation in order to capture higher

moment dependencies (volatility spillovers):

Ht = A'A + B'Ht-1 B + C'εt-1εt-1'C + S1'u1,t-1u1,t-1'S1 + S2'u2,t-1u2,t-1'S2 + E'(zt-1)2E (8)

where, A is a (2x2) lower triangular matrix of coefficients, B and C are (2x2) diagonal coefficient

matrices, S1 and S2 are the matrices of the spillover effect parameters, u1,t-1 and u2,t-1 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,t-1 is the volatility spillover effect from the FFA

market to the commodity futures market and u2,t-1 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) (see Lee, 1994). Once

again, when no cointegration is discovered between FFA and commodity futures price series, a

BEKK VAR-GARCH model is estimated, as in Equation (9), but without including the lagged

squared ECT, (zt-1)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:

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Ht = exp [A'A + B'Ht-1 B + C'εt-1εt-1'C + D' εt-1εt-1'D + S1'u1,t-1u1,t-1'S1 + S2'u2,t-1u2,t-1'S2] (9)

where, the coefficients are as previously defined and the diagonal (2x2) D matrix measures the

asymmetry effects of shocks on volatility (dii):

, 1 , 1 , 1 , 1ii ii t i ii t ii t ii td E (10)

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 = A'A + B'Ht-1 B + C'εt-1εt-1'C + D'ζt-1ζt-1'D + S1'u1,t-1u1,t-1'S1 + S2'u2,t-1u2,t-1'S2 (11)

 

where, D is a 2x2 diagonal matrix of the coefficients of asymmetry, ζt-1 = εt-1Gt-1, and Gt-1 is a 2x1

vector of indicator variables which take the value of 1 if εt-1 < 0 and 0 otherwise. If the coefficient

of the indicator variable (Gt-1) is positive 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

t 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 (see Broyden, 1967) is used, which maximize the log-likelihood function, in

order to estimate the parameters of the GARCH models.

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3. DATA AND PRELEMINARY STATISTICS

The dataset used in the paper consists of daily Baltic Forward Assessments (BFAs) obtained from

Reuters and commodity futures price series from Bloomberg, Datastream International and Tick

Data. The period investigated extends from May 2006 to October 2009, yielding a total of 868

daily observations. Nearby (prompt) BFAs and commodity futures are used in order to include

contracts with the highest liquidity among the contracts of different durations. These are rolled

over to the next nearest contract before the nearby contract expires to circumvent the issues of thin

market and expiration effects. 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 mid bid and offer FFA market prices based on average FFA prices reported by a panel

of dry-bulk FFA brokers (namely, the panelists) appointed by the Baltic Exchange. Every business

day, the panelists submit their expert estimation of mid FFA market prices for the trading shipping

routes defined by the Baltic Exchange. BFAs are regarded as the most representative FFA data, as

they include information from the most active FFA brokers. 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 routes of the Capesize, Panamax,

Supramax and Handysize indices. The composition of each FFA time-charter basket 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. 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. Coal futures refers to the Richards Bay All Publication

Index-4 (API4) coal futures, which trade in the European Energy Exchange (EEX) and are

regarded as the underlying commodities of the Capesize trades. Corn, wheat and soybeans grain

futures contracts trade at the Chicago Mercantile Exchange (CME) and are regarded as the

14  

underlying commodities of the Panamax and Supramax trades. All commodity futures are quoted

in free on board prices. The inclusion criteria of the aforementioned commodity futures 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, sulfur, iron

ore and minor commodity futures contracts (salt, clinker, and pet coke) do not trade in an

organized exchange, and thus, were not included in the analysis.

Due to the different commodities transported by the investigated vessel 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 proxies

the cargoes of the Supramax trades and includes wheat, corn, soybean futures. As there is no

futures contract for iron ore, a synthetic commodity futures basket could not be constructed for the

cargoes of Capesize trades, and therefore, Capesize FFA trades are compared only with coal

futures contracts.

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 Baltic Exchange 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. In the literature, instead of using daily close-to-close prices, daily open-to-close

prices from daily close-to-open prices are separated (see Lin et al., 1994, among others). Others

researchers lead one day ahead the market data for the market that closes before the other markets

in their samples (see Kao and Wan, 2009, among others). Others use overlapping (rolling)

multiday returns (see Forbes and Rigobon, 2002), while others revert to lower-frequency (e.g.

weekly) data sets (see Chulia and Torro, 2008, among others). However, all the above solutions

are not suitable when returns are autocorrelated or when testing for information spillovers

(predictability). Thus, in order to ensure that the spillover inferences are not biased by a non-

15  

synchronous trading problem among the markets a “time-matched” data set is created by intra-day

data purchased from Tick Data, 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 London16.

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-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 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.

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. Support for the log-

first difference stationary assumption is also provided by the Kwiatkowski, et al. (KPSS, 1992)

test. 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. As different markets have different speeds of adjustment and reaction to breaks

                                                            16 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.

16  

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.

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, Schwarz, 1978), 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 found to be cointegrated with the freight derivatives markets by either the

Johansen (1988) or the Gregory and Hansen (1996) tests.

17  

Overall, cointegration results seem to be related with the type and importance of commodity

cargoes transported by each type of vessel. 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 commodity (corn, hog and soybean) 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. As it can be seen, for the

Capesize trades (CTC–Coal, C4–Coal, and C7–Coal) and the STC-Soybean pair an asymmetric

VECM-EGARCH process is found to provide a better fit to the data, while for the PTC–Soybean

pair a VECM-GJR-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. 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 in all cases are 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.

18  

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, and in accordance to the statistical significance of the

Granger causality (Wald) tests, it seems that commodity futures returns have a unidirectional

positive impact on FFA returns in all investigated Panamax and Supramax cases. 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, while

grains account for about 30% of the CIF price of grains. This in turn, may erode the signaling

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. On the other hand, and according to the

19  

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 ( kkc ) and

lagged variance-terms ( kkb ) 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 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 standardized residuals and

Engle’s (1982) test, presented in panel C, indicate absence of any serial correlation and

heteroskedasticity, respectively.

20  

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 Granger causality 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 ( kkc ) and lagged variance-terms ( kkb ) of the

variance equations indicates once again that volatility is time-varying 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

21  

volatilities. In only two cases (P2A–Corn and STC–Corn), there is no evidence of volatility

spillovers in either direction.

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. Figure 1 presents the time paths of the

FFA and commodity futures price innovations for a ten 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

time-charter basket with soybeans futures (STC-SOY) are shown in order to conserve space17.

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.

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 Granger causality test results.

                                                            17 The responses for the remaining markets are available from the authors upon request. 

22  

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. 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 were found. In contrast, it seems that there is no relationship in returns between Capesize

and coal derivatives markets. Regarding volatility spillovers, again it seems, in most cases, that

there is a unidirectional relationship from 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. Finally, the

synthetic commodity futures baskets, which aim to replicate the structure of the FFA contracts in

the Panamax and Supramax trades, also seem to be able to spill new information to the FFA

markets, both in returns and volatilities.

The above empirical findings can be explained as follows: First, commodity futures, which trade

in well-organised markets, are more liquid than FFAs, which trade OTC, with their average daily

contract trading volume being roughly triple that of FFA contracts. As such, commodity futures

are regarded as more efficient markets, subjected to less market frictions and mispricing.

McMillan and Ülkü (2009) argue that as the volume of trades increase 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 to a higher market efficiency. Chung and Hrazdil (2010) also

report that increased liquidity enhances market efficiency, after controlling for the effects of

market capitalization, trading volume and trading frequency. Second, less trading costs result to

higher trading and to a more efficient market (see Chordia, et al., 2011). The examined

commodity futures have less transactions costs in comparison to the FFA trades, as in a FFA trade

the brokerage fee is typically 0.25% of the value of the contract, in addition to the fees of the

clearing-house if the trade is cleared.

23  

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, it is not expected to attract as much trading interest from

institutional investors as the mainstream commodity futures markets examined in the paper. In the

literature, institutional investors are well-informed and rational, while individual investors are

treated as uniformed, exhibiting disposition effects and overconfidence (see Dhar and Zhu, 2006;

and Kim and Nofsinger, 2007, among others). As a consequence, commodity futures contracts are

accessible not only to a larger spectrum of investors, with more diverse trading needs, but to a

larger number of institutional investors who possess more and better information. This results in a

higher ratio of unsophisticated investors to the total number of investors participating in the FFA

markets, compared to the commodity futures markets. 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.

Fourth, as the FFA market is an emerging (newly-established) market, it is expected to

informationally lag the well-established and liquid commodity markets. McMillan and Ülkü

(2009) argue that as a market matures, more informed investors arrive overpowering the impact of

disposition trading on 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 organized 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 reasoning behind the empirical findings and partially explain the information superiority

of commodity futures markets in comparison to FFA markets.

 

The implications of the linkages uncovered here are extremely important both from a theoretical

and a practical perspective. On the theoretical front, an economic relationship developed in this

paper, for the first time, explains the link between commodity futures and forward freight markets.

This relationship may offer fruitful implications for a future research agenda on topics related to

the cost of carry and arbitrage relationships between commodity and freight (spot or derivatives)

markets and the pricing of commodity and freight derivatives contracts, amongst others. On the

practical front, investors may utilize the revealed linkages to construct profitable investment

24  

strategies; that is, take trading positions on the FFA market according to the direction of the

forward curves of the commodity futures markets or take trading positions on the freight option

market to gain from volatility changes spilled from the commodity options markets. Additionally,

hedgers can monitor the freight and commodity derivatives markets to implement the hedges in a

more effective manner.

6. CONCLUSION

This paper examines return and volatility spillover effects between different freight and

commodity futures markets, as such effects are economically important for all participants active

in the examined markets. The economic relationship proposed and tested empirically links the

derivative market of the commodity transported with that of the non-storable freight market of the

vessel transporting it. The paper investigates various types of commodities transported under

different types of freight contracts and over a period that includes a global economic crisis.

According to the results, in most investigated cases, new information seems to appear 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, together with the theoretical

economic relation developed in this paper, can help improve the understanding of the information

transmission mechanisms between freight and commodity derivatives, and consequently spot,

markets. The results can further assist to a more precise pricing of the non-storable freight

derivatives contracts, where the theory of storage does not hold. These results are of great value to

market participants in the international shipping and commodity markets, as they can use them to

enter into more effective trading, investment, chartering and hedging decisions.

25  

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28  

Table 1. Dry-bulk Time-charter Baskets Route Description Weights Cargoes Panel A: Capesize time-charter BFA basket (172,000 dwt vessels) C8_03 Gibraltar/Hamburg Trans-Atlantic round voyage 10% Iron ore, Coal C9_03 Continent/Mediterranean trip Far East 5% Iron ore C10_03 North Pacific round voyage 20% Iron ore, Coal C11_03 China/Japan trip Mediterranean/Continent 15% Coal Panel B: Panamax time-charter BFA basket (74,000 dwt vessels) P1A_03 Trans-Atlantic round voyage 25% Grains, Coal, Iron ore, Bauxite P2A_03 Skaw-Gibraltar/Far East 25% Grains, Iron ore P3A_03 Japan-S.Korea North Pacific round voyage 25% Grains, Coal, Sulphure P4A_03 Far East via North Pacific /Skaw-Passero 25% Grains, Coal, Sulphure Panel C: Supramax time-charter BFA basket (52,000 dwt vessels) S1A Antwerp - Skaw (Denmark) trip to Far East 12.5% Grains, Fertilizers S1B Canakkale (Turkey) trip to Far East 12.5% Steel, Fertilizers S2 Japan - South Korea / North Pacific or

Australia round voyage 25% Fertilizers

S3 Japan - South Korea trip from Gibraltar - Skaw (Denmark) range

25% Steel

S4A US Gulf - Skaw-Passero 12.5% Grains, Petcoke, Scrap S4B Skaw-Passero - US Gulf 12.5% Steel

Note: Sources: Baltic Exchange and Authors Grains include wheat, corn and soybeans. The four time-charter routes of the Capesize basket correspond to 50% of the weighting of the Baltic

Capesize Index (BCI). The remaining 50% weight is allocated in the five voyage routes of the index – for more details see the Baltic Exchange website.

 

29  

Table 2. Descriptive Statistics of Daily Logarithmic First-Differences of FFA and Commodity Futures Prices (05/2006 – 10/2009)

Panel A: FFA Price Series T Mean Std Skew Kurt J-B Q(12) Q2(12) ARCH(5)

CTC 868 0.00022 0.0620 -2.644 101.445 372,776.7 74.221 0.521 0.049

[0.917] [0.000] [0.000] [0.000] [0.000] [1.000] [1.000]

C4 868 0.00004 0.0302 -0.021 16.467 9,795.3 231.307 23.604 17.743

[0.971] [0.797] [0.000] [0.000] [0.000] [0.023] [0.003]

C7 868 0.00023 0.0299 0.763 17.664 11,355.3 245.594 54.311 44.362

[0.824] [0.000] [0.000] [0.000] [0.000] [0.000] [0.000]

PTC 868 0.00027 0.0497 1.714 88.410 282,792.1 33.458 0.772 0.525

[0.872] [0.000] [0.000] [0.000] [0.001] [1.000] [0.991]

P2A 868 0.00069 0.0308 -1.152 20.288 15,060.5 389.584 26.597 10.760

[0.510] [0.000] [0.000] [0.000] [0.000] [0.009] [0.056]

STC 868 0.00002 0.0399 -5.310 151.226 830,228.1 46.098 0.142 0.057

[0.988] [0.000] [0.000] [0.000] [0.000] [1.000] [1.000]

Panel B: Commodity Futures Price Series

Coal 868 0.00029 0.0233 -0.611 3.959 620.08 14.381 383.779 113.643

[0.711] [0.000] [0.000] [0.000] [0.277] [0.000] [0.000]

Corn 868 0.00043 0.0233 -0.090 1.446 76.717 12.801 40.294 16.196

[0.579] [0.282] [0.000] [0.000] [0.384] [0.000] [0.006]

Wheat 868 0.00026 0.0252 0.114 1.232 56.661 9.959 92.899 51.562

[0.579] [0.172] [0.000] [0.000] [0.620] [0.000] [0.000]

Soybean 868 0.00046 0.0196 -0.573 2.773 325.098 13.635 145.800 53.037

[0.760] [0.000] [0.000] [0.000] [0.325] [0.000] [0.000]

Synthetic Basket 1 868 0.00039 0.0185 -0.269 2.277 197.735 22.129 129.028 66.895 [0.530] [0.001] [0.000] [0.000] [0.036] [0.000] [0.000]

Synthetic Basket 2 868 0.00040 0.0190 -0.248 2.234 189.189 22.812 122.458 64.206

[0.536] [0.003] [0.000] [0.000] [0.029] [0.000] [0.000]

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 deviation. Skew and

Kurt are the estimated centralized third and fourth moments of the data; their asymptotic distributions under the null are ˆ (0, 6)3 ~Ta N and

ˆ 3 ~ (0, 24)4T a N . J-B is the Jarque-Bera (1980) test for normality; the statistic is distributed as χ2(2). Q(12) and Q2(12) are the Ljung-

Box (1978) Q-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 χ2(12). ARCH(5) is the Engle (1982) test for ARCH effects; the statistic is distributed as χ2(5).

30  

Table 3. Unit Root Tests of FFA and Commodity Futures Prices (05/2006 – 10/2009) ADF PP KPSS LS Two Breaks in Intercept LS One Break in Intercept

Levels 1st

Differences Levels

1st Differences

Levels TB1{λ1} TB2{λ2} B1t B2t LM test statistic

TB1{λ1} B1t LM test statistic

CTC -1.276 (1) -22.284 (0) -1.280 (9) -22.297 (4) 0.713 (23) 417 {0.5} 545 {0.6} 2,461.7 7,364.6* -1.659 (8) 545 {0.6} 1,819.6 -1.545 (8)

24/12/07 30/06/08 (0.722) (2.201) 30/06/08 (-0.534)

C4 -1.172 (1) -21.331 (0) -1.306 (12) -21.720 (7) 0.771 (23) 379 {0.4} 540 {0.6} 0.533 3.947* -1.892 (9) 540 {0.6} 3.930* -1.829 (9)

31/10/07 23/06/08 (0.778) (5.494) 23/06/08 (5.474)

C7 -1.330 (2) -14.845 (1) -1.470 (16) -23.005 (13) 0.654 (23) 379 {0.4} 524 {0.6} 0.858 1.097 -1.894 (9) 533 {0.6} -0.038 -1.840 (9)

31/10/07 30/05/08 (1.270) (1.576) 12/06/08 (-0.055)

PTC -1.006 (1) -23.506 (0) -1.168 (14) -24.583 (12) 0.848 (23) 425 {0.5} 609 {0.7} 1,511.5 5,034.7* -1.366 (10) 568 {0.7} -1,016.4 -1.152 (5)

08/01/08 29/09/08 (1.360) (4.238) 01/08/08 (-0.853)

P2A -1.301 (2) -14.529 (1) -1.361 (15) -20.619 (12) 0.723 (23) 392 {0.5} 524 {0.6} 1,888.1** 5,149.6* -1.559 (4) 524 {0.6} 5,001.4* -1.465 (4)

19/11/07 30/05/08 (1.676) (4.330) 30/05/08 (4.210)

STC -0.828 (1) -24.239 (0) -1.005 (14) -25.628 (13) 0.918 (23) 417 {0.5} 545 {0.6} 1,959.6* -860.06 -1.133 (5) 545 {0.6} -944.69 -1.070 (5)

24/12/07 30/06/08 (2.309) (-1.020) 30/06/08 (-1.119)

Coal -1.132 (0) -28.296 (9) -1.261 (0) -28.497 (8) 1.080 (23) 395 {0.5} 563 {0.6} 4.604** 3.310 -1.480 (5) 599 {0.7} -6.455* -1.416 (5)

22/11/07 24/07/08 (2.001) (1.392) 15/09/08 (-2.773)

Corn -1.634 (0) -27.598 (0) -1.758 (10) -27.742 (9) 1.037 (23) 544 {0.6} 680 {0.8} -27.780* -31.864* -1.731 (4) 589 {0.7} -34.608* -1.659 (4)

27/06/08 09/01/09 (-2.827) (-3.299) 01/09/08 (-3.561)

Wheat -1.602 (0) -28.878 (0) -1.580 (6) -28.884 (7) 0.939 (23) 323 {0.4} 589 {0.7} 42.005* -48.831* -1.523 (0) 589 {0.7} -48.907* -1.452 (0)

13/08/07 01/09/08 (2.270) (-2.638) 01/09/08 (-2.636)

Soybean -1.518 (0) -28.943 (0) -1.573 (9) -28.985 (8) 1.857 (23) 477 {0.5} 620 {0.7} 102.095* -57.721* -1.739 (6) 599 {0.7} -77.823* -1.660 (6)

20/03/08 14/10/08 (4.764) (-2.723) 15/09/08 (-3.663) Synthetic Basket 1

-1.493 (0) -29.531 (0) -1.537 (10) -29.577 (10) 1.418 (23) 477 {0.5} 636 {0.7} 54.407* -21.689** -1.514 (6) 571 {0.7} -32.648* -1.422 (8) 20/03/08 05/11/08 (5.040) (-2.040) 05/08/08 (-3.056)

Synthetic Basket 2

-1.535 (0) -29.780 (0) -1.566 (10) -29.797 (10) 1.419 (23) 477 {0.5} 680 {0.8} 72.280* -50.172* -1.580 (6) 599 {0.7} -44.834* -1.446 (6) 20/03/08 09/01/09 (5.125) (-3.665) 15/09/08 (-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 minimizing 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. λi= ΤΒi/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 i-th structural break in the intercept, which is standard normally distributed. Figures in parentheses are t-statistics, while * and ** indicate significance at the 5% and 10% significance levels, respectively. 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.

 

31  

Table 4. Cointegration Tests between FFA and Commodity Futures Prices

Price Series Lags Johansen Gregory-

Hansen Estimated Cointegrating Vector

λmax λtrace H0 H1 H0 H1 Zt*{λ} Zt*{λ} Johansen (J): β' = [1, β1, β2] Gregory-Hansen (C): [1, a1, a2, β1] Gregory-Hansen (C/S): [1, α1, α2, β1,β2 ] r = 0 r =1 r = 0 r >=1 C C/S β1, β2 α1 α2 β1 α1 α2 β1 β2 r <=1 r =2 r <=1 r =2

CTC – Coal 2 25.80 34.62 - - [1, -1,491.2 34,783.2 ] 8.82 8.82 (-5.20) (1.44) C4 – Coal 2 26.25 33.53 - - [1, -0.37 5.16 ] 7.29 7.29 (-5.33) (0.88) C7 – Coal 2 25.77 32.91 - - [1, -0.40 6.18 ] 7.14 7.14 (-5.58) (1.03) PTC – Corn 2 [4, 4] 10.65 12.94 -2.69 -2.65 2.30 2.30 {0.50} {0.50} PTC – Wheat 2 [1, 1] 7.02 8.09 -3.36 -3.38 1.07 1.07 {0.46} {0.47} PTC – Soybean 2 [0, 0] 7.13 9.24 -4.98* -5.01* [1, -41,082.3 -53,075.8 113.39] [1, -44,544.2 -46,584.1 117.93 -7.18] 2.11 2.11 {0.48} {0.48} (-21.26) (-41.03) (47.39) (-14.44) (-10.03) (29.70) (-1.45) PTC – Synthetic 1 2 [0, 0] 9.19 11.46 -4.67* -4.79** [1, -37,127.2 -41,959.6 191.68] [1, -43,753.1 -30,883.4 207.18 -22.97] 2.27 2.27 {0.48} {0.48} (-22.18) (-40.50) (52.58) (-15.84) (-8.00) (32.91) (-2.99) P2A – Corn 2 [6, 6] 10.33 12.72 -2.84 -2.85 2.39 2.39 {0.51} {0.70} P2A – Wheat 2 [1, 1] 8.07 9.59 -3.27 -3.50 1.52 1.52 {0.68} {0.70} P2A – Soybean 2 [6, 6] 6.28 8.57 -4.67* -4.67 [1, -50,171.7 -51,729.1 129.14] - - - - 2.28 2.28 {0.48} {0.48} (-22.38) (-34.45) (46.50) - - - - P2A – Synthetic 1 2 [4, 4] 9.03 11.16 -4.21 -4.21 2.13 2.13 {0.49} {0.47} STC – Corn 2 [3, 3] 13.23 15.89 -2.68 -2.63 2.66 2.66 {0.50} {0.50} STC – Wheat 2 [1, 0] 8.72 9.73 -3.39 -3.47 1.01 1.01 {0.47} {0.70} STC – Soybean 2 [0, 0] 8.48 10.81 -4.78* -4.77** [1, -26,919.7 -41,468.9 86.38] [1, -25,722.8 -43,639.8 84.79 2.44] 2.33 2.33 {0.48} {0.48} (-17.67) (-40.72) (45.85) (-10.62) (-11.91) (27.24) (0.63) STC – Synthetic 2 2 [0, 0] 10.34 12.65 -4.61* -4.60 [1, -25,336.5 -32,981.4 116.00] - - - -

2.31 2.31 {0.48} {0.48} (-19.54) (-41.72) (52.82) - - - - 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 minimizing 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. λ̂ i, in the λmax and λtrace cointegration tests, are the estimated eigenvalues of the Π matrix in Equation (5). 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 λmax and λtrace 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. * and ** indicate significance at the 5% and 10% significance levels, respectively. The coefficients a1, a2, β1, β2 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.

32  

Table 5. Maximum-Likelihood Estimates of Restricted BEKK VECM-GARCH Models

FFAt =

1

1

p

i

aFFA,iFFAt-i +

1

1

p

i

bFFA,iFUTt-i + qFFAzt-1 + ε1,t (7a)

FUTt =

1

1

p

i

aFUT,iFFAt-i +

1

1

p

i

bFUT,iFUTt-i + qFUTzt-1 + ε2,t (7b)

Ht = A'A + B'Ht-1 B + C'εt-1εt-1'C + S1'u1,t-1u1,t-1'S1 + S2'u2,t-1u2,t-1'S2 + E'(zt-1)2E (8)

Ht =exp [A'A + B'Ht-1 B + C'εt-1εt-1'C + D' εt-1εt-1' D + S1'u1,t-1u1,t-1'S1 + S2'u2,t-1u2,t-1'S2+ EC'(zt-1)2EC] (in CTC, C4, C7 with Coal) (9)

Ht = A'A + B'Ht-1 B + C'εt-1εt-1'C + D'ζt-1ζt-1'D + S1'u1,t-1u1,t-1'S1 + S2'u2,t-1u2,t-1'S2 (in PTC with Soybean) (10) VECM-EGARCH(1,1) VECM-EGARCH(1,1) VECM-EGARCH(1,1) VECM-GJR-GARCH(1,1) CTC Coal C4 Coal C7 Coal PTC Soybean Panel A: Conditional Mean Parameters

qj, j = FFA, FUT 8.118E-08**

(1.921) 7.371E-08*

(4.644) 1.299E-04

(1.614) 2.979E-04*

(4.559) 1.367E-04**

(1.714) 3.081E-04*

(4.770) -4.318E-07*

(-2.482) 1.921E-07*

(2.757) aj,i, j = FFA, FUT i = 1, 2

0.161* (4.704)

-0.009 (-0.676)

0.281* (8.220)

-0.040 (-1.448)

0.213* (6.294)

-0.046** (-1.691)

0.123* (3.616)

-0.015 (-1.100)

- - 0.117*

(3.428) 0.036

(1.312) 0.173* (5.087)

0.024 (0.872)

- -

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

-0.027 (-0.299)

0.049 (1.454)

0.042 (0.997)

0.054 (1.597)

0.050 (1.204)

0.055 (1.622)

0.218* (2.536)

0.028 (0.825)

Wald Test 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] Panel B: Conditional Variance Parameters

ω11 -1.1150* (-2.472) -0.4332* (-5.371) -0.0683 (-1.301) -0.0524** (-1.913) ω21 0.0255 (0.959) 0.0534** (1.864) 0.0565 (1.312) -0.0557 (-1.385) ω22 -0.2291 (-0.992) -0.4452* (-3.849) -0.2140* (-2.839) -0.2072 (-0.819)

bkk, k = 1, 2 0.826*

(11.560) 0.970* (31.78)

0.936*

(82.37) 0.942* (63.64)

0.986* (131.8)

0.970* (101.3)

0.989* (44.287)

0.973* (30.83)

ckk, k = 1, 2 -0.021

(-0.689) 0.053

(1.075) 0.151* (2.510)

0.150* (3.258)

0.166* (2.996)

0.124* (3.201)

0.034* (3.353)

0.026* (2.787)

si, i = 1, 2 0.0175 (0.978)

0.1819 (1.470)

0.0051 (0.172)

0.1750*

(3.668) 0.0699*

(4.337) 0.1265*

(2.903) 0.0545 (0.911)

0.008 (0.815)

eci, i = 1, 2 -0.0001*

(-2.222) -0.0001 (-1.154)

-0.002 (-1.403)

-0.003* (-3.194)

-0.001 (-1.469)

-0.002* (-3.317)

- -

dii, i = 1, 2 2.053

(1.265) -1.655** (-1.788)

-0.293 (-1.361)

-0.710*

(-2.235) -0.004

(-0.031) -0.709*

(-2.332) - -

gii, i = 1, 2 - - - - - - 3.909*

(4.849) 0.257** (1.647)

 

33  

 

Panel C: Diagnostic Tests on Standardized Residuals CTC Coal C4 Coal C7 Coal PTC Soybean

Log-Likelihood 3,707 4,109

4,229 4,035 Skewness 1.245 [0.000] -0.020 [0.809] -0.815 [0.000] 0.155 [0.063] -0.081 [0.331] 0.118 [0.156] -0.588 [0.000] -0.267 [0.001] Kurtosis 26.252 [0.000] 2.742 [0.000] 14.595 [0.000] 3.005 [0.000] 11.566 [0.000] 2.874 [0.000] 24.737 [0.000] 1.419 [0.000]

J-B 25,061.6 [0.000] 271.05 [0.000] 7,772.6 [0.000] 328.97 [0.000] 4,822.1 [0.000] 299.69 [0.000] 22,069 [0.000] 82.765 [0.000] Q(12) 13.861 [0.241] 9.296 [0.595] 26.597 [0.005] 10.009 [0.530] 28.038 [0.003] 11.881 [0.373] 11.981 [0.365] 13.769 [0.246] Q2(12) 0.801 [1.000] 18.684 [0.067] 4.096 [0.967] 4.913 [0.935] 5.463 [0.907] 5.556 [0.901] 4.205 [0.963] 13.256 [0.277]

ARCH(12) 0.041 [0.839] 0.066 [0.797] 0.032 [0.859] 0.098 [0.755] 1.093 [0.296] 1.221 [0.269] 0.324 [0.985] 1.159 [0.308] SBIC -7,271 -8,075 -8,317 -7,929

Sign Bias 0.232 [0.817] -1.620 [0.106] -0.873 [0.383] -1.806 [0.071] -1.489 [0.137] -1.892 [0.059] -0.161 [0.872] 0.328 [0.743] Negative Size Bias -0.792 [0.429] -0.581 [0.561] -1.248 [0.213] 0.245 [0.807] -0.356 [0.722] 0.385 [0.700] 0.115 [0.885] 0.943 [0.346] Positive Size Bias -0.689 [0.491] 1.004 [0.316] 0.073 [0.942] 0.343 [0.731] 1.179 [0.239] 0.582 [0.561] 0.933 [0351] -1.428 [0.154]

Joint Bias Test 0.351 [0.789] 2.086 [0.101] 1.524 [0.207] 1.693 [0.167] 1.277 [0.281] 1.614 [0.185] 0.313 [0.815] 1.123 [0.339] All variables are in natural logarithms. Figures in parentheses (.) and in squared brackets [.] indicate t-statistics and exact significance levels, respectively, while * and ** indicate significance at the 5% and 10% significance levels, respectively. In all FFA and commodity futures pairs, the GARCH models are estimated utilizing the QMLE, while the Broyden, et al. (BFGS) algorithm is used. qt-1 represents the lagged ECT (qt-1 = β'Xt-1). Wald Test is the Granger (1988) causality test, distributed as χ2(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-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: u 2t = a0 + bY

1t + t (sign bias test); u 2t = a0 + bY

1t εt-1 + t (negative size bias test); u 2t = a0 +

bY 1t εt-1+ t (positive size bias test), where u 2

t are the squared standardised residuals (ε 2t /ht). Y

1t is a dummy variable taking the value of one when εt-1 is negative and

zero otherwise, and Y 1t = 1 - Y

1t . The joint bias test is based on the regression u 2t = a0 + b1Y

1t + b2Y

1t εt-1 + b3Y

1t εt-1 + t. 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.

34  

Table 5. Maximum-Likelihood Estimates of Restricted BEKK VECM-GARCH Models (Cont.) VECM-GARCH(1,2) VECM-GARCH(1,1) VECM-EGARCH(1,1) VECM-GARCH(1,1) PTC Synthetic 1 P2A Soybean STC Soybean STC Synthetic 2 Panel A: Conditional Mean Parameters

qj, j = FFA, FUT -3.245E-07**

(-1.687) 1.908E-07*

(2.635) -2.513E-07*

(-3.009) 1.480E-07*

(2.436) -3.751E-07*

(-2.117) 2.670E-07*

(3.031) -3.659E-07**

(-1.815) 2.719E-07*

(2.814) aj,i, j= FFA, FUT

i = 1, 2 0.130* (3.862) -0.015 (-1.212) 0.386* (11.357) -0.047** (1.883) 0.119*

(3.519) -0.018

(-1.052) 0.126* (3.693)

-0.023 (-1.407)

- - 0.075* (2.069) 0.012 (0.461) - - - - - - 0.086* (2.535) 0.041** (1.668) - - - -

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

0.247* (2.708) -1.740E-03 (-0.051) 0.128* (2.711) 0.028 (0.809) 0.184* (2.672) 0.027 (0.773) 0.223* (3.119) -0.012 (-0.344)

Wald Test 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] Panel B: Conditional Variance Parameters

ω11 -0.0121* (-4.030) 1.653E-05 (0.211) -0.0491* (-1.411) 0.0092* (5.426) ω21 -0.0024* (-2.769) -1.674E-04 (-1.036) 0.0521 (1.682) 0.0018* (3.429) ω22 -0.0005 (-0.582) 1.694E-03* (3.490) 0.0025 (0.0683) 0.0004 (0.432)

bkk, k = 1, 2 0.0031 (0.050) 0.960* (77.66) 0.992* (387.94) 0.967* (192.99) 0.994* (299.03) 0.996* (202.63) 0.028 (1.268) 0.975* (171.63) ckk, k = 1, 2 -0.593* (-3.446) 0.053 (0.890) -0.087* (-2.295) 0.223* (9.212) 0.042* (2.229) 0.097* (3.202) 2.235* (6.711) -0.189* (-7.984)

-0.025 (-0.657) -0.229* (-5.847) - - - - - - si, i = 1, 2 0.0159 (0.886) -1.2214* (-2.484) 0.0710* (3.022) -2.86E-05 (-4.5E05) -0.2113* (-4.728) 0.0884* (3.862) 8.271E-04 (0.008) -0.2498* (-2.797)

eci, i = 1, 2 -0.0270E-04*

(-2.866) -0.010E-05

(-0.961) -2.244E-07*

(-5.940) -6.933E-08**

(-1.738) 2.357E-06*

(2.454) -1.125E-06

(-1.634) 1.548E-05*

(2.695) -2.070E-06*

(-3.331) dii, i = 1, 2 - - - - 0.766* (4.858) -0.064 (-0.525)

Panel C: Diagnostic Tests on Standardized Residuals PTC Synthetic 1 P2A Soybean STC Soybean STC Synthetic 2

Log-Likelihood 3,815 4,254 4,295 4,142 Skewness 1.578 [0.000] -0.085 [0.307] -0.758 [0.000] -0.341 [0.000] -0.130 [0.112] -0.056 [0.501] -1.147 [0.000] -0.118 [0.157] Kurtosis 47.496 [0.000] 1.242 [0.000] 17.305 [0.000] 2.117 [0.000] 17.646 [0.000] 1.824 [0.000] 36.535 [0.000] 1.254 [0.000]

J-B 81,664 [0.000] 56.611 [0.000] 10,851 [0.000] 177.87 [0.000] 11,211 [0.000] 120.18 [0.000] 48,242 [0.000] 58.609 [0.000] Q(12) 7.268 [0.777] 14.150 [0.205] 14.845 [0.190] 12.345 [0.338] 19.539 [0.052] 11.891 [0.372] 27.569 [0.004] 19.365 [0.0648] Q2(12) 0.889 [0.999] 9.693 [0.558] 4.875 [0.937] 9.749 [0.553] 9.001 [0.622] 10.472 [0.489] 1.358 [0.999] 11.237 [0.424]

ARCH(12) 0.079 [0.999] 0.772 [0.679] 0.375 [0.972] 0.811 [0.639] 0.789 [0.662] 0.852 [0.596] 0.122 [0.999] 0.913 [0.533] SBIC -7,488 -8,353 -8,448 -8,142

Sign Bias 1.959 [0.051] 0.170 [0.865] 0.205 [0.837] 0.176 [0.860] -0.207 [0.836] 0.565 [0.573] 0.365 [0.715] 0.263 [0.792] Negative Size Bias -0.301 [0.764] -0.110 [0.912] -1.139 [0.255] -0.852 [0.394] -0.418 [0.676] -1.484 [0.138] 0.059 [0.953] 0.057 [0.954] Positive Size Bias -0.725 [0.469] -1.267 [0.206] 0.431 [0.667] -1.249 [0.212] 0.855 [0.393] -1.286 [0.199] -0.386 [0.699] -1.602 [0.109]

Joint Bias Test 1.339 [0.260] 0.743 [0.527] 0.609 [0.609] 0.981 [0.401] 0.348 [0.790] 1.272 [0.283] 0.080 [0.971] 1.167 [0.321]

 

35  

Table 6. Vector Autoregressive (VAR) Restricted BEKK-GARCH Parameter Estimates

FFAt =

1

1

p

i

aFFA,iFFAt-i +

1

1

p

i

bFFA,iFUTt-i + ε1,t (without an ECT term) (7a)

FUTt =

1

1

p

i

aFUT,iFFAt-i +

1

1

p

i

bFUT,iFUTt-i + ε2,t (without an ECT term) (7b)

Ht = A'A + B'Ht-1 B + C'εt-1εt-1'C + S1'u1,t-1u1,t-1'S1 + S2'u2,t-1u2,t-1'S2 (without a squared ECT term) (8)

Ht =exp [A'A + B'Ht-1 B + C'εt-1εt-1'C + D' εt-1εt-1' D + S1'u1,t-1u1,t-1'S1 + S2'u2,t-1u2,t-1'S2] (in P2A with Corn ) (9) Ht = A'A + B'Ht-1 B + C'εt-1εt-1'C + D'ζt-1ζt-1'D + S1'u1,t-1u1,t-1'S1 + S2'u2,t-1u2,t-1'S2 (in PTC with Corn) (10)

VAR(1)-GJR-GARCH(1,1) VAR(1)-GARCH(1,2) VAR(2)-EGARCH(1,1) VAR(2)-GARCH(1,2) PTC Corn PTC Wheat P2A Corn P2A Wheat

Panel A: Conditional Mean Parameters aj,i, j= FFA, FUT

i = 1, 2 0.129* (3.855)

-0.021 (-1.351)

0.133* (3.957)

-0.015 (-0.851)

0.404* (11.968)

-0.071* (-2.496)

0.406* (11.970)

-0.046 (-1.455)

- - - - 0.107* (3.148)

0.035 (1.241)

0.105* (3.114)

1.492 (0.136)

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

0.182* (2.482)

0.035 (0.1.03)

0.165* (2.481)

-0.019 (-0.568)

0.057 (1.409)

0.038 (1.104)

0.064** (1.748)

-0.019 (-0.557)

Wald Test 6.375 [0.011] 1.836 [0.175] 6.329 [0.011] 0.729 [0.393] 2.915 [0.232] 6.279 [0.043] 2.815 [0.093] 0.857 [0.355] Panel B: Conditional Variance Parameters

a11 0.0252* (5.162) 0.0253* (2.299) -0.0100 (-0.563) 0.0195* (6.507) a21 0.0009 (0.911) 0.0009 (0.967) 0.0018 (0.056) 0.0009 (1.066) a22 0.0049* (3.796) 0.0047* (2.122) -0.2961* (-2.052) 0.0044* (2.899)

bkk, k = 1, 2 -0.013

(-0.108) 0.956*

(54.173) 0.0001 (0.011)

0.946*

(28.777) 0.997*

(461.97) 0.959*

(50.509) 0.222

(0.682) 0.947*

(44.627)

ckk,1, k = 1, 2 0.496* (2.417)

-0.093 (-0.979)

1.818 (1.023)

-0.008 (-0.096)

0.038* (2.089)

0.006 (0.183)

0.403* (3.397)

-0.139 (-1.034)

- - -0.008

(-0.208) 0.260* (4.317)

- - 0.306

(1.111) -0.216** (-1.759)

si, i = 1, 2 1.204E-05

(1.497E-04) 1.364* (3.136)

-0.0265 (-1.312)

1.0158* (3.494)

0.0016 (0.202)

0.0352 (1.585)

0.0643* (2.513)

0.5567* (1.975)

dii, i = 1, 2 - - - - 1.358

(1.244) 9.030

(0.210) - -

gii, i = 1, 2 -2.442

(-3.627) -0.251

(-3.256) - - - - - -

 

 

 

36  

 

Panel C: Diagnostic Tests on Standardized Residuals PTC Corn PTC Wheat P2A Corn P2A Wheat

Log-Likelihood 3,532 3,438 4,073 3,879

Skewness 2.034 [0.000] 0.124 [0.138] 2.937 [0.000] 0.234 [0.154] -1.024 [0.000] 0.049 [0.550] -0.837 [0.000] 0.237 [0.005]

Kurtosis 57.492 [0.000] 1.339 [0.000] 75.525 [0.000] 0.703 [0.000] 13.653 [0.000] 1.380 [0.000] 27.362 [0.000] 0.661 [0.000]

J-B 11,972 [0.000] 66.881 [0.000] 20,682 [0.000] 25.683 [0.000] 6,862 [0.000] 68.919 [0.000] 27,053 [0.000] 23.813 [0.000]

Q(12) 10.409 [0.494] 10.222 [0.510] 8.724 [0.404] 7.469 [0.759] 14.508 [0.206] 8.324 [0.684] 14.534 [0.205] 7.845 [0.727]

Q2(12) 0.504 [0.999] 3.550 [0.981] 0.512 [0.999] 15.709 [0.152] 4.199 [0.964] 8.965 [0.625] 2.795 [0.993] 16.925 [0.110]

ARCH(12) 0.045 [1.000] 0.272 [0.993] 0.046 [1.000] 1.311 [0.206] 0.342 [0.981] 0.668 [0.783] 0.221 [0.997] 1.369 [0.175]

SBIC -6,963 -6,775 -8,019 -7,631

Sign Bias -0.017 [0.986] 0.751 [0.453] 1.204 [0.229] -1.088 [0.277] -0.939 [0.348] 1.001 [0.317] 0.919 [0.358] -0.585 [0.559]

Negative Size Bias 0.121 [0.904] -0.909 [0.363] -0.208 [0.835] 1.145 [0.253] -0.777 [0.438] -0.957 [0.339] -0.392 [0.695] 1.371 [0.171]

Positive Size Bias -0.209 [0.835] -1.269 [0.205] -0.577 [0.564] 0.720 [0.472] 1.339 [0.181] -1.310 [0.191] -0.247 [0.805] 0.384 [0.701]

Joint Bias Test 0.022 [0.996] 0.643 [0.587] 0.512 [0.674] 0.509 [0.677] 1.244 [0.292] 0.643 [0.587] 0.294 [0.830] 0.675 [0.567]

See notes in Table 5.

37  

Table 6. Vector Autoregressive (VAR) Restricted BEKK-GARCH Parameter Estimates (Cont.) VAR(3)-GJR-GARCH(1,1) 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

i = 1, 2 0.392* (11.516) -0.049* (-2.129) 0.123* (3.666) -0.026 (-1.326) 0.129* (3.825) 0.126* (3.754)

0.078* (2.121) 0.013 (0.541) - - - - 0.084* (2.486) 0.035 (1.495)

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

0.129* (2.586) -0.011 (-0.317) 0.167* (2.845) 0.035 (1.013) 0.088** (1.658) 0.161* (3.013)

0.064 (1.128) -0.052 (-1.513) - - - - -0.065 (-1.651) ** 0.058** (1.698) - - - -

Wald Test 8.995 [0.011] 3.952 [0.139] 8.154 [0.004] 1.759 [0.185] 10.629 [0.005] 3.188 [0.203] Panel B: Conditional Variance Parameters

a11 0.0176* (2.911) 0.0183* (4.304) 0.0055* (2.428) a21 0.0004 (0.938) 0.0008 (1.259) 0.0017 (0.798) a22 0.0028* (3.961) 0.0041* (3.949) 0.0040 (1.024)

bkk, k = 1, 2 0.584** (1.834) 0.959* (95.229) -0.007 (-0.316) 0.967* (79.885) -0.003 (-0.034) 0.955* (32.139) ckk,1, k = 1, 2 0.383* (2.321) -0.172* (-3.599) -2.156 (-1.640) 0.109 (1.375) -3.224* (-2.563) 0.040 (0.292)

- - - - 0.006 (0.055) 0.236* (2.445) si, i = 1, 2 0.0721* (2.723) 0.468* (1.891) 3.502E-04 (0.005) 9.563E-04 (0.006) -0.032 (-1.124) -0.8025* (-2.835) gii, i = 1, 2 0.066 (0.221) 0.179 (2.471) -3.095 (-1.537) 0.207* (3.074) - -

Panel C: Diagnostic Tests on Standardized Residuals P2A Synthetic 1 STC Corn STC Wheat

Log-Likelihood 4,179 3,666 4460.722 Skewness -0.542 [0.000] -0.128 [0.126] 0.460 [0.000] 0.115 [0.169] -4.955 (0.000) 0.209 (0.012) Kurtosis 27.329 [0.000] 1.362 [0.000] 72.409 [0.000] 1.381 [0.000] 89.869 (0.000) 0.728 (0.000)

J-B 26,898 [0.000] 69.052 [0.000] 189,001 [0.000] 70.668 [0.000] 294,627 (0.000) 25.383 (0.000) Q(12) 12.583 [0.321] 13.886 [0.239] 12.147 [0.353] 9.849 [0.544] 3.398 (0.984) 16.061 (0.139) Q2(12) 2.584 [0.995] 9.786 [0.549] 0.776 [0.999] 3.186 [0.988] 0.532 (0.999) 16.318 (0.130)

ARCH(12) 0.203[0.998] 0.833 [0.615] 0.070 [0.999] 0.247 [0.996] 0.0447 (1.000) 1.363 (0.178) SBIC -8,203 -7,243 -8,827

Sign Bias -0.192 [0.848] 0.079 [0.937] 0.209 [0.834] 0.887 [0.375] 0.838 (0.402) -0.341 (0.734) Negative Size Bias -0.222 [0.825] 0.648 [0.517] 0.124 [0.901] -1.067 [0.286] -0.134 (0.893) 0.957 (0.339) Positive Size Bias -0.246 [0.806] -1.552 [0.121] -.0425 [0.671] -1.476 [0.140] -0.694 (0.488) 0.975 (0.327)

Joint Bias Test 0.098 [0.961] 1.516 [0.209] 0.076 [0.973] 0.870 [0.456] 0.298 (0.826) 0.666 (0.573) See notes in Table 5.

 

 

38  

 

Figure 1. Generalised Impulse Responses in the FFA and Commodity Futures Markets

CTC, PTC and STC are the Capesize, Panamax and Supramax BFA four time-charter 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.

 

  

.00

.01

.02

.03

.04

.05

.06

.07

1 2 3 4 5 6 7 8 9 10

CTC API4

Response of CTC to Generalized OneS.D. Innovations

.000

.004

.008

.012

.016

.020

.024

1 2 3 4 5 6 7 8 9 10

CTC API4

Response of API4 to Generalized OneS.D. Innovations

.00

.01

.02

.03

.04

.05

1 2 3 4 5 6 7 8 9 10

PTC SYN1

Response of PTC to Generalized OneS.D. Innovations

-.005

.000

.005

.010

.015

.020

1 2 3 4 5 6 7 8 9 10

PTC SYN1

Response of SYN1 to Generalized OneS.D. Innovations

-.01

.00

.01

.02

.03

.04

1 2 3 4 5 6 7 8 9 10

STC SOYBEANS

Response of STC to Generalized OneS.D. Innovations

-.005

.000

.005

.010

.015

.020

1 2 3 4 5 6 7 8 9 10

STC SOYBEANS

Response of SOYBEANS to Generalized OneS.D. Innovations