Cullinane book chapter 2011 - Hedging Capesize

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Kavussanos, M.G. and I. Visvikis, “The hedging performance of the Capesize forward freight market”, Chapter 16, (In Eds.) Cullinane, K., ‘The International

Handbook of Maritime Business’, Edward Elgar Publishing, 2010.

THE HEDGING PERFORMANCE OF THE CAPESIZE FORWARD FREIGHT MARKET

MANOLIS G. KAVUSSANOS

Athens University of Economics and Business Department of Accounting and Finance 76 Patission St, 10434, Athens, Greece

Email: [email protected]

ILIAS D. VISVIKIS ALBA Graduate Business School,

Athinas Ave. & 2A Areos Str., 16671 Vouliagmeni, Athens, Greece Email: [email protected]

CURRENT VERSION: DECEMBER 2008

Keywords: Hedging Effectiveness, Futures and Forward Markets, Constant and Time-Varying Hedge Ratios, VECM-GARCH, Shipping.

JEL Classification: G13, G14, C32

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INTRODUCTION

Bulk shipping business is characterised by extreme volatility in rates and prices of its

assets; the vessels. This is a consequence of the very competitive freight markets, inelastic

supply of freight rates in the short-run and a demand for freight services, which is

influenced by a score of international factors that are often difficult to assess and forecast.

As a consequence of this high volatility in freight rates (and prices), cash-flows of shipping

companies, which are dependent on freight rates, are themselves volatile. This riskiness of

cash-flows and the difficulty of making them more predictable are responsible for the

spectacular failures (but also for the high returns) observed in the industry in the past.

The Capesize sector has been documented in the literature to be the riskiest in terms

of freight rate volatility, amongst the sectors of dry-bulk shipping (see for example

Kavussanos, 1996)1. The relatively limited type of trades (iron ore, coal, grains) that these

vessels are involved in, in comparison to Panamax and Handy vessels, is responsible for

this higher volatility observed in freight rates and prices of Capesize vessels. Therefore, it

makes it even more prominent to consider methods of mitigating the business risks that

arise in the riskiest sector of dry-bulk shipping – the Capesize sector. As argued in

Kavussanos and Visvikis (2006a; 2007), the use of derivatives products for business risk

management purposes provides more flexible and cheaper solutions, relative to the

traditional methods of time-chartering the vessels. The same is also true for charterers. For

the charterer, wishing to hire in vessels for transportation requirements, uncertainty of

freight rates constitutes risk over transportation costs. Freight derivatives contracts can be

used to hedge this source of risk.

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For many years now, financial derivatives have been introduced in order to provide

instruments for businesses to reduce or control the unwanted market risk of price changes,

by transferring it to others more willing to bear it. This function of derivatives markets is

performed through hedging the spot (physical) position by holding an opposite position in

the derivatives (paper) market. An important issue, in this process of hedging risks, is the

calculation of the correct number of forward contracts to use for each cash position held.

The solution to this problem depends on a number of parameters, and can influence greatly

the hedging effectiveness results. These parameters include: the models that are used to

estimate empirically the optimal hedges and whether in-sample or out-of-sample hedging

horizons are considered as relevant for the investor. This study answers these important

issues for investors wishing to engage in freight rate risk management in the Capesize

sector, through the use of the derivatives markets.

The existence of derivatives products in shipping has made risk management

cheaper, more flexible and readily available to parties exposed to adverse movements in

freight rates and other variables (such as, bunker prices, foreign exchange rates, interest

rates, vessel values, etc.) that affect the cash-flow position of the shipping company and its

customers as a consequence. By using freight derivatives, freight market participants can

secure (stabilize) their future (freight) income or (freight) costs and reduce the uncertainty

and volatility that comes from fluctuations in freight rates. Since the inception of freight

derivatives in 1985, with a freight futures contract on the general dry-bulk freight index,

namely the Baltic International Freight Futures Exchange (BIFFEX) contract, a number of

freight derivatives products have been introduced, which are tailored-made for use in the

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Capesize sector. Some of these are either Exchange-Based, while others are traded Over-

The-Counter (OTC).

The first OTC freight derivatives products that appeared in shipping markets since

1992 are the Forward Freight Agreement (FFA) contracts. FFAs are principal-to-principal

private agreements between a seller and a buyer to settle a freight rate, for a specified

quantity of cargo or type of vessel, for usually one, or a combination of the major trade

routes of the dry-bulk or tanker sectors of the shipping industry. Since they can be

“tailored-made”, to suit the needs of their users, they have become very popular with

market participants wishing to hedge freight rate fluctuations.

To see how they can be used, assume that a shipowner (or a charterer) feels that the

freight market in a specific route, with a specific vessel/cargo size, might move against him

in the future. He can approach a freight derivatives broker to sell (buy) FFA contracts,

written on the route – vessel/cargo type. The shipowner’s broker will search to find a

charterer with opposite expectations to the shipowner thereby wishing to buy (sell) FFAs

and negotiate the terms of the contract. If an agreement is reached then the FFA contract is

fixed.

In order to create freight derivatives contracts, independently set underlying freight

rate indices must be available, so that freight derivatives contracts can be settled against

these. The Baltic Exchange has undertaken this task since 1985. The dry-bulk trading

routes, which serve as the underlying assets of the 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), while the Baltic Dirty Tanker Index (BDTI)

and the Baltic Clean Tanker Index (BCTI) cater for the needs of the tanker industry. The

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Baltic indices comprise the most important routes in each segment of the industry and are

designed to reflect the daily movement in freight rates across spot voyage and time-charter

routes. Each route is given an individual weighting to reflect its importance in the world

freight market. Routes are regularly reviewed to ensure their relevance to the underlying

physical market.2

Table 1 presents the structure of the BCI, which is relevant for this chapter. It

comprises spot and time-charter routes, coded C2 to C12, involving Capesize vessels

ranging from 150,000 dwt to 172,000 dwt, carrying iron ore and coal in the routes

described in the fourth column of the table. As can be seen in the last column of the table,

the four time-charter routes are used, with equal weights, to produce the index. As can be

observed, the routes included in the index account fully for the trades that take place in the

Capesize sector today.

Voyage-based freight derivatives contracts on a particular route of the BCI are

settled on the difference between the contracted price and the average spot price of the

route over the last seven working days of the settlement month. Time-charter-based

contracts on a BCI route are settled on the difference between the contracted price and the

average price over the calendar settlement month. If freight rates fall below the agreed rate,

the buyer of FFAs (charterer) pays the difference between the agreed FFA price and the

settlement spot price; if rates increase, then the buyer of FFAs receives the difference. The

opposite is true for the seller of FFAs (shipowner).

Moreover, it should be noted that in OTC derivatives markets, each party accepts

credit-risk (counter-party risk) from the other party3. In case counterparties are concerned

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about credit risk in an FFA transaction, these can be cleared since September 2005 in the

LCH.Clearnet in London and since May 2006 in the SGX AsiaClear in Singapore4.

The primary advantage of an OTC derivatives market is that the terms and

conditions of the contract are tailored to the specific needs of the two parties. This gives

investors flexibility by letting them introduce their own contract specifications in order to

cover their specific needs. On the other hand, since November 2001 the International

Maritime Exchange (IMAREX) and since May 2005 the New York Mercantile Exchange

(NYMEX) offer freight futures contracts too. These are standardized contracts, which are

cleared at their associated clearing-houses, following a daily mark-to-market procedure that

eliminates credit risk.

This chapter contributes to the existing literature in a number of ways. First, despite

the growing importance of the FFA market in hedging freight rate risk in the Capesize

sector, to the best of our knowledge, no effort has been devoted to measuring the

effectiveness of the hedges performed in the sector. According to market estimates, during

2008, 3.17 bn tonnes of dry cargo were transported, while 3.5 bn tonnes were involved in

dry-bulk FFA trades. Around 55% of these FFA trades were conducted in the Panamax

market, 35% in the Capesize and around 10% in the Supramax/Handy markets. During

2008, Capesize trading interest has increased by 10% from the previous year.

Second, as discussed later, a potential hedger has a choice of strategies when

deciding on the optimal number of FFA contracts to use for a given freight exposure in the

underlying physical market. These alternatives are assessed and the best performing

strategy is chosen for hedging in the Capesize sector. This is achieved by estimating

different models and comparing the hedging outcomes, so as to select the model which

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takes into account the properties of both spot and FFA prices. Thus, the hedging

effectiveness of dynamic (time-varying) hedge ratios is compared and contrasted with that

of constant hedge ratios.

Third, it is deemed important to investigate the risk management function of these

contracts as the OTC FFA market is currently the most widely used derivatives market in

the shipping industry5. Special features of this market include: (i) the asymmetric

transactions costs between spot and FFA markets. These costs are higher in the spot

(physical) freight market (in relation to the FFA market) and (ii) the non-storable nature of

the underlying commodity, being that of a service. The non-storable nature of the FFA

market implies that spot and FFA prices are not linked by a cost-of-carry (storage)

relationship, as in financial and commodity derivatives markets. Therefore, it is expected

that spot and FFA prices may not be as closely “linked”, as they would be in a cost-of-carry

relationship. As a consequence, the degree of hedging effectiveness of this market is an

issue that can only be answered empirically.

Fourth, in-sample and out-of sample tests are used to determine the hedging

effectiveness of the FFA contracts in minimising the risk in the spot freight market. In-

sample tests use historical information. However, it is more relevant for practitioners to

examine the out-of-sample forecasting performance of hedging ratios, as these are forward

looking. This chapter examines the hedging performance both in-sample and out-of-sample,

for a number of alternative model specifications, identifying the appropriate model in each

case. Shipowners and charterers, whose physical operations concentrate on Capesize

trading routes, can benefit from using optimal hedge ratios that minimise their freight rate

risk.

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The remainder of this chapter is organised as follows. The next section illustrates

the derivation of constant and time-varying hedge ratio models. Section 3 presents the

empirical methodology for determining optimal hedge ratios. Section 4 discusses the

properties of the data and presents the empirical results. Section 5 evaluates the hedging

effectiveness of the proposed strategies. Finally, section 6 concludes the chapter.

ESTIMATION OF HEDGE RATIO MODELS

Constant Hedge Ratios

The Minimum Variance Hedge Ratio (MVHR) methodology of Ederington (1979) argues

that the objective of hedging is to minimise the volatility (variance) of the returns in the

hedge portfolio held by the investor. Therefore, the hedge ratio that generates the minimum

portfolio variance should be the optimal hedge ratio. The hedge ratio then is equivalent to

the ratio of the unconditional covariance between spot and FFA price changes to the

variance of FFA price changes; this is equivalent to the slope coefficient, h*, in the

following regression:

ΔSt = h0 + h*ΔFt + εt ; εt ~ iid(0,σ2) (1)

where, ΔSt = St – St-1 is the logarithmic change in the spot position between t-1 and t; ΔFt =

Ft – Ft-1 is the logarithmic change in the FFA position between t-1 and t, and h* is the

optimal hedge ratio. The coefficient of determination (R2) of the regression equation

measures the degree of variance reduction in the hedged portfolio achieved through

hedging, since it represents the proportion of risk in the spot market that is explained

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(eliminated) through the introduction of the FFA (that is, of ΔFt in the equation); the higher

the R2 the greater the effectiveness of the minimum variance hedge.

There are several issues to be noted regarding the performance of the MVHR

strategy. First, γ* and R2 of Equation (1) depend upon the historical correlation between

spot and derivatives prices and, as such, give an indication of the historical performance of

the hedging strategy (in-sample performance). A more pragmatic way to evaluate the

effectiveness of alternative hedging strategies is in an out-of-sample setting.

Second, Equation (1) implicitly assumes that the risk in cash and futures markets is

constant over time. This assumption is too restrictive and contrasts with the empirical

evidence in different markets, which indicates that cash and futures prices may be

characterised by time-varying distributions. This in turn, implies that MVHR could be

time-varying, as variances and covariances in the calculations are time-varying (updated),

as a consequence of new information arriving in the market.

Third, as the prices of the underlying “commodity” and the forward contract are

jointly (simultaneously) determined in Equation (1), the estimated hedge ratio will be

upward biased and inconsistent (simultaneity bias). Furthermore, Equation (1) is potentially

misspecified because it ignores the existence of a long-run cointegrating relationship

between cash and derivatives prices (Engle and Granger, 1987), and fails to capture the

short-run dynamics by excluding relevant lagged variables, resulting in downward biased

non-optimal hedge ratios (see later in the text for more details). Lien et al. (2002) argue that

the cointegration relationship is the only truly indispensable component when comparing ex

post performance of various hedging strategies, in the sense that hedge ratios and hedging

performance may change sharply when the cointegrating variable is omitted from the

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statistical model. These issues raise concerns regarding the risk reduction properties of the

hedge ratios generated from Equation (1).

Time-Varying Hedge Ratios

Consider a freight market hedger (shipowner or charterer) who wants to hedge his freight

rate exposure in the FFA market. The return on the shipowner’s hedged portfolio of spot

and FFA positions, ΔΡt, is given by:

ΔΡt = ΔSt - htΔFt (2)

where, ΔSt and ΔFt have already been defined and ht is the hedge ratio at time t. If spot and

FFA returns are time-varying, then the variance of the returns on the hedged portfolio will

also be time-varying and conditional on the information set available to the market at time

t-1, Ωt-1:

Var(ΔΡt | Ωt-1) = Var(ΔSt | Ωt-1) + ht2Var(ΔFt | Ωt-1) – 2htCov(ΔSt, ΔFt | Ωt-1) (3)

where, Var(ΔSt | Ωt-1), Var(ΔFt | Ωt-1) and Cov(ΔSt, ΔFt | Ωt-1) are, respectively, the

conditional variances and covariance of the spot and FFA returns. The shipowner must

choose the value of ht that minimises the conditional variance of his hedged portfolio

returns i.e. th

min [Var(ΔΡt | Ωt-1)]. Then, taking the partial derivative of Equation (3) with

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respect to ht, setting it equal to zero and solving for ht, yields the optimal MVHR, ht*,

conditional on the information available at t-1:

ht* | Ωt-1 =

)(),(

1

1

−

−

Ω∆

Ω∆∆

tt

ttt

FVarFSCov

(4)

The conditional MVHR of Equation (4) is the ratio of the conditional covariance of

spot and FFA price changes over the conditional variance of FFA price changes. Since the

conditional moments can change as new information arrives in the market and the

information set is updated, the time-varying hedge ratios may provide superior risk

reduction compared to static (constant) hedges.

EMPIRICAL METHODOLOGY

To estimate ht* in Equation (4), the conditional means of spot and FFA returns are

measured using a Vector Error-Correction Model (VECM) (Engle and Granger, 1987 and

Johansen, 1988) and the conditional variances are measured using a Generalised

Autoregressive Conditional Heteroskedasticity (GARCH) error structure (Bollerslev,

1986). This framework meets the criticisms of possible model misspecifications and time-

varying hedge ratios, since the Error-Correction Term (ECT) describes the long-run

cointegration relationship between spot and FFA prices and the GARCH error structure

permits the variances and the covariance to change over time. The time-varying hedge

ratios are then calculated from the estimated time-varying variance-covariance matrix using

the nearby (prompt) FFA contract as the hedging instrument. The hedging effectiveness of

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the estimated dynamic hedge ratios are compared and contrasted with the effectiveness of

constant hedge ratios both in-sample and out-of-sample.

The selection criterion (loss function) for the optimum model to use is the following

variance (risk) reduction statistic, which compares the variance of the hedged portfolio

from each model with that of the unhedged position:

VR = 100*)(

)()(t

tt

SVarPVarSVar

∆∆−∆ (5)

Models that produce higher values of VR are deemed to be better. For the empirical

estimation of hedge ratio models, Augmented Dickey-Fuller (ADF, 1981), Phillips and

Perron (PP, 1988) and Kwiatkowski, et al. (KPSS, 1992) unit root tests are used first to

determine the order of integration of each price series. Given a set of two I(1) series6,

Johansen (1988, 1991) tests are used to determine whether the series stand in a long-run

relationship between them; that is, whether they are cointegrated7. Therefore, the following

VECM is estimated:

ΔXt = μ + ∑−

=

1p

1i

ΓiΔXt-i + ΠXt-1 + εt ; εt | Ωt-1 ~ dist(0, Ht) (6)

where, Xt is the 2x1 vector (St, Ft)' of log-spot and log-FFA prices, respectively, Δ denotes

the first difference operator, and εt is a 2x1 vector of error-terms (εS,t, εF,t)' that follow an as-

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

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matrix, Ht. The VECM specification contains information on both the short- and long-run

adjustment to changes in Xt, via the estimated parameters in Γi and Π, respectively.

The conditional second moments of spot and FFA returns are specified as a VECM-

GARCH-X model using the following Baba et al. (1987) augmented positive definite

parameterisation (henceforth, BEKK)8:

Ht = A'A + B'Ht-1B + C'εt-1εt-1'C + E' (z 1−t )2E (7)

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

coefficient matrices, (z 1−t )2 is the lagged squared basis, and E is a 1x2 vector of coefficients

of the lagged squared basis. Matrices B and C are restricted to be diagonal because this

results in a more parsimonious representation of the conditional variance. Moreover, the

model incorporates the lagged squared basis as an ECT in order to examine the relation

between the two markets, as a factor that influences the variances of the two variables. We

call this the GARCH-X model (see for example, Lee, 1994). The most parsimonious

specification for each model is estimated by excluding insignificant variables. Finally, the

Student-t (Bollerslev, 1987) and the Quasi-Maximum Likelihood Estimation (QMLE,

Bollerslev and Wooldridge, 1992) are both employed in the estimation of the models and

the one that fits the data best is used9.

DESCRIPTION OF DATA AND EMPIRICAL RESULTS

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The C4 route and CTC basket of FFAs are used for the analysis as they represent the most

popular contracts, in terms of liquidity. More specifically, according to market estimates,

85% of the Capesize FFA trades are conducted in the CTC basket, 10% of the trades take

place in the various voyage routes (mostly in C4) and 5% of the trades are conducted in

freight options. Thus, the data sets used consist of weekly dry-bulk spot and OTC FFA

prices on Capesize route C4 (Richards Bay to Rotterdam) from September 2004 to October

2008, and on the Capesize average time-charter basket (CTC) from September 2005 to

October 2008.10 Spot (physical) data are from Clarkson’s Shipping Intelligent Network and

consist of Baltic Exchange freight rates, while FFA data are from Reuters and consist of

Baltic Forward Assessments (BFAs). BFAs are reported for each Baltic index publication

day, for the routes defined by the Baltic Exchange, and are based on average FFA

assessments made by a panel of FFA brokers appointed by the Baltic Exchange. BFAs are

regarded as the most representative FFA data, as they include information from the top ten

(at the time of writing) FFA brokers (the panelists).

Most studies in the economic literature use weekly data to calculate hedge ratios of

derivatives contracts. The choice seems to be justified as it implies that hedgers in the

market rebalance their derivatives positions at no less than a weekly basis, firstly, due to the

long horizon of operations in the shipping industry, which may extend over a period of one

or two months and secondly, due to excessive transactions costs, which would be incurred

if rebalancing takes place more frequently than once a week. Time-varying hedging

strategies have higher implementation costs than constant strategies, since they require

frequent updating and rebalancing of hedged portfolios. Thin trading, relatively low

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liquidity, high bid-ask spreads and high transactions costs can make daily rebalancing

expensive.

Spot and BFA (from now on they will be referred to as FFA) price data are sampled

every Wednesday. When a holiday occurs on Wednesday, Tuesday’s observation is used in

its place. FFA prices are always those of the nearby contract because it has the highest

liquidity amongst different duration contracts. However, to avoid thin markets and

expiration effects (when futures and forward contracts approach their settlement day, the

trading volume decreases sharply) we rollover to the next nearest contract one week before

the nearby contract expires. All price series are transformed into natural logarithms.

Summary statistics of logarithmic first-differences of weekly spot and FFA prices

are presented in Table 2. The results indicate excess skewness and kurtosis. In turn, Jarque-

Bera (1980) tests indicate departures from normality for FFA and spot prices. The Ljung-

Box Q(12) statistics (Ljung and Box, 1978) on the first 12 lags of the sample

autocorrelation function of the level series indicate significant serial correlation in all price

series. Serial correlation in spot prices may be induced by the way freight rates are

estimated by shipbroking companies. These rates are based either on actual fixtures or in

the absence of an actual fixture, on the shipbroker’s expert view of what the rate would be

if there was a fixture. In this case, shipbrokers may report a freight rate which is a mark-up

over the previous day’s rate, thereby inducing autocorrelation in the data. The Q2(12)

statistics (Ljung and Box, 1978) on the first 12 lags of the sample autocorrelation function

of the squared series and the ARCH(1) statistic (Engle, 1982) show evidence of

heteroskedasticity and ARCH(1) effects in FFA prices, respectively. However, there is no

evidence of heteroskedasticity or ARCH(1) effects in spot return weekly series.

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ADF(1981), PP (1988) unit root tests on the log-levels and log-first differences of the

weekly spot and FFA price series, indicate that all variables are log-first difference

stationary, all having a unit root on the log-levels representation. The results of the KPSS

(1992) test, which has stationarity as the null hypothesis, confirm these conclusions.

Having identified that spot and FFA prices are I(1) variables, cointegration

techniques are used next to examine the existence of a long-run relationship between these

series (Table 3). The Schwartz Bayesian Information Criterion (SBIC, Schwartz, 1978),

used to determine the lag length in the VECM, indicates that 4 lags are appropriate both in

route C4 and in the CTC basket. Johansen’s (1991) λmax and λtrace statistics show that the

spot and FFA prices in all cases are cointegrated, and thus, stand in a long-run relationship

between them. The normalised coefficient estimates of the cointegrating vector of Equation

(6) are also presented in Table 3. In order to examine whether the exact lagged basis should

be included as an ECT in the VECM model, the following hypothesis β' = (1, 0, –1) is

tested on the cointegrating vector zt = β'Xt = (St β1 Ft)', implying that the equilibrium

regression is the lagged basis, zt-1 = St-1 – Ft-1. Results in the last column of Table 3 indicate

that in route C4 the restrictions hold, while in the CTC time-charter basket the restrictions

are not accepted. This discrepancy in the results may arise from the different economic and

trading conditions that are reflected in each FFA market. That is, the CTC basket

assimilates information from four time-charter routes, while route C4 reflects only the

economic conditions of the Richards Bay to Rotterdam trades.

The maximum-likelihood estimates of the preferred VECM-GARCH-X models, for

each contract are presented in Panels A and B of Table 4. Insignificant variables have been

excluded from the model to reach a more parsimonious specification. In all cases, the

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GARCH(1,1) specification provides a good description of the joint distribution of spot and

FFA price returns. In terms of the significance of the ECT, in the CTC basket it seems that

both spot (dS = -0.279) and FFA (dF = 0.443) prices respond to shocks in the system to

restore the long-run equilibrium in this market. In route C4 it seems that only spot prices

(dS = -0.461) respond to shocks in the system, as the ECT coefficient in the FFA equation

(dF = 0.147) is statistically insignificant. In terms of the short-run dynamics, measured by

the ai and bi coefficients, in both markets it takes two periods (weeks) for adjustment to

shocks to take place in spot markets, while adjustments take half this time in FFA markets.

Moreover, the intensity of the adjustment, as shown by the sum of the lagged coefficients in

the spot equation is 0.421 versus 0.194 in the FFA market for route C4. For the CTC

basket, this discrepancy is even larger with the sum of the lagged spot coefficients standing

at 0.524, while for the FFA market the adjustment has only a magnitude of 0.153. This

longer and stronger adjustment of spot prices in comparison to the FFA market is perceived

to be a consequence of the relative rigidities of the physical market in comparison to the

FFA one.

Turning to the parameters describing the conditional variance in each market, it can

be seen that, in both spot and FFA variance equations, the coefficients of the lagged

variance (bkk) and of the lagged error-terms (ckk) are significant. Thus, the volatility of spot

and FFA rates is characterised as time-varying. The results of the coefficients of the lagged

squared basis (ejj), that is of the disequilibrium in the market, entering the variance

equations, indicate that the basis is significant and affects positively the volatility of spot

and FFA markets. That is, disequilibria in the mean values of spot and FFA markets

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increase the volatility (riskiness) in both spot and FFA markets. Therefore, a GARCH(1,1)-

X model is used in all cases.

Panel C of Table 4, reports diagnostic tests of standardised residuals, (εt / th ).

These include, Ljung-Box (1978) statistics for 12th-order serial correlation of levels and

squared levels of standardised residuals, as well as the asymmetry test statistics (sign bias,

negative size bias, positive size bias and the joint test of sign and size bias) developed by

Engle and Ng (1993).11 They indicate absence of dependencies and asymmetries in the

standardised residuals. That is, the response of volatility to shocks (news) is “symmetric”

and is not affected by the magnitude of the shock, providing further evidence that the

GARCH specification is appropriate. The estimated implied kurtosis indicates the presence

of excess kurtosis in the residuals in all cases. As a result, the Jarque-Bera (1980) test

rejects normality in all routes. As described in Endnote 9, for the CTC basket the QMLE

estimation method is used, yielding robust standard errors, and thus, an asymptotically

consistent normal covariance matrix. On the other hand, in route C4 it is found that the

Student-t distribution characterise effectively spot and FFA returns, as the degrees of

freedom (v) is found to be 5.60. Baillie and Bollerslev (1995) show that only if v < 4 the

Student-t distribution has an undefined or infinite kurtosis. Thus, the estimated models fit

the data well.

ESTIMATED HEDGE RATIOS AND THEIR HEDGING EFFECTIVENESS

In-Sample Hedge Ratios

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In order to compare the effectiveness of the different hedge ratio models, portfolios implied

by the computed weekly ratios are constructed using Equation (2). For each case, we

consider four different hedge ratio specifications: The hedge ratio from the VECM-

GARCH-X model; the hedge ratio generated from a VECM with constant variances,

estimated using a Seemingly Unrelated Regression Equation (SURE) model (see Zellner,

1962); the constant variance OLS hedge of Equation (1); and a naïve hedge by taking a

FFA position with the same size as the spot position (i.e. setting the hedge ratio equal to 1).

The variances of these portfolios as well as the variances of the spot (underlying) positions

for the sample period are presented in Panel A of Table 5. Moreover, results from

comparisons of the variance of the hedged portfolios with that of the unhedged position, as

in Equation (5), are also reported in the table. The greater the reduction in the unhedged

variance, the better the hedging effectiveness.

Results indicate that both in route C4 (59.96 percent) and in the CTC basket (64.02

percent) time-varying hedge ratios perform better, in terms of increasing hedging

effectiveness, in comparison to constant hedge ratio models. These results reveal that the

arrival of new information affects the relationship between spot and FFA prices, and

therefore, time-varying hedging models display better performance. Amongst “constant”

hedge ratio models, the best hedging strategy is displayed by the conventional model. The

increase in variance reduction from using time-varying models, instead of constant hedge

ratio models, is much larger in the CTC basket, from 56.65 percent to 64.02 percent, as

opposed to a marginal increase from 59.24 percent to 59.96 percent in route C4, indicating

that the CTC basket, being an average of four time-charter routes, is able to assimilate more

market information into prices than the single route (C4). The evidence contrasts with the

20

widely-held belief among practitioners (and their practices) that the naïve hedging

approach, of using a position in the derivatives market, which is equivalent to that in the

spot market, yields the “best” results.

To see what this entails in practice, consider the case of a shipowner with a

Capesize 172,000 dwt vessel open for fixture during the end of September 2008, which will

be hired under a time-charter contract during the end of October 2008. The shipowner, in

order to get protected against a possible downturn of the market, decides to hedge his

physical position against a worldwide delivery / redelivery basis with a CTC FFA contract

with a hedging horizon of one month (31 days).

At the end of October, the spot market is quoted at $37,000/day, creating a physical

exposure for the shipowner of $1,147,000 (= $37,000/day x 31 days). Using weekly spot

and FFA prices, over the period September 2005 to October 2008 he estimates that the

appropriate time-varying hedge ratio from a VECM-GARCH-X model during the end of

October is 0.77. Thus, in the FFA market he needs to take a short (selling) position equal to

$883,190 (= h* x spot exposure = 0.77 x $1,147,000) of the spot position. This would have

eliminated completely the risk (volatility) of his spot position, effectively locking his

freight rate at $37,000/day and his income at $1,147,000. If instead, the shipowner chooses

to sell the full position of the spot exposure ($1,147,000), using a naive hedge ratio of h* =

1 in the FFA market, then he would have hedged $263,810 (= $1,147,000 – $883,190)

more than he has to. This $263,810 of “over-hedging” represents a speculative position for

the shipowner and a higher cost of $659.5 (= $263,810 * 0.25 percent) in terms of

transaction brokerage) fees.

21

For comparison purposes, assume that a shipowner has a Capesize 150,000 dwt

vessel and wishes to charter it under a voyage charter, say in route C4. Further, assume that

the charter rate at the end of October 2008 is quoted at $15.98/ton, representing a physical

exposure of $2,397,000 (= $15.98/ton x 150,000mt). In this case, the appropriate time-

varying hedge ratio from a VECM-GARCH-X model is 0.83. In the FFA market the

shipowner needs to take a short position of $1,989,510 (= 0.83 x $2,397,000) to completely

eliminate his risk. By using a naive hedge ratio, the “over-hedging” position in this case is

$407,490 (= $2,397,000 - $1,989,510). Thus, it seems that both under a voyage and a time-

charter, a time-varying hedge ratio creates more effective and cost efficient hedging

positions for the shipowner.

Out-of-Sample Hedge Ratios

A more realistic approach and closer to the practice of hedging is to consider the hedging

performance of different methods for out-of-sample periods, as investors are concerned

with how well they can obtain forecasts of hedge ratios at different points in time. To

simulate that, we use an initial portion of the sample for estimation and reserve the

remaining sample for out-of-sample forecasting. For that, in route C4 we withhold 30

observations of the sample (26 March 2008 to 15 October 2008, representing a period of

seven months) and in the CTC time-charter basket we withhold 20 observations of the

sample (4 June 2008 to 15 October 2008, representing a period of five months) and

estimate the models using only the data up to this date. Then, we perform one-week-ahead

forecasts of covariances and variances and use them to forecast the one-week-ahead hedge

ratios. The following week this exercise is repeated, with the new observation included in

22

the data set. We continue updating the models and forecasting the hedge ratios until the end

of our data set.

The results for out-of-sample hedging effectiveness, presented in Panel B of Table

5, indicate that both in route C4 (85.69 percent) and in the CTC basket (65.73 percent)

naïve hedge ratios produce the highest variance reduction. This result validates the practice

of using positions in the FFA markets, which are equal in magnitude with the underlying

freight rate exposures. Miffre (2004) reports the same results for weekly out-of-sample

forecasts of the US$/BP£ hedge ratios. He argues that the simplicity of the naïve method

and the very low transaction costs it involves might be more attractive to market

participants. Fung and Leung (2007) examine the ex ante hedging performance of foreign

exchange forward markets and report that the naive hedge performs similarly to the optimal

hedge ratios used in the study. They argue that market participants should simply follow a

one-to-one approach when hedging foreign exchange risk in forward markets. Moreover,

this result may be partially justified by the choice of the (weekly) hedging horizon. Chen et

al. (2004) report that if the hedging horizon is long, then the naïve hedge ratio is close to (if

not) the optimum hedge ratio. The hedging performance results in this study, with the

greatest variance reduction of 86 percent, compares favourably with results, achieved

through the use of futures contracts, in other markets. Kavussanos (2002) reports hedging

effectiveness evidence uncovered in research on BIFFEX contracts, with the highest

variance reduction to be 23.25 percent.

In the literature, empirical results concerning the performance of GARCH hedge

ratios are generally mixed. In-sample comparisons show that, in some cases, dynamic

hedging generates much better performance in terms of risk reduction (Koutmos and

23

Pericli, 1999) but in others the benefits seem too minimal to warrant the efforts (Wilkinson

et al., 1999). Out-of-sample comparisons are mostly in favour of constant hedge strategies.

Bystrom (2003) report that OLS hedge ratios perform better than time-varying ones in the

electricity futures market in Norway. Lien et al. (2002) finds that the OLS hedge strategy

outperforms the GARCH strategy in ten futures markets, covering currency, commodity

and stock index futures. Tong (1996) finds that in the case of foreign-exchange risk

hedging, dynamic hedging is not substantially better than static hedging. He attributes this

to the rather stable relationship between the spot asset and the direct hedging instrument.

Broadly speaking, it is not easy to forecast variances, covariances, and hence time-varying

hedge ratios, and this can explain the results in the out-of-sample tests. Therefore, it seems

that the additional complexity of specifying and estimating GARCH models may be

justified for some commodities but not for others.

CONCLUSION

This chapter examines for the first time the reduction in freight rate risk that can be

achieved by utilising Forward Freight Agreements (FFAs) in the Capesize sub-sector of the

bulk shipping industry. Capesize vessels have been documented in the literature to bear the

highest volatility in freight rates and prices, in comparison to smaller size vessels, such as

Panamax and Handy vessels. As a consequence, it is extremely important for principals, but

also for charterers, to have some strategy for freight rate risk management. Both in-sample

and out-of-sample hedging performances are examined for each FFA contract, considering

alternative methods, both constant and time-varying, for computing more effective hedge

ratios.

24

Overall, the results reveal that shipping companies with Capesize vessels operating

worldwide and trading companies that transport commodities to different parts of the world

can use the FFA contracts effectively to reduce their freight rate risk, since the variability of

their cash-flows can be significantly explained by the fluctuations of the FFA rates up to 64

percent in-sample and 86 percent out-of-sample. In-sample results indicate that time-

varying hedge ratios perform better in increasing hedging effectiveness, while out-of-

sample results indicate that naïve hedge ratio strategies produce the highest variance

reductions, essentially validating the practice of using positions in FFA markets, which are

equal in magnitude with the freight rate exposures in the spot C4 and CTC markets. Market

agents can benefit from this result by developing appropriate hedge ratios and thus,

controlling their freight rate risk more efficiently.

ENDNOTES 1 Kavussanos (1996) reports that in the dry-bulk sector there is a clear ranking of volatilities by vessel size,

with the freight markets of the larger Capesize vessels displaying higher volatilities compared to the smaller

Panamax ones, while Panamax volatilities are higher than those of the Handy ones. As a consequence, risk-

averse investors in shipping can diversify risks in their portfolios by heavier weighting towards smaller size

vessels. 2 For an analytical description of the composition of the Baltic Exchange indices see Kavussanos and Visvikis

(2006a, Chapter 3). 3 However, it should be noted that during the recent years, with the arrival of banks, hedge funds and other

financial institutions into the freight derivatives market, the credit risk issue has decreased even further, as

these institutions are, most of the time, ready to take some of the credit risk, as being the other counterparty to

the derivatives transactions. 4 For details of existing exchanges clearing freight derivatives, see Kavussanos and Visvikis (2006a, b). 5 According to market sources, during 2007, 66 percent of the dry-bulk freight derivatives trades were

conducted OTC and 34 percent were cleared through a clearing-house. In total, for 2007 it is estimated that

3600 million tonnes of freight were hedged in the dry-bulk FFA market, whereas the physical market

represented 3017 million tonnes.

25

6 I(1) stands for a price series which is integrated of order 1; that is, it needs to be differenced once to become

stationary. 7 If two or more time-series variables are themselves non-stationary, but a linear combination of them is

stationary, then the variables are said to be cointegrated. 8 Several other specifications are also used, such as a bivariate VECM-EGARGH and a VECM-GJR-

GARCH, but yield inferior results judged by the evaluation of the log-likelihood and in terms of residual

specification tests (not reported). 9 The Student-t distribution converges to the normal distribution as the degrees of freedom (v) approach

infinity. However, for v < 4, the Student-t distribution has an undefined or infinite degree of kurtosis and in

such cases the QMLE method is used for estimation, which uses robust standard errors, and thus, yields an

asymptotically consistent normal covariance matrix. Preliminary evidence suggests that in route C4 (v =

5.600) the Student-t distribution is appropriate, while in the CTC time-charter basket (v = 3.651) the QMLE is

more appropriate. 10 The Capesize time-charter basket consists of the following routes: C8 (Delivery Gibraltar-Hamburg range,

redelivery Gibraltar-Hamburg range), C9 (Delivery ARA or passing Passero, redelivery China-Japan range),

C10 (Delivery China-Japan range round voyage, redelivery China-Japan range) and C11 (Delivery China-

Japan range, redelivery ARA or passing Passero). 11 The test statistics for the Engle and Ng (1993) tests are the t-ratio of b in the regressions:

u 2t = a0 + bY −

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

−1t εt-1 + ωt (negative size bias test);

u 2t = a0 + bY +

−1t εt-1+ ωt (positive size bias test), where u 2t 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 test is based on the regression u 2t = a0 + b1Y

−−1t + b2Y

−−1t εt-1 + b3Y

+−1t εt-1 + ωt.

The joint test H0: b1 = b2 = b3 = 0, is an F-test with 95% critical value of 2.60.

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28

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29

Table 1. Baltic Capesize Index (BCI) – Route Definitions

Routes Vessel Size (dwt) Cargo Route Description Weights

C2 160 000 Iron Ore Tubarao (Brazil) to Rotterdam (Netherlands) 0%

C3 150 000 Iron Ore Turabao/Beilun and Baoshan (China) 0%

C4 150 000 Coal Richards Bay (S. Africa) to Rotterdam 0%

C5 150 000 Iron Ore W. Australia/Beilun-Baoshan 0%

C7 150 000 Coal Bolivar (Columbia)/Rotterdam 0%

C8_03 172 000 T/C Delivery Gibraltar-Hamburg range, redelivery Gibraltar-Hamburg range

25%

C9_03 172 000 T/C Delivery ARA or passing Passero, redelivery China-Japan range

25%

C10_03 172 000 T/C Delivery China-Japan range round voyage, redelivery China-Japan range

25%

C11_03 172 000 T/C Delivery China-Japan range, redelivery ARA or passing Passero

25%

C12 150 000 Coal Gladston (Australia) to Rotterdam 0%

Source: Baltic Exchange

30

Table 2. Descriptive Statistics of Weekly Logarithmic First-Differences of Spot and FFA Prices Panel A: Route C4, Logarithmic First-Differences of Spot and FFA Price Series (09/04 to 10/08)

N Mean Skew Kurt J-B Q(12) Q2(12) ARCH(1) ADF Lev PP Lev ADF 1st Diffs PP 1st Diffs KPSS Spot 209 -0.0029 -1.015 7.066 179.88

[0.000] 30.228 [0.003]

8.712 [0.727]

1.151 [0.283]

-1.447 (1) -1.618 (7) -9.051 (0) -9.251 (5) 1.085

FFA 209 -0.0025 -0.696 5.443 68.88 [0.000]

26.293 [0.000]

24.599 [0.017]

4.219 [0.040]

-1.525 (2) -1.548 (7) -6.631 (1) -11.103 (5) 1.125

Panel B: Logarithmic First-Differences of Time-charter Basket CTC, Spot and FFA Price Series (09/05 to 10/08) N Mean Skew Kurt J-B Q(12) Q2(12) ARCH(1) ADF Lev PP Lev ADF 1st Diffs PP 1st Diffs KPSS

Spot 159 -0.0064 -3.805 30.356 5,341.4 [0.000]

23.181 [0.026]

3.067 [0.995]

0.089 [0.765]

-0.382 (2) -1.045 (7) -4.048 (1) -7.399 (5) 1.134

FFA 159 -0.0042 -2.219 13.847 909.99 [0.000]

57.238 [0.000]

35.411 [0.000]

5.935 [0.015]

-1.157 (5) -1.124 (7) -10.028 (3) -7.567 (4) 1.189

N is the number of observations. Mean is the sample mean of the series. Skew and Kurt are the estimated centralised third and fourth moments of the data. J-B is the Jarque-Bera (1980) test for normality; the statistic is distributed as χ2(2). Figures in square brackets [.] indicate exact significance levels. 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; these statistics are distributed as χ2(12). ARCH(1) is the Engle (1982) test for ARCH effects; the statistic is distributed as χ2(1). ADF is the Augmented Dickey Fuller (1981) test. The ADF regressions include an intercept term; the lag-length of the ADF test (in parentheses) is determined by minimising the SBIC (1978). PP is the Phillips and Perron (1988) test; the truncation lag for the test is in parentheses. Lev and 1st Diffs correspond to price series in log-levels and log-first differences, respectively. The 95% critical value for the ADF and PP tests is –2.88. The critical values for the KPSS test are 0.146 and 0.119 for the 5% and 10% levels, respectively.

31

Table 3. Johansen (1988) Test for the Number of Cointegrating Vectors between Spot and FFA Prices

Lags Hypothesis (Maximal)

Test Statistic

Hypothesis (Trace)

Test Statistic

95% Critical Values

Cointegrating Vector

Hypothesis Test

H0 H1 λmax H0 H1 λtrace λmax λtrace β' = (1, β1, β2) β' = (1, 0, -1) Route C4 4 r = 0 r =1 32.259 r = 0 r >=1 35.325 15.87 20.18 (1, -0.051, -0.999) 0.364 [0.834] r <=1 r =2 3.066 r <=1 r =2 3.066 9.16 9.16 Basket CTC 4 r = 0 r =1 47.839 r = 0 r >=1 49.214 15.87 20.18 (1, 0.079, -1.006) 5.135 [0.077]

r <=1 r =2 1.375 r <=1 r =2 1.375 9.16 9.16 Lags is the lag length of the Vector Autoregressive (VAR) models; the lag length is determined using the SBIC (1978). Figures in square

brackets [.] indicate exact significance levels. r represents the number of cointegrating vectors. λmax(r,r+1) = -Tln(1 – λ r+1) and λtrace(r) = -

T ∑+=

n

1ri

ln(1 – λ i), where λ i are the estimated eigenvalues of the Π matrix in Equation (6). Estimates of the coefficients in the cointegrating

vector are normalised with respect to the coefficient of the spot rate, St. The statistic for the parameter restrictions on the coefficients of the

cointegrating vector is –T [ln(1 - λ *1) –ln(1 - λ 1)], where λ *

1 and λ 1 denote the largest eigenvalues of the restricted and the unrestricted models, respectively. The statistic is distributed as χ2 with degrees of freedom equal to the total number of restrictions minus the number of the just identifying restrictions, which equals the number of restrictions placed on the cointegrating vector.

32

Table 4. Maximum Likelihood Estimates and Diagnostic Tests of VECM-GARCH-X Models

(Route C4: 2004:09-2008:10, Basket CTC: 2005:09-2008:10)

ΔSt = ∑−

=

1p

1i

aS, iΔSt-i + ∑−

=

1p

1i

bS,iΔFt-i + dSzt-1 + εS,t

ΔFt = ∑−

=

1p

1i

aF,iΔSt-i + ∑−

=

1p

1i

bF,iΔFt-i + dFzt-1 + εF,t (6)

Ht = A'A + B'Ht-1B + C'εt-1εt-1'C + E'(z 1−t )2E (7) VECM-GARCH(1,1)-X VECM-GARCH(1,1)-X

Coefficients Spot C4 FFA C4 Spot CTC FFA CTC Panel A: Conditional Mean Parameters

dj, j = S, F -0.461 [0.000] 0.147 [0.159] -0.279 [0.029] 0.443 [0.000] ai, i = 1, 2 0.145 [0.042] 0.194 [0.001] 0.375 [0.000] 0.153 [0.023] bi, i = 1, 2 0.276 [0.000] - 0.149 [0.056] -

Panel B: Conditional Variance Parameters a11 0.010 [0.023] 0.039 [0.000] a21 0.006 [0.057] 0.032 [0.000] a22 0.004 [0.253] 0.025 [0.000]

bkk , k = 1, 2 0.951 [0.000] 0.962 [0.000] 0.753 [0.000] 0.463 [0.000] c1,kk , k = 1, 2 0.203 [0.000] 0.112 [0.012] -0.059 [0.374] 0.122 [0.056] ekk , k = 1, 2 0.253 [0.023] 0.385 [0.000] 0.523 [0.000] 0.772 [0.000]

v 5.600 - Panel C: Diagnostic Tests on Standardi zed Residuals

Spot C4

FFA C4

Spot CTC

FFA CTC

System Log-Likelihood 643.352 717.333 Skewness -0.534 [0.003] -0.278 [0.115] -0.858 [0.000] -0.818 [0.000] Kurtosis 3.529 [0.000] 3.557 [0.000] 3.322 [0.000] 3.054 [0.000]

J-B 110.49 [0.000] 105.35 [0.000] 86.801 [0.000] 74.530 [0.000] Q(12) 5.105 [0.926] 3.874 [0.973] 4.454 [0.955] 10.924 [0.449] Q2(12) 2.466 [0.996] 5.681 [0.893] 1.733 [0.999] 8.563 [0.662]

ARCH(12) 0.189 [0.998] 0.403 [0.961] 0.139 [0.999] 0.822 [0.627] AIC -1,256.71 -1,406.67

SBIC -1,207.61 -1,364.61 Sign and Si ze Bias Tests (see Endnote 11 for details)

Sign Bias -0.051 [0.959] 0.342 [0.732] 1.677 [0.096] 1.716 [0.089] Negative Size Bias -0.004 [0.996] -0.722 [0.471] -0.631 [0.529] -1.603 [0.111] Positive Size Bias -0.155 [0.877] 0.277 [0.782] -1.061 [0.290] -1.139 [0.257]

Joint Test for 3 Effects 0.024 [0.995] 0.312 [0.817] 1.072 [0.363] 1.230 [0.301] All variables are transformed in natural logarithms. Figures in squared brackets [.] indicate exact significance levels. The GARCH models are estimated in the CTC time-charter basket using the QMLE, while in route C4 are estimated using the Student-t distribution; v is the estimate of the degrees of freedom from the Student-t distribution. The Broyden, et al. (BFGS) algorithm (Shanno and Phua, 1980), which utilizes derivatives to maximize the log-likelihood, is used. zt-1 represents the lagged ECT (zt-1 = β'Xt-1). The ECT is restricted to be the lagged basis (St-1 – Ft-1) in route C4, while in the time-charter basket, the ECT is the following spread: ECT = St-1 – 1.006*Ft-1 + 0.079. 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 and heteroskedasticity in the standardised residuals and in the standardised squared residuals, respectively. ARCH(12) is the Engle’s (1982) F-test for Autoregressive Conditional Heteroskedasticity. AIC and SBIC are the Akaike Information Criterion (1973) and Schwartz Bayesian Information Criterion (1978), respectively. The sign and size bias tests are the Engle and Ng (1993) tests.

33

Table 5. In-Sample and Out-of-Sample Portfolio Variances and Hedging Effectiveness

Panel A: In-Sample Portfolio Variances and Hedging Effectiveness

Hedged Portfolio Variances Var(ΔΡt) = Var(ΔSt ) + ht

2Var(ΔFt ) – 2htCov(ΔSt, ΔFt ) (3)

Route C4 Basket CTC Unhedged (spot) 0.00635 0.00974 Naïve (h* = 1) 0.00277 0.00438 Conventional (h* = constant) 0.00259 0.00422 VECM (ht

*) 0.00260 0.00448 VECM-GARCH-X (ht

*) 0.00254 0.00350 Variance Reduction of Hedged vs. Unhedged Position (%)

VR = 100*)(

)()(StVar

PtVarStVar∆

∆−∆ (5)

Unhedged - - Naïve 56.41 54.99 Conventional 59.24 56.65 VECM 59.22 54.01 VECM-GARCH-X 59.96* 64.02* Panel B: Out-of-Sample Portfolio Variances and Hedging Effectiveness

Hedged Portfolio Variances Route C4 Basket CTC Unhedged (spot) 0.01516 0.05938 Naïve (h* = 1) 0.00217 0.02035 Conventional (h* = constant) 0.00312 0.02125 VECM (ht

*) 0.00298 0.02185 VECM-GARCH-X (ht

*) 0.00269 0.04034 Variance Reduction of Hedged vs. Unhedged Position (%)

Unhedged - - Naïve 85.69* 65.73* Conventional 79.41 64.22 VECM 80.37 32.07 VECM-GARCH-X 82.24 63.19

Variance is the variance of the hedged portfolios of spot and FFA positions, as in Equation (3). Variance reduction is the variance reduction of the hedged portfolio from each model in comparison to the unhedged position, as in Equation (5). * denotes the model with the greatest variance reduction.