Are freight futures markets efficient? Evidence from IMAREX

International Journal of Forecasting 28 (2012) 644–659

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Are freight futures markets efficient? Evidence from IMAREX Lambros Goulas a , George Skiadopoulos b,c,d,∗ a

Systemic Risk Management, Greece

b

Department of Banking and Financial Management, University of Piraeus, Greece

c

Financial Options Research Centre, Warwick Business School, University of Warwick, UK

d

Cass Business School, City University, UK

article

info

Keywords: Freight markets Freight rate IMAREX freight futures Interval forecasts Market efficiency Model confidence set

abstract The International Maritime Exchange (IMAREX) is the leading regulated marketplace for trading and clearing shipping freight derivatives. We investigate for the first time whether the IMAREX freight futures market is efficient over the daily and weekly horizons. To this end, we address the question in both a statistical setting and an economic setting by employing an extensive dataset of freight futures prices. In the statistical setting, we form both point and interval forecasts using alternative models, and evaluate them using a number of statistical tests. We assess the economic significance of the obtained forecasts by means of trading strategies, taking into account the presence of transactions costs. We find that IMAREX is not efficient over the shorter daily horizon. The results have implications for the economics of freight futures markets and the pricing of freight derivatives. © 2012 International Institute of Forecasters. Published by Elsevier B.V. All rights reserved.

1. Introduction The primary task of the shipping industry is to move cargo around the world; it is estimated to account for the transfer of 80% of the world’s merchandise trade (United Nations Conference on Trade and Development, 2008). The freight rate is the cost of hiring/leasing transportation (chartering). Freight rates differ depending on the type of cargo to be carried, the vessel size and the route to be followed, and are determined in the freight market where the sea transport is bought and sold (see Stopford, 1997, for the factors that determine demand and supply in the freight markets). Typically, they exhibit cyclicality, extreme volatility and seasonality, and are affected by the international business environment. Consequently, they entail a significant market risk (see Angelidis & Skiadopoulos, 2008), which calls for the development of

∗ Correspondence to: University of Piraeus. Department of Banking and Financial Management, Karaoli and Dimitriou 80, Piraeus 18534, Greece. Tel.: +30 210 4142363. E-mail addresses: [email protected] (L. Goulas), [email protected] (G. Skiadopoulos).

hedging schemes and motivates the implementation of speculative strategies. As a response, freight derivatives have been being traded in the over-the-counter market and exchanges over the last three decades (see Kavussanos & Visvikis, 2006a,b, and Alizadeh & Nomikos, 2009, for an extensive description of the markets).1 Focusing on exchange-traded freight derivatives, the first freight futures contract, termed BIFFEX (Baltic International Freight Futures Exchange), was introduced in the

1 Forward Freight Agreements (FFAs) are the most well-known overthe-counter freight derivatives. They are agreements between two principals that set a freight rate for a specified volume of cargo and vessel type on certain routes on a given date in the future. A charterer would be a natural buyer of an FFA, in order to protect herself against a potential rise in the physical market, which would force her to pay higher freight rates. Similarly, a ship owner would sell futures to cancel out the losses in his revenues from a potential decline in freights. FFAs usually negotiate through a broker (e.g., Clarksons, Simpson Spence & Young). However, FFAs entail a significant credit risk, and the position cannot be closed prior to expiry. To circumvent this problem, FFAs have started being markedto-market daily in the Norwegian Futures & Options Clearinghouse (NOS) since 2001, and in LCH. Clearnet (formed following a merger of the London Clearing House and the French Clearing House Clearnet) since 2005.

0169-2070/$ – see front matter © 2012 International Institute of Forecasters. Published by Elsevier B.V. All rights reserved. doi:10.1016/j.ijforecast.2011.11.004

L. Goulas, G. Skiadopoulos / International Journal of Forecasting 28 (2012) 644–659

London International Financial Futures Exchange (LIFFE) in 1985; BIFFEX was written on the Baltic Freight Index (BFI). In April 2002, LIFFE ceased the trading of BIFFEX due to its low liquidity.2 In November 2001, the International Maritime Exchange (IMAREX) was founded, and freight derivatives written on various freight indices and routes were introduced among the other derivative products traded in the Exchange. In partnership with the Norwegian Options and Futures clearing house (NOS), IMAREX is the leading regulated marketplace for trading and clearing shipping freight derivatives written on various freight indices, with freight futures being the most liquid instrument.3 Currently, it has over 200 direct members, including oil companies, ship owners, traders and financial companies. It is estimated that the total nominal trade volume in IMAREX amounted to US$18 billion in 2008. This paper investigates for the first time whether the IMAREX freight futures market is efficient, by assessing both the statistical and economic significance of formed forecasts of futures prices. Given the role of this particular market and the vast body of literature on the efficiency of other futures markets, the question of the efficiency of the IMAREX is of particular importance to academics. It is also important to practitioners, since fluctuations in freight rates affect shipowners’ cash flows, charterers’ costs, and commodity and energy producers. There is already an extensive body of literature investigating the question of whether the prices of stock index, interest rate, currency, commodity, and volatility futures can be forecasted. The significance of the results has been evaluated using either statistical or economic (trading profits) metrics. A number of studies have documented a statistically predictable pattern in futures returns (see Bessembinder & Chan, 1992, for commodity and currency futures returns; Miffre, 2001a, for the FTSE 100 futures; and Miffre, 2001b, for commodity and financial futures). On the other hand, the empirical evidence of predictability in futures markets under an economic metric is mixed. For instance, Hartzmark (1987), employing daily data of all contract maturities, finds that, in aggregate, speculators do not earn significant profits in commodity and interest rate futures markets. Yoo and Maddala (1991), considering daily data for a number of futures maturities, study commodity and currency futures and find that speculators tend to be profitable. Similar findings are reported by Hartzmark (1991), Kho (1996) and Wang (2004). On the other hand, Konstantinidi,

2 The demise of the BIFFEX market was attributed to the fact that the BIFFEX contract did not serve as an efficient hedging instrument; this was because the underlying Baltic Freight Index (BFI) was not taking all routes and vessels into account, giving rise to a basis risk in the case of crosshedging strategies (see e.g., Kavussanos & Nomikos, 2000, Haigh & Holt, 2002). As a response to this, BFI was split into the Baltic Capesize Index (BCI) and the Baltic Panamax Index (BPI) in April 1999, and the Baltic Handymax Index (BHMI) was added in November 1999 for even greater transparency. 3 Freight futures and options have also been being traded in the New York Mercantile Exchange (NYMEX) and the Singapore Exchange (SGX) since 2005 and 2006, respectively (see also Kavussanos & Visvikis, 2006a, and references therein, for a detailed review of the advances in the freight derivatives market).

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Skiadopoulos, and Tzagkaraki (2008) and Konstantinidi and Skiadopoulos (2011) find that the VIX volatility futures market is efficient using both statistical and economic settings. Chincarini (2011) also reaches similar conclusions for the weather derivatives market. In the case of the freight markets, a number of papers have examined whether spot freight rates can be forecasted rather than futures (see e.g., Cullinane, Mason, & Cape, 1999, Jonnala, Fuller, & Bessler, 2002, Adland & Strandenes, 2006, and Glen, 2006, for a review of the approaches employed for modeling the dry and tanker markets). The implicit hypothesis is that predictability in the underlying freight spot rate implies predictability of the corresponding derivative contract, as well. However, from a theoretical point of view this is not a valid implication, since the standard cost-of-carry relationship for financial futures does not hold for the freight ones. This is because the underlying asset is not tradable, and hence the pricing by arbitrage argument cannot be applied. Hence, there may be other factors/information flows which also affect freight futures markets. This is analogous to the interest rate derivatives literature, where it is well documented that models which describe the dynamics of the underlying interest rate quite well, cannot account for the properties of the prices of the corresponding interest rate derivative (‘‘unspanned stochastic volatility problem’’, see e.g. Jarrow, Li, & Zhao, 2007, and references therein). To circumvent this constraint, a series of papers have examined the efficiency of the BIFFEX market (see e.g., Haigh, 2000, Kavussanos & Nomikos, 1999, 2003), as well as those of various forward freight markets (see e.g., Kavussanos & Visvikis, 2004, Kavussanos, Visvikis, & Menachof, 2004), written on alternative spot freight rates (for various routes and both dry and wet cargoes). The analysis is carried out within a statistical setting which tests the unbiasedness hypothesis of the market, i.e. whether the current futures price is the best predictor of the future value of the underlying spot freight rate that will prevail on the maturity date of the contract. The acceptance of this hypothesis implies that futures prices evolve as martingales, and hence that the market is efficient. The literature finds mixed results, depending on the market and type of contract under investigation (see Kavussanos & Visvikis, 2006a, for a review). Adland and Cullinane (2005) argue that time-varying premia are the source of the rejection of the martingale property. Batchelor, Alizadeh, and Visvikis (2007) also study whether freight forward prices can be predicted, by performing a horse race of alternative forecasting models. They find that all models outperform the random walk model, but do not test the economic significance of the outperformance. This paper, however, takes a different research approach and makes at least three contributions to the literature on whether freight derivatives markets are efficient. First, we employ an extensive dataset from IMAREX and analyze the futures prices of various maturities written on various major freight indices of the dry and wet markets. The use of alternative indices is necessary, given that freight markets are highly segmented. To the best of our knowledge, this is the first study to investigate the efficiency of this growing market; the previous literature

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has only examined the efficiency of the BIFFEX or the over-counter market.4 Second, we examine the question under consideration within both statistical and economic settings. Previously, the literature has only examined the statistical significance of forecasts of freight futures prices. However, the ultimate test for market efficiency involves examining whether abnormal economic profits can be obtained; Jensen (1978) defines a market as efficient with respect to an information set if it is impossible to make economic profits by trading on the basis of this set. In addition, from a practitioner’s point of view, a trading rule has to deliver economically significant profits in order to be acceptable; statistical predictability alone does not suffice. To this end, we also employ an economic setting where we assess the performances of trading strategies based on models employed in the statistical setting (see also Dorfleitner & Wimmer, 2010, for a similar approach). Most importantly, we also take into account the transaction costs incurred. Third, in the statistical setting, we address our research question by forming both point and interval out-of-sample forecasts; the previous literature has only considered point forecasts, and yet interval forecasts may also be useful for trading purposes (see Christoffersen, 1998). We test the statistical significance of the point forecasts obtained, by using the Model Confidence Set methodology of Hansen, Lunde, and Nason (2011). This approach identifies the set of models that perform best in terms of forecasting. It has the advantage that, in contrast to previous methods which test the predictive ability of any model (see e.g., Harvey, Leybourne, & Newbold, 1997, Clark & McCracken, 2001), it does not require the assessment of the performance of any model against that of an ad-hoc chosen benchmark model. To check the robustness of our results, we perform the analysis across futures series of various maturities and by employing a number of alternative model specifications. The latter is necessary because the question of predictability is inevitably tested jointly with the assumed forecasting model. Furthermore, we conduct the analysis for two alternative forecasting horizons (daily and weekly), since a number of traders in the IMAREX market do not close their positions within a day but tend to keep them open for slightly longer periods of time. The remainder of this paper is structured as follows. Section 2 describes the dataset. Section 3 presents the forecasting models to be used. Sections 4 and 5 evaluate the out-of-sample predictive performances of the various models in statistical and economic terms, respectively. The last section concludes, discusses the implications of the results, and suggests topics for future research. 2. Dataset The bulk cargo market is a highly segmented one; freights depend on the size of the vessel (e.g., tankers,

4 Surprisingly, not much research has been devoted to IMAREX. To the best of our knowledge, Prokopczuk (2011) is the only one to focus on this market, using IMAREX freight futures data to examine the pricing and hedging performances of alternative freight derivative models.

bulk carriers and container ships), the type of cargo that is carried, the route that is followed and the delivery period. They also depend on the type of chartering.5 To capture this segmentation, the Baltic Exchange publishes a number of spot freight indices on a daily basis (see the Baltic Exchange, 2009). Their values are reported once every day and are determined by the individual daily quotes of the member companies (panelists) of the Exchange. The dataset consists of daily settlement prices of a set of IMAREX freight futures written on various Baltic indices, and a number of economic variables over the period April 5, 2005 until July 17, 2009. The period of April 5, 2005–September 29, 2006 is used as the in-sample period, when we initially estimate the models described in Section 3. We obtain data on IMAREX freight futures from IMAREX. The dataset consists of futures written on three major Baltic spot freight indices, separately. In particular, futures written on a basket of four time-chartered Capesize routes (CS4TC), a basket of four time-chartered Panamax routes (PM4TC) and the dirty tanker TD3 route are used. The CS4TC and PM4TC indices are expressed in US dollars per day, and measure the cost to hire the vessel for one day. They are simple averages of four time-chartered indices that are included in the construction of the Capesize and Panamax indices, respectively. Table 1 defines these time-chartered indices for BPI and BCI (Panels A and B, respectively); the vessel size and route description are provided. The TD3 index is used to construct the Baltic Dirty Tanker Index (BDTI). It measures the freight rate of vessels of size 260,000 metric tons (mt) that transfer crude oil, have a maximum age of 15 years, and travel on the route from the Middle East Gulf to Japan (see Table 1, Panel C).6 On any given day, IMAREX lists for trading four serial months, six quarters, two half-years and five years maturity series for the dry-bulk futures contracts, and six serial months, six quarters and two years maturity series for the tanker futures contracts. The delivery period lasts from the first to the last trading day of the contract period. The contracts are cash-settled. The settlement price is the arithmetic average of the spot prices of the underlying index over the number of days in the delivery period. Contracts are traded from 09:00 to 18:30 Central European time on any business day. The minimum lot is one voyage

5 There are four types of charters: voyage charters, bareboat charters, time charters, and contracts of affreightment (COA). In a voyage charter, the vessel is chartered for a specific voyage. Bareboat charters are solely equipment leases for a specified period of time. In a time charter, the vessel and all the operations (e.g., crew, maintenance, insurance) are chartered for a certain length of time, rather than for a certain voyage. A COA is similar to a time charter, but it expresses a minimum number of cargoes that the charterer is obliged to provide to the owner in the course of a stated time period. 6 Tanker voyage rates are based and reported on the Worldscale index, published by the Worldscale Association. Under the Worldscale system, the spot freight rate is expressed in terms of the nominal freight rate (flat rate) for a particular route. Hence, Worldscale 100 would mean the actual rate for the voyage in question, as calculated and issued by the Worldscale Association, whereas Worldscale 150 would mean 150% of that rate and Worldscale 50 would mean 50% of that rate.

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Table 1 Description of the Baltic Time Chartered (TC) sub indices. The TC sub indices that are included in the Baltic Panamax Index (BPI) and the Baltic Capesize Index (BCI), as well as the TD3 index that is included in the Baltic Dirty Tanker Index (BDTI), are reported in panels A, B and C, respectively. The vessel size is measured by its carrying capacity (dwt: deadweight tons), and includes the effective cargo, bunkers, lubricants, water, food rations, crew and any passengers. In any given index, each shipping route is given an individual weighting to reflect its importance in the world-wide freight market. VLCC stands for Very Large Crude Carrier. Source: Baltic Exchange. Panel A: Baltic Panamax Index (BPI) time chartered indices Routes Vessel size (dwt) Route description P1A

74,000

P2A

74,000

P3A

74,000

P4

74,000

Weights (%)

Transatlantic (including east coast of South America) round of 45/60 days on the basis of delivery and redelivery Skaw–Gibraltar range Basis delivery Skaw–Gibraltar range, for a trip to the Far East, redelivery Taiwan–Japan range, duration 60–65 days Transpacific round of 35/50 days either via Australia or Pacific (but not including short rounds such as Vostochy (Russia)/Japan), delivery and redelivery Japan/South Korea range Delivery Japan/South Korea range for a trip via US West Coast–British Columbia range, redelivery Skaw–Gibraltar range, duration 50–60 days

20 12.5 20

15

Panel B: Baltic Capesize Index (BCI) time chartered indices Vessel size (dwt) C8

172,000

C9

172,000

C10

172,000

C11

172,000

Delivery Gibraltar–Hamburg range, 5–15 days ahead of the index date, transatlantic round voyage duration 30–45 days, redelivery Gibraltar–Hamburg range Delivery ARA or passing Passero, 5–15 days ahead of the index date, redelivery China–Japan range, duration about 65 days Delivery China–Japan range, 5–15 days ahead of the index date, round voyage duration 30–40 days, redelivery China–Japan range Delivery China–Japan range, 5–15 days ahead of the index date, redelivery ARA or passing Passero, duration about 65 days

10

Middle East Gulf to Japan: Ras Tanura to Chiba (Japan)

–

5 20 5

Panel C: TD3 Vessel size (mt)/type of vessel TD3

250,000/VLCC

day for the dry-bulk derivatives and 1000 mt for the tanker derivatives. In this study, we employ data for the four shortest futures maturities for any given underlying index, because these are the most liquid ones. To minimize the impact of noisy data, we perform roll-over to the next maturity contract five trading days prior to the expiry of the contract. Overall, 1073 daily observations are available for each series. The economic variables dataset consists of daily closing prices on (i) the West Texas Intermediate (WTI) spot crude oil price, (ii) the S&P GSCI Grains Spot Index, which is part of the S&P GSCI Agriculture Index that serves as a reliable benchmark for investment performance in the agricultural commodity markets, (iii) spot coal prices, (iv) the S&P GSCI Industrial Metals Spot Index, which is a basket of industrial metals prices; we employ the S&P GCSI Industrial Metals index as a benchmark for investment performance in industrial metals, and (v) the ten-year US government bond. Furthermore, we use the Baltic Capesize (BCI), Baltic Panamax (BPI), and Baltic Dirty Tanker TD3 spot freight indices. We choose this economic variables dataset because it has been found to determine the demand for shipping services (see for instance Beenstock & Vergottis, 1989a,b; Poulakidas & Joutz, 2009). Finally, we use daily prices of the S&P 500 index and the one-month Libor rate for the purposes of performance evaluation of the trading strategies. The S&P 500 index serves as a performance benchmark for global investment. We obtain all data from Bloomberg, with the exception of WTI, which is obtained from the Energy Information Association.

Fig. 1 shows the daily evolution of the prices of each one of the four shortest monthly IMAREX futures series written on CS4TC, PM4TC, and the Dirty Tanker TD3 route, separately. We can see that futures series for different underlying indices are highly correlated. Furthermore, we can see that the employed period incorporates both the bullish period of 2005–2008 and the subsequent bearish one (for instance, the shortest Panamax futures price dropped from a high of $94,110 to a low of $6,889). The incorporation of alternative regimes in the sample employed serves as a robustness test for the subsequent analysis. Table 2 reports the summary statistics of the freight futures (in both levels and first differences), as well as the Jarque–Bera test for normality of the distribution of returns. Values for the augmented Dickey–Fuller (ADF) test are also reported. We can see that the distribution of futures changes departs from the normal. In addition, the ADF test indicates that all of the variables are non-stationary in levels and stationary in first differences; similar results are also obtained for the economic variables employed. Finally, unreported results from the application of the standard ARCH test for heteroskedasticity effects and the Engle and Ng (1993) asymmetric (leverage) tests to the futures return series revealed that the futures volatility is time-varying and asymmetrically correlated with the futures price. This motivates the use of GARCH and asymmetric volatility type models, as will be discussed in Section 3.

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Fig. 1. Evolution of the four shortest maturity IMAREX Capesize (T/C Basket), Panamax (T/C Basket) and TD3 futures over the period April 5, 2005–July 17, 2009.

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649

Table 2 Descriptive statistics for freight futures. Entries report the summary statistics for the Capesize (panel A), Panamax (panel B) and Dirty Tanker TD3 (panel C) IMAREX futures on levels and first differences across the four shortest maturity series. The first order autocorrelation ρ1 , and the Jarque–Bera and Augmented Dickey Fuller (ADF) test values are also reported. The null hypothesis for the Jarque–Bera and ADF tests is that the series is normally distributed and has a unit root, respectively. The sample period is from April 5, 2005–July 17, 2009. Levels

Differences

Panel A: Capesize (T/C Basket) IMAREX futures on levels and differences

Mean Standard dev. Minimum Maximum Skewness Kurtosis Jarque–Bera

ρ1

ADF Observations

1st shortest

2nd shortest

3rd shortest

4th shortest

1st shortest

2nd shortest

3rd shortest

4th shortest

73924.9 50501.7 3644 222,125 0.8 2.54 123.89* 0.997 −0.93 1073

72068.5 48508.3 6844 188,010 0.75 2.28 123.88* 0.997 −0.97 1073

71179.3 48050.3 6844 184,719 0.77 2.25 131.65* 0.997 −0.98 1073

69835.8 47554.1 6844 184,719 0.80 2.28 138.18* 0.997 −0.97 1073

−0.0002

−0.0002

−0.0003

−0.0003

0.06

0.06

0.05

0.05

−0.36

−0.36

−0.41

−0.42

0.92 2.74 53.72 116262.0* 0.199 −18.45* 1072

0.45 0.45 12.32 3919.61* 0.268 −19.05* 1072

−0.0005 0.05 −0.36 0.76 3.50 52.88 113331* 0.125 −20.64* 1072

0.24

0.25

−0.79

−0.78

10.16 2401.13* 0.310 −19.60* 1072

10.29 2482.19* 0.281 −19.60* 1072

−0.0005

−0.0005

−0.0004

0.05 −0.21 0.38 0.78 12.10 3811.1* 0.232 −19.75* 1072

0.05 −0.22 0.33 0.14 8.13 1180.56* 0.221 −21.16* 1072

−0.0009

−0.001

−0.0009

0.06 −0.61 0.35 −0.64 17.59 9583.30* 0.138 −21.19* 1072

0.05 −0.49 0.31 −0.65 13.44 4942.59* 0.158 −20.35* 1072

0.04 −0.32 0.29 −0.37 11.91 3567.55* 0.115 −22* 1072

Panel B: Panamax (T/C Basket) IMAREX futures on levels and differences Mean Standard dev. Minimum Maximum Skewness Kurtosis Jarque–Bera

ρ1

ADF Observations

36097.5 23141.8 4688 94,110 0.74 2.34 116.75* 0.998 −0.82 1073

35929.7 22778.8 6889 94,110 0.74 2.28 121.78* 0.997 −0.93 1073

35729.3 22575.7 7390 90,225 0.73 2.16 127.9* 0.997 −0.91 1073

35277.1 22295.1 7390 90,225 0.76 2.18 133.59* 0.997 −0.89 1073

0.05

−0.22 0.27

−0.15 7.34 846.71* 0.226 −20.56* 1072

Panel C: Dirty Tanker TD3 IMAREX futures on levels and differences Mean Standard dev. Minimum Maximum Skewness Kurtosis Jarque–Bera

ρ1

ADF Observations *

94.97 42.18 28 240 1.03 4.05 243.43* 0.987 −1.37 1073

91.95 34.86 30.5 212 0.59 3.33 67.74* 0.987 −1.32 1073

90.01 33.02 31 184 0.36 2.88 24.30* 0.991 −1.15 1073

89.24 33.28 30.5 181 0.41 2.95 30.59* 0.993 −1.07 1073

−0.0009 0.04

−0.43 0.29

−0.97 23.75 19393.25* 0.087 −22.45* 1072

Denotes rejection of the null hypothesis at the 1% level.

+ α3 ∆BCIt −1 + a4 Et (COALt +1 ) + a5 COALt −1 + α6 Et (IMt +1 ) + α7 IMt −1 + α8 Et (it +1 ) + α9 it −1

3. Forecasting models In this section, we describe the models that will be used to test the market efficiency hypothesis of the futures IMAREX market in the statistical setting. Overall, we use eleven different models: the economic variables model, the univariate autoregressive model, the Vector Error Correction model (VECM), and a number of GARCH-type models.

+ α10 Et (yst +1 ) + α11 yst −1 + εtCS4TC ,T ∆FtPM4TC ,T

∆FtCS4TC = c + α1 ∆FtCS4TC ,T −1,T + α2 Et (∆BCIt +1 )

(1)

+ β2 Et (∆BPIt +1 )

+ β3 ∆BPIt −1 + β4 Et (GNt +1 ) + β5 GNt −1 + β6 Et (it +1 ) + β7 it −1

3.1. Economic variables model The economic variables model uses a number of economic variables to forecast the evolution of futures freight prices (see e.g. Beenstock & Vergottis, 1989a,b, Jonnala et al., 2002, Poulakidas & Joutz, 2009). Given that the futures dataset consists of futures written on three alternative freight indices, we develop three respective model specifications to account for the unique characteristics associated with the route vessel size and cargo type of each freight index. These are:

= c+β

PM4TC 1 ∆Ft −1,T

+ β8 Et (yst +1 ) + β9 yst −1 + εtPM4TC ,T ∆FtTD3 ,T

(2)

= c+γ + γ2 Et (∆TD3t +1 ) + γ3 ∆TD3t −1 + γ4 Et (WTIt +1 ) + γ5 WTIt −1 + γ6 Et (it +1 ) + γ7 it −1 TD3 1 ∆Ft −1,T

+ γ8 Et (yst +1 ) + γ9 yst −1 + εtTD3 , ,T

(3)

where ∆Ftk,T denotes the daily changes in the futures price of the futures written on the kth freight index (k = CS4TC, PM4TC, TD3) between times t − 1 and t for a given maturity T (T = 1, 2, 3, 4); c is a constant;

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L. Goulas, G. Skiadopoulos / International Journal of Forecasting 28 (2012) 644–659

∆BCI, ∆PBI and ∆TD3 are the daily log-returns of the Baltic Capesize, Baltic Panamax and Baltic TD3 route indexes, respectively; COAL, IM, GN, and WTI are the daily logreturns of the coal spot prices, industrial metals index, grain spot index and West Texas Intermediate spot crude oil, respectively; i is the one-month Libor rate; ys is the slope of the yield curve (the difference between the price of the ten year US government bond and the one month interbank rate); and εtk,T is the corresponding error term, with mean zero and a constant variance. These variables are the main determinants of dry and wet spot freight rates (see Beenstock & Vergottis, 1989a,b) and have been found to forecast spot freight rates accurately (see Jonnala et al., 2002). Hence, they may also have forecasting power in freight futures markets. Notice that in the above specifications, we also use the conditional expectations of the lagged variables, since they may also affect the dynamics of the indexes; market participants may take into account both lagged and leading (i.e. forward-looking formed expectations) values of the variables considered. For estimation purposes, we replace the expected future variables with their actual outcomes and estimate models using the Generalized Method of Moments. 3.2. Univariate autoregressive moving average models and vector error correction models (VECM) We employ univariate autoregressive moving average models for examining whether the evolution of IMAREX futures for any given maturity and underlying index can be forecasted using its previous values; this is because their daily returns exhibit positive autocorrelation. This would be consistent with the weak form market efficiency hypothesis. Lags of the ARMA (p, q) models based on the Schwartz information criterion (in a range of up to ten lags) are used. Finally, we choose an AR (1) specification. Next, we employ a VECM model in order to take into account any long-run relationships between futures series, written on any given freight index (see Alexander, 2008, for a review of the evidence of cointegration in various financial markets). The VECM models the evolution of the whole term structure of futures prices. This is consistent with the empirical evidence that there are various common factors (usually three) which drive the evolution of the term structure of futures prices over time; this pattern is detected by the application of Principal Components Analysis (PCA; see for example Chantziara & Skiadopoulos, 2008, and references therein). In fact, we apply PCA to the changes of freight futures prices across the four maturities and find that the first three principal components explain about 96% of the total variance of the changes in freight rates. Hence, there is scope for the VECM model to answer the question as to whether the co-movements in freight rates for different maturities prevail in the long-run, too. We choose a VECM(1) model based on the Schwartz information criterion. For futures written on any particular freight index, we use a (4 × 1) vector that contains the differences of the prices of the four IMAREX futures series written on any given underlying spot freight index. The application of Johansen’s (1988) tests to the in-sample dataset demonstrates that there are three cointegrating vectors for all futures series.

3.3. GARCH models We use a number of standard GARCH-type models for forecasting the evolution of futures freight indices. In particular, we employ the GARCH (Bollerslev, 1986), EGARCH (Nelson, 1991), GJR-GARCH (Glosten, Jagannathan, & Runkle, 1993) and GARCH-M (Engle, Lilien, & Robins, 1987) models (see also Alexander, 2008, for a description of these models). This family of models has been used widely in the freight literature for describing the properties of spot freight rates, which are characterized by heteroskedasticity, asymmetric effects, and extreme kurtosis, as has already been discussed in Section 2 (see Glen, 2006, for a review, and Angelidis & Skiadopoulos, 2008, for an application of GARCH-type models to freight indices in a Valueat-Risk setting). We estimate all models for two conditional probability functions of the indices returns: the normal and Student-t distributions. 4. Out-of-sample evidence: statistical significance We form point and interval forecasts of the changes of futures prices for each of the three index IMAREX futures and each maturity in order to assess the outof-sample performances of each of the models described in Section 3. To this end, we generate one-day-ahead and one-week-ahead out-of-sample forecasts over the period 2 October 2006–17 July 2009. When forming the point forecasts, we first estimate the models over the insample period (April 5, 2005–September 29, 2006); this yields 375 and 75 non-overlapping observations for the daily and weekly horizon forecasts, respectively. Then, to form the remaining out-of-sample point forecasts, we reestimate each model recursively using fixed-length rolling windows of 375 and 75 non-overlapping observations for the one-day-ahead and one-week-ahead forecasting horizons, respectively. We construct the 95% interval forecasts for the AR and VECM(1) by applying the bootstrap methodology of Pascual, Romo, and Ruiz (2001) to take into account the non-normality of the residuals of the models and the parameter uncertainty.7 In the case of the GARCH, EGARCH, GJR, GARCH-M, and economic variables models, we generate the interval forecasts by Monte Carlo simulation, instead.8 To construct the prediction intervals, we form 10,000 bootstrap samples or 10,000 simulation runs at each time step, depending on the model. 7 Given a sample of past observations of the variable to be forecasted and an assumed forecasting model, the calculation of Pascual et al. (2001) bootstrapped interval forecasts is performed in five steps. First, the assumed model is estimated and the centered residuals are retained. Second, a bootstrap sample of the residuals is generated using sampling with replacement from the empirical distribution of the residuals. Third, using the bootstrapped sample of residuals and the model estimated coefficients from the first step, a bootstrap replicate of the series is generated. Fourth, a bootstrapped sample of the coefficient estimates is obtained by estimating the assumed model for the replicated series obtained in the previous step. In the final step, the bootstrapped future value for the one-step-ahead forecast is obtained by using the bootstrap sample of coefficients. The five steps are repeated B times to obtain a set of B future values. The lower and upper bounds of the prediction intervals are constructed as the (α/2)100th and (1 − α/2)100th percentiles, respectively, of the empirical distribution of the B futures forecasts. 8 Pascual, Romo, and Ruiz (2006) propose a non-parametric methodology for generating bootstrapped interval forecasts from GARCH-type

L. Goulas, G. Skiadopoulos / International Journal of Forecasting 28 (2012) 644–659

4.1. Point forecasts: statistical testing To assess the statistical significance of the out-ofsample point forecasts obtained, we use the Model Confidence Set methodology of Hansen et al. (2011). The method selects a set of best performing model(s) with a given level of confidence. Its main feature is that it does not require the ad-hoc choice of a benchmark model against which the performance of any model is evaluated, as is the case with previous tests, and it also acknowledges the information content of the underlying data. In particular, uninformative data yield a larger number of best models, whereas informative data yield a MCS containing only a few models. The MCS is constructed through a sequential testing procedure, which requires an equivalence test, an elimination rule and an updating algorithm. Let M0 be the set that contains a finite number of candidate forecasting models, where each model is indexed by i = 1, . . ., m0 .For any given maturity T , consider the forecast series Fˆit ,T



Fˆjt ,T

n

n

and

t =1

of the freight futures prices written on the kth

t =1

underlying freight index generated by the ith and jth model specifications, respectively (k is suppressed to  hereafter, 



simplify the notation). Let eit ,T

n

t =1

j

and et ,T

n

be the

t =1

respective series of forecast errors for each of the model specifications, and  denote  the corresponding loss functions



j



by g eit ,T and g et ,T . The set M ∗ of superior models in M0 is defined as





 ≤ 0 for all j ∈ M0 , (4)      = g eit ,T − g ejt ,T is the loss differential ij

M ∗ ≡ i ∈ M0 : E dt ,T ij

where dt ,T



that measures the performance of model i relative to j at any point in time. The set of the best forecasting models, M ∗ , is determined by a sequential testing procedure that removes one inferior model from the initial set of candidate models at every iteration. Thus, the MCS procedure starts off with the full set of candidate models M0 and drops models until it reaches M ∗ . In order to judge statistically whether M ∗ has been reached or not, the following hypothesis tests are carried out at each run: H0,M : E (dij,t ) = 0

for all i, j ∈ M vs.

HA,M : E (dij,t ) ̸= 0

for some i, j ∈ M ,

(5)

where M ⊂ M0 is the set of remaining candidate models for M ∗ . If H0,M is rejected at an iteration, a model is removed from the set of candidates M and the hypotheses are then tested again on the reduced set of models. This procedure is repeated until H0,M is not rejected at some predetermined confidence level α . The set of models ˆ 1∗−α , and included in M at this point is denoted by M

referred to as the Model Confidence Set. Where the MCS consists of one model, this model outperforms the set of models. Where two or more models belong in the MCS, the models have an equal forecasting ability and outperform the eliminated models. In order to empirically implement the MCS procedure, one needs an equivalence test δM which allows H0,M to be tested, as well as an elimination rule eM that selects the model to be removed from M, if necessary. The equivalence test δM is based on the range statistic, defined as TM ≡ max tij  ,

 

(6)

i,j∈M

where tij

d = √ ij

var(dij )

= T −1

with dij

T

t =1

dij,t . The

elimination rule associated with TM is set to be the following: the model i selected by eM to be eliminated is the one for which teM ,j = TM for some j ∈ M . The asymptotic distribution of the test statistic TM under the null hypothesis is non-standard. We implement the MCS using two alternative loss functions. The first is the root mean squared prediction error (RMSE), calculated as the square root of the average squared deviations of the actual futures prices from the model based forecasts, averaged over the number of observations. The second metric is the mean absolute prediction error (MAE), calculated as the average of the absolute differences between the actual futures prices and the model based forecasts, averaged over the number of observations (see also Gonçalves & Guidolin, 2006, Konstantinidi et al., 2008, Konstantinidi & Skiadopoulos, 2011, for similar choices). In addition, we bootstrap the distribution of the test statistic by implementing the algorithm suggested by Hansen et al. (2011). 4.2. Interval forecasts: statistical testing To assess the out-of-sample performance of the constructed interval forecasts for the period under consideration, we use Christoffersen’s (1998) likelihood ratio test of unconditional coverage. To fix ideas, let the sample  n path of each one of the freight futures be Ft ,T t =1 , and their respective series of interval forecasts be



n

Lit /t −1,T (1 − a) , Uti/t −1,T (1 − a)

t =1

. Lit /t −1,T (1 − a) and

Uti/t −1,T (1 − a) denote the lower and upper bounds, respectively, of the (1 − α)% prediction interval at time t, constructed at time t − 1, for the ith model specification. The test checks whether the percentage of cases where the realized futures price violates (i.e., does not fall within) the constructed interval equals α %. To this end, an indicator function that takes a value of one or zero, depending on whether or not the realized futures price violates the constructed prediction intervals, is used, i.e. Iti,T 0,

if Ft ,T ∈ [Lit /t −1,T (1 − a), Uti/t −1,T (1 − a)]

1,

if Ft ,T ̸∈ [Lit /t −1,T (1 − a), Uti/t −1,T (1 − a)].

 models; the main feature of the method is that no assumption about the distribution of the error term needs to be made. However, the application of this method is inherently inconsistent, since the estimation of any GARCH-type model is based on an assumption about the conditional distribution of the error term.

651

=

(7)

The null hypothesis   of an efficient (1 − α)% interval forecast is H0 : E Iti,T = a and the alternative hypothesis is

652

L. Goulas, G. Skiadopoulos / International Journal of Forecasting 28 (2012) 644–659





H1 : E Iti,T ̸= a. This is tested by the likelihood ratio LRunc , given by:

 LRunc = 2 ln

1−

N T

T −N  N  N T

 − 2 ln (1 − α)T −N α N ∼ χ 2 (1) , 

(8)

where N is the number of times that a violation has occurred. The test statistic follows a Chi-square distribution with one degree of freedom. However, the power of the test may be sensitive to the sample size. Therefore, in accordance with the work of Christoffersen (2003), we generate Monte Carlo simulated p-values for assessing the statistical significance of the results. For calculating them, we simulate a sample of n i.i.d. Bernoulli(α ) variables. Next, for the simulated sample, we obtain Christoffersen’s (1998) test statistic. We repeat this procedure K = 9999 times and obtain the empirical distribution of Christoffersen’s (1998) test statistic under the null. 4.3. Point and interval forecasts: results We apply the MCS methodology to all maturities and underlying indices using the RMSE and MSE loss functions, separately. Table 3 reports the results on the statistical evaluation of the point forecasts obtained from each of the models described in Section 3 for the one-day forecasting horizon; we evaluate forecasts under both of the statistical measures for each of the four maturity series for the Capesize, Panamax, and TD3 futures. We can see that under the MAE, the random walk and economic variables models are excluded from the MCS in all 12 cases. Furthermore, under the RMSE, the random walk and economic variables models are excluded from the MCS in 11 of the 12 cases (i.e. 91% of the cases). In the case of the one-week-ahead forecasts, unreported results show that the random walk and economic variables models are again excluded from the set of best performing models under the MAE in all 12 cases. In addition, under the RMSE, the random walk model is excluded from the set in eight cases (i.e. 66.7% of cases) and the economic variables model is excluded in five (i.e. 41.7% of cases). These results indicate that freight futures prices are statistically predictable point-wise over the one-day and one-week forecast horizons.9 Regarding the evaluation of the constructed interval forecasts, Table 4 reports the results from the statistical

9 We have also assessed the forecasting predictability of each model using the modified Diebold–Mariano (MDM; see Harvey et al., 1997) and encompassing (ENC) tests, based on the test of Clark and McCracken (2001). The MDM test for equal forecasting accuracy tests whether a forecast generated by the ith model outperforms a forecast generated by the jth model, which is defined as the benchmark model. The ENC test tests the null hypothesis that the ith model forecast encompasses the jth model. To this end, the random walk model is chosen as the benchmark. We find that all models outperform the random walk model (see also Batchelor et al., 2007, for similar results in the case of freight forward markets), which supports the evidence of predictability documented by the MCS methodology. The results hold irrespective of the underlying index. However, the MCS approach is more flexible, since it does not require the selection of a benchmark model, which is inevitably ad-hoc.

evaluation of the constructed one-day-ahead interval forecasts for the case of the Capesize futures; the percentage of observations that fall outside the constructed 95% interval forecasts (violations) and the p-value of Christoffersen’s test are reported for every maturity series. We can see that there are seven cases out of 36 (19.5% of cases) where the null hypothesis that the constructed interval is efficient cannot be rejected; this occurs mostly for the longer maturities. Unreported results show that in the case of the Panamax futures, there are five cases out of 40 (12.5% of cases) where the null hypothesis cannot be rejected. Finally, in the case of the TD3 futures, there are 15 cases out of 38 (39% of cases) where the null hypothesis cannot be rejected; 11 of the 12 cases refer to the shortest and secondshortest maturities. This indicates that efficient interval forecasts can be constructed for freight futures prices at a one-day forecasting horizon (by assuming the independence of cases at the 5% significance level). In the case of the constructed one-week-ahead interval forecasts, unreported results show that in the case of the Capesize futures, there are only four cases out of 44 (9.1% of cases) where the null hypothesis that the constructed interval is efficient cannot be rejected; this occurs mostly for the longer maturities. In the case of the Panamax futures, there are four cases out of 40 (10% of cases) where the null hypothesis cannot be rejected. Finally, in the case of the TD3 futures, there is only one case out of 43 (2.3% of cases) where the null hypothesis cannot be rejected. This indicates that, in line with the results from the one-dayahead interval forecasts, efficient interval forecasts can be constructed for freight futures prices at the one-week forecasting horizon, with the exception of the TD3 futures. 5. Out-of-sample evidence: economic significance The results discussed in Section 4 suggest that the market efficiency hypothesis may be questioned by means of both point and interval forecasts, especially at the oneday horizon. However, the ultimate test of this hypothesis is whether the derived forecasts are economically significant. Hence, we assess the economic significance by performing trading strategies based on the point and interval forecasts obtained from the models described in Section 3 for each futures maturity and underlying index. The trading strategies involve a single freight futures contract throughout the trading period. Transaction costs are also taken into account; the transaction fees in the dry-bulk time-chartered basket futures and tanker TD3 futures are 0.25% and 0.35% of the contract nominal value, respectively (see www.imarex.com). 5.1. Economic significance: performance measures To evaluate the out-of-sample economic significance of the point and interval forecasts, we compute two alternative performance measures for each model specification: the Sharpe Ratio (SR) and Leland’s (1999) alpha Ap ; the latter is employed to account for the presence of nonnormality in the distribution of the trading strategies’ returns. Leland’s Ap is defined as: Ap = E rp − Bp E (rm ) − rf − rf ,

 





(9)

L. Goulas, G. Skiadopoulos / International Journal of Forecasting 28 (2012) 644–659

653

Table 3 Model Confidence Set (MCS) test for freight futures: one-day forecasting horizon. Entries report the forecasting models contained in the MCS at a significance level α = 0.05. The composition of the MCS for each index and maturity is reported based on MAE and RMSE, separately. The one-day-ahead out-of-sample assessment is conducted over the period 2 October 2006–17 July 2009. IMAREX Capesize (T/C basket) futures

MAE (α = 0.05%)

RMSE (α = 0.05%)

1st shortest

2nd shortest

3rd shortest

4th shortest

AR(1) VECM(1) AR/GARCH(1, 1) − n, AR/GARCH(1, 1) − t, AR/EGARCH(1, 1) − n, AR/EGARCH(1, 1) − t, AR/GARCH(1, 1) − M − n, AR/GARCH(1, 1) − M − t,

AR(1) VECM(1) AR/GARCH(1, 1) − n, AR/GARCH(1, 1) − t, AR/EGARCH(1, 1) − n, AR/EGARCH(1, 1) − t, AR/GARCH(1, 1) − M − n, AR/GARCH(1, 1) − M − t,

AR(1) VECM(1) AR/GARCH(1, 1) − n, AR/GARCH(1, 1) − t, AR/EGARCH(1, 1) − n, AR/EGARCH(1, 1) − t, AR/GARCH(1, 1) − M − n, AR/GARCH(1, 1) − M − t,

AR(1) VECM(1) AR/GARCH(1, 1) − n, AR/GARCH(1, 1) − t, AR/EGARCH(1, 1) − n, AR/EGARCH(1, 1) − t, AR/GARCH(1, 1) − M − n, AR/GARCH(1, 1) − M − t,

All models

AR(1) VECM(1) AR/GARCH(1, 1) − n, AR/GARCH(1, 1) − t, AR/EGARCH(1, 1) − n, AR/EGARCH(1, 1) − t, AR/GARCH(1, 1) − M − n, AR/GARCH(1, 1) − M − t,

AR(1) VECM(1) AR/GARCH(1, 1) − n, AR/GARCH(1, 1) − t, AR/EGARCH(1, 1) − n, AR/EGARCH(1, 1) − t, AR/GARCH(1, 1) − M − n, AR/GARCH(1, 1) − M − t,

AR(1) VECM(1) AR/GARCH(1, 1) − n, AR/GARCH(1, 1) − t, AR/EGARCH(1, 1) − n, AR/EGARCH(1, 1) − t, AR/GARCH(1, 1) − M − n, AR/GARCH(1, 1) − M − t,

AR(1) VECM(1) AR/GARCH(1, 1) − n, AR/GARCH(1, 1) − t, AR/GJR(1, 1) − t, AR/EGARCH(1, 1) − t, AR/GARCH(1, 1) − M − n, AR/GARCH(1, 1) − M − t,

AR(1) VECM(1) AR/GARCH(1, 1) − n, AR/GARCH(1, 1) − t, AR/EGARCH(1, 1) − n, AR/EGARCH(1, 1) − t, AR/GJR(1, 1) − n, AR/GJR(1, 1) − t, AR/GARCH(1, 1) − M − n, AR/GARCH(1, 1) − M − t,

AR(1) VECM(1) AR/GARCH(1, 1) − n, AR/GARCH(1, 1) − t, AR/EGARCH(1, 1) − n, AR/EGARCH(1, 1) − t, AR/GARCH(1, 1) − M − n, AR/GARCH(1, 1) − M − t,

AR(1) VECM(1) AR/GARCH(1, 1) − n, AR/GARCH(1, 1) − t, AR/GJR(1, 1) − t, AR/EGARCH(1, 1) − t, AR/GARCH(1, 1) − M − n, AR/GARCH(1, 1) − M − t,

AR(1) VECM(1) AR/GARCH(1, 1) − n, AR/GARCH(1, 1) − t, AR/EGARCH(1, 1) − n, AR/GJR(1, 1) − n, AR/GJR(1, 1) − t, AR/EGARCH(1, 1) − t, AR/GARCH(1, 1) − M − n, AR/GARCH(1, 1) − M − t,

AR(1) VECM(1) AR/GARCH(1, 1) − n, AR/GARCH(1, 1) − t, AR/EGARCH(1, 1) − n, AR/EGARCH(1, 1) − t, AR/GARCH(1, 1) − M − n, AR/GARCH(1, 1) − M − t,

AR(1) VECM(1) AR/GARCH(1, 1) − n, AR/GARCH(1, 1) − t, AR/EGARCH(1, 1) − n, AR/GJR(1, 1) − t, AR/GARCH(1, 1) − M − n, AR/GARCH(1, 1) − M − t,

AR(1) VECM(1) AR/GARCH(1, 1) − n, AR/GARCH(1, 1) − t, AR/EGARCH(1, 1) − n, AR/EGARCH(1, 1) − t, AR/GJR(1, 1) − n, AR/GJR(1, 1) − t, AR/GARCH(1, 1) − M − n, AR/GARCH(1, 1) − M − t,

AR(1) VECM(1) AR/GARCH(1, 1) − n, AR/GARCH(1, 1) − t, AR/EGARCH(1, 1) − t, AR/GJR(1, 1) − n, AR/GARCH(1, 1) − M − n, AR/GARCH(1, 1) − M − t,

AR(1) VECM(1) AR/GARCH(1, 1) − n, AR/GARCH(1, 1) − t, AR/EGARCH(1, 1) − n, AR/GJR(1, 1) − n, AR/GARCH(1, 1) − M − n, AR/GARCH(1, 1) − M − t,

AR(1) VECM(1) AR/GARCH(1, 1) − n, AR/GARCH(1, 1) − t, AR/EGARCH(1, 1) − n, AR/GJR(1, 1) − t, AR/GARCH(1, 1) − M − n, AR/GARCH(1, 1) − M − t,

AR(1) VECM(1) AR/GARCH(1, 1) − n, AR/GARCH(1, 1) − t, AR/EGARCH(1, 1) − n, AR/EGARCH(1, 1) − t, AR/GJR(1, 1) − n, AR/GJR(1, 1) − t, AR/GARCH(1, 1) − M − n, AR/GARCH(1, 1) − M − t

AR(1) VECM(1) AR/GARCH(1, 1) − n, AR/GARCH(1, 1) − t, AR/EGARCH(1, 1) − t, AR/GJR(1, 1) − n, AR/GARCH(1, 1) − M − n, AR/GARCH(1, 1) − M − t,

AR(1) VECM(1) AR/GARCH(1, 1) − n, AR/GARCH(1, 1) − t, AR/EGARCH(1, 1) − n, AR/EGARCH(1, 1) − t, AR/GJR(1, 1) − n, AR/GJR(1, 1) − t, AR/GARCH(1, 1) − M − n, AR/GARCH(1, 1) − M − t

IMAREX Panamax (T/C basket) futures

MAE (α = 0.05%)

RMSE (α = 0.05%)

AR(1) VECM(1) AR/GARCH(1, 1) − n, AR/GARCH(1, 1) − t, AR/EGARCH(1, 1) − n, AR/EGARCH(1, 1) − t, AR/GJR(1, 1) − n, AR/GJR(1, 1) − t, AR/GARCH(1, 1) − M − n, AR/GARCH(1, 1) − M − t,

All models

Dirty tanker TD3 route futures

MAE (α = 0.05%)

RMSE (α = 0.05%)

654

L. Goulas, G. Skiadopoulos / International Journal of Forecasting 28 (2012) 644–659

Table 4 Statistical efficiency of the one-day-ahead interval forecasts for IMAREX Capesize futures. Entries report the percentage of observations that fall outside the constructed intervals (violations), and the p-values of Christoffersen’s (1998) likelihood ratio test of unconditional coverage (LRunc) for each futures maturity. The null hypothesis is that the percentage of times that the actual index prices fall outside the constructed (1 – α )% interval forecasts is α %. Results are reported for daily 95% interval forecasts generated by the economic variables model (panel A), the AR(1) model (panel B), the VECM(1) model (panel C), the GARCH, EGARCH and GARCH-in-mean models with normal distributions (Panels D, F and H, respectively), and the GARCH, EGARCH and GARCH-in-mean models with Student-t distributions (panels E, G and I, respectively). On each day, 10,000 bootstrap samples (panels A, B and C) and simulation runs (panels D, E, F, G, H and I) are formed. The models are estimated recursively over the period 2 October 2006–17 July 2009. IMAREX Capesize (T/C basket) futures 1st shortest

2nd shortest

3rd shortest

4th shortest

15.5 0.0001*

17.93 0.0001*

18.536 0.0001*

15.21 0.0001*

9.04 0.0001*

10.47 0.0001*

10.62 0.0001*

8.75 0.0001*

44.48 0.0001*

54.09 0.0001*

59.97 0.0001*

54.23 0.0001*

6.17 0.022**

6.46 0.0100*

6.17 0.0220**

4.45 0.0595

7.32 0.0010*

5.88 0.0390**

5.6 0.0525

4.59 0.0741

6.17 0.0200**

8.18 0.0001*

6.89 0.0034*

6.6 0.0080*

6.74 0.0040*

6.03 0.0285**

6.6 0.0066*

5.88 0.0372**

6.31 0.0180**

6.89 0.0046*

4.73 0.0888

5.45 0.0675

5.45 0.0663

4.88 0.1020

Panel A: economic variables Violations (%) p-value Panel B: AR(1) Violations (%) p-value Panel C: VECM(1) Violations (%) p-value Panel D: AR/GARCH(1, 1) − n Violations (%) p-value Panel E: AR/GARCH(1, 1) − t Violations (%) p-value Panel F: AR/EGARCH(1, 1) − n Violations (%) p-value Panel G: AR/EGARCH(1, 1) − t Violations (%) p-value

Panel H: AR/GARCH(1, 1)-in-mean − n Violations (%) p-value

6.74 0.0060*

Panel I: AR/GARCH(1, 1)-in-mean − t Violations (%) p-value * **

7.46 0.0010*

Denotes rejection of the null at the 1% significance level. Denotes rejection of the null at the 5% significance level.

where rp denotes the return on the trading strategy, rm is the market portfolio return, rf is the risk-free rate, Bp =

( (m

) and λ = )

cov rp ,−(1+rm )−λ cov r ,−(1+r )−λ m

(

ln[E (1+rm )]−ln 1+rf var[ln(1+rm )]

). B p

is a measure of risk, similar to CAPM’s beta, and λ is the coefficient of relative risk aversion. We employ a two-step procedure for calculating Leland’s alpha. First, we compute λ and Bp for each time step. To this end, we use the one-month continuously compounded LIBOR rate and the return on the S&P 500 index as proxies for rf and rm , respectively.10 Second, we

10 We have also computed Leland’s alpha by using the FTSE ST Maritime Index as an alternative benchmark index. The FTSE ST Maritime Index is part of the FTSE ST Index Series and is published jointly by Singapore Press Holdings, Singapore Exchange and FTSE Group. It serves as a performance benchmark for maritime investments, and includes twelve maritimerelated companies. The results were similar.

estimate the following regression: rpi ,t − Bip,t rm,t − rf ,t − rf ,t = Aip + εti ,





(10)

where Aip and rpi ,t are Leland’s alpha and the return on the trading strategy, respectively, based on the forecasts from the ith model If Ap > 0, then the trading strategy offers an expected return in excess of its normal risk adjusted level. We assess the statistical significance of the two performance measures by bootstrapping their 95% confidence intervals (CI). For this purpose, we employ the stationary bootstrap method of Politis and Romano (1994), using 1000 bootstrap repetitions; this is because the returns on the trading strategies employed have been found to be stationary.11 Following Sullivan, Timmermann,

11 The stationary bootstrap is applicable to stationary and weakly dependent time series. To construct the bootstrapped time series, the

L. Goulas, G. Skiadopoulos / International Journal of Forecasting 28 (2012) 644–659

and White (1999), we choose a mean block size of 10. As a robustness check, we have also performed bootstrap repetitions choosing alternative mean block sizes of 2, 20 and 30. We find that the results are not sensitive to the choice of the mean block size. 5.2. Trading strategies and results Given the forecasts Fˆti|t −1,T formed at time t − 1 by the ith model for the T -expiry freight futures price to be realized at time t, the following trading rule is employed to assess the economic significance of the constructed point forecasts: If Ft −1,T (1 + TC ) ≤ Fˆti|t −1,T ,

then go long;

If Ft −1,T (1 − TC ) ≥ Fˆti|t −1,T ,

then go short;

If Ft −1,T (1 − TC ) > Fˆti|t −1,T > Ft −1,T (1 + TC ), then do nothing; where TC denotes the transaction cost. The rationale for the rule is the following. When the current futures price is greater (lower) than the forecasted futures price plus (minus) transaction costs, the index is expected to decrease (increase). In this case the investor will take a short (long) position in the IMAREX futures. If the current futures price is inside the spread of the forecasted futures price, the investor takes no action and maintains her position. We use the TC in the triggering rule so as to avoid triggering trades based on small signals (see also Szakmary, Shen, & Sharma, 2010, for a similar idea). In addition, we employ the following trading rule in order to assess the economic significance of the constructed interval forecasts. If Ft −1,T (1 + TC )

≤

Uˆ ti|t −1,T (1 − α) + Lˆ it |t −1,T (1 − α)

then go long.

2

,

If Ft −1,T (1 − TC )

≥

Uˆ ti|t −1,T (1 − α) + Lˆ it |t −1,T (1 − α)

then go short.

2

,

If Ft −1,T (1 − TC )

>

Uˆ ti|t −1,T (1 − α) + Lˆ it |t −1,T (1 − α)

> Ft −1,T (1 + TC ),

2

then do nothing.

Again, the rationale is that, when the current futures price is close to the lower (upper) bound of the forecasted intervals plus (minus) transaction costs, the index price is expected to increase (decrease). Hence, the investor will take a long (short) position in the IMAREX futures.

stationary bootstrap re-samples blocks of a random size from the original time series. The block size follows a geometric distribution, with a mean block length of 1/q. The main feature of this procedure is that the re-sampled pseudo time series retains the stationarity property of the original series.

655

Table 5 reports the results from the evaluation of the performances of the trading strategies based on the oneday-ahead point forecasts from the models described in Section 3 for the case of the Capesize futures; the values of SR and Ap , as well as their bootstrapped 95% CI, are reported for each model and futures maturity. We can see that both performance measures are positive and statistically significant. Unreported results show that in the case of the Panamax futures, positive and statistically significant performance measures are observed in 36 cases (out of 39). In the case of the TD3 futures, both performance measures are positive and statistically significant in 18 cases out of 38. In total, the trading strategies based on point forecasts yield economically significant profits in 92 cases out of 113 (i.e., 81.4% of the cases). Table 6 reports the results from the performance evaluation of the trading strategies based on the oneday-ahead interval forecasts of the models described in Section 3 for the case of the Capesize futures. We can see that the two performance measures are positive and statistically significant in all cases. This also holds for the Panamax and TD3 futures. Therefore, the trading strategies yield economically significant profits at the daily forecasting horizon, regardless of whether they are based on point or interval forecasts. However, these trading strategies do not yield economically significant profits at the weekly forecasting horizon. In particular, we find that the performance measures are statistically insignificant in all cases for all indices and maturities. This holds whether the strategies are based on point or interval forecasts.12 6. Conclusions We investigate for the first time whether the International Maritime Exchange (IMAREX) freight futures market is efficient. To this end, we employ an extensive dataset of freight futures that takes the segmented nature of the maritime industry into account. We study the research question first in a statistical setting, then in an economic setting. In particular, we form statistical out-of-sample point and interval forecasts of futures prices and evaluate them. Then, we assess the performance of trading strategies based on the statistical forecasts formed. To ensure the robustness of the analysis, we consider a number of model specifications (11 overall); the specifications account for any mean-reversion and time-varying volatility that the dynamics of freight futures prices may exhibit. In addition, we also evaluate the performances of the trading strategies by taking into account the departure from normality of the returns of the strategy, as well as the presence of transaction costs. We examine the question under scrutiny by considering both daily and weekly forecast horizons.

12 We have also estimated a restricted version of the economic variables model (Eqs. (1)–(3)) that employs only the lagged variables (i.e. lagged information). We find that the lagged economic variables model performs better than the augmented model in the case of point forecasts, whereas it performs worse in the case of interval forecasts. These results hold over both the one-day and one-week forecasting horizons. The performances of the two models are similar under the economic setting.

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Table 5 Trading strategy with IMAREX Capesize futures, based on one-day-ahead point forecasts. The Sharpe ratio (SR) and Leland’s alpha (Ap ) are reported, with their respective bootstrapped 95% confidence intervals (95% CI) in parentheses. The strategy is based on point forecasts obtained from the economic variables model (panel A), the AR(1) model (panel B), the VECM(1) model (panel C), the GARCH, EGARCH and GARCH-in-mean models with normal distributions (panels D, F, H respectively), and the GARCH, EGARCH and GARCH-in-mean models with Student-t distributions (panels E, G, I respectively). The naïve buy and hold strategy yields SR values equal to −0.006 (−0.12, 0.08), −0.007 (−0.1, 0.08), −0.011 (−0.1, 0.09) and −0.009 (−0.09, 0.09) for the 1st, 2nd, 3rd and 4th maturities, respectively. IMAREX Capesize (T/C basket) futures 1st shortest

2nd shortest

3rd shortest

4th shortest

0.1202 (0.06, 0.18) 0.0064 (0.002, 0.011)

0.1124 (0.09, 0.21) 0.005 (0.001, 0.009)

0.1044 (0.03, 0.18) 0.004 (0.001, 0.007)

0.0974 (0.02, 0.18) 0.0039 (0.001, 0.007)

0.145 (0.08, 0.23) 0.0072 (0.003, 0.012)

0.1821 (0.12, 0.25) 0.0071 (0.004, 0.011)

0.1909 (0.11, 0.27) 0.007 (0.003, 0.01)

0.1878 (0.11, 0.27) 0.007 (0.004, 0.011)

0.149 (0.09, 0.23) 0.0077 (0.003, 0.012)

0.1694 (0.10, 0.23) 0.0072 (0.004, 0.011)

0.1772 (0.10, 0.25) 0.0065 (0.003, 0.01)

0.1732 (0.10, 0.25) 0.0065 (0.003, 0.01)

0.141 (0.08, 0.21) 0.0074 (0.003, 0.012)

0.1805 (0.10, 0.25) 0.0073 (0.004, 0.011)

0.2022 (0.12, 0.27) 0.0073 (0.004, 0.011)

0.1848 (0.11, 0.26) 0.0067 (0.003, 0.01)

0.1578 (0.10, 0.25) 0.0082 (0.004, 0.013)

0.1914 (0.12, 0.26) 0.0076 (0.004, 0.011)

0.1831 (0.09, 0.25) 0.0069 (0.003, 0.01)

0.1848 (0.10, 0.25) 0.0073 (0.004, 0.01)

0.1535 (0.09, 0.23) 0.008 (0.004, 0.013)

0.1685 (0.10, 0.23) 0.0068 (0.003, 0.009)

0.1864 (0.11, 0.26) 0.0068 (0.004, 0.01)

0.184 (0.10, 0.25) 0.0073 (0.004, 0.011)

0.1537 (0.09, 0.23) 0.008 (0.004, 0.013)

0.1782 (0.10, 0.25) 0.007 (0.004, 0.011)

0.1842 (0.11, 0.27) 0.0068 (0.004, 0.01)

0.1827 (0.10, 0.24) 0.0072 (0.003, 0.01)

0.1937 (0.12, 0.26) 0.0075 (0.004, 0.011)

0.2117 (0.13, 0.28) 0.0072 (0.004, 0.01)

0.1697 (0.09, 0.24) 0.006 (0.003, 0.01)

0.1818 (0.11, 0.25) 0.0068 (0.004, 0.01)

0.1864 (0.1, 0.26) 0.0067 (0.004, 0.01)

0.1712 (0.09, 0.24) 0.0065 (0.003, 0.01)

Panel A: economic variables Sharpe ratio 95% CI Ap 95% CI Panel B: AR(1) Sharpe ratio 95% CI Ap 95% CI Panel C: VECM(1) Sharpe ratio 95% CI Ap 95% CI Panel D: AR/GARCH(1, 1) − n Sharpe ratio 95% CI Ap 95% CI Panel E: AR/GARCH(1, 1) − t Sharpe ratio 95% CI Ap 95% CI Panel F: AR/EGARCH(1, 1) − n Sharpe ratio 95% CI Ap 95% CI Panel G: AR/EGARCH(1, 1) − t Sharpe ratio 95% CI Ap 95% CI

Panel H: AR/GARCH(1, 1)-in-mean − n Sharpe ratio 95% CI Ap 95% CI

0.1308 (0.07, 0.21) 0.0064 (0.002, 0.011)

Panel I: AR/GARCH(1, 1)-in-mean − t Sharpe ratio 95% CI Ap 95% CI

0.1641 (0.10, 0.25) 0.0083 (0.004, 0.013)

We find that the daily evolution of the IMAREX freight futures prices can be forecasted, regardless of the underlying freight index and the maturity of the futures contract. Furthermore, the predictability of freight futures prices is particularly evident in the case of point forecasts, where all models considered outperform the random walk

model. Most importantly, the futures trading strategies based on the formed daily forecasts yield a positive, economically significant risk premium, even after taking transaction costs into account. However, the statistical and economic significance of the daily forecasts deteriorates when we consider weekly horizons.

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657

Table 6 Trading strategy with IMAREX Capesize futures based on one-day-ahead interval forecasts. The Sharpe ratio (SR) and Leland’s alpha (Ap ) are reported, with their respective bootstrapped 95% confidence intervals (95% CI) in parentheses. The strategy is based on interval forecasts obtained from the economic variables model (panel A), the AR(1) model (panel B), the VECM(1) model (panel C), the GARCH, EGARCH and GARCH-in-mean models with normal distributions (panels D, F, H respectively), and the GARCH, EGARCH and GARCH-in-mean models with Student-t distributions (panels E, G, I respectively). The naïve buy and hold strategy yields SR values equal to −0.006 (−0.12, 0.08), −0.007 (−0.1, 0.08), −0.011 (−0.1, 0.09) and −0.009 (−0.09, 0.09) for the 1st, 2nd, 3rd and 4th maturities, respectively. IMAREX Capesize (T/C basket) futures 1st shortest

2nd shortest

3rd shortest

4th shortest

0.0845 (0.02, 0.19) 0.0047 (0.003, 0.01)

0.1663 (0.08, 0.26) 0.0085 (0.004, 0.014)

0.2072 (0.12, 0.29) 0.0091 (0.005, 0.014)

0.1898 (0.11, 0.26) 0.0077 (0.004, 0.012)

0.117 (0.03, 0.24) 0.0064 (0.001, 0.012)

0.1757 (0.09, 0.26) 0.0083 (0.004, 0.013)

0.1791 (0.10, 0.25) 0.0074 (0.004, 0.011)

0.1629 (0.09, 0.24) 0.0064 (0.003, 0.01)

0.2002 (0.11, 0.29) 0.0087 (0.004, 0.014)

0.1713 (0.09, 0.27) 0.0082 (0.004, 0.013)

0.1941 (0.12, 0.25) 0.008 (0.004, 0.012)

0.2061 (0.13, 0.29) 0.008 (0.004, 0.012)

0.2073 (0.11, 0.29) 0.0091 (0.004, 0.015)

0.172 (0.09, 0.27) 0.0083 (0.004, 0.013)

0.1901 (0.12, 0.26) 0.0079 (0.004, 0.011)

0.213 (0.13, 0.29) 0.0082 (0.005, 0.012)

0.2074 (0.12, 0.3) 0.0091 (0.004, 0.015)

0.1695 (0.09, 0.27) 0.0082 (0.004, 0.013)

0.195 (0.12, 0.27) 0.0081 (0.005, 0.012)

0.2039 (0.13, 0.29) 0.008 (0.004, 0.012)

0.2126 (0.12, 0.31) 0.0092 (0.005, 0.015)

0.1704 (0.09, 0.26) 0.0082 (0.004, 0.013)

0.197 (0.12, 0.27) 0.0081 (0.005, 0.012)

0.209 (0.13, 0.29) 0.0082 (0.005, 0.012)

0.2045 (0.11, 0.29) 0.0087 (0.004, 0.015)

0.1753 (0.09, 0.27) 0.0084 (0.004, 0.013)

0.2014 (0.13, 0.27) 0.0083 (0.005, 0.012)

0.2085 (0.13, 0.29) 0.0082 (0.005, 0.012)

0.1799 (0.09, 0.27) 0.0086 (0.004, 0.013)

0.1914 (0.12, 0.26) 0.0078 (0.005, 0.012)

0.2128 (0.13, 0.3) 0.0082 (0.005, 0.012)

0.1869 (0.09, 0.28) 0.0089 (0.004, 0.014)

0.189 (0.12, 0.26) 0.0079 (0.005, 0.012)

0.2171 (0.14, 0.39) 0.0084 (0.005, 0.012)

Panel A: economic variables Sharpe ratio 95% CI Ap 95% CI Panel B: AR(1) Sharpe ratio 95% CI Ap 95% CI Panel C: VECM(1) Sharpe ratio 95% CI Ap 95% CI Panel D: AR/GARCH(1, 1) − n Sharpe ratio 95% CI Ap Ap 95% CI Panel E: AR/GARCH(1, 1) − t Sharpe ratio 95% CI Ap 95% CI Panel F: AR/EGARCH(1, 1) − n Sharpe ratio 95% CI Ap 95% CI Panel G: AR/EGARCH(1, 1) − t Sharpe ratio 95% CI Ap 95% CI

Panel I: AR/GARCH(1, 1)-in-mean − n Sharpe ratio 95% CI Ap 95% CI

0.1941 (0.11, 0.29) 0.0085 (0.004, 0.014)

Panel J: AR/GARCH(1, 1)-in-mean − t Sharpe ratio 95% CI Ap 95% CI

0.1983 (0.11, 0.29) 0.0086 (0.004, 0.014)

Our findings have at least four implications for the economics of the freight futures market and the pricing of freight derivatives. First, the IMAREX futures market is not informationally efficient for very short (daily) horizons. Second, the existence of a daily positive risk premium in the freight futures market implies that the unbiasedness

hypothesis does not hold for IMAREX, and questions the price discovery role of freight futures prices. Furthermore, the results suggest that risk-neutral valuation cannot be used for the purpose of pricing freight derivatives. Instead, an equilibrium pricing approach has to be adopted, given the presence of the market price of freight risk. Finally, a

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mean-reverting process for the underlying freight index with time-varying volatility should be assumed when building a freight derivative model. Further research should investigate whether the reported results also hold for other derivative products traded in IMAREX, such as the BDI freight futures introduced in 2008, as well as for other types of strategies (e.g., spread strategies). In addition, it would be worth investigating the determinants of the freight risk premium (see also Adland & Cullinane, 2005). Given that there is anecdotal evidence that freights derivatives are used mostly for hedging purposes, the theory of normal backwardation may be appropriate for explaining its existence (see e.g. Geman, 2005). Finally, intra-day data should be used to study the market efficiency hypothesis; unfortunately, such data are currently unavailable. These topics are well beyond the scope of the current paper, but deserve to be topics for future research. Acknowledgments We are grateful to Graham Elliott (the Editor), an Associate Editor and an anonymous referee for their stimulating, thorough and constructive comments. We would also like to thank Roar Adland, Timotheos Angelidis and Eirini Konstantinidi for useful discussions and comments, and IMAREX Exchange for providing us with the data. Any remaining errors are our responsibility alone. References Adland, R., & Cullinane, K. (2005). A time-varying risk premium in the term structure of bulk shipping freight rates. Journal of Transport Economics and Policy, 39, 191–208. Adland, R., & Strandenes, S. (2006). Market efficiency in the bulk freight market revisited. Maritime Policy and Management, 33, 107–117. Alexander, C. (2008). Market risk analysis. In Practical financial econometrics: vol. II. John Wiley & Sons Publishers. Alizadeh, A., & Nomikos, N. (2009). Shipping derivatives and risk management. London: Palgrave McMillan. Angelidis, T., & Skiadopoulos, G. (2008). Measuring the market risk of freight rates: a value-at-risk approach. International Journal of Theoretical and Applied Finance, 11, 447–469. Baltic exchange (2009). Manual for panelists: a guide to freight reporting and index production. Batchelor, R., Alizadeh, A., & Visvikis, I. D. (2007). Forecasting spot and forward prices in the international freight market. International Journal of Forecasting, 23, 101–114. Beenstock, M., & Vergottis, A. (1989a). An econometric model of the world market for dry cargo freight and shipping. Applied Economics, 21, 339–356. Beenstock, M., & Vergottis, A. (1989b). An econometric model of the world tanker market. Journal of Transport Economics and Policy, 23, 263–280. Bessembinder, H., & Chan, K. (1992). Time varying risk premia and forecastable returns in futures markets. Journal of Financial Economics, 32, 169–193. Bollerslev, T. (1986). Generalized autoregressive conditional heteroskedasticity. Journal of Econometrics, 31, 307–327. Chantziara, T., & Skiadopoulos, G. (2008). Can the dynamics of the term structure of petroleum futures be forecasted? Evidence from major markets. Energy Economics, 30, 962–985. Chincarini, L. (2011). No chills or burns from temperature surprises: an empirical analysis of the weather derivatives market. Journal of Futures Markets, 31, 1–33. Christoffersen, P. F. (1998). Evaluating interval forecasts. International Economic Review, 39, 841–862. Christoffersen, P. F. (2003). Elements of financial risk management. San Diego, CA: Academic Press. Clark, T. E., & McCracken, M. W. (2001). Tests of equal forecast accuracy and encompassing for nested models. Journal of Econometrics, 105, 85–110.

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Wang, C. (2004). Futures trading activity and predictable foreign exchange market movements. Journal of Banking and Finance, 28, 1023–1041. Yoo, J., & Maddala, G. S. (1991). Risk premia and price volatility in futures markets. Journal of Futures Markets, 11, 165–177. Lambros Goulas is a software analyst at Systemic Risk Management, a software development company based in Athens, Greece. He holds a B.Sc. in Business Administration from the University of Piraeus and an M.Sc. in Banking and Financial Management from the University of Piraeus. George Skiadopoulos is Associate Professor in the Department of Banking and Financial Management of the University of Piraeus. He is also an Associate Research Fellow at the Financial Options Research Centre of the University of Warwick and an Honorary Senior Visiting Fellow at the Faculty of Finance, Cass Business School, City University London. He has published in academic journals such as the International Journal of Forecasting, Journal of Banking and Finance, Management Science, etc. He is a member of the editorial boards of the Journal of Business, Finance and Accounting and Journal of Derivatives, and also serves on the Academic Advisory Council of the Professional Risk Managers International Association (PRMIA). For more information, please visit http://web.xrh.unipi.gr/faculty/gskiadopoulos/.