《船舶采购、销售和运营 Ship Purchase, Sales and Operations》课程教学资源（资料）Investment timing and trading strategies in the sale and purchase market for ships

Available online at www.sciencedirect.com ScienceDirect TRANSPORTATION RESEARCH PART B ELSEVIER Transportation Research Part B 41(2007)126-143 www.elsevier.com/locate/trb Investment timing and trading strategies in the sale and purchase market for ships Amir H.Alizadeh *Nikos K.Nomikos Faculty of Finance,Cass Business School,London ECIY 8TZ.United Kingdom Received 14 September 2005:received in revised form 13 April 2006:accepted 25 April 2006 Abstract The aim of this paper is to investigate,for the first time,the performance of trading strategies based on the combination of technical trading rules and fundamental analysis in the sale and purchase market for dry bulk ships.Using a sample of price and charter rates over the period January 1976 to September 2004,we establish the existence of a long-run cointe- grating relationship between price and earnings and use this relationship as an indicator of investment or divestment timing decisions in the dry bulk shipping sector.In order to discount the possibility of data snooping biases and to evaluate the robustness of our trading models,we also perform tests using the stationary bootstrap approach.Our results indicate that trading strategies based on earnings-price ratios significantly out-perform buy and hold strategies in the second-hand market for ships,especially in the market for larger vessels,due to higher volatility in these markets. 2006 Elsevier Ltd.All rights reserved. Keywords:Trading strategies;Cointegration;Shipping;Stationary bootstrap 1.Introduction Investors in shipping markets have always been faced with important and difficult decisions on investment and/or divestment timing because of the complex and volatile nature of the shipping industry.It is not sur- prising therefore that the dynamic behaviour of ship prices and their conditional volatilities have been the focus of many empirical studies in maritime economics literature.Traditional approaches for modelling ship prices are mainly based on general and partial equilibrium models using structural relationships between a number of variables such as orderbook,newbuilding deliveries,scrapping rates,freight rates,bunker prices, etc.(see Strandenes,1984;Beenstock and Vergottis,1989;Tsolakis et al.,2003,among others).More recent studies have applied real options analysis for determining ship prices;this valuation framework takes explicitly into account the operational flexibility in ship management,in terms of choosing between entry and exit from the market,spot and period time-charter operations,and switching between lay-up and trading modes(see Dixit and Pindyck,1994;Tvedt,1997;Bendall and Stent,2004,among others). Corresponding author.Tel.:+44 207 040 0199;fax:+44 207 040 8681. E-mail addresses:a.alizadeh@city.ac.uk(A.H.Alizadeh),n.nomikos@city.ac.uk (N.K.Nomikos). 0191-2615/S-see front matter 2006 Elsevier Ltd.All rights reserved. doi:10.1016j.trb.2006.04.002

Investment timing and trading strategies in the sale and purchase market for ships Amir H. Alizadeh *, Nikos K. Nomikos Faculty of Finance, Cass Business School, London EC1Y 8TZ, United Kingdom Received 14 September 2005; received in revised form 13 April 2006; accepted 25 April 2006 Abstract The aim of this paper is to investigate, for the first time, the performance of trading strategies based on the combination of technical trading rules and fundamental analysis in the sale and purchase market for dry bulk ships. Using a sample of price and charter rates over the period January 1976 to September 2004, we establish the existence of a long-run cointe￾grating relationship between price and earnings and use this relationship as an indicator of investment or divestment timing decisions in the dry bulk shipping sector. In order to discount the possibility of data snooping biases and to evaluate the robustness of our trading models, we also perform tests using the stationary bootstrap approach. Our results indicate that trading strategies based on earnings–price ratios significantly out-perform buy and hold strategies in the second-hand market for ships, especially in the market for larger vessels, due to higher volatility in these markets. 2006 Elsevier Ltd. All rights reserved. Keywords: Trading strategies; Cointegration; Shipping; Stationary bootstrap 1. Introduction Investors in shipping markets have always been faced with important and difficult decisions on investment and/or divestment timing because of the complex and volatile nature of the shipping industry. It is not sur￾prising therefore that the dynamic behaviour of ship prices and their conditional volatilities have been the focus of many empirical studies in maritime economics literature. Traditional approaches for modelling ship prices are mainly based on general and partial equilibrium models using structural relationships between a number of variables such as orderbook, newbuilding deliveries, scrapping rates, freight rates, bunker prices, etc. (see Strandenes, 1984; Beenstock and Vergottis, 1989; Tsolakis et al., 2003, among others). More recent studies have applied real options analysis for determining ship prices; this valuation framework takes explicitly into account the operational flexibility in ship management, in terms of choosing between entry and exit from the market, spot and period time-charter operations, and switching between lay-up and trading modes (see Dixit and Pindyck, 1994; Tvedt, 1997; Bendall and Stent, 2004, among others). 0191-2615/$ - see front matter 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.trb.2006.04.002 * Corresponding author. Tel.: +44 207 040 0199; fax: +44 207 040 8681. E-mail addresses: a.alizadeh@city.ac.uk (A.H. Alizadeh), n.nomikos@city.ac.uk (N.K. Nomikos). Transportation Research Part B 41 (2007) 126–143 www.elsevier.com/locate/trb

A.H.Alizadeh.N.K.Nomikos Transportation Research Part B 41 (2007)126-143 127 The price formation in the second-hand market for ships has also been examined to determine whether markets for ships are efficient and whether prices are formed rationally.For example,Kavussanos and Ali- zadeh (2002a),Hale and Vanags(1992)and Glen (1997),test the validity of the Efficient Market Hypothesis (EMH)in the formation of second-hand dry bulk prices.These studies argue that the failure of the EMH may either be attributed to the existence of time-varying risk premia,or reflect arbitrage opportunities in the mar- ket.The latter suggests that if prices for vessels are found to deviate consistently from their rational values, then trading strategies can be adapted to exploit excess profit making opportunities.For example,when ship prices are lower than their fundamental values,then buying and operating these vessels may be profitable since they are under-priced in comparison to their future profitability (i.e.the earnings from freight operations).On the other hand,when prices are higher than their corresponding rational values,then from a shipowner's point of view it may be more profitable to charter in vessels,rather than buying them,since they are overpriced in comparison to their expected future profitability. Despite numerous studies in the literature on ship price formation,on testing the validity of the EMH in shipping markets,and on the behaviour of ship prices and their volatilities,there has been little empirical evi- dence on whether sale and purchase decisions of merchant ships,based on fundamental and/or technical anal- ysis,can be profitable.For example,Adland(2000)and Adland and Koekebakker (2004)investigate the performance of technical trading rules and argue that if the market for ships is efficient,then trading strategies based on these rules should not produce wealth in excess of what can be gained through simple buy and hold strategies.Using both in-and out-of-sample tests,they report that,in general,trading rules do not yield excess returns that can compensate for transaction costs.Although their study seems to provide support for the EMH,given the nature of technical analysis there may be two points that could be raised.First,as they point out,their results might be dependent on the variables and set of rules used for constructing the tech- nical trading strategies.Second,the use of technical trading rules on their own,and not in conjunction with the underlying economic theory,may not be as effective in this market.This is because the historical pattern of the underlying series alone is not enough to extract information on the future behaviour of prices,since it is widely documented that ship prices follow random walk processes. Therefore,in this study we overcome these shortcomings by developing a theoretical economic framework which links prices and earnings,and then combining such a relationship with technical rules,to extract infor- mation from the market for investment and trading purposes.In other words,we do not rely only on the past price behaviour for trading strategies,but we combine technical trading rules with fundamental analysis by using the cointegration relationship between prices and earnings.In particular,we use the price-earnings ratio as an indicator for investment or divestment timing decisions in the dry bulk shipping sector.The motivation for this stems from the importance of economic indicators and,in particular,the price-earnings(P/E)ratio (or its inverse the earnings-price,E/P,ratio)in predicting asset returns in financial markets.For instance,P/E ratios of individual stocks or portfolios are regularly used to explain the returns in the stock market and a number of studies document the ability of P/E ratios to predict future returns of individual stocks or portfo- lios.For instance,Campbell and Shiller(1998)show that P/E ratios are negatively correlated with subsequent stock returns over a ten-year period.Other studies on the information content of P/E ratio in predicting stock returns include Fama and French (1992),Fuller et al.(1993),Jaffe et al.(1989),and Roll (1994). The spread between P/E ratios and interest rates is also used to forecast movements of broad stock market indices.For example,Lander et al.(1997)use various linear combinations of the P/E ratio and bond yields to predict returns on the S&P 500 index in a regression framework,while,Pesaran and Timmermann (1995) include both interest rates and P/E ratios as possible explanatory variables of stock market movements.In addition,a number of studies in financial economics literature examine the performance of various strategies that may be useful in timing the market.For example,Lander et al.(1997)test their models'ability to time the market,while Fuller and Kling(1990,1994)study regression-based market timing strategies using dividend yields,and highlight the inherent difficulties in finding market timing strategies. I Here by fundamental or rational value of assets we mean the discounted present value of the expected stream of income that the assets will generate over their lifetime. 2 Adland and Koekebakker(2004)use historical prices for VLCC and Aframax tankers,as well as capesize and panamax dry bulk carriers

The price formation in the second-hand market for ships has also been examined to determine whether markets for ships are efficient and whether prices are formed rationally. For example, Kavussanos and Ali￾zadeh (2002a), Hale and Vanags (1992) and Glen (1997), test the validity of the Efficient Market Hypothesis (EMH) in the formation of second-hand dry bulk prices. These studies argue that the failure of the EMH may either be attributed to the existence of time-varying risk premia, or reflect arbitrage opportunities in the mar￾ket. The latter suggests that if prices for vessels are found to deviate consistently from their rational values, then trading strategies can be adapted to exploit excess profit making opportunities.1 For example, when ship prices are lower than their fundamental values, then buying and operating these vessels may be profitable since they are under-priced in comparison to their future profitability (i.e. the earnings from freight operations). On the other hand, when prices are higher than their corresponding rational values, then from a shipowner’s point of view it may be more profitable to charter in vessels, rather than buying them, since they are overpriced in comparison to their expected future profitability. Despite numerous studies in the literature on ship price formation, on testing the validity of the EMH in shipping markets, and on the behaviour of ship prices and their volatilities, there has been little empirical evi￾dence on whether sale and purchase decisions of merchant ships, based on fundamental and/or technical anal￾ysis, can be profitable. For example, Adland (2000) and Adland and Koekebakker (2004) investigate the performance of technical trading rules and argue that if the market for ships is efficient, then trading strategies based on these rules should not produce wealth in excess of what can be gained through simple buy and hold strategies.2 Using both in- and out-of-sample tests, they report that, in general, trading rules do not yield excess returns that can compensate for transaction costs. Although their study seems to provide support for the EMH, given the nature of technical analysis there may be two points that could be raised. First, as they point out, their results might be dependent on the variables and set of rules used for constructing the tech￾nical trading strategies. Second, the use of technical trading rules on their own, and not in conjunction with the underlying economic theory, may not be as effective in this market. This is because the historical pattern of the underlying series alone is not enough to extract information on the future behaviour of prices, since it is widely documented that ship prices follow random walk processes. Therefore, in this study we overcome these shortcomings by developing a theoretical economic framework which links prices and earnings, and then combining such a relationship with technical rules, to extract infor￾mation from the market for investment and trading purposes. In other words, we do not rely only on the past price behaviour for trading strategies, but we combine technical trading rules with fundamental analysis by using the cointegration relationship between prices and earnings. In particular, we use the price–earnings ratio as an indicator for investment or divestment timing decisions in the dry bulk shipping sector. The motivation for this stems from the importance of economic indicators and, in particular, the price–earnings (P/E) ratio (or its inverse the earnings–price, E/P, ratio) in predicting asset returns in financial markets. For instance, P/E ratios of individual stocks or portfolios are regularly used to explain the returns in the stock market and a number of studies document the ability of P/E ratios to predict future returns of individual stocks or portfo￾lios. For instance, Campbell and Shiller (1998) show that P/E ratios are negatively correlated with subsequent stock returns over a ten-year period. Other studies on the information content of P/E ratio in predicting stock returns include Fama and French (1992), Fuller et al. (1993), Jaffe et al. (1989), and Roll (1994). The spread between P/E ratios and interest rates is also used to forecast movements of broad stock market indices. For example, Lander et al. (1997) use various linear combinations of the P/E ratio and bond yields to predict returns on the S&P 500 index in a regression framework, while, Pesaran and Timmermann (1995) include both interest rates and P/E ratios as possible explanatory variables of stock market movements. In addition, a number of studies in financial economics literature examine the performance of various strategies that may be useful in timing the market. For example, Lander et al. (1997) test their models’ ability to time the market, while Fuller and Kling (1990, 1994) study regression-based market timing strategies using dividend yields, and highlight the inherent difficulties in finding market timing strategies. 1 Here by fundamental or rational value of assets we mean the discounted present value of the expected stream of income that the assets will generate over their lifetime. 2 Adland and Koekebakker (2004) use historical prices for VLCC and Aframax tankers, as well as capesize and panamax dry bulk carriers. A.H. Alizadeh, N.K. Nomikos / Transportation Research Part B 41 (2007) 126–143 127

128 A.H.Alizadeh.N.K.Nomikos Transportation Research Part B 41 (2007)126-143 However,although these studies provide empirical evidence on the performance of trading rules in financial markets,there has been little evidence for markets that trade real assets,in particular for the transportation and shipping markets.The aim of this paper is therefore to investigate the performance of trading strategies for investment decisions in the market for second-hand ships.In doing so,the paper contributes to the liter- ature in a number of ways.First,there has been no prior evidence on the performance of trading strategies based on signals provided by fundamental market price indicators such as the price-earnings (P/E)ratio and how effective these strategies are for investment decisions in the shipping markets.We consider ships as real capital assets which can,not only generate income through operation but also capital gain (loss) through price appreciation(depreciation).In this setting we examine whether the P/E ratio can be used to identify the optimal time to buy or sell second-hand vessels.Second,we compare the profitability and risk- return characteristics of our proposed strategies with a simple benchmark strategy-the "buy and hold", where one invests in the shipping market at all times.This comparison enables us to assess whether the dynamic investment strategy,in which one invests in ships most of the time but switches to risk-free invest- ments(e.g.t-bills)when the P/E ratio is too high,is superior to "static"trading strategies.As a matter of fact, if the information contained in the P/E ratio is economically important,one would expect the dynamic strat- egies to have higher risk-adjusted returns.Third,we also compare the profitability of the trading strategies across different vessel sizes and attribute any differences in the results to the idiosyncratic features of each mar- ket.Finally,we also use stationary bootstrap as a technique to re-generate the underlying series and hence replicate the trading results from the different strategies in a simulation environment;this is done in order to discount the possibility that our results may be due to data snooping or statistical chance. Our methodology is motivated by the fact that the ratio of ship prices to operating earnings(price-earnings ratio)is a measure of whether the market for second-hand ships is under or overvalued,relative to its funda- mentals.Shipowners,ship operators and charterers regularly use this ratio as an indicator of whether to buy or charter-in tonnage.The findings of this paper also have important practical implications and can be of interest to investors in shipping markets regarding the timing of investment and divestment.In addition, recent developments in the areas of shipping investment and finance,such as the development of shipping funds and derivative contracts for ship values,may enable participants not only to invest in ships as an alter- native investment but also to speculate on the future outlook of the market without incurring the costs of physically owning or operating a ship.Although the focus of the paper is in the market for ships,the same methodology can also be used for the valuation and investment analysis of other tangible assets in the trans- portation sector,such as the airline industry.Since airlines are often faced with the choice of whether to lease or buy aircrafts,the ratio of aircraft prices to operational earnings can also be used in the same setting to iden- tify investment timing opportunities. The structure of this paper is as follows.Section 2 presents the theoretical background and the methodol- ogies proposed in the asset pricing literature,which are used to relate prices and earnings for second-hand ships.The data and their properties are discussed in Section 3.Section 4 presents the empirical results and discussion on the performance of trading strategies using simulations.Finally,Section 5 concludes this paper. 2.The theoretical relationship between price and earnings Investors in the shipping industry,like investors in any other sector of the economy,are not only interested in income from the day to day operation of ships,but also interested in gains from capital appreciation in the value of the vessels.Therefore,from the investors'point of view expected one period returns,E,R+1,on ship- ping investments are equal to the expected one period capital gains between time t and t+1(E,P+-P,)/P, plus the expected return from operation,E,/P,where E,P+is the expected ship price at time t+1 and E,I+is the expected operating profit between period t and t+1.3 Mathematically, E,R+1= EP+l-P,+E,Ⅱ4l P (1) 3 See Section 3 of the paper for the description of operating profits and TC earnings

However, although these studies provide empirical evidence on the performance of trading rules in financial markets, there has been little evidence for markets that trade real assets, in particular for the transportation and shipping markets. The aim of this paper is therefore to investigate the performance of trading strategies for investment decisions in the market for second-hand ships. In doing so, the paper contributes to the liter￾ature in a number of ways. First, there has been no prior evidence on the performance of trading strategies based on signals provided by fundamental market price indicators such as the price–earnings (P/E) ratio and how effective these strategies are for investment decisions in the shipping markets. We consider ships as real capital assets which can, not only generate income through operation but also capital gain (loss) through price appreciation (depreciation). In this setting we examine whether the P/E ratio can be used to identify the optimal time to buy or sell second-hand vessels. Second, we compare the profitability and risk￾return characteristics of our proposed strategies with a simple benchmark strategy—the ‘‘buy and hold’’, where one invests in the shipping market at all times. This comparison enables us to assess whether the dynamic investment strategy, in which one invests in ships most of the time but switches to risk-free invest￾ments (e.g. t-bills) when the P/E ratio is too high, is superior to ‘‘static’’ trading strategies. As a matter of fact, if the information contained in the P/E ratio is economically important, one would expect the dynamic strat￾egies to have higher risk-adjusted returns. Third, we also compare the profitability of the trading strategies across different vessel sizes and attribute any differences in the results to the idiosyncratic features of each mar￾ket. Finally, we also use stationary bootstrap as a technique to re-generate the underlying series and hence replicate the trading results from the different strategies in a simulation environment; this is done in order to discount the possibility that our results may be due to data snooping or statistical chance. Our methodology is motivated by the fact that the ratio of ship prices to operating earnings (price–earnings ratio) is a measure of whether the market for second-hand ships is under or overvalued, relative to its funda￾mentals. Shipowners, ship operators and charterers regularly use this ratio as an indicator of whether to buy or charter-in tonnage. The findings of this paper also have important practical implications and can be of interest to investors in shipping markets regarding the timing of investment and divestment. In addition, recent developments in the areas of shipping investment and finance, such as the development of shipping funds and derivative contracts for ship values, may enable participants not only to invest in ships as an alter￾native investment but also to speculate on the future outlook of the market without incurring the costs of physically owning or operating a ship. Although the focus of the paper is in the market for ships, the same methodology can also be used for the valuation and investment analysis of other tangible assets in the trans￾portation sector, such as the airline industry. Since airlines are often faced with the choice of whether to lease or buy aircrafts, the ratio of aircraft prices to operational earnings can also be used in the same setting to iden￾tify investment timing opportunities. The structure of this paper is as follows. Section 2 presents the theoretical background and the methodol￾ogies proposed in the asset pricing literature, which are used to relate prices and earnings for second-hand ships. The data and their properties are discussed in Section 3. Section 4 presents the empirical results and discussion on the performance of trading strategies using simulations. Finally, Section 5 concludes this paper. 2. The theoretical relationship between price and earnings Investors in the shipping industry, like investors in any other sector of the economy, are not only interested in income from the day to day operation of ships, but also interested in gains from capital appreciation in the value of the vessels. Therefore, from the investors’ point of view expected one period returns, EtRt+1, on ship￾ping investments are equal to the expected one period capital gains between time t and t +1(EtPt+1 Pt)/Pt, plus the expected return from operation, EtPt+1/Pt, where EtPt+1 is the expected ship price at time t + 1 and EtPt+1 is the expected operating profit between period t and t + 1.3 Mathematically, EtRtþ1 ¼ EtPtþ1 Pt þ EtPtþ1 Pt ð1Þ 3 See Section 3 of the paper for the description of operating profits and TC earnings. 128 A.H. Alizadeh, N.K. Nomikos / Transportation Research Part B 41 (2007) 126–143

A.H.Alizadeh.N.K.Nomikos Transportation Research Part B 41 (2007)126-143 129 Eq.(1)can be rearranged to represent the present value relationship,where the current ship price,P,is ex- pressed in terms of the expected price of the vessel,expected operational profits and expected rate of return,in the following expression P,= rE,P41+E,Ⅱ+ 1+E,R+1 (2) Eq.(2)is in fact a one period present value model;through recursive substitution and some algebraic manip- ulation,P,can be written as the sum of the present values of the future profits plus the terminal or resale value, Pof the asset.Mathematically +E,R+)厂 E,+H+ +E,R+） (3) Eq.(2)can also be written in logarithmic form;however,in this case it is not possible to perform recursive substitutions to write the log of price (InP,)in terms of the log of discounted expected earnings and log of discounted expected terminal value of the asset.Campbell and Shiller(1987)suggest a way round this by using a first-order Taylor series expansion and linearising(1)around the geometric mean of P and IT(P and IT)to give In(1+E,R+1)=pIn(E,P+)+(1-p)In(E:I+1)-In P:+k (4) where p=P/(P+IT)and k =-In(p)-(1 p)In(1/p-1).Letting Ep+1 In(E,P:+1),Ei+1=In(1 E,R+1) and E+=In(E,I,+1),Eq.(2)can be written as P,=pEP+1+(1-p)E元+1-E+1+k (5) which can be solved recursively forward to yield =∑l-pE4a-pPE4+prE+k1-p/0- (6) Since prices and operating profit series are non-stationary,Eq.(6)should be transformed in such a way so as to derive a model with stationary variables.Following Campbell and Shiller(1987),we use the cointegration relationship between the log-price and the log-earning series for such transformation;that is the log P/E ratio.This is done by subtracting n,from both sides of(6)which results in A-元= ∑pl-p）E4H--∑pE41H+Ep+kl-p)/I-p) (7) or Cp'(E,△元+1+H-E+1+i)+p(EpPn-E+)+k(1-p)/(1-p） (8) i-0 In the above setting p,-n,and p-n,are the log P/E ratio and log resale price-earning ratio,respectively. According to Campbell and Shiller(1987),the left hand side of Eq.(8)is the actual spread,and the right hand 4 It has been argued that many financial and economic time series are non-stationary.Such variables tend to have an increasing variance and do not show a tendency to revert to a long-run mean.In order to detect such behaviour in a variable one should use unit root tests such as the Phillips and Perron (1988)and Kwiatkowski et al.(1992).In general,it has been shown that correlation between non- stationary series does not accurately represent the true relationship between variables.However,there might be cases where two non- stationary variables can be related in the long-run through an equilibrium relationship,but deviate from such an equilibrium in the short run.Such a relationship is called a cointegrating relationship and implies that a linear combination of the two non-stationary series is stationary(Engle and Granger,1987).In our case for instance,although the log of ship prices and the log of earnings are non-stationary time series,their difference(i.e.the P/E ratio)should be stationary because ship prices and earnings are linked through the fundamental pricing relationship of Eq.(6).Thus,if the P/E ratio is too high or too low,we expect it to revert back to its long-run mean due to corrective movements in the level of earnings and ship prices

Eq. (1) can be rearranged to represent the present value relationship, where the current ship price, Pt, is ex￾pressed in terms of the expected price of the vessel, expected operational profits and expected rate of return, in the following expression Pt ¼ EtPtþ1 þ EtPtþ1 1 þ EtRtþ1 ð2Þ Eq. (2) is in fact a one period present value model; through recursive substitution and some algebraic manip￾ulation, Pt can be written as the sum of the present values of the future profits plus the terminal or resale value, Psc tþn of the asset. Mathematically Pt ¼ Xn i¼1 Yi j¼1 ð1 þ EtRtþjÞ 1 !EtPtþi þ Yn j¼1 ð1 þ EtRtþjÞ 1 !EtPsc tþn ð3Þ Eq. (2) can also be written in logarithmic form; however, in this case it is not possible to perform recursive substitutions to write the log of price (lnPt) in terms of the log of discounted expected earnings and log of discounted expected terminal value of the asset. Campbell and Shiller (1987) suggest a way round this by using a first-order Taylor series expansion and linearising (1) around the geometric mean of P and P (P and P) to give lnð1 þ EtRtþ1Þ ¼ q lnðEtPtþ1Þþð1 qÞlnðEtPtþ1Þ ln Pt þ k ð4Þ where q ¼ P=ðP þ PÞ and k = ln(q) (1 q)ln(1/q 1). Letting Etpt+1 = ln(EtPt+1), Etrt+1 = ln(1 + EtR+1) and Etpt+1 = ln(EtPt+1), Eq. (2) can be written as pt ¼ qEptþ1 þ ð1 qÞEptþ1 Ertþ1 þ k ð5Þ which can be solved recursively forward to yield pt ¼ Xn1 i¼0 qi ð1 qÞEtptþ1þi Xn1 i¼0 qi Etrtþ1þi þ qn Etpsc tþn þ kð1 qn Þ=ð1 qÞ ð6Þ Since prices and operating profit series are non-stationary, Eq. (6) should be transformed in such a way so as to derive a model with stationary variables. Following Campbell and Shiller (1987), we use the cointegration relationship between the log-price and the log-earning series for such transformation; that is the log P/E ratio.4 This is done by subtracting pt from both sides of (6) which results in pt pt ¼ Xn1 i¼0 qi ð1 qÞEtptþ1þi pt Xn1 i¼0 qi Etrtþ1þi þ qn Etpsc tþn þ kð1 qn Þ=ð1 qÞ ð7Þ or pt pt ¼ Xn1 i¼0 qi ðEtDptþ1þi Etrtþ1þiÞ þ qn ðEtpsc tþn EtptþnÞ þ kð1 qn Þ=ð1 qÞ ð8Þ In the above setting pt pt and psc t pt are the log P/E ratio and log resale price–earning ratio, respectively. According to Campbell and Shiller (1987), the left hand side of Eq. (8) is the actual spread, and the right hand 4 It has been argued that many financial and economic time series are non-stationary. Such variables tend to have an increasing variance and do not show a tendency to revert to a long-run mean. In order to detect such behaviour in a variable one should use unit root tests such as the Phillips and Perron (1988) and Kwiatkowski et al. (1992). In general, it has been shown that correlation between non￾stationary series does not accurately represent the true relationship between variables. However, there might be cases where two non￾stationary variables can be related in the long-run through an equilibrium relationship, but deviate from such an equilibrium in the short run. Such a relationship is called a cointegrating relationship and implies that a linear combination of the two non-stationary series is stationary (Engle and Granger, 1987). In our case for instance, although the log of ship prices and the log of earnings are non-stationary time series, their difference (i.e. the P/E ratio) should be stationary because ship prices and earnings are linked through the fundamental pricing relationship of Eq. (6). Thus, if the P/E ratio is too high or too low, we expect it to revert back to its long-run mean due to corrective movements in the level of earnings and ship prices. A.H. Alizadeh, N.K. Nomikos / Transportation Research Part B 41 (2007) 126–143 129

130 A.H.Alizadeh.N.K.Nomikos Transportation Research Part B 41 (2007)126-143 side is the theoretical spread which is based on the expected values of earnings,discount rates and resale values of the asset.Under efficient market conditions,the two spread series should be statistically equal with similar volatility,which can be tested empirically(see Kavussanos and Alizadeh,2002a).This model also suggests that the difference between the actual and theoretical spreads contains very useful information for investment pur- poses.For example,when the actual spread is greater than the theoretical one,this implies that the actual price is above the theoretical price,which is the discounted present value of future earnings;that is,vessels are over- priced relative to their future earnings potential.Therefore,the above model suggests that the P/E ratio (spread)contains important information regarding investment timing and trading strategies in shipping markets. 2.1.Cointegration and causality An alternative but related way of explaining the information content of the P/E ratio is through the coin- tegrating relationship between these two variables.In order to test the existence of cointegration between sec- ond-hand prices and operational earnings,we use the Johansen's(1988)reduced rank cointegration technique and estimate the following vector error correction model (VECM) 4g,=2a4p4+2A4+a-1-m1-)+ =1 (9) △m,=∑cAp-+d,Am-+zp-1-0m-1-0o)+ The above VECM model can be used to establish the cointegrating relationship between log-prices and log earnings which then can be used to set up a trading strategy for shipping investment.The important element of the cointegration relationship is the error correction term(ECT)which is in fact the difference between log- prices and log earnings(p,1-01-00).The constant term in the error correction term,00,represents the long-run equilibrium relationship;it is in other words the long-run average of the P/E ratio.In order to set up a trading model then,at any month we estimate the deviation of the log P/E ratio from its long-run mean (cointegration constant).For example,when the log P/E ratio is greater than its long-run average,this indi- cates that earnings are low relative to ship prices or,alternatively,ship prices are overvalued relative to their earnings potential.In this case,ship prices in the market are expected to adjust in future periods by falling relative to their current levels.Similarly,when the P/E ratio is lower than its long-run average,this can be regarded as an indication that ship prices are undervalued relative to their potential earnings and,hence,it is expected that prices will increase in the next period,so that the long run earnings-price relationship is restored. The VECM model of Eq.(9)also provides a framework for testing the causal linkages between ship prices and earnings.According to the Granger Representation Theorem(Granger,1986),if two variables are coin- tegrated,then at least one variable should Granger-cause the other.Since ship prices are determined through the discounted present value of expected earnings and the latter are determined exogenously,through the interaction between the supply and demand schedules for shipping services,we expect the causality to be uni- directional;that is,we expect earnings to Granger-cause ship prices but not the other way round.Hence,any change in earnings should affect the spread between log-prices and log earnings and result in a change in ship prices over the next period.Therefore,in this case one can argue that the log P/E ratio contains information on future changes in ship prices,which can be used for investment strategies. 5 A time series,is said to Granger cause another time series,P if the present value of p can be predicted more accurately by using past values of than by not doing so,considering also other relevant information including past values of p,(Granger,1969).Therefore. the criterion for Granger causality is whether or not the variance of the predictive error of p,is reduced when past,values are included in its prediction.In terms of the VECM of Eq.(9),n,Granger causes p,if some of the b;coefficients,i=1,2,...,g are not zero and/or y,the error correction coefficient in the equation for ship prices,is significant at conventional levels

side is the theoretical spread which is based on the expected values of earnings, discount rates and resale values of the asset. Under efficient market conditions, the two spread series should be statistically equal with similar volatility, which can be tested empirically (see Kavussanos and Alizadeh, 2002a). This model also suggests that the difference between the actual and theoretical spreads contains very useful information for investment pur￾poses. For example, when the actual spread is greater than the theoretical one, this implies that the actual price is above the theoretical price, which is the discounted present value of future earnings; that is, vessels are over￾priced relative to their future earnings potential. Therefore, the above model suggests that the P/E ratio (spread) contains important information regarding investment timing and trading strategies in shipping markets. 2.1. Cointegration and causality An alternative but related way of explaining the information content of the P/E ratio is through the coin￾tegrating relationship between these two variables. In order to test the existence of cointegration between sec￾ond-hand prices and operational earnings, we use the Johansen’s (1988) reduced rank cointegration technique and estimate the following vector error correction model (VECM) Dpt ¼ Xq i¼1 aiDpti þXq i¼1 biDpti þ c1ðpt1 hpt1 h0Þ þ e1;t Dpt ¼ Xq i¼1 ciDpti þXq i¼1 diDpti þ c2ðpt1 hpt1 h0Þ þ e2;t ð9Þ The above VECM model can be used to establish the cointegrating relationship between log-prices and log earnings which then can be used to set up a trading strategy for shipping investment. The important element of the cointegration relationship is the error correction term (ECT) which is in fact the difference between log￾prices and log earnings (pt1 hpt1 h0). The constant term in the error correction term, h0, represents the long-run equilibrium relationship; it is in other words the long-run average of the P/E ratio. In order to set up a trading model then, at any month we estimate the deviation of the log P/E ratio from its long-run mean (cointegration constant). For example, when the log P/E ratio is greater than its long-run average, this indi￾cates that earnings are low relative to ship prices or, alternatively, ship prices are overvalued relative to their earnings potential. In this case, ship prices in the market are expected to adjust in future periods by falling relative to their current levels. Similarly, when the P/E ratio is lower than its long-run average, this can be regarded as an indication that ship prices are undervalued relative to their potential earnings and, hence, it is expected that prices will increase in the next period, so that the long run earnings–price relationship is restored. The VECM model of Eq. (9) also provides a framework for testing the causal linkages between ship prices and earnings. According to the Granger Representation Theorem (Granger, 1986), if two variables are coin￾tegrated, then at least one variable should Granger-cause the other.5 Since ship prices are determined through the discounted present value of expected earnings and the latter are determined exogenously, through the interaction between the supply and demand schedules for shipping services, we expect the causality to be uni￾directional; that is, we expect earnings to Granger-cause ship prices but not the other way round. Hence, any change in earnings should affect the spread between log-prices and log earnings and result in a change in ship prices over the next period. Therefore, in this case one can argue that the log P/E ratio contains information on future changes in ship prices, which can be used for investment strategies. 5 A time series, pt, is said to Granger cause another time series, pt, if the present value of pt can be predicted more accurately by using past values of pt than by not doing so, considering also other relevant information including past values of pt (Granger, 1969). Therefore, the criterion for Granger causality is whether or not the variance of the predictive error of pt is reduced when past pt values are included in its prediction. In terms of the VECM of Eq. (9), pt Granger causes pt if some of the bi coefficients, i = 1, 2,...,q are not zero and/or c1, the error correction coefficient in the equation for ship prices, is significant at conventional levels. 130 A.H. Alizadeh, N.K. Nomikos / Transportation Research Part B 41 (2007) 126–143

A.H.Alizadeh.N.K.Nomikos Transportation Research Part B 41 (2007)126-143 131 2.2.Trading strategies The aim of this analysis is to utilise the relationship between variables in shipping markets and devise strat- egies to identify the timing for sale and purchase of merchant ships.To do so,we develop a strategy which is based on the relationship between price and earnings of such vessels.As mentioned earlier,theoretically,the price of a vessel is linked to her expected operational earnings which are in turn determined by current and expected conditions in the shipping market and the world economy.This theoretical relationship between prices and earnings allows us to use the historical (empirical)spread between them to identify buy and sell opportunities in the market. In practice,the universe of potential trading rules is vast,as there are multiple combinations of relation- ships between variables that can produce a trading signal as well as multiple parameterizations for a given family of rules;for instance,there are different combinations of Moving Average(MA)rules reflecting differ- ent time spans in the estimation of MA prices as well as different filter rules depending on the distance from the mean.As it is beyond the scope of this study to evaluate an exhaustive set of trading rules,we focus our efforts on two simple cases of MA rules based on the relationship between ship prices and earnings. The moving average trading strategy is mainly based on the comparison of a fast(short)and a slow(long) moving average of the PE ratio.For example,a simple MA trading strategy in the sale and purchase market for ships could be a comparison of a 12 month MA with 3 month MA of the PE ratio.This means that in a given month,a positive difference between the 12-month MA and the 3-month MA of the PE ratios should signal a buy decision;similarly,a negative difference signals a sell decision. 3.Description of data For the purpose of this study,monthly prices for 5-year old ships are collected for three different size dry bulk carriers(capesize,panamax and handysize)from Clarkson's Shipping Intelligence Network from January 1976 to September 2004.Capesize prices are for the period April 1979 to September 2004.All prices are quoted in million dollars and represent the average value of vessels traded in each category in any particular month In shipping,operating profits can be defined as time-charter rates,or the time-charter equivalent of spot rates when a vessel is operating in the spot market,minus operating costs.In this study,we use time-charter rates as a proxy for earnings,I,,for two reasons.First,because time-charter rates do not include voyage costs and represent the net earnings from chartering activities of the vessel.Second,since time-charter rates are hire contracts for a number of consecutive periods,they are considered to contain information about future earn- ings of the vessel during these periods(see Kavussanos and Alizadeh,2002b,for a detailed discussion of time- charter rates formation).As a result,it is believed that time-charter rates(earnings)may explain price changes better than current spot rates.Monthly time-charter rates for handysize,panamax and capesize vessels over the period January 1976(April 1979 for capesize vessels)to September 2004 are also obtained from Clarkson's Shipping Intelligence Network.Finally,monthly operating expenses for each vessel size are also collected from the same source. Table I reports descriptive statistics of levels and logarithmic first differences of second-hand prices,as well as operational earnings for capesize,panamax and handysize vessels.The results indicate that mean levels of prices for larger vessels are higher than for smaller ones.Unconditional volatilities of prices(standard devi- ation)also follow a similar pattern;that is,prices for larger vessels fluctuate more than prices for smaller ves- sels.Jarque and Bera(1980)tests indicate significant departures from normality for TC earnings and price returns in all markets,while price levels for all size classes seem to be normally distributed.The Ljung and Box(1978)O statistics for 12th-order autocorrelations in levels and logarithmic first differences of earnings are all significant,indicating that serial correlation is present in all price and profit series.Finally,Engle's 6For the strategy implemented in this paper,a sell decision will be executed only if the investor has already bought a ship.In other words short-selling is not permitted since practically it is not possible for an investor to take a short position in a vessel.However,the development of new "paper"contracts on ship prices,such as the Baltic Sale and Purchase Agreement (BSPA)could allow investors to short sell the vessel values and benefit from falling ship prices

2.2. Trading strategies The aim of this analysis is to utilise the relationship between variables in shipping markets and devise strat￾egies to identify the timing for sale and purchase of merchant ships. To do so, we develop a strategy which is based on the relationship between price and earnings of such vessels. As mentioned earlier, theoretically, the price of a vessel is linked to her expected operational earnings which are in turn determined by current and expected conditions in the shipping market and the world economy. This theoretical relationship between prices and earnings allows us to use the historical (empirical) spread between them to identify buy and sell opportunities in the market. In practice, the universe of potential trading rules is vast, as there are multiple combinations of relation￾ships between variables that can produce a trading signal as well as multiple parameterizations for a given family of rules; for instance, there are different combinations of Moving Average (MA) rules reflecting differ￾ent time spans in the estimation of MA prices as well as different filter rules depending on the distance from the mean. As it is beyond the scope of this study to evaluate an exhaustive set of trading rules, we focus our efforts on two simple cases of MA rules based on the relationship between ship prices and earnings. The moving average trading strategy is mainly based on the comparison of a fast (short) and a slow (long) moving average of the PE ratio. For example, a simple MA trading strategy in the sale and purchase market for ships could be a comparison of a 12 month MA with 3 month MA of the PE ratio. This means that in a given month, a positive difference between the 12-month MA and the 3-month MA of the PE ratios should signal a buy decision; similarly, a negative difference signals a sell decision.6 3. Description of data For the purpose of this study, monthly prices for 5-year old ships are collected for three different size dry bulk carriers (capesize, panamax and handysize) from Clarkson’s Shipping Intelligence Network from January 1976 to September 2004. Capesize prices are for the period April 1979 to September 2004. All prices are quoted in million dollars and represent the average value of vessels traded in each category in any particular month. In shipping, operating profits can be defined as time-charter rates, or the time-charter equivalent of spot rates when a vessel is operating in the spot market, minus operating costs. In this study, we use time-charter rates as a proxy for earnings, Pt, for two reasons. First, because time-charter rates do not include voyage costs and represent the net earnings from chartering activities of the vessel. Second, since time-charter rates are hire contracts for a number of consecutive periods, they are considered to contain information about future earn￾ings of the vessel during these periods (see Kavussanos and Alizadeh, 2002b, for a detailed discussion of time￾charter rates formation). As a result, it is believed that time-charter rates (earnings) may explain price changes better than current spot rates. Monthly time-charter rates for handysize, panamax and capesize vessels over the period January 1976 (April 1979 for capesize vessels) to September 2004 are also obtained from Clarkson’s Shipping Intelligence Network. Finally, monthly operating expenses for each vessel size are also collected from the same source. Table 1 reports descriptive statistics of levels and logarithmic first differences of second-hand prices, as well as operational earnings for capesize, panamax and handysize vessels. The results indicate that mean levels of prices for larger vessels are higher than for smaller ones. Unconditional volatilities of prices (standard devi￾ation) also follow a similar pattern; that is, prices for larger vessels fluctuate more than prices for smaller ves￾sels. Jarque and Bera (1980) tests indicate significant departures from normality for TC earnings and price returns in all markets, while price levels for all size classes seem to be normally distributed. The Ljung and Box (1978) Q statistics for 12th-order autocorrelations in levels and logarithmic first differences of earnings are all significant, indicating that serial correlation is present in all price and profit series. Finally, Engle’s 6 For the strategy implemented in this paper, a sell decision will be executed only if the investor has already bought a ship. In other words short-selling is not permitted since practically it is not possible for an investor to take a short position in a vessel. However, the development of new ‘‘paper’’ contracts on ship prices, such as the Baltic Sale and Purchase Agreement (BSPA) could allow investors to short sell the vessel values and benefit from falling ship prices. A.H. Alizadeh, N.K. Nomikos / Transportation Research Part B 41 (2007) 126–143 131

132 A.H.Alizadeh.N.K.Nomikos Transportation Research Part B 41 (2007)126-143 Table1 Descriptive statistics of price (P)and time charter earnings(TC)for different size dry bulk carriers Mean SD Skew Kurt. J-B Q12) ARCH(12) Capesize Second-hand prices,P(Sm) 22.54 10.11 -0.073 -0.396 2.557 3346 2867 {0.583} {0.137} {0.278} {0.0001 {0.0001 I year TC earnings,I(Sm) 3.960 1.183 1.200 2.709 167.01 1950 1662 {0.000 {0.0001 {0.000} {0.0001 (0.0001 Log return△p(o) 0.007 0.071 2.097 17.737 4761 58.15 24.76 {0.000} {0.000} {0.0001 {0.0001 {0.016} Log change,△Π(% 0.003 0.101 0.248 1.753 42.16 53.25 37.83 {0.0791 {0.000} {0.000} {0.0001 {0.000} Panamax Second-hand prices,P(Sm) 15.83 6.240 0.233 0.033 3.140 3164 2691 {0.078} {0.902} {0.208} {0.0001 (0.0001 I year TC earnings.II(Sm) 3.131 1.495 2.034 9.674 1583 1901 910.9 {0.0001 {0.000} {0.000} {0.000} {0.0001 Log return△p(% 0.004 0.058 0.263 3.767 207.4 57.33 71.59 {0.047} {0.000} {0.000} {0.000} {0.0001 Log change,△Ⅱ(y% 0.006 0.093 -0.467 8.995 1172 44.29 117.3 {0.0001 {0.0001 {0.000} {0.000} (0.0001 Handysize Second-hand prices,P(Sm) 10.54 3.996 -0.066 -0.693 6.138 3390 3118 {0.613} {0.016} {0.046} {0.000} (0.0001 1 year TC earnings,I(Sm) 2.300 0.896 1.687 6.395 751 2652 1904 {0.000} {0.0001 {0.000} {0.000} (0.0001 Log return△p(o 0.002 0.052 -0.011 2.571 94.77 97.56 54.20 {0.933} {0.000} {0.000} {0.000} {0.000} Log change,△Ⅱ(yo 0.005 0.056 0.357 2.893 127.3 94.08 184.2 {0.007} {0.0001 {0.0001 {0.0001 {0.0001 Sample period is January 1976 to September 2004 for the Handysize and Panamax series and April 1979 to September 2004 for the capesize series. Figures in are p-values. Skew.and Kurt.are the estimated centralised third and fourth moments of the data,denoted and (-3),respectively.Their asymp- totic distributions,under the null,are vT~N(0,6)and vT(3)~N(0,24). .J-B is the Jarque and Bera(1980)test statistics for normality:it is (2)distributed. .(12)is the Ljung and Box(1978)O statistic on the 12th-order sample autocorrelations of the raw series.distributed as (12). .ARCH(12)is the Engle's(1982)test for 12th-order ARCH effect:the statistic has a(12)distribution. (1982)ARCH tests for 12th-order ARCH effects indicate the existence of autoregressive conditional hetero- scedasticity in all series. Phillips and Perron(1988)(PP),unit root tests are performed on the log-levels and log-differences of sec- ond-hand prices and time-charter rates(earnings),for the three size dry bulk carriers.Results from these tests suggest that log-levels of all price and earnings series are non-stationary,while their first differences are sta- tionary,indicating that variables are integrated of order one,I(1).Also,PP unit root tests on the spread between logs of second-hand prices and time-charter rates for different size vessels indicate that all spread ser- ies are stationary.Studies in the literature argue that PP tests may have low power in rejecting the unit root null hypothesis in favour of the alternative of stationarity (see Harris,1995;Maddala and Kim,1998).Lee et al.(2000)suggest that one way of overcoming this problem is by conducting unit root tests which test the null of stationarity against the alternative of a unit root,such as the test developed by Kwiatkowski et al.(1992),henceforth KPSS test.In the KPSS test,the null hypothesis of stationarity is rejected in favour

(1982) ARCH tests for 12th-order ARCH effects indicate the existence of autoregressive conditional hetero￾scedasticity in all series. Phillips and Perron (1988) (PP), unit root tests are performed on the log-levels and log-differences of sec￾ond-hand prices and time-charter rates (earnings), for the three size dry bulk carriers. Results from these tests suggest that log-levels of all price and earnings series are non-stationary, while their first differences are sta￾tionary, indicating that variables are integrated of order one, I(1). Also, PP unit root tests on the spread between logs of second-hand prices and time-charter rates for different size vessels indicate that all spread ser￾ies are stationary. Studies in the literature argue that PP tests may have low power in rejecting the unit root null hypothesis in favour of the alternative of stationarity (see Harris, 1995; Maddala and Kim, 1998). Lee et al. (2000) suggest that one way of overcoming this problem is by conducting unit root tests which test the null of stationarity against the alternative of a unit root, such as the test developed by Kwiatkowski et al. (1992), henceforth KPSS test. In the KPSS test, the null hypothesis of stationarity is rejected in favour Table 1 Descriptive statistics of price (P) and time charter earnings (TC) for different size dry bulk carriers Mean SD Skew. Kurt. J–B Q(12) ARCH(12) Capesize Second-hand prices, P ($m) 22.54 10.11 0.073 0.396 2.557 3346 2867 {0.583} {0.137} {0.278} {0.000} {0.000} 1 year TC earnings, P ($m) 3.960 1.183 1.200 2.709 167.01 1950 1662 {0.000} {0.000} {0.000} {0.000} {0.000} Log return Dp (%) 0.007 0.071 2.097 17.737 4761 58.15 24.76 {0.000} {0.000} {0.000} {0.000} {0.016} Log change, DP (%) 0.003 0.101 0.248 1.753 42.16 53.25 37.83 {0.079} {0.000} {0.000} {0.000} {0.000} Panamax Second-hand prices, P ($m) 15.83 6.240 0.233 0.033 3.140 3164 2691 {0.078} {0.902} {0.208} {0.000} {0.000} 1 year TC earnings, P ($m) 3.131 1.495 2.034 9.674 1583 1901 910.9 {0.000} {0.000} {0.000} {0.000} {0.000} Log return Dp (%) 0.004 0.058 0.263 3.767 207.4 57.33 71.59 {0.047} {0.000} {0.000} {0.000} {0.000} Log change, DP (%) 0.006 0.093 0.467 8.995 1172 44.29 117.3 {0.000} {0.000} {0.000} {0.000} {0.000} Handysize Second-hand prices, P ($m) 10.54 3.996 0.066 0.693 6.138 3390 3118 {0.613} {0.016} {0.046} {0.000} {0.000} 1 year TC earnings, P ($m) 2.300 0.896 1.687 6.395 751 2652 1904 {0.000} {0.000} {0.000} {0.000} {0.000} Log return Dp (%) 0.002 0.052 0.011 2.571 94.77 97.56 54.20 {0.933} {0.000} {0.000} {0.000} {0.000} Log change, DP (%) 0.005 0.056 0.357 2.893 127.3 94.08 184.2 {0.007} {0.000} {0.000} {0.000} {0.000} • Sample period is January 1976 to September 2004 for the Handysize and Panamax series and April 1979 to September 2004 for the capesize series. • Figures in {Æ} are p-values. • Skew. and Kurt. are the estimated centralised third and fourth moments of the data, denoted ^a3 and (^a4–3), respectively. Their asymp￾totic distributions, under the null, are ffiffiffi T p ^a3 Nð0; 6Þ and ffiffiffi T p ð^a4–3Þ Nð0; 24Þ. • J–B is the Jarque and Bera (1980) test statistics for normality; it is v2 (2) distributed. • Q(12) is the Ljung and Box (1978) Q statistic on the 12th-order sample autocorrelations of the raw series, distributed as v2 (12). • ARCH(12) is the Engle’s (1982) test for 12th-order ARCH effect; the statistic has a v2 (12) distribution. 132 A.H. Alizadeh, N.K. Nomikos / Transportation Research Part B 41 (2007) 126–143

A.H.Alizadeh,N.K.Nomikos Transportation Research Part B 41 (2007)126-143 133 40 40.0 35 35.0 3 30.0 25 d 25. 0 20.0 15.0 at000:6 10.0 5.0 0 0.0 6 8 00 00m .PANAMAX Price PANAMAX TC rate Fig.1.Historical prices and time-charter rates for panamax dry bulk carriers. of the unit root alternative,if the calculated test statistic exceeds the corresponding critical values.KPSS test results also confirm that the log-price and time-charter earnings series are non-stationary,I(1),while the spreads between prices and time-charter earnings are in fact stationary.'These results also provide early evi- dence that log prices and time-charter earnings are cointegrated,and render support for the use of the VECM specification for modelling ship price changes. Finally,Fig.I plots the second-hand prices along with one year time-charter rates for a panamax dry bulk carrier over the sample period.It can be seen that while prices and time-charter rates move together in the long-run,they tend to vary over time and under different market conditions.For example,it can be observed that just before any shipping market recovery,the spread between TC earnings and prices tends to narrow (e.g.in 1978,1987-1988,and 2002-2003),while the spread between TC earnings and prices tends to widen during market downturns (e.g.in 1980,1990 and 1997)which is another indication of the importance of price-earning relationship in investment timing in shipping markets.Graphs for the capesize and handysize TC earnings and prices,not presented here,indicate a similar pattern.In addition,comparison of behaviour of prices across different vessel sizes reveals that prices for all three categories of dry bulk carriers tend to move close together over the long-run while their short run behaviour seems to be different and show idiosyncratic stochastic behaviour over time.Different short-term dynamics of different size ship prices might be related to differences in the supply and demand for each type of vessel and the prevailing conditions in the shipping industry. 4.Empirical results Having identified that ship prices and earnings are I(1)variables,cointegration techniques are used next to examine the existence of a long-run relationship between these series.The lag length(g=1)in the VECM of Eq.(9)is chosen on the basis of the Schwarz Bayesian Information Criterion(SBIC)(Schwarz,1978).LR tests indicate that an intercept term should be included in the long-run relationship.s Johansen's (1988)reduced rank cointegration method is then used to establish the cointegration relationship between ship prices and earnings.This method involves assessing the rank of the long-run coefficients matrix,I,through the max and statistics.The rank ofI in turn determines the number of cointegrating relationships;for instance, 7 Unit root results are not presented here but are available from the authors. s Johansen(1991)proposes the following statistic to test for the appropriateness of including an intercept term in the cointegrating vector against the alternative that there are linear trends in the level of the series;-T[n(1)-In(1-(n-r)where and represent the i smallest eigenvalues of the model that includes an intercept term in the cointegrating vector and an intercept term in the short run model,respectively.Acceptance of the null hypothesis indicates that the VECM in Eq.(9)should be estimated with an intercept term in the cointegrating vector.These results are not presented here and are available from the authors.It should also be noted that the inclusion of an intercept term is also justified on the basis that the intercept term reflects the mean value of the P/E ratio. I is the coefficient of x,-1,in the matrix representation of VECM of Eq.(9),where x=(p:)',Ax,==,Ax+x1+h

of the unit root alternative, if the calculated test statistic exceeds the corresponding critical values. KPSS test results also confirm that the log-price and time-charter earnings series are non-stationary, I(1), while the spreads between prices and time-charter earnings are in fact stationary.7 These results also provide early evi￾dence that log prices and time-charter earnings are cointegrated, and render support for the use of the VECM specification for modelling ship price changes. Finally, Fig. 1 plots the second-hand prices along with one year time-charter rates for a panamax dry bulk carrier over the sample period. It can be seen that while prices and time-charter rates move together in the long-run, they tend to vary over time and under different market conditions. For example, it can be observed that just before any shipping market recovery, the spread between TC earnings and prices tends to narrow (e.g. in 1978, 1987–1988, and 2002–2003), while the spread between TC earnings and prices tends to widen during market downturns (e.g. in 1980, 1990 and 1997) which is another indication of the importance of price–earning relationship in investment timing in shipping markets. Graphs for the capesize and handysize TC earnings and prices, not presented here, indicate a similar pattern. In addition, comparison of behaviour of prices across different vessel sizes reveals that prices for all three categories of dry bulk carriers tend to move close together over the long-run while their short run behaviour seems to be different and show idiosyncratic stochastic behaviour over time. Different short-term dynamics of different size ship prices might be related to differences in the supply and demand for each type of vessel and the prevailing conditions in the shipping industry. 4. Empirical results Having identified that ship prices and earnings are I(1) variables, cointegration techniques are used next to examine the existence of a long-run relationship between these series. The lag length (q = 1) in the VECM of Eq. (9) is chosen on the basis of the Schwarz Bayesian Information Criterion (SBIC) (Schwarz, 1978). LR tests indicate that an intercept term should be included in the long-run relationship.8 Johansen’s (1988) reduced rank cointegration method is then used to establish the cointegration relationship between ship prices and earnings. This method involves assessing the rank of the long-run coefficients matrix, C, through the kmax and ktrace statistics.9 The rank of C in turn determines the number of cointegrating relationships; for instance, 0 5 10 15 20 25 30 35 40 1976- 01 1977-06 1978-11 1980-04 1981-09 1983-02 1984-07 1985-12 1987-05 1988-10 1990-03 1991-08 1993- 01 1994-06 1995-11 1997-04 1998-09 2000-02 2001-07 2002-12 2004-05 Price m$ 0.0 5.0 10. 0 15. 0 20. 0 25. 0 30. 0 35. 0 40. 0 TC rate 000'$ PANAMAX Price PANAMAX TC rate Fig. 1. Historical prices and time-charter rates for panamax dry bulk carriers. 7 Unit root results are not presented here but are available from the authors. 8 Johansen (1991) proposes the following statistic to test for the appropriateness of including an intercept term in the cointegrating vector against the alternative that there are linear trends in the level of the series; T Pn i¼rþ1½lnð1 ^k i Þ lnð1 ^kiÞ v2ðn rÞ where ^k i and ^ki represent the i smallest eigenvalues of the model that includes an intercept term in the cointegrating vector and an intercept term in the short run model, respectively. Acceptance of the null hypothesis indicates that the VECM in Eq. (9) should be estimated with an intercept term in the cointegrating vector. These results are not presented here and are available from the authors. It should also be noted that the inclusion of an intercept term is also justified on the basis that the intercept term reflects the mean value of the P/E ratio. 9 C is the coefficient of xt 1, in the matrix representation of VECM of Eq. (9), where xt ¼ ðpt ptÞ 0 ;Dxt ¼ Pk i¼1 Q i Dxti þ Cxt1 þ et. A.H. Alizadeh, N.K. Nomikos / Transportation Research Part B 41 (2007) 126–143 133

134 A.H.Alizadeh.N.K.Nomikos Transportation Research Part B 41 (2007)126-143 Table 2 Result of Johansen's reduced rank cointegration test of log-prices (p)and log time-charter ( △p= b△r-+P-1-0π-l-o)+r △= dA-+2p-1-m-l-0）+ Pair of variables Lags Amax imax 90%CVs Atrace Atrace Atrace 90%CVs Normalised Ho H Ho H coint.vector Handysize [100o] In P and InTC 9=1 r=0r≥1 17.22 15.67 r=0r=1 20.1819.96 [1-1.455-1.09) (pandπ) r≤1r=2 2.94 9.24 r0,ship prices the following period will decrease and earnings will 10 Similarly,if rank(T)=0.r is a 2x2 null matrix and the VECM is reduced to a VAR model in first differences.Finally,if rank(T)=2. then all variables in X-1 are /(0)and a VAR model in levels is appropriate

if rank(C) = 1 then there is a single cointegrating vector describing the long-run equilibrium relationship between the variables. In this case, C can be factored as C = ch0 , where c and h are 2 · 1 vectors.10 Using this factorisation, h0 represents the vector of cointegrating parameters and c is the vector of error correction coef- ficients measuring the speed of convergence to the long-run steady state. Results from these tests are reported in Table 2. The kmax and ktrace statistics indicate the existence of one cointegrating vector between ship prices and TC earnings in each market. This means that log-prices and TC earnings are linked through a unique long-run relationship and any deviation from this equilibrium is restored through the short-term adjustment of these variables. The estimated cointegrating vectors, i.e. [1h h0] from Eq. (9), are also presented in the same table. These unrestricted cointegrating vectors are then used in the estimation of the VECM model; estimation results for the models are presented in Table 3. Residual diagnostics indicate that autocorrelation and heteroscedas￾ticity are present in the residuals of all the regressions. Consequently a Newey and West (1987) correction for serial correlation and heteroscedasticity is applied to the standard errors of the regressions. Examination of the vector of error correction coefficients, c, provides insight into the adjustment process of the different vari￾ables towards equilibrium. Consider first, the system of equations for the capesize market. The cointegrating vector, h, is significant in both equations, and the signs of the speed of adjustment coefficient (negative for ship prices and positive for TC earnings) are consistent with convergence of ship prices and TC earnings towards their long-run relationship. For instance, in response to a positive deviation from their long-run relationship at period t 1, i.e. pt1 hpt1 h0 > 0, ship prices the following period will decrease and earnings will Table 2 Result of Johansen’s reduced rank cointegration test of log-prices (p) and log time-charter (p) Dpt ¼ Xq i¼1 aiDpti þXq i¼1 biDpti þ c1ðpt1 hpt1 h0Þ þ e1;t Dpt ¼ Xq i¼1 ciDpti þXq i¼1 diDpti þ c2ðpt1 hpt1 h0Þ þ e2;t Pair of variables Lags kmax kmax kmax 90% CVs ktrace ktrace ktrace 90% CVs Normalised coint. vector H0 HA H0 HA Handysize [1 h h0] lnP and lnTC q = 1 r = 0 r P 1 17.22 15.67 r = 0 r = 1 20.18 19.96 [1 1.455 1.095] (p and p) r 6 1 r = 2 2.94 9.24 r 6 1 r = 2 2.94 9.24 Panamax lnP and lnTC q = 1 r = 0 r P 1 37.29 15.67 r = 0 r = 1 40.71 19.96 [1 1.237 1.348] (p and p) r 6 1 r = 2 3.41 9.24 r 6 1 r = 2 3.41 9.24 Capesize lnP and lnTC q = 1 r = 0 r P 1 17.40 15.67 r = 0 r = 1 20.37 19.96 [1 1.134 1.707] (p and p) r 6 1 r = 2 2.98 9.24 r 6 1 r = 2 2.98 9.24 • Sample period is January 1976 to September 2004 for the Handysize and Panamax series and April 1979 to September 2004 for the capesize series. • Johansen’s (1988) reduced rank cointegration tests for each pair are estimated using a model with a constant in the cointegrating vector and no trend. • The appropriate number of lags in each case is chosen by minimising SBIC. • kmaxðr;r þ 1Þ¼T lnð1 ^krþ1Þ tests the null hypothesis of r cointegrating vectors against the alternative of r + 1. • ktrace ¼ T Pn i¼rþ1 lnð1 ^kiÞ tests the null that there are at most r cointegrating vectors against the alternative that the number of coin￾tegrating vectors is greater than r, where n is the number of variables in the system (n = 2 in this case). • CVs represent critical values from Osterwald-Lenum (1992). 10 Similarly, if rank(C) = 0, C is a 2 · 2 null matrix and the VECM is reduced to a VAR model in first differences. Finally, if rank(C) = 2, then all variables in Xt1 are I(0) and a VAR model in levels is appropriate. 134 A.H. Alizadeh, N.K. Nomikos / Transportation Research Part B 41 (2007) 126–143

A.H.Alizadeh,N.K.Nomikos Transportation Research Part B 41 (2007)126-143 135 Table 3 Result of VECM for three size dry bulk carriers Ap: 〉aAp-4+>b△-+hP-1-r--o)+1r △：= cAp-+ d4-+2pr-l-m-l-o）+ Estimated model for: Capesize Panamax Handysize △p △元 △p, △T, △p, △元4 ai=1,2 -0.030 0.043 -0.028 0.078 -0.027 0.023 (-0.012) (-0.018) -0.011 -0.018 (-0.010) (-0.010) [-2.541 [2.421] [-2.402] [4.289] [-2.868] [2.214] △p-1 0.203 0.071 0.145 0.166 0.241 0.123 (-0.057 (-0.085) -0.056 -0.088 (-0.052) (-0.056) [3.579] [0.828] [2.579 [1.880] [4.608] [2.181] △t-1 0.142 0.358 0.144 0.319 0.208 0.416 (-0.039) (-0.059) -0.036 -0.056 (-0.049) (-0.053) [3.646] [6.092] [4.056 [5.697] [4.230] [7.875] R 0.153 0.129 0.123 0.140 0.189 0.196 Causality test Statistics p-Value DF Statistics p-Value DF Statistics p-Value DF △r,→△p 13.29 0.0001 2 16.45 {0.0001 2 18.16 {0.0001 2 Ap,一△： 0.685 0.408} 3.534 {0.060} 2 4.028 {0.045} 2 Sample period is January 1976 to September 2004 for the Handysize and Panamax series and April 1979 to September 2004 for the capesize series. Standard errors,in(),are corrected for serial correlation and/or heteroscedasticity using the Newey and West(1987)method. .Numbers in [are t-statistics;DF are the degrees of freedom for the causality tests. increase,thus restoring equilibrium in the market.The same pattern is evident in the panamax and handysize markets. More rigorous investigation of the interactions between the variables can be obtained by performing Granger causality tests,which are presented in the same table.According to the Granger(1986)representation theorem,if two price series are cointegrated,then causality must exist in at least one direction.Theoretically, we expect operational earnings to Granger-cause ship prices.We test such causality between the variables by imposing the appropriate restrictions on the VECM model.Tests for the joint significance of the lagged cross-market returns and error correction coefficients,confirm the conjecture that TC earnings Granger-cause ship prices.On the other hand,ship prices cause TC earnings only in the handysize market at the 5%level,and there is no evidence of causality at the 1%level. 4.1.Profitability of trading rules There can be unlimited number of ways to set up trading strategies based on MA or filter rules,depending on factors such as the variable on which the rule is applied,the length of MA series considered,and the dis- tance from the mean in the case of filter rules.However,we choose to apply two simple MA based rules to illustrate the importance of the price-earnings relationship(ratio)in determining ship prices and consequently market timing in the sale and purchase market for ships. Our trading strategy is based on the deviation of the log P/E ratio from its long-run mean.In order to determine the timing of sale and purchase,we devise two MA series using the deviation of log P/E ratio from its long-run mean,one slow [e.g.MA(12)or MA(6)]and one fast [MA(1)],as shown in Fig.2 for the panamax market.The difference between the two constructed MA series is then used as an indicator for buy and sell

increase, thus restoring equilibrium in the market. The same pattern is evident in the panamax and handysize markets. More rigorous investigation of the interactions between the variables can be obtained by performing Granger causality tests, which are presented in the same table. According to the Granger (1986) representation theorem, if two price series are cointegrated, then causality must exist in at least one direction. Theoretically, we expect operational earnings to Granger-cause ship prices. We test such causality between the variables by imposing the appropriate restrictions on the VECM model. Tests for the joint significance of the lagged cross-market returns and error correction coefficients, confirm the conjecture that TC earnings Granger-cause ship prices. On the other hand, ship prices cause TC earnings only in the handysize market at the 5% level, and there is no evidence of causality at the 1% level. 4.1. Profitability of trading rules There can be unlimited number of ways to set up trading strategies based on MA or filter rules, depending on factors such as the variable on which the rule is applied, the length of MA series considered, and the dis￾tance from the mean in the case of filter rules. However, we choose to apply two simple MA based rules to illustrate the importance of the price–earnings relationship (ratio) in determining ship prices and consequently market timing in the sale and purchase market for ships. Our trading strategy is based on the deviation of the log P/E ratio from its long-run mean. In order to determine the timing of sale and purchase, we devise two MA series using the deviation of log P/E ratio from its long-run mean, one slow [e.g. MA(12) or MA(6)] and one fast [MA(1)], as shown in Fig. 2 for the panamax market. The difference between the two constructed MA series is then used as an indicator for buy and sell Table 3 Result of VECM for three size dry bulk carriers Dpt ¼ Xq i¼1 aiDpti þXq i¼1 biDpti þ c1ðpt1 hpt1 h0Þ þ e1;t Dpt ¼ Xq i¼1 ciDpti þXq i¼1 diDpti þ c2ðpt1 hpt1 h0Þ þ e2;t Estimated model for: Capesize Panamax Handysize Dpt Dpt Dpt Dpt Dpt Dpt ci i = 1, 2 0.030 0.043 0.028 0.078 0.027 0.023 (0.012) (0.018) 0.011 0.018 (0.010) (0.010) [2.541] [2.421] [2.402] [4.289] [2.868] [2.214] Dpt1 0.203 0.071 0.145 0.166 0.241 0.123 (0.057) (0.085) 0.056 0.088 (0.052) (0.056) [3.579] [0.828] [ 2.579] [1.880] [4.608] [2.181] Dpt1 0.142 0.358 0.144 0.319 0.208 0.416 (0.039) (0.059) 0.036 0.056 (0.049) (0.053) [3.646] [6.092] [4.056] [5.697] [4.230] [7.875] R2 0.153 0.129 0.123 0.140 0.189 0.196 Causality test Statistics p-Value DF Statistics p-Value DF Statistics p-Value DF Dpt ! Dpt 13.29 {0.000} 2 16.45 {0.000} 2 18.16 {0.000} 2 Dpt ! Dpt 0.685 {0.408} 2 3.534 {0.060} 2 4.028 {0.045} 2 • Sample period is January 1976 to September 2004 for the Handysize and Panamax series and April 1979 to September 2004 for the capesize series. • Standard errors, in (Æ), are corrected for serial correlation and/or heteroscedasticity using the Newey and West (1987) method. • Numbers in [Æ] are t-statistics; DF are the degrees of freedom for the causality tests. A.H. Alizadeh, N.K. Nomikos / Transportation Research Part B 41 (2007) 126–143 135