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 cointegrating 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 surprising 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 Alizadeh (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 market. 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 evidence on whether sale and purchase decisions of merchant ships, based on fundamental and/or technical analysis, 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 technical 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 information 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 portfolios. 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 literature 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 riskreturn 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 investments (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 strategies 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 market. 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 fundamentals. 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 alternative 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 transportation 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 identify investment timing opportunities. The structure of this paper is as follows. Section 2 presents the theoretical background and the methodologies 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 shipping 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 expressed 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 manipulation, 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 nonstationary series does not accurately represent the true relationship between variables. However, there might be cases where two nonstationary 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 purposes. 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 overpriced 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 cointegrating relationship between these two variables. In order to test the existence of cointegration between second-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 logprices 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 indicates 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 cointegrated, 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 unidirectional; 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