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