Investment Timing and Trading Strategies in the Sale and Purchase Market for Ships

Transportation Research Part B 41 (2007) 126–143

www.elsevier.com/locate/trb

Investment timing and trading strategies in the saleand 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 combinationof technical trading rules and fundamental analysis in the sale and purchase market for dry bulk ships. Using a sample ofprice 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 timingdecisions in the dry bulk shipping sector. In order to discount the possibility of data snooping biases and to evaluate therobustness of our trading models, we also perform tests using the stationary bootstrap approach. Our results indicate thattrading strategies based on earnings–price ratios significantly out-perform buy and hold strategies in the second-handmarket 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 investmentand/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 thefocus of many empirical studies in maritime economics literature. Traditional approaches for modelling shipprices are mainly based on general and partial equilibrium models using structural relationships between anumber 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 recentstudies have applied real options analysis for determining ship prices; this valuation framework takes explicitlyinto account the operational flexibility in ship management, in terms of choosing between entry and exit fromthe market, spot and period time-charter operations, and switching between lay-up and trading modes (seeDixit 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: [email protected] (A.H. Alizadeh), [email protected] (N.K. Nomikos).

mailto:[email protected]

mailto:[email protected]

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 whethermarkets 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 mayeither 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 shipprices are lower than their fundamental values, then buying and operating these vessels may be profitable sincethey are under-priced in comparison to their future profitability (i.e. the earnings from freight operations). Onthe other hand, when prices are higher than their corresponding rational values, then from a shipowner’s pointof view it may be more profitable to charter in vessels, rather than buying them, since they are overpriced incomparison to their expected future profitability.

Despite numerous studies in the literature on ship price formation, on testing the validity of the EMH inshipping 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 theperformance of technical trading rules and argue that if the market for ships is efficient, then trading strategiesbased on these rules should not produce wealth in excess of what can be gained through simple buy and holdstrategies.2 Using both in- and out-of-sample tests, they report that, in general, trading rules do not yieldexcess returns that can compensate for transaction costs. Although their study seems to provide supportfor the EMH, given the nature of technical analysis there may be two points that could be raised. First, asthey 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 withthe underlying economic theory, may not be as effective in this market. This is because the historical pattern ofthe underlying series alone is not enough to extract information on the future behaviour of prices, since it iswidely documented that ship prices follow random walk processes.

Therefore, in this study we overcome these shortcomings by developing a theoretical economic frameworkwhich 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 pastprice behaviour for trading strategies, but we combine technical trading rules with fundamental analysis byusing the cointegration relationship between prices and earnings. In particular, we use the price–earnings ratioas an indicator for investment or divestment timing decisions in the dry bulk shipping sector. The motivationfor this stems from the importance of economic indicators and, in particular, the price–earnings (P/E) ratio (orits inverse the earnings–price, E/P, ratio) in predicting asset returns in financial markets. For instance, P/Eratios of individual stocks or portfolios are regularly used to explain the returns in the stock market and anumber 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 subsequentstock returns over a ten-year period. Other studies on the information content of P/E ratio in predicting stockreturns 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 marketindices. For example, Lander et al. (1997) use various linear combinations of the P/E ratio and bond yields topredict 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. Inaddition, a number of studies in financial economics literature examine the performance of various strategiesthat may be useful in timing the market. For example, Lander et al. (1997) test their models’ ability to time themarket, while Fuller and Kling (1990, 1994) study regression-based market timing strategies using dividendyields, 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 assetswill generate over their lifetime.

2 Adland and Koekebakker (2004) use historical prices for VLCC and Aframax tankers, as well as capesize and panamax dry bulkcarriers.

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 financialmarkets, there has been little evidence for markets that trade real assets, in particular for the transportationand shipping markets. The aim of this paper is therefore to investigate the performance of trading strategiesfor 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 strategiesbased on signals provided by fundamental market price indicators such as the price–earnings (P/E) ratioand how effective these strategies are for investment decisions in the shipping markets. We consider shipsas 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 toidentify 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 thedynamic 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 strategiesacross 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 hencereplicate the trading results from the different strategies in a simulation environment; this is done in orderto 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–earningsratio) 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 buyor charter-in tonnage. The findings of this paper also have important practical implications and can be ofinterest 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 shippingfunds 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 ofphysically owning or operating a ship. Although the focus of the paper is in the market for ships, the samemethodology 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 leaseor 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-handships. The data and their properties are discussed in Section 3. Section 4 presents the empirical results anddiscussion 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 interestedin income from the day to day operation of ships, but also interested in gains from capital appreciation in thevalue 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 andEtPt+1 is the expected operating profit between period t and t + 1.3 Mathematically,

3 See

EtRtþ1 ¼EtP tþ1 � P t þ EtPtþ1

P t

� �ð1Þ

Section 3 of the paper for the description of operating profits and TC earnings.


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, inthe following expression

4 It hand dosuch astationstationrun. Sstationtime sepricingcorrect

P t ¼EtP tþ1 þ EtPtþ1

1þ 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,P sc

tþn of the asset. Mathematically

P t ¼Xn

i¼1

Yi

j¼1

ð1þ EtRtþjÞ�1

!EtPtþi þ

Yn

j¼1

ð1þ EtRtþjÞ�1

!EtP sc

tþn ð3Þ

Eq. (2) can also be written in logarithmic form; however, in this case it is not possible to perform recursivesubstitutions to write the log of price (lnPt) in terms of the log of discounted expected earnings and log ofdiscounted expected terminal value of the asset. Campbell and Shiller (1987) suggest a way round this by usinga first-order Taylor series expansion and linearising (1) around the geometric mean of P and P (P and P) togive

lnð1þ EtRtþ1Þ ¼ q lnðEtP tþ1Þ þ ð1� qÞ lnðEtPtþ1Þ � ln P t þ k ð4Þ
where q ¼ P=ðP þPÞ 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 ¼Xn�1

i¼0

qið1� qÞEtptþ1þi �Xn�1

i¼0

qiEtrtþ1þi þ qnEtpsctþn þ kð1� qnÞ=ð1� qÞ ð6Þ

Since prices and operating profit series are non-stationary, Eq. (6) should be transformed in such a way so asto derive a model with stationary variables. Following Campbell and Shiller (1987), we use the cointegrationrelationship between the log-price and the log-earning series for such transformation; that is the log P/Eratio.4 This is done by subtracting pt from both sides of (6) which results in

pt � pt ¼Xn�1

i¼0

qið1� qÞEtptþ1þi � pt �Xn�1

i¼0

qiEtrtþ1þi þ qnEtpsctþn þ kð1� qnÞ=ð1� qÞ ð7Þ

or

pt � pt ¼Xn�1

i¼0

qiðEtDptþ1þi � Etrtþ1þiÞ þ qnðEtpsctþn � EtptþnÞ þ kð1� qnÞ=ð1� qÞ ð8Þ

In the above setting pt � pt and psct � 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

as been argued that many financial and economic time series are non-stationary. Such variables tend to have an increasing variancenot 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

s the Phillips and Perron (1988) and Kwiatkowski et al. (1992). In general, it has been shown that correlation between non-ary series does not accurately represent the true relationship between variables. However, there might be cases where two non-ary variables can be related in the long-run through an equilibrium relationship, but deviate from such an equilibrium in the short

uch a relationship is called a cointegrating relationship and implies that a linear combination of the two non-stationary series isary (Engle and Granger, 1987). In our case for instance, although the log of ship prices and the log of earnings are non-stationaryries, their difference (i.e. the P/E ratio) should be stationary because ship prices and earnings are linked through the fundamentalrelationship 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

ive movements in the level of earnings and ship prices.


side is the theoretical spread which is based on the expected values of earnings, discount rates and resale valuesof the asset. Under efficient market conditions, the two spread series should be statistically equal with similarvolatility, which can be tested empirically (see Kavussanos and Alizadeh, 2002a). This model also suggests thatthe 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 priceis 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 shippingmarkets.

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 techniqueand estimate the following vector error correction model (VECM)

5 A tpast vathe criits preerror c

Dpt ¼Xq

i¼1

aiDpt�i þXq

i¼1

biDpt�i þ c1ðpt�1 � hpt�1 � h0Þ þ e1;t

Dpt ¼Xq

i¼1

ciDpt�i þXq

i¼1

diDpt�i þ c2ðpt�1 � hpt�1 � h0Þ þ e2;t

ð9Þ

The above VECM model can be used to establish the cointegrating relationship between log-prices and logearnings which then can be used to set up a trading strategy for shipping investment. The important elementof the cointegration relationship is the error correction term (ECT) which is in fact the difference between log-prices and log earnings (pt�1 � hpt�1 � h0). The constant term in the error correction term, h0, represents thelong-run equilibrium relationship; it is in other words the long-run average of the P/E ratio. In order to set upa 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 theirearnings potential. In this case, ship prices in the market are expected to adjust in future periods by fallingrelative to their current levels. Similarly, when the P/E ratio is lower than its long-run average, this can beregarded as an indication that ship prices are undervalued relative to their potential earnings and, hence, itis expected that prices will increase in the next period, so that the long run earnings–price relationship isrestored.

The VECM model of Eq. (9) also provides a framework for testing the causal linkages between ship pricesand 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 throughthe discounted present value of expected earnings and the latter are determined exogenously, through theinteraction 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, anychange in earnings should affect the spread between log-prices and log earnings and result in a change in shipprices over the next period. Therefore, in this case one can argue that the log P/E ratio contains informationon future changes in ship prices, which can be used for investment strategies.

ime series, pt, is said to Granger cause another time series, pt, if the present value of pt can be predicted more accurately by usinglues of pt than by not doing so, considering also other relevant information including past values of pt (Granger, 1969). Therefore,

terion for Granger causality is whether or not the variance of the predictive error of pt is reduced when past pt values are included indiction. 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, theorrection coefficient in the equation for ship prices, is significant at conventional levels.


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 isbased on the relationship between price and earnings of such vessels. As mentioned earlier, theoretically, theprice of a vessel is linked to her expected operational earnings which are in turn determined by current andexpected conditions in the shipping market and the world economy. This theoretical relationship betweenprices and earnings allows us to use the historical (empirical) spread between them to identify buy and sellopportunities 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 givenfamily 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 themean. As it is beyond the scope of this study to evaluate an exhaustive set of trading rules, we focus our effortson 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 marketfor ships could be a comparison of a 12 month MA with 3 month MA of the PE ratio. This means that in agiven month, a positive difference between the 12-month MA and the 3-month MA of the PE ratios shouldsignal 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 drybulk carriers (capesize, panamax and handysize) from Clarkson’s Shipping Intelligence Network from January1976 to September 2004. Capesize prices are for the period April 1979 to September 2004. All prices arequoted in million dollars and represent the average value of vessels traded in each category in any particularmonth.

In shipping, operating profits can be defined as time-charter rates, or the time-charter equivalent of spotrates when a vessel is operating in the spot market, minus operating costs. In this study, we use time-charterrates as a proxy for earnings, Pt, for two reasons. First, because time-charter rates do not include voyage costsand represent the net earnings from chartering activities of the vessel. Second, since time-charter rates are hirecontracts 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 changesbetter than current spot rates. Monthly time-charter rates for handysize, panamax and capesize vessels overthe period January 1976 (April 1979 for capesize vessels) to September 2004 are also obtained from Clarkson’sShipping Intelligence Network. Finally, monthly operating expenses for each vessel size are also collected fromthe same source.

Table 1 reports descriptive statistics of levels and logarithmic first differences of second-hand prices, as wellas operational earnings for capesize, panamax and handysize vessels. The results indicate that mean levels ofprices 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 pricereturns in all markets, while price levels for all size classes seem to be normally distributed. The Ljung andBox (1978) Q statistics for 12th-order autocorrelations in levels and logarithmic first differences of earningsare 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 wordsshort-selling is not permitted since practically it is not possible for an investor to take a short position in a vessel. However, thedevelopment of new ‘‘paper’’ contracts on ship prices, such as the Baltic Sale and Purchase Agreement (BSPA) could allow investors toshort sell the vessel values and benefit from falling ship prices.

Table 1Descriptive 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 thecapesize 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, areffiffiffiffiTp

a3 � Nð0; 6Þ andffiffiffiffiTpða4–3Þ � 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.


(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 testssuggest 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 spreadbetween 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 rootnull hypothesis in favour of the alternative of stationarity (see Harris, 1995; Maddala and Kim, 1998). Leeet al. (2000) suggest that one way of overcoming this problem is by conducting unit root tests which testthe null of stationarity against the alternative of a unit root, such as the test developed by Kwiatkowskiet al. (1992), henceforth KPSS test. In the KPSS test, the null hypothesis of stationarity is rejected in favour

0

510

15

20

2530

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

Pric

e m

$

0.0

5.010. 0

15. 0

20. 0

25. 030. 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.


of the unit root alternative, if the calculated test statistic exceeds the corresponding critical values. KPSS testresults also confirm that the log-price and time-charter earnings series are non-stationary, I(1), while thespreads 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 VECMspecification for modelling ship price changes.

Finally, Fig. 1 plots the second-hand prices along with one year time-charter rates for a panamax dry bulkcarrier over the sample period. It can be seen that while prices and time-charter rates move together in thelong-run, they tend to vary over time and under different market conditions. For example, it can be observedthat 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 widenduring market downturns (e.g. in 1980, 1990 and 1997) which is another indication of the importance ofprice–earning relationship in investment timing in shipping markets. Graphs for the capesize and handysizeTC earnings and prices, not presented here, indicate a similar pattern. In addition, comparison of behaviourof prices across different vessel sizes reveals that prices for all three categories of dry bulk carriers tend to moveclose together over the long-run while their short run behaviour seems to be different and show idiosyncraticstochastic behaviour over time. Different short-term dynamics of different size ship prices might be related todifferences in the supply and demand for each type of vessel and the prevailing conditions in the shippingindustry.

4. Empirical results

Having identified that ship prices and earnings are I(1) variables, cointegration techniques are used next toexamine the existence of a long-run relationship between these series. The lag length (q = 1) in the VECM ofEq. (9) is chosen on the basis of the Schwarz Bayesian Information Criterion (SBIC) (Schwarz, 1978). LR testsindicate that an intercept term should be included in the long-run relationship.8 Johansen’s (1988) reducedrank cointegration method is then used to establish the cointegration relationship between ship prices andearnings. 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,

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; �TPn

i¼rþ1½lnð1� k�i Þ � lnð1� kiÞ� � v2ðn� rÞ where k�iand ki represent the i smallest eigenvalues of the model that includes an intercept term in the cointegrating vector and an intercept term inthe short run model, respectively. Acceptance of the null hypothesis indicates that the VECM in Eq. (9) should be estimated with anintercept term in the cointegrating vector. These results are not presented here and are available from the authors. It should also be notedthat 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 ptÞ0;Dxt ¼Pk

i¼1

QiDxt�i þ Cxt�1 þ et.

Table 2Result of Johansen’s reduced rank cointegration test of log-prices (p) and log time-charter (p)

Dpt ¼Xq

i¼1

aiDpt�i þXq

i¼1


Dpt ¼Xq

i¼1

ciDpt�i þXq

i¼1


Pair of variables Lags kmax kmax kmax 90% CVs ktrace ktrace ktrace 90% CVs Normalisedcoint. vectorH0 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


• Johansen’s (1988) reduced rank cointegration tests for each pair are estimated using a model with a constant in the cointegrating vectorand no trend.

• The appropriate number of lags in each case is chosen by minimising SBIC.• kmaxðr; r þ 1Þ ¼ �T lnð1� krþ1Þ tests the null hypothesis of r cointegrating vectors against the alternative of r + 1.• ktrace ¼ �T

Pni¼rþ1 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).


if rank(C) = 1 then there is a single cointegrating vector describing the long-run equilibrium relationshipbetween the variables. In this case, C can be factored as C = ch 0, where c and h are 2 · 1 vectors.10 Using thisfactorisation, h 0 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 reportedin Table 2. The kmax and ktrace statistics indicate the existence of one cointegrating vector between ship pricesand TC earnings in each market. This means that log-prices and TC earnings are linked through a uniquelong-run relationship and any deviation from this equilibrium is restored through the short-term adjustmentof these variables.

The estimated cointegrating vectors, i.e. [1hh0] from Eq. (9), are also presented in the same table. Theseunrestricted cointegrating vectors are then used in the estimation of the VECM model; estimation resultsfor 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 forserial correlation and heteroscedasticity is applied to the standard errors of the regressions. Examination ofthe 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 cointegratingvector, h, is significant in both equations, and the signs of the speed of adjustment coefficient (negative for shipprices and positive for TC earnings) are consistent with convergence of ship prices and TC earnings towardstheir long-run relationship. For instance, in response to a positive deviation from their long-run relationship atperiod t � 1, i.e. pt�1 � hpt�1 � h0 > 0, ship prices the following period will decrease and earnings will

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 Xt�1 are I(0) and a VAR model in levels is appropriate.

Table 3Result of VECM for three size dry bulk carriers

Dpt ¼Xq

i¼1

aiDpt�i þXq

i¼1


Dpt ¼Xq

i¼1

ciDpt�i þXq

i¼1


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]

Dpt�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]

Dpt�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]

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} 2Dpt! Dpt 0.685 {0.408} 2 3.534 {0.060} 2 4.028 {0.045} 2


• 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.


increase, thus restoring equilibrium in the market. The same pattern is evident in the panamax and handysizemarkets.

More rigorous investigation of the interactions between the variables can be obtained by performingGranger causality tests, which are presented in the same table. According to the Granger (1986) representationtheorem, 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 byimposing the appropriate restrictions on the VECM model. Tests for the joint significance of the laggedcross-market returns and error correction coefficients, confirm the conjecture that TC earnings Granger-causeship prices. On the other hand, ship prices cause TC earnings only in the handysize market at the 5% level, andthere 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, dependingon 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 toillustrate the importance of the price–earnings relationship (ratio) in determining ship prices and consequentlymarket 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 todetermine the timing of sale and purchase, we devise two MA series using the deviation of log P/E ratio fromits long-run mean, one slow [e.g. MA(12) or MA(6)] and one fast [MA(1)], as shown in Fig. 2 for the panamaxmarket. The difference between the two constructed MA series is then used as an indicator for buy and sell

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Fig. 2. Plot of moving average 12 (MA12) and moving average 1 (MA1) of historical log-price–earning ratio in panamax market.


signals in the second-hand market. A positive difference between the slow and the fast MA series signals a selldecision, while a negative difference signals a buy decision. If investors do not hold a position in the shippingmarket then we assume that they invest their funds in treasury-bills.

In assessing the performance of our strategies, we also consider transaction costs, the income from operat-ing the vessels in the charter markets as well as the depreciation in the value of the vessel. More specifically:transaction costs are incurred every time a buy or sell decision is implemented; they typically come in the formof brokerage commission for the sale and purchase shipbrokers who arrange the deals. Operating profits arecalculated as the difference between monthly charter earnings and operating expenses for each month the ves-sel is in our portfolio.11 Finally, depreciation represents the reduction in the value of the vessel due to wear andtear each month the investor holds the vessel in his/her portfolio. This is estimated as the average decline in thevalue between a 5-year old and a 10-year old vessel and is 0.5% per month for each type of vessel. It shouldalso be noted that the proposed strategy is structured and implemented in a way that is entirely forward look-ing. In other words, investment decisions at any point in time are decided on the basis of information that isavailable to investors at that specific point in time. This way we provide a more realistic and accurate repre-sentation regarding the performance of the trading strategies.

We then apply the outlined MA trading model to each sub-market within the dry bulk shipping sector. Forcomparison purposes we also consider the performance of a benchmark buy-and-hold strategy. This strategymimics the behaviour of a ship operating company which owns a ship and operates her in the charter marketthroughout her economic life. Hence, the performance of this strategy reflects primarily the income from theoperation of the vessel in the charter market. Since in the ‘‘buy and hold’’ strategy one is always an investor inthe market, it is an appropriate benchmark for the proposed dynamic trading strategy which suggests invest-ing in the shipping market only when the timing is right. Table 4 presents the annualized mean returns, annu-alized standard deviations of returns and Sharpe ratios, which scale the mean returns by their standarddeviations, for the different strategies. It can be noted that both the MA(6,1) and MA(12, 1) strategies out-per-form the buy and hold strategy as indicated by the Sharpe ratios across all markets. For example, whenMA(12, 1) trading rule is applied, the Sharpe ratios for handysize, panamax and capesize investmentsincreased to 0.667, 0.982 and 0.798, respectively, reflecting the joint effect of increase in mean returns andreduction in standard deviations of return on the investment in each market. It can also be seen that the gainthrough such investment strategies and trading rules is greater in the markets for larger vessels due to highervolatility in these markets compared to the market for handysize vessels and better or more frequent tradingopportunities arising due to such variation in prices.

11 Monthly time-charter earnings are estimated on the assumption that the vessel will be on-hire 29 days per month or 348 days per year.The remaining 17 days per year represent time off-hire for repairs and maintenance.

Table 4Result of empirical simulation of trading strategies

Handysize Panamax Capesize

MA12/MA1 on P/E ratio

Mean return 0.08611 0.14814 0.16127St. Dev. 0.12907 0.15083 0.20209Sharpe ratio 0.66713 0.98216 0.79800

MA6/MA1 on P/E ratio

Mean return 0.07332 0.14017 0.15751St. Dev. 0.13346 0.15353 0.20197Sharpe ratio 0.54936 0.91296 0.77983

Buy and hold

Mean return 0.08487 0.11459 0.08097St. Dev. 0.18406 0.20967 0.25288Sharpe Ratio 0.46109 0.54651 0.32019

• Mean return and St. Dev. are the annualized mean returns (monthly mean return · 12) and standard deviation of returns(monthly standard deviation�

ffiffiffiffiffi12p

), respectively, for the different trading strategies. Sharpe ratio is the ratio of mean returns overthe standard deviation of returns.

• Sample period is January 1976 to September 2004 for handysize and panamax series and April 1979 to September 2004 for the capesizeseries.


The cumulative returns on the MA(12,1) trading rule and ‘‘buy and hold’’ investment strategy in thehandysize, panamax and capesize markets are shown in Figs. 3–5, respectively. The significant increase incumulative returns when the active MA(12,1) trading rule is employed, compared to ‘‘buy and hold’’ strategy,is evident for the larger vessels (panamax and capesizes). In fact, it is also interesting to note that the proposedtrading model correctly identifies the buy signal during the lucrative shipping markets of 2003–2004 whenearnings increased sharply compared to ship prices.

4.2. Data snooping and the stationary bootstrap

The results in the previous section are encouraging regarding the performance of our proposed tradingstrategies. However, an important issue which arises when evaluating technical trading rules, is that of datasnooping. According to Sullivan et al. (1999) and White (2000) data snooping occurs when a dataset is usedmore than once for data selection and inference purposes. In other words, using the same dataset frequentlyfor testing trading strategies, may increase the probability of having satisfactory results purely due to chanceor due to the use of posterior information rather than the superior ability of the trading strategies.

The method most commonly used in the literature to assess the performance of trading strategies and testfor data snooping is bootstrap. The bootstrap, introduced by Efron (1979), is a resampling method thatuses the empirical distribution of the statistic of interest, rather than the theoretical distribution implied by

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MA Cum Ret BH Cum Ret

Fig. 3. Cumulative return on MA trading strategy for handysize bulk carrier.

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Fig. 4. Cumulative return on MA trading strategy for panamax bulk carrier.

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Fig. 5. Cumulative return on MA trading strategy for capesize bulk carrier.


statistical theory, to conduct statistical inference. The main advantage of bootstrap is that it can approximatethe properties of the sampling distribution of the underlying statistic even when such a distribution is not para-metrically defined, or the underlying statistic is complex and not easy to obtain. Bootstrap techniques havealso been used by Brock et al. (1992), who test whether trading results from some trading rules can beexplained by time-series models, as well as Sullivan et al. (1999) who use bootstrap to test the joint perfor-mance of several technical rules.

However, the ordinary bootstrap method is only valid in the case of iid observations. When ordinary boot-strap techniques are applied to serially dependent observations, as is the case with ship-prices and earnings, theresampled series will not retain the statistical properties of the original dataset and yield inconsistent resultsand statistical inference (see Ruiz and Pacual, 2002). In view of that, several non-parametric methods for deal-ing with serially dependent data have been developed. One such method is the stationary bootstrap method ofPolitis and Romano (1994). This procedure is based on re-sampling blocks of random length, where the lengthof each block follows a geometric distribution. This way it generates random samples which preserve the serialdependence property of the original series and are also stationary. This is important since our proposed trad-ing strategy relies on the premise that the P/E ratio is stationary; see Appendix A for technical details.

Therefore, in order to statistically assess the performance of our trading strategies, we use the stationarybootstrap technique to regenerate random paths that ship prices and earnings may have possibly followedover the sample period, whilst maintaining the distributional properties of the original series. We then imple-ment the proposed trading strategies using the simulated price and earnings series which, in turn, generate adistribution of trading statistics under the different trading rules. Therefore, our approach in using bootstrap isdifferent from the previous literature in the sense that we bootstrap to generate paths of price and earning ser-ies and assess the profitability of PE based trading strategies.

We start by bootstrapping the log-difference series. Then these bootstrapped series are transformed backinto levels to construct P/E ratios which are used to trigger buy and sell decisions based on the MA trading


strategies. In implementing these strategies, we consider transaction costs, the depreciation in the value of thevessel and operating profit, along the lines described in the previous section of the paper. As a benchmarkmodel, we also consider the buy and hold strategy in which one is always long in the market and hence benefitsfrom a constant stream of income, arising from the operation of the vessel in the charter market, irrespectiveof the level of the P/E ratio. Both the MA and the buy and hold strategies are implemented for each one of the1000 bootstrapped series, thus generating a series of empirical distributions of mean returns and Sharpe ratios.Under the null hypothesis that a dynamic trading strategy is no better than a buy and hold strategy or, equiv-alently, that there is no information or signals in the original P/E ratio, the profit from the MA strategiesshould be no better than the profit from a buy and hold strategy.

The results of the bootstrap simulations, are reported in Table 5. The table contains the mean annual return(obtained as the mean return from the trading strategies implemented on the 1000 bootstrapped series), thestandard deviation of the mean returns, as well as the average Sharpe ratio across the bootstrapped series.Several points merit discussion here. First, it can be observed that the mean returns and Sharpe ratios fromthe different strategies are similar to those observed in the empirical series under the same trading rule. Fur-thermore, their comparative performance is also similar; in other words, in the simulated series, capesizereturns are higher than panamax returns and panamax returns are higher than handysize returns. The tradingrules based on log-price–earnings ratio seem to out-perform the static investment tactics both in terms of

Table 5Result of stationary bootstrap simulation of trading strategies

Handysize Panamax Capesize

Panel A: mean returns and Sharpe ratios

MA12/MA1 on P/E ratioMean return 0.05676 0.11113 0.12820St. Dev. 0.02569 0.02407 0.03004Sharpe ratio 0.50964 0.94118 0.77713

MA6/MA1 on P/E ratioMean return 0.04892 0.11109 0.12996St. Dev. 0.02623 0.02306 0.02725Sharpe ratio 0.42321 0.87162 0.77702

Buy and hold returnMean return 0.04404 0.07399 0.06266St. Dev. 0.04435 0.03922 0.03711Sharpe ratio 0.24268 0.38178 0.27708

Panel B: 90% Empirical Confidence Intervals and p-values

Excess returnsMA12 relative to buy and hold (�0.0418, 0.0604) (�0.0241, 0.0853) (0.0076, 0.1150)**

{0.329} {0.133} {0.024}MA6 relative to buy and hold (�0.0485, 0.0516) (�0.0152, 0.0781) (0.0169, 0.1100)**

{0.411} {0.108} {0.008}

Sharpe ratios

MA12 relative to buy and hold (�0.0555, 0.5825) (0.1719, 0.9911)** (0.2300, 0.8150)**

{0.084} {0.008} {0.000}MA6 relative to buy and hold (�0.1367, 0.4845) (0.1838, 0.7810)** (0.2483, 0.7642)**

{0.182} {0.003} {0.000}

• Results are based on 1000 realisations of the trading strategies based on the stationary bootstrap of Politis and Romano (1994).• Mean return and Sharpe ratio are the average mean returns and Sharpe ratios across 1000 simulations. St. Dev. is the standard devi-

ation of mean returns across 1000 simulations.• p-Values are in {Æ} and measure the significance level for which we can reject a one-tail test on the null that mean returns or Sharpe

ratios are not different between the MA and the buy and hold strategies.• 90% Empirical Confidence Intervals are in brackets (Æ).• Numbers in [Æ] are t-statistics; DF are the degrees of freedom for the causality tests.• Sample period is January 1976 to September 2004 for handysize and panamax series and April 1979 to September 2004 for the capesize

series.


increasing average returns and in terms of the Sharpe ratios. For instance, a comparison of Sharpe ratios inTable 5 reveals a threefold increase in capesize and panamax markets and a twofold increase in handysize ves-sels, compared to the buy and hold strategy, when the MA(12, 1) trading rule is used.

More formal statistical tests are conducted by considering the empirical confidence intervals for excessreturns and Sharpe ratios. More specifically, for each simulated series we estimate the excess return of theMA trading strategy relative to the buy and hold strategy as well as the excess performance of the Sharpe ratiorelative to the Sharpe ratio in the buy and hold strategy. We then construct 90% empirical confidence intervalsfor the excess returns based on the bootstrap simulations to test whether excess returns are significantly dif-ferent from zero (or in other words, whether the P/E based trading strategies provide significantly higherreturns compared to the static strategy). These are constructed as the 5% and 95% percentiles of the orderedexcess returns series. If the value of zero is not contained within the confidence interval then returns under theMA strategy are significantly better, at the 10% level, compared to the buy and hold strategy. For comparisonpurposes, we also construct the empirical p-values for the tests. These are simply calculated as the ratio of fre-quency of occurrence of negative excess returns over the total number of simulations (1000 replications) andreflect the significance level, for which the null hypothesis that there is not significant difference between thereturns can be rejected, using a one-tail test. Overall, these results indicate that the MA strategies provide sig-nificant increases in Sharpe ratios compared to the ordinary buy and hold strategies for the panamax and cap-esize markets.

Figs. 6–8 plot the distributions of simulated returns of MA(12,1), MA(6,1) and static trading strategies forhandysize, panamax and capsize markets, respectively. These graphs clearly illustrate the benefits of usingtrading signals derived from ship prices and earnings in shipping investment, as the distribution of simulatedreturns based on MA rules show significant shifts to the right with relatively lower dispersion.

Overall, our simulation analysis confirms that the relationship between price and earnings in shipping mar-kets contains important information about the future behaviour of ship prices. This relationship reflects andresponds to changes in market fundamentals and deviations from this relationship can be used to identifyinvestment and divestment timing in shipping markets and, hence, exploit significant returns in the market.Our results also reveal that the combination of technical trading and fundamental analyses could be more

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Fig. 6. Comparison of simulated return distribution of active and passive trading strategies in the handysize market.

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Fig. 7. Comparison of simulated return distribution of active and passive trading strategies in the panamax market.

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Fig. 8. Comparison of simulated return distribution of active and passive trading strategies in the capesize market.


effective in the market for larger vessels (panamax and capesize) due to higher volatility and price fluctuationsin these markets compared to the market for handysize ships. This can be attributed to the fact that the mar-kets for smaller ships are more efficient in the sense that there are more participants and these ships are moreflexible to operate in terms of the cargo that they can carry and the routes in which they operate. It can also beargued that while larger ships could be more suitable for the purpose of asset play in the shipping markets, thetiming of investment is of crucial importance as potential gains and losses are higher in these sectors of theshipping industry.

5. Summary and conclusions

In this study we propose a new approach for timing investment and divestment decisions in shipping mar-kets. In particular, we utilise the relationship between variables in shipping markets and devise strategies toidentify the timing for sale and purchase of merchant ships. The theoretical relationship between ship pricesand TC earnings, based on the discounted present value model, is discussed in detail and a cointegration rela-tionship is established between ship prices and earnings. Based on this cointegration relationship, we develop atrading strategy which measures the deviation of the P/E ratio, which is also the cointegrating vector, from itslong-run equilibrium and signals sale and purchase opportunities using moving average trading rules. Suchstrategies are then applied to historical series which reveal promising results when compared with staticbuy and hold strategies. To ensure the consistency of our model, we also perform simulations which confirmthe superiority of the MA trading rules further.

Overall, our results show that the relationship between price and earnings in shipping markets containsimportant information about future behaviour of ship prices, which can be used for investment timing in ship-ping markets. We also show that investors in shipping markets can benefit from applying technical tradingrules when making sale and purchase decisions.

Acknowledgements

We would like to thank Professor Ken Small and three anonymous referees for their extremely helpful com-ments. This paper has also largely benefited from the comments of participants at the 2004 Shipping Invest-ment Seminar at Cass Business School, at the Hong Kong Shipowner’s Association seminar and at the 2005International Association of Maritime Economists Conference, Limassol, Cyprus where it was awarded the‘‘Most Innovative Paper of the Conference’’ prize.

Appendix A

Here we present the algorithm that is used to implement the stationary bootstrap resampling technique ofPolitis and Romano (1994). The description of the algorithm here follows from Appendix C of Sullivan et al.(1999).


The stationary bootstrap is calculated as follows: Given the original sample of T observations, X(t),t = {1, . . . ,T}, we start by selecting a ‘‘smoothing parameter’’, q = qT, 0 < qT 6 1, TqT!1 as T!1,and then form the bootstrapped series, X(t)*, as follows:

1. At t = 1, select X(1)* at random, independently and uniformly from {X(1), . . . ,X(T)}. Say for instance thatX(1)* is selected to be the Jth observation in the original series, X(1)* = X(J) where 1 6 J 6 T.

2. Increment t by 1. If t > T, then stop. Otherwise draw a standard uniform random variable U independentlyof all other random variables(a) if U < q, then select X(2)* at random, independently and uniformly from {X(1), . . . ,X(T)},(b) if U > q, then expand the block by setting X(2)* = X(J + 1), so that the X(2)* is the next observation in

the original series following X(J). If J + 1 > T, then reset J + 1 to 1, so that the block continues fromthe first observation in the sample.

3. Repeat step 2 until we reach X(T)*.4. Repeat steps 1–3, 1000 times.

Therefore, the stationary bootstrap re-samples blocks of varying length from the original data, where theblock length follows a geometric distribution, with mean block length 1/q. In general, given that X(t)* is deter-mined by the Jth observation X(J) in the original series, then X(t + 1)* will be equal to the next observation inthe block X(J + 1) with probability 1-q and picked at random from the original observations with probabilityq. Regarding the choice of q, a large value of q is appropriate for data with little dependence, and a smallervalue of q is appropriate for data that exhibit more serial dependence. The value of q chosen in our experi-ments is 0.1, corresponding to a mean block length of 10. This follows other studies in the literature, mostnotably Sullivan et al. (1999). Furthermore, we also perform sensitivity tests with different values of q, andfind that the results presented in this section are not sensitive to the choice of q.

References

Adland, R.O., 2000. Technical trading rule performance in the second-hand asset markets in bulk shipping. Foundation for Research inEconomics and Business Administration, Bergen, Norway, Working Paper No. 04/2000.

Adland, R.O., Koekebakker, S., 2004. Market efficiency in the second-hand market for bulk ships. Maritime Economics and Logistics 6(1), 1–15.

Beenstock, M., Vergottis, A., 1989. An econometric model of the world market for dry cargo freight and shipping. Applied Economics 21,339–359.

Bendall, H.B., Stent, A., 2004. Ship investment under uncertainty: a real option approach. Working Paper, University of Technology,Sydney, Australia.

Brock, W., Lakonishok, J., LeBaron, B., 1992. Simple technical trading rules and the stochastic properties of stock returns. Journal ofFinance 47 (5), 1731–1764.

Campbell, J.Y., Shiller, R.J., 1987. Cointegration and test of present value models. Journal of Political Economy 95, 1062–1088.Campbell, J.Y., Shiller, R.J., 1998. Valuation ratios and the long-run stock market outlook. The Journal of Portfolio Management 24 (2),

11–26.Dixit, A.K., Pindyck, R.S., 1994. Investment Under Uncertainty. Princeton University Press.Efron, B., 1979. Bootstrap methods: another look at the jackknife. Annals of Statistics 7, 1–26.Engle, R.F., 1982. Autoregressive conditional heteroskedasticity with estimates of the variance of United Kingdom inflation.

Econometrica 50 (4), 987–1008.Engle, R.F., Granger, C.W., 1987. Cointegration and error correction: representation, estimation, and testing. Econometrica 55 (2), 251–

276.Fama, E., French, K., 1992. The cross-section of expected stock returns. Journal of Finance 46 (2), 427–466.Fuller, R.J., Kling, J.L., 1990. Is the stock market predictable? The Journal of Portfolio Management 15 (4), 28–36.Fuller, R.J., Kling, J.L., 1994. Can regression-based models predict stock and bond returns. The Journal of Portfolio Management 19 (3),

56–63.Fuller, R.J., Huberts, L.C., Levinson, M.J., 1993. Returns to E/P strategies, Higgledy–Piggledy growth, analysts’ forecast errors, and

omitted risk factors. The Journal of Portfolio Management 19 (2), 13–24.Glen, D.R., 1997. The market for second-hand ships: further results on efficiency using cointegration analysis. Maritime Policy and

Management 24 (3), 245–260.Granger, C., 1969. Investigating causal relations by econometric models and cross-spectral methods. Econometrica 37 (3), 424–438.Granger, C., 1986. Developments in the study of cointegrated variables. Oxford Bulletin of Economics and Statistics 48 (3), 213–227.


Hale, C., Vanags, A., 1992. The market for second-hand ships: some results on efficiency using cointegration. Maritime Policy andManagement 19 (1), 31–39.

Harris, R., 1995. Using Cointegration Analysis in Econometric Modelling. Prentice Hall/Harvester Wheatsheaf, UK.Jaffe, J., Keim, D., Westerfield, R., 1989. Earnings yields, market values, and stock returns. Journal of Finance 44 (1), 135–148.Jarque, C.M., Bera, A.K., 1980. Efficient test for normality, homoscedasticity and serial dependence of regression residuals. Economics

Letters 6, 255–259.Johansen, S., 1988. Statistical analysis of cointegration vectors. Journal of Economic Dynamics and Control 12 (2/3), 231–254.Johansen, S., 1991. Estimation and hypothesis testing of cointegration vectors in Gaussian vector autoregressive models. Econometrica 59

(6), 1551–1580.Kavussanos, M.G., Alizadeh, A.H., 2002a. Efficient pricing of ships in the dry bulk sector of the shipping industry. Maritime Policy and

Management 29 (3), 303–330.Kavussanos, M.G., Alizadeh, A., 2002b. The expectations hypothesis of the term structure and risk premia in dry bulk shipping freight

markets; An EGARCH-M approach. Journal of Transport Economics and Policy 36 (2), 267–304.Kwiatkowski, D.P., Phillips, C.B., Schmidt, P., Shin, Y., 1992. Testing the null hypothesis of stationarity against the alternative of a unit

root. Journal of Econometrics 54 (1/2/3), 159–178.Lander, J., Orphanides, A., Douvogiannis, M., 1997. Earnings forecasts and the predictability of stock returns: evidence from trading the

S&P. The Journal of Portfolio Management 23 (4), 24–35.Lee, C.I., Gleason, K.C., Mathur, I., 2000. Efficiency tests in the French derivatives market. Journal of Banking and Finance 24 (5),

787–807.Ljung, G.M., Box, G.E.P., 1978. On a measure of lack of fit in time series models. Biometrika 65, 297–303.Maddala, G.S., Kim, I., 1998. Unit Roots, Cointegration and Structural Change. Cambridge University Press, UK.Newey, W.K., West, K.D., 1987. A simple positive definite heteroskedasticity and autocorrelation consistent covariance matrix.

Econometrica 55 (3), 703–708.Osterwald-Lenum, M., 1992. A note with the quantiles of the asymptotic distribution of the ML cointegration rank test statistics. Oxford

Bulletin of Economics and Statistics 54 (3), 461–472.Pesaran, M.H., Timmermann, A., 1995. Predictability of stock returns: robustness and economic significance. Journal of Finance 50 (4),

1201–1228.Phillips, P.C.B., Perron, P., 1988. Testing for a unit root in time series regressions. Biometrica 75, 335–346.Politis, D.N., Romano, J.P., 1994. The stationary bootstrap. Journal of the American Statistical Association 89 (428), 1303–1314.Roll, R., 1994. Style return differentials: illusions, risk Premia, or investment opportunities? Working Paper, University of California, Los

Angeles.Ruiz, E., Pacual, L., 2002. Bootstrapping financial time series. Journal of Economic Surveys 16 (3), 271–300.Schwarz, G., 1978. Estimating the dimension of a model. Annals of Statistics 6, 461–464.Strandenes, S.P., 1984. Price determination in the time-charter and second-hand markets. Working Paper No. 06, Centre for Applied

Research, Norwegian School of Economics and Business Administration.Sullivan, R., Timmermann, A., White, H., 1999. Data-snooping, technical trading rule performance, and the bootstrap. Journal of

Finance 54 (5), 1647–1691.Tsolakis, S.D., Cridland, C., Haralambides, H.E., 2003. Econometric modelling of second-hand ship prices. Maritime Economics and

Logistics 5 (4), 347–377.Tvedt, J., 1997. Valuation of VLCCs under income uncertainty. Maritime Policy and Management 24 (2), 159–174.White, H., 2000. A reality check for data snooping. Econometrica 68 (5), 1097–1126.

Documents

Investment Timing and Trading Strategies in the Sale and Purchase Market for Ships