Integrating The Four Shipping Markets: A New Approach By

Integrating The Four Shipping Markets: A New Approach

By

George N. Dikos

M.Eng. Naval Architecture and Marine Engineering, N.T.U.A., 1999

M.S. Shipping, Trade and Finance, City University Business School, 2001

SUBMITTED TO THE DEPARTMENT OF OCEAN ENGINEERING INPARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF

MASTER OF SCIENCE IN OCEAN SYSTEMS MANAGEMENT

AT THE

MASSACHUSETTS INSTITUTE OF TECHNOLOGY

FEBRUARY 2003

@ 2003 Massachusetts Institute of TechnologyAll rights reserved

Signature of Author............/ 'U

/J- /

Certified by............

Accepted by..............................

............Department of Ocean Engineering

December 19, 2003

................Henry Marcus

Professor of Marine SystemsThesis Supervisor

........ .i ...... ...............

Arthur BaggeroerProfessor of Ocean Engineering and Electrical Engineering

Chairman, Department Committee on Graduate Studies

BARKER

I

MASAoUil S INSTITUTEOF TECHNOLOGY

JUL 1 5 2003

LIBRARIES

The Four Shipping Markets: An IntegratedApproach

by

George Dikos

Submitted to the Depratment of Ocean Engineering on December 20, 2002

in Partial Fulfillment of the Requirements for the degree of

Master in Science in Ocean Systems Management

Abstract

Using the approach of modern financial economics, several questions re-garding the four shipping markets are addressed. These markets are themarket for new vessels, the second hand market, the scrapping market andthe freight rate market. Using "no arbitrage" arguments, the four marketsare integrated and equilibrium valuation of vessels is derived. Finally, ques-tions of market efficiency and rational expectations are tested empirically,using modern econometric theory.

Thesis Supervisor: Henry S. MarcusTitle: Professor of Ocean Systems Management

Massachusetts Institute of TechnologyThe Four Shipping Markets: An Integrated Approach

ACKNOWLEDGMENTS

First of all I would like to thank the Eugenides Foundation, the A. Onassis PublicBenefit Foundation and the Fulbright Foundation for funding my studies at M.I.T.My thanks go out especially to the President of the Eugenides Foundation, Mr. L.Eugenides-Demetriades, for his encouragement and belief in my work and in the oldfriendship between our families. I would also like to thank Professor Henry Marcusfor supervising both this thesis and my PhD research. I am also grateful to ProfessorNick Patrikalakis and Professor Jerry Hausman. Thanks also go to my co-authorsProfessor Henry Marcus and Nick Papapostolou for allowing me to use parts of ourjoint work from the following working papers: 'Market Efficiency in the ShippingSector', 'Second Hand Prices, New Buildings and Time Charter Rates' and'Integrating the Four Shipping Markets: The End of the Puzzle'. Thanks also go toVassilis Papakonstantinou and Mr. N. Teleionis.

I dedicate this thesis to my parents, with all my love.

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TABLE OF CONTENTS

1. The Four Shipping Markets: Towards an Integrated Approach................ 41.1 Introduction and Motivation......................................................................42. Empirical Analysis of Second Hand Prices ............................................... 72.1 EBITDA/CAPEX as a leading indicator for depreciation ........................ 7

2.1.1 Testing the Hypotheses...................................................................................................... 92.1.2 H ypothesis Testing ................................................................................................................ 102.1.3 R esults ................................................................................................................................... 11

2.2 Specification of the Depreciation Curves ............................................. 162.3 Out of Sample Testing and Benchmark Testing....................................22

2.3.1 R esidual D iagram .................................................................................................................. 232.3.2 Structural Analysis of our Empirical Findings .................................................................. 25

2.4 Econometric Analysis of the Second Hand Price and New Vessel Price Dyanmics ................ 31

THE COST OF RUNNING VESSELS......................................................................................... 33H andysize ....................................................................................................................................... 34Table 2: Summary Statistics Of Price & Profit Series.............................................................. 38

ESTIMATION RESULTS ................................................................................................................. 40Table 3: Summary Statistics of the Excess Returns in the Four Tanker Carriers...................... 42Table 4: Predictability of Excess Returns on Shipping Investments .......................................... 43

COINTEGRATION TESTS...............................................................................................................44Table 5:Cointegration Test For Prices and Operational Profits................................................. 45Table 6: Estimated VECM of Handysize Prices & Profits.............................................................48Table 7: Estimated VECM of Suezmax Prices & Profits ............................................................... 49Table 8: Estimated VECM of VLCC Prices & Profits ................................................................... 50

C O N C LU SIO N .................................................................................................................................. 593. A Stochastic Model for the Depreciation Curves..................643.1Introduction and Motivation....................................................................643.2 The Relation between Renewal Value and Market Value of Ships..........663.3 Modelling the Evolution of New Building Prices, Second Hand Prices andTime Charter Rates.................................................................................... 69

3.3.1.1 The M odel...............................................................................................................................693.3.1.2 Economic Interpretation of the Depreciation Curves........................................................ 723.3.1.3 The Form of Depreciation Curves .................................................................................... 74

3.4 Empirical Analysis.................................................................................753.4.1.1 D ata A nalysis.......................................................................................................................... 753.4.1.2 Empirical Reuslts....................................................................................................................76

T a b le 2 ..................................................................................................... . . 7 73.5 Summary and Topics for Further Research ......................................... 784. Integrating the Four Shipping Markets using the Contingent ClaimsA p pro ach .................................................................................................... . 8 0

4.1 A Structural Model for the Second Hand Prices.......................................................................804.2.1 Risk Factors and Replicating Strategies ................................................................................ 81

4.3 A two-factor market model ....................................................................... 874.3.1 Valuation in an incomplete market....................................................................................... 87

4.4 Generalized formulation of the 'Good Deal' Problem ........................... 905. Towards a General Equilibrium...............................................................94

5.1 Partial Equilibrium Pricing...................................................................................................... 945.2 Market Microstructure and Open Problems..............................................................................96

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1. The Four Shipping Markets: Towards an IntegratedApproach

Historically, the market for new vessels, the market for second hand vessels, thefreight rate dynamics and finally the market for scrap have been considered asdifferent markets that obey their own laws of supply and demand. The main aim ofthis dissertation is to identify the dynamics of second hand prices from a financialor Real Options approach.

1.1 Introduction and Motivation

After the pioneering work of Zannetos (1966) and others, who set the

foundations of Maritime Economics from a microeconomic or Industrial

Organisation point of view, very little has been done in using financial tools to

identify 'pricing links' between the different markets that constitute the

shipping industry. The dynamics of the freight rates are determined by the

supply and demand for transportation and the same applies for the orderings

of new building vessels and scrapping decisions. However, since the second

hand vessels do not affect the supply and demand patterns, their value

should be determined by their payoffs and their opportunity or

replacement cost. This observation will be the motivation for this paper and

the link that will allow us to integrate our approach towards the different

shipping markets, by using intuition from finance.

Since the market for second hand vessels doesn't depend on capacity

replacement and speculation and given that ships exist in order to provide

demand capacity, ideally it should not exist. However not only it exists, but

also it is one of the driving forces of shipping economics and shipping

investment. This implies that it functions, on the one hand as a market for

assets and on the other hand (and this is the key idea in this paper) as a

proxy for the market value of a vessel compared to the replacement cost,

given by the prices of new vessels.

The first part of this observation is not new in maritime economics.

Beenstock and Vergottis (1989) came up with a model in order to explain the

prices of second hand values. This model, which was a CAPM type model,

relied on quadratic utility functions for shipping investors and the assumption

4


that markets are complete. Since then, few significant research efforts have

been made to understand the financial aspects of the market for second hand

vessels and their role in the shipping industry.

Without the strict assumptions required in a CAPM type approach, we

know that the value of the asset is determined by the value of its expected

payoff, for which time charter rates are a sufficient statistic. Furthermore,

decisions in the second hand market depend on the comparison between

market values (second hand prices) and new building prices (replacement

costs). If these two factors are sufficient statistics for

investment/replacement decisions in the second hand market, then they

should also be sufficient statistics for the pricing of second hand ships. This

was the main intuition of the seminal paper (1992) by Marcus et.al.

Furthermore, the intuition behind the relationship of second hand prices and

new vessels has close connections to Tobin's q-theory. This approached will

provide the theoretical background for our empirical analysis in Chapter 2.

From an empirical point of view, 10 years later after the 'Buy Low - Sell

High' approach, Haralambides et.al (2002) conducted an excellent

econometric analysis for the determination of the factors that affect second

hand prices. Once these factors are identified empirically, one has good

estimates about the sources of risk involved in pricing the uncertain payoffs.

Then by assuming that we are able to trade continuously in a portfolio that

spans the payoffs of the second hand ship (which is the case under

complete markets) we may use 'arbitrage' arguments to derive the value of

the second hand ship, contingent on the factors of risk. In Chapter 2 we derive

empirically these risk factors by running an econometric analysis on the prices

of the second hand values. In Chapter 3 and Chapter 4 we use the

assumption of continuous trading and elements of the Real Options literature

to derive closed form formulas for the prices of second hand vessels as a

function of the underlying risk factors. In Chapter 5 we abandon the

assumption of continuous trading and describe a dynamic model for the

shipping industry, using elements from Dynamic Optimization and extensions

of the Devanney (1971) model.

The introduction of continuous time methods and contingent claim

valuation methods in shipping is not new: Goncalves (1992) used future

5


contracts as an underlying instrument and Dixit and Pindyck (1994) derived

threshold ratios that trigger investment in the tanker industry. As we shall

observe from our empirical analysis in Chapter 2, the functional relationship

between second hand values is highly non-linear. This non-linearity provides

significant evidence for a hidden 'real option' value in the second hand market

asset play. The introduction of contingent claim methods and the justification

for these methods is the main idea in Chapters 3 and 4; the integrated

dynamic model is finally presented in Chapter 5. By pricing second hand

vessels in terms of their replacement cost (the price of a new vessel) and their

market value (in terms of the expected revenue generated by the time charter

rates) and using the scrap value as a terminal condition we manage to

establish a link between the 'four shipping markets', or what economists

would identify as the market for services and the market for capital

replacement. From this point of view we hope this will provide an integrated

approach for comparative valuation of equilibrium prices in the second hand

market.

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2. Empirical Analysis of Second Hand Prices

2.1 EBITDA/CAPEX as a leading indicator for depreciation

Our empirical analysis relies heavily on the previous work by Marcus

et. al. (1992) In this paper it was identified that efficient buy-low sell strategies

can be conducted using Time Charter Rates and prices of New Vessels as

sufficient statistics for prices of Second Hand Vessels. We shall conduct our

empirical analysis by identifying the relationship between second hand prices

of 5, 10 and 15 year old ships, the prevailing time charter rates and prices of

new vessels. Before proceeding with our analysis let us define two important

variables that will appear in our empirical analysis: EBITDA/CAPEX will

denote the ratio of the revenue earned by the one year time charter rate

minus operating expenses divided by the expenses incurred by investing in a

new vessel:

Formally we define:

EBITDACAPEX= (TC/ Day- OPEXI Da) * DaysEmplagd andCAPEX

CAPEX stands for the capital expenses associated with investing in a new

vessel. Furthermore, depreciation or Depr will stand for:

CAPEX(t) - Pr iceSH(t)Depr(t) = , where PriceSH(t) is the price of a

CAPEXsecond hand vessel at time t.

In the heart of our analysis lies the observation that the

EBITDA/CAPEX ratio is a leading indicator of (real incurred) depreciation.

Behind this empirical observation underlies the following economic intuition:

EBITDA/CAPEX is a proxy to the Return on Equity or to the economic returns

that the cash-flow generating asset-ship yields; it is a 'measure' of its true

value, whereas depreciation is a measure of its replacement cost.

(EBITDA/CAPEX)/Depreciation is a proxy for the long-term return on the

investment compared to its replacement cost and it can be considered as a Q-

ratio equivalent. According to Tobin's Q-Theory when the true value of an

7


asset exceeds its replacement cost, one should invest and the reverse.

According to the intuition in our model, an increase of the economic rent (or

EBITDA/CAPEX ratio) which corresponds to an increase in the true value and

the Q-ratio should result in an increased demand and investment activity;

thus, depreciation should decrease. Therefore, EBITDA/CAPEX should be

negatively correlated with depreciation, which would imply that an increase in

the expected cash flow would result in the appreciation of the ship price (or

lower levels of depreciation). For a more rigorous analysis of the relationship

between Q-Theory and Industrial Organisation see Ross (1981) and Tobin

(1969).

However, a negative correlation between EBITDA/CAPEX and

Depreciation, which is in line with Economic Theory, would also imply some

other important relations: It implies that EBITDA adjusts more slowly than

replacement costs and depreciation. This is supportive to the evidence of

sticky prices in investment theory and provides us with partial explanations to

the fact that time charter rates adjust far more quickly than ship market prices

(replacement costs).

The shipping industry possesses a unique characteristic: The

replacement cost of the underlying asset is tradable in a relatively liquid

market and the true value of the asset can be estimated fairly accurately given

the long-term time charters. Therefore, the Depreciation ratio provides us with

consistent estimates of the Q-ratio.

In our economy prices serve to equilibrate supply and demand and in

an equilibrium they reflect all information available. The Q-ratio is a measure

of how far the economy is from equilibrium and can be considered as a

measure of economic efficiency. However, economic efficiency does not

necessarily imply asset market efficiency, as pointed out in Waldman and

Dow (1997). This is the case in the Banking System and this will be the case

in the Shipping Industry. Although asset players can exploit profitable

strategies (old versus new, small versus large) similar to strategies of

investors in capital markets, and is therefore not market efficient it is

economically efficient. And this will be verified by proving the EBIDTA/CAPEX

/Depreciation relationship or Q-Theory equivalent.

8


Since this market is found to be market-inefficient, strategies that lead to

excess profits can be exploited. According to Investment Theory the Q-ratio or

EBITDA/CAPEX/Depreciation can be considered as a leading indicator for the

demand for the asset. If the second-hand market verifies this relationship, we

will be able to infer that it is economically efficient. Having verified this

coefficient we will have an industrial example in line with Waldman and Dow,

where market efficiency is not a necessity for economic-investment efficiency.

Being able to test the relationship between the order book and the Q-

ratio would suggest a test for the economic efficiency of the Newbuilding

market, which is questioned by numerous studies.

Due to the above economic intuition we shall not follow the trivial

procedure in empirical analysis and regress second hand prices on prices of

new vessels and time charter rates directly, including age and ship type as

dummies in our model. Based on our previous discussion we shall use the

equivalent q-type formulation approach and test the empirical relation with

dimensionless parameters. Therefore, we shall regress Depreciation rates for

the age of 5, 10 and 15 years with EBITDA/CAPEX rates, including dummies

for ship type. Imposing this additional structure, we are testing two

hypotheses. On the one hand we are testing for the effect of new building

prices and time charter rates on second hand prices and on the other hand

we are testing for a negative correlation between Depreciation ratios and

economic rents (measured with the EBITDA/CAPEX proxy). A negative

relation will be a strong indicator of economic efficiency in this market.

Furthermore if our intuition is correct, we are gaining in statistical efficiency by

using economic information in our statistical tests.

2.1.1 Testing the Hypotheses

In order to test these hypotheses we conduct the following statistical

tests:

1) We run the incurred depreciation on the EBITDA/CAPEX ratio, including

dummies for the age of each ship. We perform this regression separately

for each type and then for a generalised data set including dummies for

category. In this way we see if there is a significant relationship between

9


EBITDA/CAPEX and Depreciation for each category separately and how

significance changes with category.

2) From Economic Theory a decrease in economic rents (or a decrease in

the ratio EBITDA/CAPEX) should result with an increase of depreciation.

Since the potential profits are less than expected, investors are willing to

sell this asset. In order to check our economic intuition we run the first

difference of the EBITDA/CAPEX ratio on depreciation and on the first

difference of depreciation. In this way we can check for spurious

regression and fixed effects. If the supportive statistics remain high after

taking first differences, this makes our case even stronger. Finally, we run

EBITDA/CAPEX ratio on passed ratios and depreciation in order to verify

our hypothesis of the elastic behaviour of long term rates (EBITDA) to

market price fluctuations.

2.1.2 Hypothesis Testing

The first hypothesis we test is the causality between the

EBITDA/CAPEX ratio and depreciation. We run a linear regression and

perform all the tests for heteroscedasticity and autocorrelation. We finally

check for the statistical significance of the beta's, that would imply a strong

causal relation.

EBIDAa + p BD +IF t =A CA PEXt- Hypothesis 1

CAPEX,

The second hypotheses we check is the one that underlies our

economic intuition. Namely:

EBIDAPA +EK 9 = a + ACAPEX,,,_, Hypothesis2CAPEX,

and

Finally we check the EBITDA/CAPEX ratio for autocorrelation of 5th order:

10


S1= - P AJ( EBIDAJ15 CAPEX )+, =a+ ACAPEX Hypothesis3

2.1.3 Results

The AFRAMAX Case

A) We performed our tests using the LimDep Econometric Analysis Package

of William Greene:

In order to test the first hypothesis we run OLS (Ordinary Least Squares) for

AFRAMAX on the model:

Depr = fage5 + P 2 agel0 + f3 agel 5 + P 4EBIDA / CAPEX +

and we obtained the following results:

Ordinary Least Squares Regression - Weighting Variable = none

Dep.var.= DEPR Mean=.4777638889E-01 S.D.=.1373611057E-01

Model size: Observations = 108 Parameters = 4 Deg.Fr.= 104

Residuals Sum of squares= .1602804337E-01 Std.Dev.= .01241

Fit R-squared= .206094 Adjusted R-equared .18319

Autocorrel: Durbin-Watson Statistic = .21900 Rho .89050

Variable Coefficient Standard Error t-ratio P[ITI>t] Mean of X

AGE1 .7283863620E-01 .54038009E-02 13.479 .0000 .33333333

AGE2 .7463808064E-01 .54038009E-02 13.812 .0000 .33333333

AGE3 .7299502509E-01 .54038009E-02 13.508 .0000 .33333333

EC -2486298001 48267514E-01 -5.151 .0000 10342361

The reported statistics are significant and a strong causal relationship

between EBITDA/CAPEX versus Depreciation cannot be challenged.

Even though R square is found to be low this doesn't imply anything about the

relationship we want to examine. The only statistic that leads us to accept

our reject causality is the t-statistic, which is highly above the critical

value of 1.96. We performed OLS using robust matrices to correct for

heteroscedasticity and the statistical significance remained high. An important

11


observation is that age is a significant factor in determining depreciation. The

most sensitive category is the 10-year-old ships and the less sensitive is the

five-year-old ships. This observation is counterintuitive indeed and shall be

furthered examined.

In order to perform an elementary test for autocorrelation and to check our

economic intuition we run OLS for the first differences of our data:

First Differences

Ordinary Least Squares Regression - Weighting Variable = none

Dep. Var. = DEPR Mean= -.3403738318E-03 S.D.= .6364871838E-02

Model size: Observations = 107 Parameters = 4 Deg.Fr= 103

Residuals: Sum of squares= .3453686171E-02 Std.Dev.=.00579

Fit: R-squared= .195738, Adjusted R-squared =.17231

Model test: F[3, 103] = 8.36 Prob value = .00005

Diagnostic: Log-L = 401.4247 Restricted (b=0) Log-L = 389.7708

LogAmemiyaPrCrt.= -10.266, Akaike Info. Crt.= -7.428

Autocorrel: Durbin-Watson Statistic = 1.21498 Rho = .39251

Variable Coefficient Standard Error t-ratio P[TI>t Mean of X

AGE1 -. 1252421124E-02 .97909397E-03 -1.279 .2037 .32710280

AGE2 .3649028066E-03 .96509837E-03 .378 .7061 .33644860

AGE3 -.4593052670E-04 .96509837E-03 -.048 .9621 .33644860

EC -.1861053410 .38529597E-01 -4.830 .0000 .20429907E-03

What we observe is that the strong relation between Depreciation and

EBITDA/CAPEX remains statistically significant and the t-statistic remains in

the same levels. Therefore, the regression cannot be considered as spurious.

What we observe is that although size is a factor when forecasting, it doesn't

really explain the percentage variations of the two factors. This implies that

incorporating age can yield a better explanation of Depreciation; however, it is

not a causal force to its variations. As we can observe, the Durbin-Watson

statistic is now inconclusive for autocorrelation; however, in the first panel it

indicated that autocorrelation might be present. Since the finite differences

indicate no autocorrelation, the presence of a common trend is strong.

We then regress the Depreciation change in the period t, t+2 with the change

in EBITDA/CAPEX that we observe at time t and we still derive high t-

statistics, which implies that EBITDA/CAPEX is indeed a leading

indicator and can be used to forecast incurred depreciation.

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We now want to check how 'sticky' is the EBITDA/CAPEX ratio and we

therefore run OLS on its history:

What we documented is a very strong positive relationship between the

today's EBITDA/CAPEX ratio and the ratio six observations before. We

therefore run the Depreciation ratio with EBITDA/CAPEX and the history of

EBITDA/CAPEX to specify if the history can improve our forecast. We still

observe that the observation two years ago can improve our forecast for

depreciation. Whether this is due to seasonality or due to 'stickyness' is a fact

that has to be further examined. Before proceeding to checking these

hypotheses for other types, we run OLS with correction for autocorrelation on

the Data in the first Panel:

From the following results it is evident that the tested relationship survives

easily all the tests:

Ordinary Least Squares Regression - Weighting Variable = noneDep. Var. = DEPR Mean= .4777638889E-01 S.D.=1373611057E-01Model size: Observations = 108 Parameters = 4 Deg.Fr.=104Residuals: Sum of squares=.1602804337E-01 Std.Dev.= 01241Fit: R-squared=.206094 Adjusted R-squared = .18319Model test: F[ 3, 104] = 9.00 Prob value = .00002Diagnostic: Log-L = 322.7942 Restricted(b=0) Log-L = 310.3315LogAmemiyaPrCrt.= -8.741 Akaike Info. Crt.= -5.904Autocorrel: Durbin-Watson Statistic = .21900 Rho = .89050Autocorrelation consistent covariance matrix for lags of6 periods

Variable Coefficient Standard Error t-ratio P[ITI>t] Mean of XAGE1 .7283863620E-01 .94738787E-02 7.688 .0000 .33333333AGE2 .7463808064E-01 .91076161E-02 8.195 .0000 .33333333AGE3 .7299502509E-01 .79729283E-02 9.155 .0000 .33333333EC -.2486298001 .77457980E-01 -3.210 .0018 .10342361

Challenging Tasks for further Analysis:

Provided that the above relations are verified for the other types of ship, we

can argue that the second hand market is economicly efficient (the Q-ratio is

an indicator of economic activity). In some sense the asset play market is

efficient too and therefore the imbalance in supply could be attributed to the

newbuilding market. A Dynamic Analysis with time series method could reveal

more information about the interaction between the Q-ratio and the industry

dynamics.

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The VLCC Case

Following the same steps we now run the Depreciation

EBITDA/CAPEX ratio for the VLCC, accounting for size:

Ordinary least squares regression Weighting variable = noneDep. var. = DEPR Mean= .5963129630E-01 S.D.= .1362702442E-01Model size: Observations = 108 Parameters = 4 Deg.Fr.= 104Residuals: Sum of squares= .3903941156E- Std.Dev.= .01937

01Fit: R-squared= -.964796 Adjusted R-squared = -1.02147Diagnostic: Log-L = 274.7216 Restricted (b=0) Log-L = 311.1926LogAmemiyaPrCrt.= -7.851 Akaike Info. Crt.= -5.013Autocorrel: Durbin-Watson Statistic = .38163 Rho = .80918Results Corrected for heteroskedasticityBreusch - Pagan chi-squared = 162.7924 with 3 degrees of freedom

Variable Coefficient Standard Error t-ratio P[ITI>t Mean of X

AGE1 .6997216916E-01 .80811075E-02 8.659 .0000 .33333333AGE2 .6727099467E-01 .72206230E-02 9.317 .0000 .37037037AGE3 .6678394635E-01 .46288619E-02 14.428 .0000 .33333333EC -.1704179991 .57061315E-01 -2.987 .0035 .81344444E-01

The relationship remains statistically significant, however it is less sensitive

to EBITDA/CAPEX and more sensitive to age, especially for the 15 year

old ship. Possibly this puzzle could be explained if we took into account the

fact that old VLCC's were traded for a premium, due to the extra steel that

was placed in them before the introduction of more high-tensile steel and

thinner scantlings.

However we still have to adjust for autocorrelation and we include the passed

six lags:

Ordinary Least Squares Regression - Weighting Variable = noneDep. var. = DEPR Mean= .5963129630E-01 S.D.= .1362702442E-01Model size: Observations = 108 Parameters = 4 Deg.Fr.= 104Residuals: Sum of squares= .3903941156E-01 Std.Dev.= .01937Fit: R-squared= -.964796 Adjusted R-squared = -1.02147Diagnostic: Log-L = 274.7216 Restricted (b=0) Log-L = 311.1926LogAmemiyaPrCrt.= -7.851 Akaike Info. Crt.= -5.013Autocorrel: Durbin-Watson Statistic = .38163 Rho = .80918Autocorrelation consistent covariance matrix for lags of 6 periods

Variable Coefficient Standard Error t-ratio P[ITI>t Mean of XAGE1 .6997216916E-01 .14813474E-01 4.724 .0000 .33333333AGE2 .6727099467E-01 .10572965E-01 6.363 .0000 .37037037AGE3 .6678394635E-01 .62887299E-02 10.620 .0000 .33333333EC -.1704179991 .76954789E-01 -2.215 .0290 .81344444E-01

14

on the


The relationship remains statistically strong having corrected for six period's

lags.

15


2.2 Specification of the Depreciation Curves

2.2.1 Testing for non-linearity

At this point there are two main assumptions on which our analysis relies:

We have assumed that there is no trend in our data and have treated them as

Panel Data using no time series techniques. It has been verified that beyond

the high correlation and the strong causality there is also a significant

underlying economic intuition. However, we have not tested for any time-

series effects or common trends. Finding a common trend could on the one

hand justify further the strong causality and on the other hand it could improve

our forecastability significant. If for example there is a common force that

drives this causality, then this could be exploited further and used as an

additional factor in our forecasting procedure. However, this is a task that

requires additional data and analysis and at the end of the day it can only

result in advanced forecasting techniques and by no means reverses the

results we have found until now.

A second important assumption is the one of linear conditional expectation.

When regressing Depreciation on the EBIDTA/CAPEX the standard

underlying econometric assumption is namely the following one: The

conditional expectation (or the best prediction) of the Depreciation based on

the EC observation is namely a linear function of EC. We are now going to

test if this is a correct specification. At this point we have to bear in mind that

adding terms in a model always results in a higher fit. We shall therefore

examine if the incremental fit gained is worth the extra parameters.

We now test the relation between the observations of the Depreciation on the

stochastic regressors of age and EC. At this point the treat age as an input

and not as a dummy.

This has the following consequence: We shall determine joint coefficients for

age, EC and their functions for both VLCC and AFRAMAX- the only term that

will remain variable will be the constant. This will keep the number of variables

16


needed for prediction as low as possible and will allow our model to be easily

updated.

Specifying a complex functional form for a model is a significant drawback: On

the one hand the economic intuition and rationale becomes questionable

(which leads people to test the hypotheses) and on the other hand updating

the model requires an update in the functional form. Therefore, keeping the

number of dependent variables as low as possible is a true 'asset'.

VLCC and AFRAMAX joint results

We run OLS on the joint data for VLCC and AFRAMAX with age and EC and

the 'goodness of fit' or R2 turned out to be 42%. All the t-statistics remained

statistically significant, indeed.

At that point we decided to 'weighting' the EBITDA/CAPEX ratio with respect

to age. The intuition is that older ships will be more efficiently priced than

younger ships and less volatile to large market movements. Furthermore,

based on the Q-renewal theory the replacement cost of an old asset should

be much closer to its true value, since much less uncertainty is associated to

his future.

The result from this cross-product term, turned out to be beyond expectations.

The t-statistic of this cross term is close to 15 (indicates cointegration) and

the R2 has reached 58%. We now include the square of the age and the EC

ratio as independent terms and we present our results. At this point we have

to bear in mind that adding the data from the other sectors and including other

types of ships can only increase the forecasting power of our model.

17


Joint AFRAMAX and VLCC Results - Specification

Ordinary least squares regression - Weighting variable = noneDep. var. = DEPR Mean=.5370384259E-01 S.D.=.148867641 1E-01Model size: Observations = 216 Parameters = 7 Deg.Fr.= 209Residuals: Sum of squares=.1652254741E-01 Std.Dev.= .00889Fit: IR-squared= .69323 Adjusted R-squared =.64328Model test: F[6, 209] = 65.62 Prob value =.00000Diagnostic: Log-L = 717.1665 Restricted(b=0) Log-L =602.7835LogAmemiyaPrCrt.= -9.413, Akaike Info. Crt.= -6.576Autocorrel: Durbin-Watson Statistic =.30577 Rho =.84712

Variable Coefficient Standard Error t-ratio P[ITI>t Mean of X

AGE -.2319671183E-02 .11188717E-02 -2.073 .0394 10.000000VLCC .1253398320 .74237274E-02 16.884 .0000 .50000000AFRA .1202226475 .77673709E-02 15.478 .0000 .50000000

EC -.8855295396 .10003614 -8.852 .0000 .92384028E-01EA .4478081079E-01 .45390247E-02 9.866 .0000 .92384773AA -.1171356135E-03 .51333956E-04 -2.282 .0235 116.66667EE .8564916386 .42653632 2.008 .0459 .96011111E-02

Predicted Values(* => observation was not in estimating sample.)

Observation Observed1 .82130E-012 .81280E-013 .80500E-014 .78410E-015 .68360E-016 .61330E-017 .58610E-018 .56290E-019 .59060E-0110 .62980E-0111 .63980E-0112 .56930E-0113 .43510E-0114 .35080E-0115 .35080E-0116 .30980E-0117 .22780E-0118 .25000E-0119 .24830E-0120 .26970E-0121 .20400E-0122 .23900E-0123 .45870E-0124 .64060E-0125 .68740E-0126 .66810E-0127 .66810E-0128 .59920E-0129 .52940E-0130 .43670E-0131 .31720E-0132 .16220E-0133 .13720E-0134 .16040E-0135 .17610E-0136 .33960E-0137 .69680E-0138 .68620E-0139 .66460E-0140 .63310E-0141 .59410E-0142 .55670E-0143 .54800E-0144 .52480E-0145 .51130E-0146 .50580E-0147 .50640E-0148 .49700E-01

Y Predicted Y.53132E-01.50228E-01.47253E-01.45531E-01.43548E-01.43135E-01.41381E-01.38479E-01.60432E-01.56894E-01.56732E-01.55916E-01.54892E-01.53923E-01.53526E-01.51201E-01.47843E-01.47670E-01.45208E-01.45830E-01.42796E-01.44441E-01.47615E-01.52875E-01.52436E-01.60538E-01.66143E-01.67725E-01.54457E-01.41362E-01.32845E-01.19435E-01.15735E-01.22403E-01.34628E-01.42192E-01.52883E-01.51268E-01.49648E-01.48722E-01.47669E-01.47451E-01.46534E-01.45041E-01.57037E-01.55003E-01.54911E-01.54447E-01

18

Residual.0290.0311.0332.0329.0248.0182.0172.0178

-. 0014.0061.0072.0010

-. 0114-. 0188-. 0184-. 0202-. 0251-. 0227-. 0204-. 0189-. 0224-. 0205-. 0017

.0112

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.0168

.0174

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.0117

.0082

.0083

.0074-. 0059-. 0044-. 0043-. 0047

95% Forecast.0354.0325.0296.0278.0258.0254.0237.0207.0427.0392.0390.0382.0372.0362.0358

.0335

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Interval.0708.0679.0650.0632.0613.0609.0591.0562.0782.0746.0744.0736.0726.0716.0712.0689.0655.0654.0629.0635.0605.0622.0653.0706.0701.0783.0839.0856.0722.0591.0507.0378.0345.0406.0524.0599.0706.0690.0673.0664.0654.0651.0642.0627.0748.0727.0726.0722

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We have included the following variables:

- Age

- Type

- EBIDTA/CAPEX

- The product of EC with Age

- Age2

- EC 2

And this 'simple' second order quadratic conditional expectation yields an

R2=69%, with all coefficients statistically significant at 95%. We have

now a powerful prediction benchmark in our hands, which can easily be

extended to all types of ships. This still remains a static model and large

improvements can be expected when we account for Time Series

Analysis and Dynamic Effects.

Finally, since our economic intuition is that EBITDA/CAPEX is a leading

indicator for Depreciation and our practical target is to be able to make

inference about future Depreciation based on today's EBITDA/CAPEX we run

OLS of the observation at time t on the result at time t+1.

We obtain statistically supportive results; however, the problem with leading

indicators (as addressed by Hendry) is whether the elasticity remains constant

over time. This issue could be addressed in a dynamic analysis and we could

test the model for structural changes over time.

21


2.3 Out of Sample Testing and Benchmark Testing

In this section we perform an out of the sample testing of our above

specification and compare our depreciation curves to other forms of

depreciation curves, such as the Lin Cai Depreciation curves (LC hereafter)

and compare the results.

The LC model outperforms our model for the first 25% of our

observations. This is obvious since it was designed on a fitting-sorting

algorithm. However, as time goes by the forecast error becomes huge relative

to our simple 5-factor model. The Forecast error is actually ten times higher

than our variance, whereas our forecast accuracy is 90% for the last 30% of

the observations with minimal error. For the last observations that are

relatively explosive (due to the bullish shipping market) the LC error formula

explodes.

From the diagram that compares the two errors the supremacy of the

specification in 2.1.2 is obvious.

Note: The Lin -Cai formula we used in our analysis for the depreciation

curves is the following:

=1F((C$28*($R$95*C$118*25/$G$16*C$118*25/$G$16+$R$97*C$118*25/$G

$16)+$R$96*C$118*25/$G$16*C$118*25/$G$16+$R$98*C$118*25/$G$16+$

R$99)*$V$95+ C$118*25/$G$16*$V$96+$V$97>0,

C$28*($R$95*C$118*25/$G$16*C$118*25/$G$16+$R$97*C$118*25/$G$16)

+$R$96*C$118*25/$G$16*C$118*25/$G$16+$R$98*C$118*25/$G$16+$R$9

9,

C$28*($T$95*(C$i I8*25I$G$1 6-25)*(C$11I8*25I$G$1 6-

25)+$T$97*(C$118*25/$G$16 25))+$T$96*(C$118*25/$G$16-

25)*(C$118*25/$G$16 25)+$T$98*(C$118*25/$G$16-25)+$T$99)

The first part of the formula is a sorting condition that decides the fit:

The second part can be simplified if we assume a Life of 25 years for our ship:

Then it simply collapses to the following:

C28*(R95+R97*C 18)+R96+R98*C118+R99 or equivalently:

22


DeprLnKai= (D(EBITDA/CAPEX (a + 0 * age) + y + *age) +

Where the Greek Letters correspond to the estimated residual parameters

s2,s21,sl,sl 1,sQ and are adapted based on the sorting condition. The sorting

condition results in different formulas for each observation set and requires

many parameters. It gives a very good fit when passed data occur and is

strongly outperformed by our formula. Another reason that leads to its

outperformance is the omission of the non-linear terms and the model

misspecification.

2.3.1 Residual Diagram

The Lin Cai formula outperforms the MITSIM05 model only on the first

25% of the observations.

23

AFRAMAXVLCC Observations

o 14

0.12

0.1

0 0.08

0 D8

CL'I.

a) 0.04

0.02

0

-0.02

Observations


VLCC

y = 0.8565x2 - 0.2137x + 0.0642

0.12

0.1

0.08-

.0 + MIT-50 MIT-10

0.06

-(

4 ---- ."..~.4-4MIT-15

0.04-

0.02

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2EBITDA-CAPEX

Fitted Curves for VLCC vessels with age 5, 10 and 15 years

24


2.3.2 Structural Analysis of our Empirical Findings

In our previous analysis we concluded that the following factors appear

to determine the prices of second hand vessels:

1. A constant that differs for each industry (Random Effect)

2. A beta factor for Age.

3. A beta factor for EBITDA/CAPEX.

4. A beta factor for the AGEA2 and EBITDA/CAPEXA2

5. A beta factor for weighted EBITDA/CAPEX*Age

Thus our intuition about the parameters has turned out to be correct. There is

however significant evidence that there are important non-linearities in these

relationships. In the Paragraphs 3 and 4 we shall construct some dynamic

models that will justify these non-linearities.

25


Appendix

Joint Formula for the AFRAMAX-VLCC SUEZMAX

Following our previous analysis we derive the formulas for the joint

AFRAMAX-VLCC and SUEZMAX and we compare the coefficients derived

with the AFRA-VLCC coefficients derived on page 20. We stack our data in

Panel Data form and use a total of 323 observations. Running LIMDEP and

correcting for multicollinearity we obtain the following results:

Ordinary Least Squares Regression - Weighting Variable = noneDep. var. = DEPR Mean= .5284492260E-01 S.D.= .1578811278E-01Model size: Observations = 323Residuals: Sum of squares= .2237366571E-01Fit: R-squared= .721246Model test: F[ 7, 315] = 116.43Diagnostic: Log-L = 1088.4528LogAmemiyaPrCrt.= -9.528Autocorrel: Durbin-Watson Statistic = .35024

Parameters = 8Std.Dev.= .00843Adjusted R-squared = .71505Prob value =.00000Restricted (b=0) Log-L = 882.1485Akaike Info. Crt.= -6.690Rho = .82488

Deg.Fr.= 315

Variable coefficient Standard Error t-ratio P[ITI>t] Mean of X

AGE -.3431757693E-02 .85803367E-03 -4.000 .0001 9.9845201SUEZ .1366533138 .55342457E-02 24.692 .0000 .33126935VLCC .1405608564 .54618293E-02 25.735 .0000 .33436533AFRA .1372882790 .57097227E-02 24.045 .0000 .33436533EC -1.086932388 .66560000E-01 -16.330 .0000 .93676594E-01EA .4536886420E-01 .32199621E-02 14.090 .0000 .93524467AA 1.579992417 .25874240 6.106 .0000 .10048235E-01EE -.6489909736E-04 .39760161E-04 -1.632 .1036 116.33127

We now compare the 2-industry case coefficients with the3- industry case:

Coefficients2by2 3by3-0.0023 -0.00343

AgeSuez 0.1366VLCC 0.1253 0.1405AFRA 0.1202 0.1372E/C -0.8855 -1.0869AGE*E/C 0.04478 0.04536ECA2 0.856 1.5799AGEA2 -0.0002 -0.00006

The industry constants that display the higher statistics do not change

significantly and neither does the EBITDA/CAPEX coefficient that becomes

even higher implying that SUEZMAX is the most sensitive industry to E/C

variations. Dynamic Effects of age become less important (age is not a non-

26


linear effect); however, EBITDA/CAPEX squared becomes even higher

implying that SUEZMAX is very sensitive to its changes especially in a good

market.

(The coefficient of the squared term is the coefficient of the Taylor expansion

and the second derivative- a positive second derivative implies that the E/C

coefficient rises in a booming market and is less sensitive to a bad market.)

This is in line with the empirical observation that in a bad market ships cannot

depreciate more than their 'natural' depreciation rate; therefore, depreciation

becomes independent of E/C at rock-bottom prices. The positive coefficient of

the squared E/C term is in line with Maritime Economic Theory and empirical

observations.

Tanker Industry Prediction ModelPredicted Values

(* => observation was not in estimating sample.)

Observation Observed Y1 .82130E-012 .81280E-013 .80500E-014 .78410E-015 .68360E-016 .61330E-017 .58610E-018 .56290E-019 .59060E-0110 .62980E-0111 .63980E-0112 .56930E-0113 .43510E-0114 .35080E-0115 .35080E-0116 .30980E-0117 .22780E-0118 .25000E-0119 .24830E-0120 .26970E-0121 .20400E-0122 .23900E-0123 .45870E-0124 .64060E-0125 .68740E-0126 .66810E-0127 .66810E-0128 .59920E-0129 .52940E-0130 .43670E-0131 .31720E-0132 .16220E-0133 .13720E-0134 .16040E-0135 .17610E-0136 .33960E-0137 .69680E-0138 .68620E-0139 .66460E-0140 .63310E-0141 .59410E-0142 .55670E-0143 .54800E-0144 .52480E-0145 .51130E-0146 .50580E-0147 .50640E-0148 .49700E-01

Predicted Y.53951E-01.50671E-01.47363E-01.45470E-01.43307E-01.42859E-01.40970E-01.37883E-01.62353E-01.58248E-01.58061E-01.57127E-01.55954E-01.54848E-01.54393E-01.51762E-01.48017E-01.47825E-01.45114E-01.45792E-01.42492E-01.44276E-01.47764E-01.53655E-01.53159E-01.62478E-01.69082E-01.70966E-01.55453E-01.40951E-01.32057E-01.19240E-01.16039E-01.21931E-01.33876E-01.41842E-01.52323E-01.50349E-01.48414E-01.47327E-01.46107E-01.45856E-01.44815E-01.43156E-01.57539E-01.54957E-01.54841E-01.54264E-01

Residual.0282.0306.0331.0329.0251.0185.0176.0184

-. 0033.0047.0059

-. 0002-. 0124-. 0198-. 0193-. 0208-. 0252-. 0228-. 0203-. 0188-. 0221-. 0204-. 0019

.0104

.0156

.0043-. 0023-. 0110-. 0025

.0027-. 0003-. 0030-. 0023-. 0059-. 0163-. 0079

.0174

.0183

.0180

.0160

.0133

.0098

.0100

.0093-. 0064-. 0044-. 0042-. 0046

95% Forecast.0370.0337.0304.0285.0264.0259.0240.0209.0454.0413.0411.0402.0390.0379.0375.0348.0311.0309.0282.0288.0255.0273.0308.0367.0362.0455.0521.0540.0385.0240.0150.0020

-.0013.0048.0169.0249.0356.0336.0317.0306.0294.0291.0281.0264.0408.0382.0381.0375

Interval.0709.0676.0643.0624.0603.0598.0579.0549.0793.0752.0750.0741.0729.0718.0713.0687.0650.0648-.0621.0627.0594.0612.0647.0706.0701.0794.0860.0879.0724.0579.0491.0364.0334.0391.0509.0588.0691.0671.0652.0641.0628.0626.0616.0599.0743.0717.0716.0710

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The predicted values generated by the model are displayed and the prediction

error is in many cases less than 3%. In addition, the R2 has achieved a value

of 72%, which is an excellent fit for panel data. Finally, we display the

prediction errors and their pattern confirms their white noise charaterisation.

We shall now proceed with an econometric analysis of the dynamics of the

relationship between second hand prices and prices of new vessels. This

econometric analysis will allow us to identify the main dynamics of these two

markets and any long run (cointegration) relationships between these two

processes.

2.4 Econometric Analysis of the Second Hand Price and New Vessel

Price Dyanmics

Ship prices and their movements over time are of great importance to

shipowners taking decisions regarding purchase and sale of vessels. As

Stopford (1997) notes: 'Typically, second-hand prices will respond sharply to

changes in market conditions, and it is not uncommon for prices paid to

double, or halve, within a period of a few months'. Furthermore, investors in

the shipping industry rely not only on the profits generated from shipping

operations, but also on capital gains from buying and selling merchant

vessels. In fact, some investors consider the latter activity more important

than the former one since correct timing of sale and purchase can be highly

rewarding compared to operating the vessel.

Thus, it is important to investigate whether the markets for newbuilding,

second-hand, and scrap tanker vessels are efficient and include rational

31


agents, i.e. assets are priced rationally, since failure of the EMH, if it not due

to the existence of time-varying risk premia, may signal arbitrage

opportunities. For instance, if vessel prices are found to be different from their

rational values, then trading strategies can be utilized to exploit excess profit

opportunities. Consequently, when prices are lower than their fundamental

values (fundamental or rational value is the discounted present value of the

expected stream of income generated over the vessel's lifetime), then vessels

are under-priced compared to their future profitability (i.e. the earnings from

freight operations). In that case it would be profitable to buy and operate the

vessel or sell it when prices are high. In contrast, when prices are higher than

their fundamental values, then vessels are over-priced in comparison to their

future profitability. As a result, it would be profitable for the agent to charter

the vessel rather than buying it. Hence, from the point of view of both the

charterer and shipowner, it is crucial to understand the price mechanism as

well as the efficiency of the market for vessels because both of them might

affect the economic efficiency of the shipping industry. The remaining part of

this section is structured as follows: The Efficient Market Hypothesis (EMH) in

the price formation for the VLCC, Suezmax, and Handysize vessels is tested.

The sources of data are given followed by the econometric analysis.

DATA ON VESSEL PRICES, TIME-CHARTER EARNINGS AND

OPERATING COSTS

The data used for the analysis of this study are as follow: monthly

newbuliding, second-hand, scrap prices and time-charter earnings for VLCC

(250,000 Dwt), Suezmax (140,000 Dwt), and Handysize (30,000 Dwt)

vessels. The data was collected from Clarksons (www.Clarksons.net) and

covers the period from January 1981 to August 2001. Newbuilding, second-

hand and scrap prices are quoted in million dollars for each size and

represent the average value of the vessel in any particular month. Time-

charter earnings are quoted in dollars per day and once more represent the

average value of the vessel in each month. Operating costs were collected

from Drewry Shipping Consultants in daily basis for the period 1990 up to

32


2001 and they represent international averages excluding American flag

vessels. We converted these operating costs to monthly observations by

multiplying the daily figures by 30. This yields a monthly operating cost series

for the period 1990 to 2001. As operating costs do not fluctuate dramatically

over time and increase at an inflationary rate, a non-linear exponential growth

model is used to fit the data and backcast them to 1981. A more detailed

analysis of the operating costs is given in the next section.

THE COST OF RUNNING VESSELS

First of all, the vessel sets the broad framework of costs through its fuel

consumption, the number of crew required to operate it, and its physical

condition, which dictates the requirement for repairs and maintenance.

Second, the cost of bought-in items, specifically bunkers, crew wages, and

ship repair costs, which rise at the inflation rate and follow different

economic trends outside the shipowners's control. Third, costs -like

administrative overhead- depend solely on how efficient the company is run

by the manager.

Unfortunately, there is no internationally accepted standard cost

classification, which often leads to confusion, a matter though that is out of

the scope of this paper.

We should mention again that operating costs do not fluctuate significantly,

and in contrast to voyage costs, they grow at a constant rate, normally the

inflation rate. Within a fleet of vessels one could notice that the level of

operating costs vary. It is usual to find that the old vessels have a completely

different cost structure from the new ones. Indeed, this relationship between

cost and age is one of the central issues in the shipping industry'. Another

factor that can affect the costs is the flag under which the vessel is sailing and

The relationship defines the slope of the short run supply curve.

33


the maintenance strategy of the company as well. The model used to fit the

operating cost series has the following form:

OCt = aet +ut

where, OCt= Operating Costs

t = Time Trend

The above exponential growth model is estimated over the period January

1990 to August 2001 using a non-linear least squares method. Table 2 gives

the coefficients for the exponential growth model, which are used to backcast

the data to year 1981. Actually, the exponential growth model was found to

have a very good goodness-of-fit. As we can see from table 2, the R 2's of the

model were high and the growth rate of the sample period was reasonable.

-2More precisely, the R 's are found to be 88%, 95%, and for the Handysize,

and Suezmax respectively, indicating a high degree of accuracy, with the-2

exception of the VLCC sector, where an R of 81 % is not so high.

Table 2: Estimates of Exponential Growth Model of Operating Costs for the Four Tanker Carriers

OC,= ae" +u,

Handysize Suezmax VLCC

A 80332.6 (1446.863) [65.033] 86041.6 (1376.958) [68.334] 90141.6 (2981.797 [31.8 (4683 [6.3] 8 (1795)[834 556]

0.00239 (0.0000807 [29,684] 0.00375 (0.0000752 [49.8761 0.00516 0.000160) [32.

6 ) 2 ) 6 371]

2 0.88 0.95 0.81

* Sample Period 1990:1 to 2001:8.

. Figures in (.) and [.1 are standard errors and t-statistics,

respectively.

34

Massachusetts Institute of TechnologyThe Four Shipping Markets: An Integrated Apvroach

Figure 1 plots the actual and estimated operating costs for the Aframax

vessels. It can been seen that, estimated values are closely tracked by actual

operating costs, and there is a constant exponential growth in the series. The

operating costs series calculated using the exponential growth model will be

considered as an aggregate level of costs incurred by the shipowners, and

later in the chapter will be used to calculate the operating profits for each size

of vessel. At this point we should mention that the results obtained might not

be so accurate as shipowners do not report the actual cost that they incur. So

the fitted operating costs may represent the aggregate level of costs incurred

by the shipowners but bear in mind that some shipowner may be willing to pay

more or less than that.

Figure 1: Estimated Monthly Operating Costs for the Four Tanker

Carriers

PANEL A - HANDY SIZE (40,00Dw t)

180000

160000

c 1400000

120000

oa 100000

80000

60000,82 84 86 88 90 92 94 96 98 00

- FITTED OC - ACTUAL OC

PANEL C - S UEZM AX (140,00ODwt)

250 000

200 000 .

1500 00 -

100 0 00.

A ,9 2 94 968 2 84 86 88 90

- ACT U A L 0 C I- FITT ED O C

50000

35

0

4)

CLt

98 0 0

Massachusetts Institute of TechnologyThe Four Shipoing Markets: An Integrated Approach

INTERPRETATION OF DATA RESULTS ON PRICES AND PROFITS

In the shipping industry, operating profits (earnings) at time t, !7t, can be

defined as the time-charter rates (TCt) less the operating costs (OCt):

HI, = TC, - OCt. Time-charter rates do not include voyage costs (paid by the

charterer), and thus are appropriate to use in calculating the operating profits

because they represent the net earnings from the chartering activities.

Descriptive statistics of newbuilding, second-hand and scrap prices, as well

as of operating profits for each of the three different tanker size carriers are

reported in table 2-Panel A. A quick glance at the results reveals that mean

levels of prices and profits are higher for larger vessels than for smaller ones.

In addition, mean levels of newbuilding prices are higher than mean levels of

second-hand prices and scrap prices for each of the four different size

vessels. Furthermore, looking at the unconditional volatilities (variances), we

can argue that prices for larger ships fluctuate more than prices for smaller

vessels, a result that is consistent with Kavussanos (1997). Moreover, we can

say that second-hand prices are the most volatile with the only exception the

case of handysize sector where newbuilding prices are the most volatile.

36

PANEL D - VLCC (250,00ODw t)

0

4Lf-

92 94 96 ' 98 0082 84 8 6 88 90

-- FITT ED O C -- A C T U A L OC


According to the coefficients of excess kurtosis -which measure the

peakedness or flatness of the distribution of the series- price series appear to

be platykurtic. As far as the operating costs are concerned, they also appear

to be platykurtic with the only exception of the VLCC operating costs which

appear appear to be leptokurtic. Jarque-Bera (1980) is a test statistic for

testing whether the series is normally distributed. The test statistic measures

the difference of the skewness and kurtosis of the series with those from the

normal distribution. Jarque-Bera tests indicate significant departures from

normality for all series. The Ljung-Box Q-statistic (Lung-Box 1979) at lag k is a

test statistic for the null hypothesis that there is no autocorrelation up to order

k. As it can be seen from the table, the Q-statistic for the 1st and 1 2 th order

autocorrelation in levels of prices and operating profit series are all significant,

indicating the presence of serial correlation in both price and profit series. The

ARCH LM test, is the Lagrange multiplier (LM) test for autoregressive

conditional heteroskedasticity (ARCH) in the residuals (Engle 1982). This

particular specification of heteroskedasticity was motivated by the observation

that in many financial time series, the magnitude of residuals appeared to be

related to the magnitude of recent residuals. Engle's ARCH tests for the 1st

and 12 th order ARCH effects indicate the existence of autoregressive

conditional heteroscedasticity in all price and profit series.

37


Table 2, Panel-B, reports the Phillips-Perron (1988) unit root tests. The test

fails to reject the test in levels, i.e. all variables are found to be non-stationary.

On the other hand, the test cannot reject the test in first differences, i.e.

stationarity is found. Therefore, it can be concluded that newbuilding, second-

hand, and scrap prices, as well as operating profits contain one unit root and

are in fact integrated of order one 1(1). Kavussanos (1997) concluded that

there are no seasonal patterns in the second-hand prices, and that prices are

1(1). Thus, our unit root tests are in fact consistent with the seasonal unit root

tests results of Kavussanos (1997).

Table 2: Summary Statistics Of Price & Profit Series

Panel A - Descriptive Statistics

Handysize N Mean Var. Skew. Kurtosis J-B Q0(1) Q(12) ARCH(1) ARCH(12

Newbuilding PNB 248 25.72 47.61 -0.62 1.95 27.14 249.03 2799.5 241.30 230.79Prices

[0.00] [0.00] [0.00] [0.00] [0.00]

Second-Hand pSH 248 16.21 22.47 -0.19 2.19 8.29 244.83 2347.4 223.35 215.25Prices

[0.01] [0.00] [0.00] [0.00] [0.00]

Scrap Prices PsC 248 1.40 0.14 0.75 2.76 23.60 230.18 2053.9 183.94 182.80

[0.00] [0.00] [0.00] [0.00] [0.00]

Operating Profits n 248 0.140 0.0049 -0.25 2.39 6.45 241.19 2092.3 228.05 221.42

[0.02] [0.00] [0.00] [0.00] [0.00]

Suezmax

Newbuilding PNB 248 46.76 141.37 -0.09 2.10 8.71 248.35 2704.2 237.37 227.30Prices

[0.01] [0.00] [0.00] [0.00] [0.00]

Second-Hand pSH 248 29.79 178.49 -0.54 1.77 27.48 247.98 2627.2 240.82 231.42Prices

[0.00] [0.00] [0.00] [0.00] [0.00]

Scrap Prices PSc 248 3.95 1.12 0.72 2.72 22.44 240.94 2150.7 230.31 221.26

[0.00] [0.00] [0.00] [0.00] [0.00]

Operating Profits n 248 0.250 0.0289 0.48 2.93 9.88 244.19 2011.8 215.34 212.81

[0.00] [0.00] [0.00] [0.00] [0.00]

38


NB

PNB 248 71.52 327.25 -0.41

pSH 248 43.21 492.40 -0.57

2.29 12.05

[0.00]

1.77 29.24

[0.00] [0.00] [0.00]

Scrap Prices PSC

Operating Profits r

248 5.60 2.30 0.76 2.81 24.02 242.93 2198.2 232.42 223.38

[0.00] [0.00] [0.00] [0.00] [0.00]

248 0.347 0.0361 0.63 3.28 17.40 236.74 1591.8 205.06 203.64

[0.00] [0.00] [0.00] [0.00] [0.00]

Panel B - Philips-Perron Unit Root Tests for Log Prices & Log Profits


Levels First Diff. Levels First Diff. Levels First Diff.

Newbuilding Prices pNB -0.98 -13.70 -1.19 -14.26 -1.11 -14.85

Second-Hand Prices pSH -1.46 -13.44 -0.84 -11.51 -0.95 -12.53

Scrap Prices psc -2.31 -19.74 -2.05 -15.52 -1.97 -14.51

Operating Profits n -1.12 -14.47 -1.81 -12.29 -2.17 -11.59

* The sample for Aframax price and profit series covers the period from January 1981 to August

2001.N is the number of observations, and the figures reported are in million dollars. Figures in

] are p-values.

* Skew and Kurt are the estimated centralised third and fourth moments of the data, denoted &3

and ( (X4 -3) respectively; their asymptotic distributions under the null are -5 ~ N(0,6)

and /T(i, - 3) ~ N(0,24).

" J-B is the Jarque-Bera (1980) test for normality; the statistic is

X2 (2) distributed. Q(1) and Q(12) are the Ljung-Box (1978) Q-

statistics on the 1st and 1 2 th order sample autocorrelation of the

series. These tests are distributed as X2(1) and X2(12),

respectively.

. ARCH(1) and ARCH(12) is the Engle (1982) test for ARCH

effects. The statistic is X2 distributed with 1 and 12 degrees of

freedom, respectively.

39

VLCC

Newbuilding

Prices

Second-Hand

Prices

248.12

[0.00]

247.87

2741.9

[0.00]

2672.8

236.31

[0.00]

242.48

(0.00]

226.22

[0.00]

232.62

[0.00]


The lag length for the Philips-Perron test is set at 12. All tests

include a constant, and the McKinnon critical values for the unit

root tests are -3.46, -2.87, -2.57 for 1%, 5%, and 10%

significance level respectively.

ESTIMATION RESULTS

First, we test the implication of the EMH regarding the unpredictability of 3-

month and 6-month excess holding period returns on shipping investments.

Second, we examine the implication of the EMH regarding the RVF by using a

present value model and in addition, we test the restrictions implied by the

EMH on the VAR model and variance ratio tests on spread series. However,

before doing that, the existence of cointegrating relationships between price

and operating profit series is studied. The important part of establishing any

cointegrating relationship between operating profit and price series, is that it

could rule out the existence of rational bubbles in ship prices (Diba and

Grossman 1988), and provide the necessary condition to set up the VAR

model.

UNPREDICTABILITY OF EXCESS HOLDING PERIOD RETURNS

Descriptive statistics of 3-month and 6-month excess holding period returns of

shipping investments over the market returns (FTSE 100) are reported in

table 3. In addition, table 3 provides the Ljung-Box (1978) Q-statistic tests for

1st and 12th order autocorrelation, the Engle (1982) test for 1st and 1 2th order

ARCH effects and the Phillips-Perron (1988) unit roots tests. Results indicate

that sample means of 3-month excess holding period returns are statistically

zero (with the exception of the 3-month excess holding period returns for the

VLCC vessels). On the other hand, means of 6-month excess holding period

returns for Handysize vessels are statistically zero, whereas 6-month excess

holding period returns for Suezmax and VLLC are significantly different from

zero. Furthermore, means of 6-month excess holding period returns are

higher than 3-month excess holding period returns. In addition, unconditional

volatilities (variance) of 6-month excess holding period returns seem to be

higher than those of 3-months excess returns for all sizes, which is in

40


accordance with the literature regarding asset pricing and risk-return

relationships (Markowitz 1959).

It is obvious from table 3 that both 3-month and 6-month excess holding

period returns for all size vessels are serially correlated which is an

implication of predictability in the series. Note that, this is inconsistent with the

EMH which requires the excess return series to be independent and

unpredictable. Nevertheless, the existence of autocorrelation in the excess

returns series can be explained by the following reason. The autocorrelation

in excess return series might be due to thin trading as the number of vessels

traded in three months is limited. Therefore, prices changes might not be

exclusively due to the arrival of news between successive trades (as required

by the EMH), but information from one trade might affect the next one.

Phillips-Perron unit root test results indicate that excess holding period returns

are in fact stationary, 1(0). Given that excess holding period return series are

stationary and autocorrelated, ARMA(p,q) models are fitted in each case

using Box-Jenkins methods. The AR(2) models, plus the MA(2) terms,

appropriate for the 3-month excess returns are shown in table 4 (note that if

the insignificant values are not reported). The MA(2) terms are incorporated in

the model because the horizon over which excess returns are calculated is

greater than the frequency of the observations (monthly). This is in

accordance to Hansen and Hodrick (1982) correction for overlapping data.

The same model is also used for the 6-month excess holding period returns,

where an AR(5) model and MA(5) terms are used. As we can see from table

4, the coefficients of determination, R 's, range between 66% and 70% for

the 3-month excess returns, and between 83% and 87% for the 6-month

excess returns. Therefore, we can conclude that there is a higher degree of

predictability in the 6-month excess return series than in the 3-month excess

return series, and this might be due to the higher number of MA terms

incorporated in the model used for the 6-month series.

41


Table 3: Summary Statistics of the Excess Returns in the Four Tanker Carriers

N Mean Var. Skew. Kurtosis J-B Autocorrelation ARCH

Handysize Q(1) Q(12) ARCH(1) ARCH(12)

3-Month exr3 245 0.00491 0.0187 -0.472489 5.146887 56.16733 125.72 174.11 90.96 114.26

[0.57] [0.00] [0.001 [0.00] [0.00] [0.01]

6-Month exr6 242 0.01004 0.0412 -0.324835 4.259166 20.24302 173.30 380.22 122.63 135.45

[0.44] [0.00] [0.00] [0.00] [0.00] [0.00]

Suezmax

3-Month exr3 245 0.01252 0.0148 0.202677 3.478921 4.018787 135.11 191.80 86.84 100.72

[0.111 [0.13] [0.00] [0.00] [0.00] [0.00]

6-Month exr6 242 0.02622 0.0342 0.431222 3.847178 14.73698 182.72 421.35 135.84 147.16

[0.02] [0.00] [0.00] [0.00] [0.00] [0.00]

VLCC

3-Month exr3 245 0.02544 0.0210 0.201585 4.977612 41.58357 127.11 229.38 50.66 95.94

[0.00] [0.00] [0.00] [0.00] [0.00] [0.00]

6-Month exr6 242 0.04967 0.0524 0.532731 3.890990 19.45147 185.55 554.82 147.02 160.63

[0.00] [0.00] [0.00] [0.00] [0.00] [0.00]

Philips-Perron Unit Root Tests


Levels First Diff. Levels First Diff. Levels First Diff.

3-Month exr3 -6.51 - -5.37 - -6.19 -

6-Month exr6 -5.15 - -3.94 - -4.28 -

* The sample for Aframax, price and profit series covers the period from January 1981 to August 2001.

* Figures in [ ] are p-values.

* Skew and Kurt are the estimated centralised third and fourth moments of the data, denoted &3 and

(X 4 -3) respectively; their asymptotic distributions under the null are -.I& 3 ~ N(0,6)

and J(i 4 - 3)- N(0,24).

* J-B is the Jarque-Bera (1980) test for normality; the statistic is X2(2) distributed.

Q 0(1) and Q(12) are the Ljung-Box (1978) Q-statistics on the 1 s and 1 2 " order sample autocorrelation

of the series. These tests are distributed as X2(1) and X2(12), respectively.

* ARCH(1) and ARCH(12) is the Engle (1982) test for ARCH effects. The statistic is X2 distributed with 1

and 12 degrees of freedom, respectively.

* The lag length for the Philips-Perron test is set at 12.

42


. All tests include a constant, and the McKinnon critical values for the unit root tests are -3.46, -2.87, -

2.57 for 1%, 5%, and 10% significance level respectively.

Table 4: Predictability of Excess Returns on Shipping Investments

p qexr, =a0 + aexr,+2fs, +c, , ,~ -iid(,a2)

i=I :1=1


3-month 6-month 3-month 6-month 3-month 6-month

-0.0018 0.0203 0.0020 0.0202 0.0058 0.0457

ao (0.0157) (0.0339) (0.0141) (0.0348) (0.0142) (0.0380)

[0.9070] [0.5498] [0.8875] [0.5622] [0.6811] [0.2301]

0.0468 0.1077 0.0821 0.1220 -0.0116 0.4757

al (0.0678) (0.0734) (0.0654) (0.0690) (0.0651) (0.0709)

[0.0490] [0.0143] [0.0210] [0.0786] [0.0758] [0.0000]

-0.0690 0.0145 0.2250

a2 - (0.0742) - (0.0650) - (0.0886)

[0.0349] [0.0529] [0.0118]

0.1310 0.1619 0.2164

a3 - (0.0754) - (0.0691) - (0.0900)

[0.0717] [0.0201] [0.0171]

-0.0178 -0.3439

a 4 - (0.0773) - - - (0.0683)

[0.0817] [0.0000]

a5 - - - - - -

0.9603 0.0861 1.0148 1.0315 1.0048 0.4717

1 (0.0244) (0.0361) (0.0049) (0.0285) (0.0062) (0.0457)

[0.0000] [0.0000] [0.0000] [0.0000] [0.0000] [0.0000]

0.9374 0.9697 0.9799 0.9562 1.0071 0.3569

p2 (0.0230) (0.0294) (0.0001) (0.0277) (0.0086) (0.0586)

[0.0000] [0.0000] [0.0000] [0.0000] [0.0000] [0.0000]

0.8312 0.8634 -0.1085

3 - (0.0418) - (0.0247) - (0.0406)

[0.0000] [0.0000] [0.0081]

0.9041 0.8482 0.4858

p4 - (0.0348) - (0.0288) - (0.0474)

[0.0000] [0.0000] [0.0000]

0.8293 0.8704 0.4638

p3s - (0.0294) - (0.0277) - (0.0588)

[0.0000] [0.0000] [0.0000]

-2R 0.66 0.84 0.70 0.87 0.68 0.83

43


Q(1) 0.2753 [0.0001 0.1548 [0.000] 0.1144 [0.000] 0.1745 [0.000] 0.0205 [0.000] 1.5362 [0.000]

Q(12) 9.3866 [0.000] 38.586 [0.000] 7.2272 [0.512] 4.6193 [0.099] 12.181 [0.143] 39.751 [0.000]

ARCH(1) 5.9903 [0.014] 13.373 [0.0001 0.5144 [0.473] 0.0209 [0.884] 0.6403 [0.424] 0.0784 [0.779]

ARCH (12) 24.927 [0.015] 62.065 [0.000] 1.7298 [0.062] 1.9117 [0.034] 2.7075 [0.001] 5.8157 [0.000]

J-B 56.01 [0.0000] 31.86 [0.0000] 6.36 [0.0414] 6.26 [0.0435] 184.42 [0.00] 229.03 [0.00]

AIC -2.19 -1.87 -2.54 -2.51 -2.12 -1.79

* The sample for the price and profit series covers the period February 1980 to December 1998.

* The figures in (.) and [.] are standard error and probability values, respectively.

* The lag length for each model is chosen in order to minimise the AIC.

Q Q(1) and Q(12) are Ljung-Box tests for 1st and 12th order serial correlation in the residuals.

* ARCH(1) and ARCH(12) are F tests for 1st and 12h order autoregressive conditional heteroscedasticity.

* J-B is the Jarque- Bera (1980) test for normality.

COINTEGRATION TESTS

Given a group of non-stationary series, we may be interested in determining

whether the series are cointegrated, and if they are, in identifying the

cointegrating (long-run equilibrium) relationships. The existence of a long run

cointegrating relationship between prices and operating profits is investigated

using the Johansen (1988) cointegration method. The results are reported in

table 5. The lag length for the VECM models are determined alongside the

deterministic parts (constant and trend) using the Akaike Information Criterion

(AIC).

In the case of Handysize, the Atrace rejects the null hypothesis for all price

series except in the case of scrap price series. In the case of Suezmax, the

Atrace test statistic rejects the null hypothesis of there being no cointegrating

vector for all price series. Finally, in the case of VLCC, only second-hand and

scrap price series are cointegrated with the profit series, whereas the opposite

holds for the case of newbuilding price series. Note that even at the 95% or

99% significance level, the picture does not change dramatically. As a result,

we could say that the Atrace test statistic indicates the existence of long run

relationships between prices (newbuilding, second-hand, and scrap) and

operating profits for each size, although results are not very clear for scrap

prices of Handysize vessels, and newbuilding prices of VLCC vessels. As we

mentioned earlier, the Atrace test statistic does not reject the null hypothesis of

there being no cointegrating vector, against the alternative of there being one

44


cointegrating vector at even the 90% significance level. However, we could

use the Engle-Granger two-step method to confirm that these price series are

in fact cointegrated with operating profits.

Table 5:Cointegration Test For Prices and Operational Profits

q q

Ap,= aj,6p,_, b-1_ y(p_+0 +00)+61-,

q

qAn,~ =Zc,4O, +ZdjA~c, y 2 (Pt-1 +0 7y1- 00 )+F 2 ,f=1 =

Normalised Xtrace Ltrace Xtrace XtraceParo La Likelihoo 90 95 9%

Parae Cointegrating H o 90% 95% 99%Variables gs Vector HA CV's CV's CV's

Handysize

pNB 369 26.04 17.88 19.96 24.60

4.070] r=1 1.41 7.53 9.24 12.97

r 1

r=2

pSH and c q=2 [1 -0.322 - r=0 21.66 17.88 19.96 24.60

3.487] r=1 2.20 7.53 9.24 12.97

r 1

r=2

pSC and n q=4 [1 -0.257 - r=0 13.54 17.88 19.96 24.60

0.889] r=1 3.35 7.53 9.24 12.97

r 1

r=2

Suezmax

45

,


pNBp N and n q=3 [1 -0.296 -4.353]

pSH and t q=2 [1 -0.578 -

4.283]

pSC and iT

VLCC

pNB

pSH and n

q=3 [1 -0.308 -

1.902]

q=3 [1 -1.024 -

5.415]

q=3 [1 -2.043 -

5.909]

r0O

r=1

r 1

r=2

r=0

r=1

r 1

r=2

r=0

r=1

r 1

r=2

r0O

r=1

r 1

r=2

r=0

r=1

pSC and aT q=1 [1 -0.791

2.600]

r 1

r=2

- r=0r=1

r 1

r=2

* The appropriate number

AIC.

of lags in each case is chosen so as to minimise

* trace = -T log(1 - ,) tests the null that there are at most r cointegrating,=r-4I

vectors against the alternative that the number of cointegrating vectors is

greater than r, where n is the number of variables in the system (n=2 in

this case).

* Critical values are from Osterwald-Lenum (1992).

46

20.00

1.11

40.15

1.71

18.70

4.68

11.87

1.74

20.57

1.71

17.88

7.53

17.88

7.53

17.88

7.53

17.88

7.53

17.88

7.53

19.96

9.24

19.96

9.24

19.96

9.24

19.96

9.24

19.96

9.24

24.60

12.97

24.60

12.97

22.61

7.55

17.88

7.53

19.96

9.24

24.60

12.97

24.60

12.97

24.60

12.97

24.60

12.97


Indeed, we regress the price series (handysize scrap price series and VLCC

newbuilding price series) on the operating profits series and we look to see if

the residuals of the regression technique are actually stationary. Thus, we

perform unit root test on the residuals. Note that, the critical values of the

Engle-Granger test for cointegration when the regression contains a constant

are, -3.96, -3.37, and -3.07 for the 90%, 95% and 99% confidence interval

respectively. The results that we found are: -3.004 for the relationship

between Handysize scrap price and profits series, and -1.706 for the VLCC

newbuilding price and profits series. Thus, all the residuals series are

stationary indicating cointegration relationships. In short, by using the Engle-

Granger method we find that Handysize scrap price series as well as VLCC

newbuilding price series are in fact cointegrated with the operating profits

series for each sector respectively.

Table 6 reports the estimated VECM models along with diagnostic tests for

Handysize vessels. It can been seen that the coefficients of error correction

terms in price equations are negative and significant at the 5% level, with the

exception of the scrap market in which the coefficient is negative but not

significant. Coefficients of the error correction terms in profit equations are all

positive and significant. The fact that these coefficients have opposite signs

indicates that both variables respond to any disequilibrium in order to bring

the system back to equilibrium. Estimated VECM models for Suezmax and

VLCC price and profit series are reported in tables 7 and 8 respectively. The

situation is not so clear in the case of Suezmax and VLCC VECM models.

When newbuilding price series are considered, we can observe similar

patterns as the VECM models of Handysize. In the case of second-hand and

scrap price series though -for both Suezmax and VLCC vessels- the picture

is not so clear.

47


Table 6: Estimated VECM of Handysize Prices & Profits

q q

Ap, = aAp,,+ Zbi,_A , +y 1(p,_ +0 ,_, +00)+s,,

qq

A , = cAp,_,+ dAn,_+ Y 2(P,_, +07t,_ +0 0)+s 2,11 i=1

Newbuilding-price and operating Second-hand price and Scrap-price and operating

profit equations operating profit equations profit equations

Apt Ant, Apt At Apt Air,

ECT 1

AnttI

R-bar squared

-0.0262

(0.0060)

-4.3582

0.0042

(0.0035)

1.1861

0.1580

(0.0634)

2.4908

-0.0027

(0.0036)

-0.7610

0.0063

(0.0640)

-0.0990

-0.0045

(0.0035)

-1.2604

0.0430

(0.0644)

0.6681

-0.0030

(0.0033)

-0.9011

0.0587

0.0631

0.9302

0.206

0.2743

(0.1242)

2.2075

-0.2340

(0.0741)

-3.1576

0.1330

(1.3091)

0.1016

0.0001

(0.0754)

0.0016

-0.5954

(1.3226)

-0.4502

0.0894

(0.0741)

1.2075

1.0745

(1.3303)

0.8077

0.0468

(0.0690)

0.6785

0.0906

(1.3033)

0.0695

0.114

-0.0524

(0.0127)

-4.1048

-0.0103

(0.0086)

-1.1995

0.1263

(0.0653)

1.9338

-0.0051

(0.0080)

-0.6478

0.1312

(0.0658)

1.9935

0.096

0.3029

(0.1063)

2.8481

-0.2066

(0.0715)

-2.8876

1.0885

(0.5434)

2.0031

-0.0101

(0.0667)

-0.1523

0.1666

(0.5477)

0.3043

0.137

-0.0301

(0.0171)

-1.7569

-0.0007

(0.0100)

-0.0726

-0.1549

(0.0657)

-2.3567

0.0087

(0.0103)

0.8443

-0.0065

(0.0644)

-0.1020

0.0159

(0.0102)

1.5521

0.1326

(0.0645)

2.0558

0.0032

(0.0097)

0.3285

0.0837

(0.0639)

1.3082

0.068

0.3000

(0.1149)

2.6104

-0.2690

(0.0670)

-4.0157

-0.7633

(0.4402)

-1.7340

-0.0260

(0.0692)

-0.3760

-0.5893

(0.4316)

-1.3653

0.0657

(0.0689)

0.9547

-0.2234

(0.4320)

-0.5171

0.0471

(0.0653)

0.7225

0.1312

(0.4285)

0.3062

0.127

48

Ant-2

Apt-2

Ant-3

Apt-3

APM


LB-Q(1)

LB-Q(12)

ARCH(1)

ARCH(12)

J-B

0.0040

[0.949]

4.0354

[0.983]

1.792

[0.181]

1.040

[0.413]

111.1

[0.000]

0.0155

[0.901]

13.496

[0.334]

0.014

[0.903]

0.119

[0.999]

149653

[0.000]

0.1705

[0.680]

12.257

[0.425]

2.149

[0.143]

2.694

[0.002]

553.4

[0.00]

0.0114

[0.915]

21.761

[0.040]

0.0038

[0.950]

0.1387

[0.999]

136971

[0.00]

0.0040

[0.9501

5.3413

[0.946]

39.280

[0.000]

3.9598

[0.000]

4455.4

[0.00]

0.0202

[0.887]

15.328

[0.224]

0.0150

[0.902]

0.1089

[0.999]

139745

[0.00]

AIC -3.46 -1.86 j -1.24

* The figures in (.) and [.] are standard errors and values in bold are the t-observed values, respectively.

" The lag length for each model is chosen in order to minimise the AIC.

* Q(1) and Q(12) are Ljung-Box tests for 1st and 12th order serial correlation in the residuals, 5% critical values for

these statistics are 3.84 and 21.03, respectively.

* ARCH (12) is the Ljung-Box test for 12th order serial correlation in the squared residuals, 5% critical value for

this statistic is 21.03.

* J-B is the Jarque- Bera (1980) test for normality. The 5% critical value for this statistic is X (2)=5.99.

Table 7: Estimated VECM of Suezmax Prices & Profits

q q

Ap, = ajhp,~ +ZbjA7E,_, +y ,(p, +07c,_,+00 )+F- ,i=I 1=1

q q

on ~ P,_,+ Zd~AEI,_+Y 2( P,- +07E,_I +00o)+62.,i=1 i=1

Newbuilding-price and operating Second-hand price and Scrap-price and operating

profit equations operating profit equations profit equations

Apt At Apt Antt Apt At

ECTtI1

Apt.2

Ant-3

Apt-3

-0.0121

(0.0079)

-1.5377

-0.0053

(0.0048)

-1.0953

0.1430

(0.0644)

2.2203

-0.0014

(0.0049)

-0.2887

0.0648

(0.0650)

0.9978

0.0062

(0.0048)

1.2705

-0.0181

(0.0644)

-0.2816

0.4162

(0.1051)

3.9598

0.0365

(0.0648)

0.5625

0.5485

(0.8554)

0.6412

0.0838

(0.0650)

1.2885

0.3602

(0.8632)

0.4173

0.1515

(0.0649)

2.3330

0.6741

(0.8564)

0.7871

0.0371

(0.0093)

3.9965

0.0137

(0.0083)

1.6528

0.2269

(0.0677)

3.3522

0.0119

(0.0081)

1.4635

-0.0093

(0.0670)

-0.1390

0.4138

(0.0742)

5.5729

0.0712

(0.0665)

1.0719

-0.2536

(0.5407)

-0.4689

0.0909

(0.0654)

1.3900

0.1259

(0.5356)

0.2351

0.0029

(0.0113)

0.2620

0.0044

(0.0089)

0.4978

0.0467

(0.0634)

0.7361

0.0110

(0.0089)

1.2407

0.0029

(0.0634)

0.0469

0.0065

(0.0089)

0.7352

0.0947

(0.0636)

1.4905

0.3052

(0.0815)

3.7438

0.0163

(0.0639)

0.2556

0.0833

(0.4547)

0.1832

0.0591

(0.0639)

0.9258

-0.5870

(0.4543)

-1.2922

0.1186

(0.0639)

1.8564

-0.0030

(0.4556)

-0.0066

49

Apt-,


R-bar squared

LB-Q(1)

LB-Q(12)

ARCH(1)

ARCH(12)

J-B

AIC

See note in Table 6.

0.049

0.0173

[0.895]

19.020

[0.088]

0.1359

[0.712]

0.3042

[0.988]

1853.1

[0.000]

0.074

0.3001

[0.584]

19.298

[0.082]

6.2026

[0.013]

2.7299

[0.001]

37089

[0.000]

-3.30

Table 8: Estimated VECM of VLCC Prices & Profits

q q

Ap, =ZajAp,_, + bAat, +y 1 (p,_ +0t,_, +Oo)+s ,1=1 i=1

q q

A p,=XcAp, + dAn,_, +y 2(P,- 1 +OTIt +0 0)+e 2 ,i=1 i=1

Newbuilding-price and operating Second-hand price and Scrap-price and

profit equations operating profit equations operating profit

equations

Apt Antt Apt Antt Apt At

ECTt-1

Ant-2

Apt-3

-0.0074

(0.0047)

-1.5713

0.0111

(0.0164)

0.6809

0.0834

(0.0647)

1.2883

-0.0229

(0.0166)

-1.3807

0.1929

(0.0638)

3.0237

0.0145

(0.0166)

0.8773

0.0136

(0.0655)

0.2080

0.0479

(0.0185)

2.5799

0.1887

(0.0646)

2.9179

0.1587

(0.2552)

0.6220

0.0070

(0.0655)

0.1072

0.6233

(0.2515)

2.4781

0.0183

(0.0654)

0.2799

0.2083

(0.2583)

0.8066

0.0058

(0.0081)

0.7176

0.0587

(0.0378)

1.5503

0.0601

(0.0655)

0.9166

0.0739

(0.0388)

1.9039

0.1313

(0.0648)

2.0267

0.0800

(0.0388)

2.0602

0.0561

(0.0647)

0.8671

0.0577

(0.0137)

4.2131

0.2204

(0.0636)

3.4625

0.2086

(0.1103)

1.8912

0.0401

(0.0652)

0.6152

0.1153

(0.1090)

1.0580

0.0276

(0.0653)

0.4231

0.0164

(0.1089)

0.1509

0.0180

(0.0098)

1.8309

0.0803

(0.0285)

2.8131

0.0678

(0.0656)

1.0328

0.0799

(0.0216)

3.6942

0.2005

(0.0627)

3.1962

-0.1060

(0.1442)

-0.7352

50

0.168

0.0134

[0.908]

17.636

[0.127]

0.4047

[0.525]

3.2848

[0.002]

1157.4

[0.000]

0.138

0.0787

[0.779]

21.967

[0.038]

37.607

[0.000]

8.1329

[0.000]

20776

[0.000]

0.024

0.0006

[0.980]

4.1286

[0.981]

5.1338

[0.024]

1.0473

[0.4066]

78.953

[0.000]

0.069

0.2625

[0.608]

23.668

[0.023]

6.2441

[0.0131]

2.8115

[0.0013]

64.097

[0.000]

-2.49 -2.05

'


R-bar squared 0.076 0.085 0.096 0.137 0.058 0.085

LB-Q(1) 0.0000 0.0000 0.0066 0.0072 0.0045 0.0004

[0.994] [0.995] [0.935] [0.932] [0.947] [0.985]

LB-Q(12) 18.621 11.126 21.816 12.365 3.8960 12.620

[0.098] [0.518] [0.040] [0.417] [0.985] [0.397]

ARCH(1) 0.7737 0.8372 2.3466 1.3952 0.0011 1.2303

[0.379] [0.361] [0.126] [0.238] [0.972] [0.268]

ARCH(12) 0.8342 0.9807 4.6479 1.1234 0.3633 0.9940

[0.615] [0.468] [0.000] [0.342] [0.974] [0.455]

J-B 13.179 281.57 1320.8 406.81 209.21 297.79

[0.000] [0.000] [0.000] [0.000] [0.000] [0.000]

AIC -5.92 -4.33 -4.84

See note in Table 6.

The fact vessel prices and operating profits are 1(1) and cointegrated also

rejects the existence of rational bubbles (see Diba and Grossman 1988).

Therefore, the existence of rational bubbles in the formation of ship prices can

be ruled out as suggested by cointegration tests. Rejecting the existence of

rational bubbles in price formation is important, as failure of the EMH and RVF

in asset pricing, i.e. permanent deviations of actual prices from the theoretical

prices, can be due to the existence of such bubbles.

RESTRICTIONS ON THE VAR MODEL AND VARIANCE RATIO TESTS

Following Campbell and Shiller (1988), we consider SNB, ) (or S,H)), 7rrt and

Sscn) (or S(SH,)) to be generated by a pth order trivariate VAR model. The

general VAR model results for the combinations of "newbuilding/second-

hand", "newbuilding/scrap" and "second-hand/scrap" prices for three different

sizes of dry bulk carriers are in Tables 9, 10 and 11, respectively 2. The GMM

estimation method is used, while standard errors of the estimated parameters

are corrected for serial correlation and/or heteroscedasticity using the Newey-

West (1987) method. A lag length of one is used in all cases, chosen by AIC.

2 In the case of "newbuilding/second-hand", the present value model implies that the newbuilding price is equal tothe DPV of operating profits for the next five years plus the DPV of the second-hand price five years later. In thecase of "newbuilding/scrap", the present value model implies that the newbuilding price is equal to the DPV ofoperating profits for the entire economic life of the vessel (i.e. 20 years) plus the DPV of her scrap price at the endof this period. Similarly, for "second-hand/scrap" model, the present value model implies that the second-hand

51


For each VAR model (for each different size of tanker carrier), coefficients of

the lagged variables along with their respective standard errors and p-values

are reported in the first block of the table. For example, the first, second and

third blocks on the top of Table 9, report coefficients of the lagged spread

between newbuilding prices and operating profits, S(NB,"), the lagged

difference between changes in log profits and log returns, irrt, and the lagged

spread between second-hand prices and operating profits, SsH , for each of

the three equations in the VAR model (for VLCC, Suezmax, and handysize

vessels, respectively).

Lagged coefficients of the first spread series are found to be close to one,

which is an indication of high persistence degree in every case, except for the

Suezmax, and Handysize equation when the combination of second-hand and

scrap prices (model 3) are considered (table 11). Coefficients of

determination, R2's, for equations explaining the spread series are high, and

are in the range of 90%.

Table 9: Results of the 3 variable VAR model: Newbuilding and Second-hand

prices

S - NB,n) B + +n , t SI"') + 1,11=1 i=1 5=1

7tr, = p ZTJi" ZPjE,- JPjT 6,

S(S, aB) ) 2, t-i3,S H si=1 i=I i=1

VLCC Suezmax Handysize

S NB,n ar S(SH,7) NB,7c) r S(SH ) SNB,i nrt Sr"0

52

price of the vessel is equal to the DPV of operating profits from operating the vessel for her entire economic life(i.e. 15 years) plus the DPV of her scrap price in 15 years time.


S(NB n

0.947

(0.018

)[0.000

I

0.20

9

(0.0

76)

[0.0

06]

-0.027

(0.015

)[0.068

1

1.184

(0.127

)[0.000

I

-0.039

(0.101

)[0.693

I

0.220.044 0.041 -0.204 0.038

8(0.017 (0.015 (0.126 (0.101

(0.072)

[0.013 [0.008 [0.107 [0.706[0.001]

StsH,n)

R-bar

squared

ARCH(12)

AIC

-0.061

(0.024

)[0.013

]

0.15

2

(0.0

75)[0.0

44]

0.932

0.933

2.005

1.741

[0.025]

[0.060]

0.955

(0.019

)[0.000

]I

0.075

1.292

[0.225]

-4226.43

0.176

(0.125

)[0.159

1

-0.016

(0.101

)[0.867

]

0.881

0.786

6.681

7.370

[0.000]

[0.000]

-0.369

(0.311

)[0.235

1

0.395

(0.309

)[0.202

]

0.657

(0.305

)[0.032

]

0.105

6.932

[0.000]

-3782.11

1.26 0.25 -0.345

5 6

(0.1 (0.0 (0.164)

65) 70)

[0.0 [0.0 [0.032]

00] 00]

- - 0.368

0.28 0.25

7 0 (0.164)

(0.1 (0.0

65) 70) [0.025]

[0.0 [0.0

83]

0.32

5

(0.1

66)

[0.0

51]

00]

0.24 0.583

6

(0.0

67)

[0.0

00]

(0.165)

[0.000]

0.795 0.112

0.777

0.094 0.093

0.093

[1.000] [1.000]

[1.000]

-3712.79

53

Wald tests Statistics p-value Statistics p-value Statistics p-value

DF DF DF

Massachusetts Institute of TechnologyThe Four ShiDpine Markets: An Integrated Approach

5.196 [0.157] 4.269 [0.233] 6.966 [0.072]

3 3 3

Var ratio Var(as)Nar(ts) t- Var(as)Nar(ts) Var(as)Nar(ts) t-

tests Observed t-Observed Observed

0.512 1.471 1.432

-1.72 1.92 4.11

* The figures in (.) and [.] are standard errors and probability values,

respectively.

* sNB.-) and sJsH") are spread series between logs of newbuilding prices and

logs of operating profits, and second-hand prices and operating profits,

respectively. ar, = An - r,, represents the difference between changes in log

profits and log returns.

* VAR models are estimated by non-linear GMM. The standard errors are

corrected for serial correlation and/or heteroscedasticity using the Newey-

West method.

* The lag length for each model is chosen in order to minimise the AIC.

* ARCH(12) is the F test for 12th order ARCH.

" Wald tests are nonlinear cross equation restrictions of equation (34),

el= e2A(I- pA)~'(I- p"A")+ p"e3A, implied by the EHM on the VAR model.

They have chi-square distributions with degrees of freedom equal to the

number of restrictions. This is 3 in all cases.

* Var(as)Nar(ts) represent the variance ratio of the actual and the theoretical

spread series, respectively. T-observed is the given by

t - observed= Var(as)/Var(ts) --1 and is used for the null hypothesis of the varianceS.E.

ratio equals 1.

Variance ratio tests are also performed in order to provide additional evidence

on testing the validity of the EMH on the formation of tanker prices. We

perform the one side hypothesis test where: the null hypothesis that the

variance ratio equals one, against the alternative hypothesis that that variance

ratio exceeds unity. The t-critical value for the test at a 95% confidence

interval is 1.645.

54


Results of the VR tests for the model with combination of

"newbuilding/second-hand" prices are illustrated at the bottom of table 9. The

t-observed values are -1.72, 1.92, and 4.11 for VLCC, Suezmax, and

Handysize models respectively. Comparing these values with the t-critical

value of 1.645 we can see that the null hypothesis that the variance ratio

equals one can be rejected in the case of Handysize equation, indicating

some support of the EMH. In the case of VLCC and Suezmax the null

hypothesis cannot be rejected indicating evidence against the EMH.

Results for the model with combination of "newbuilding/scrap" prices are

illustrated at the bottom of table 10. The t-observed values are -2.98, -1.52,

and 1.42 for VLCC, Suezmax, and Handysize models respectively.

Comparing these values with the t-critical value of 1.645 we can see that the

null hypothesis that the variance ratio equals one can not be rejected in all

cases indicating evidence against the EMH.

Results of the VR tests for the model with combination of "second-hand/scrap"

prices are illustrated at the bottom of table 11. The t-observed values are

0.75, -2.04, and 2.09 for VLCC, Suezmax, and Handysize models

respectively. Comparing these values with the t-critical value of 1.645 we can

see that the null hypothesis that the variance ratio equals one can be rejected

only in the case of Handysize equation, indicating some support of the EMH.

In all the other cases the null hypothesis cannot be rejected indicating

evidence against the EMH.

Results of nonlinear cross equation restrictions implied by the EMH and the

present value model on the VAR model for "newbuilding/second-hand", are

also presented at the bottom of table 9. Wald test statistic values are 5.196,

4.269, and 6.966 for VLCC, Suezmax, and Handysize models respectively.

The results for VLCC, Suezmax, and Handysize indicate that the EMH cannot

be rejected at the 5% significance level.

55


Table 10: Results of the 3 variable VAR model: Newbuilding and Scrap prices

SI NB,.) NBx)+ l -n + 3, ,,1=1 = =

Ut 1, i B ) 2,I' t-i 3i- iS

1=11

5SsH, ) - X (Bx)+X 2 ,i t- +X 3 , , 3 ,t1=1 i=I 1=1


S(NB,T ) S (SHn) s(NBit) t (SH, ) s NBiE S(SHnF)

0.983 0.18

(0.027 7

) (0.0[0.000 75)

[0.0

13]

0.19-0.005

6(0.026 (0.0

70)[0.848 [0.0

05]

0.09

6

(0.0

79)

[0.2

25]

-0.043

(0.026

[0.098

]

0.059

(0.025

)[0.019

I

0.948

(0.025

)[0.000

I

0.065

0.926

0.963

(0.082

[0.000

I

0.005

(0.083

)[0.952

]

-0.004

(0.083

)[0.960

I

-0.011

(0.143

[0.933

]

0.006

(0.146

)[0.962

]

-0.001

(0.150

)[0.989

I

0.871

-0.029

(0.062

[0.643

0.057

(0.063

)[0.366

]

0.945

(0.062

)[0.000

I

0.019

0.882

0.94

3

(0.048)

[0.000]

0.25

9

(0.0

78)

[0.0

01]

0.020.25

44

(0.0 (.~yJ (0.049) 79)

[0.6 [0.012] 01]

-0.025

(0.047)

[0.591]

0.048

(0.048)

[0.319]

- 0.25 0.9450.25

0.02 2 (0.050)

1 [0.000](0.0 (0.0

5)72)[0.0

[0.6

80]

0.791 0.098

0.816

56

S(NB,I)

S(sH,)

R-bar

squared

0.019

(0.026

)[0.460

]

0.923

---------- - -------------- ---. t


1.577 0.839

0.988

[0.100] [0.611]

[0.462]

-4386.04

2.857

[0.001]

2.739

2.845

[0.001]

[0.002]

-3651.38

0.102 0.100

0.109

[1.000] [1.000]

[1.000]

-3583.21


DF DF DF

7.841 [0.04] 10.47 [0.014] 11.02 [0.011]

3 3 3



0.737 0.912 1.142

-2.98 -1.52 1.42

* See notes in Table 9.

* s(NB,)and S(sc,) are spread between logs of newbuilding prices and logs of

operating profits, and scrap prices and operating profits, respectively.

* Var(as)Nar(ts) represent the variance ratio of the actual and the theoretical


t -observed= Var(as)/Var(ts) -1 and is used for the null hypothesis of the varianceS.E

ratio equals 1.

Results on the VAR model for "newbuilding/scrap", are presented at the

bottom of table 10 Wald test statistic values are 7.841, 10.47, and 11.02 for

VLCC, Suezmax, and Handysize models respectively. The Wald test can

reject the validity of the EMH at the 5% confidence interval in all cases.

Finally, in the case of "second-hand/scrap" price model, table 11, Wald test

statistics indicate that the restrictions implied by the present value model and

the EMH on the VAR model are rejected at the 5% significance level for all

size of vessels except for Suezmax. Table 12, illustrates a summary of both

the variance ratio tests and Wald tests results.

57

ARCH(12)

AIC


Table 11: Results of the 3 variable VAR model: Second-hand and Scrap Prices

S NBn) N , +3,S> n

1= =1 1 =1

S [s ) X1 SB")+Z 2,ln , +2 Z- 1 3,AS +3

i= l i=1 =1sLC CB) e2,ia-i d3,iySHs e,


S(NB,ic) a SSH ,i ) SNB,n ) s O( SH ,rl) s( NB,n s (SH ,U)

0.95

(0.01

[0.00

I

0.04

(0.01

)[0.00

]

-0.035

(0.016

)[0.029

]

1 0.12 -0.050

9 5 (0.020

(0.0 )0 73) [0.014

[0.0 187]

0.219 0.068

75 (0.016

(0.0

69)1[0.0 [0.000

01]

0.11

9

(0.0

79)[0.1

32]

0.932

0.953

(0.018

)[0.000

I

0.112

0.928

0.635

(0.323

[0.050

]

0.399

(0.327

)[0.224

]

-0.372

(0.330

)[0.260

]

-0.031

(0.090

[0.730

]

0.053

(0.091

)[0.561

]

-0.045

(0.096

)[0.638

]

0.787

0.891

0.182

(0.130

[0.163

-0.195

(0.132

)[0.141

]

1.181

(0.134

)[0.000

]

0.104

0.78

7

(0.0

91)

[0.000]

0.15

2

(0.0

91)

[0.0

96]

0.23

7

(0.0

70)

[0.0

00]

0.112

(0.087)

[0.200]

0.24 0.064

4

(0.0

73)

[0.0

01]

0.240.15

21

(0.0(0.0 66)

93) [0.0[0.1

04] 00]

0.775

0.817

(0.087)

[0.456]

1.060

(0.088)

[0.000]

0.104

58

S(NB,.)

S ,s,)

R-bar

squared

......... - -------------- ------- 4 ----------- ------------------ - ------ -- . ......... . ......


ARCH(12)

AIC

1.532

1.382

[0.114]

[0.176]

1.223

[0.269]

-3979.01

7.561

6.349

[0.000]

[0.000]

6.968

[0.000]

-3421.54

0.096

0.102

[1.000]

[1.000]

0.093

[1.000]

-3159.34


DF DF DF

11.13 [0.011] 4.041 [0.256] 22.43 [0.000]

3 3 3



1.316 0.744 1.260

0.75 -2.04 2.09

* See notes in Table 9.

* S(sH-) and ssc) represent spreads between logs of second-hand prices

and logs of operating profits, and logs of scrap prices and logs of operating

profits, respectively.

" Var(as)Nar(ts) represent the variance ratio of the actual and the theoretical


t - observed= Var(as)/Var(ts) -I and is used for the null hypothesis of the varianceS.E

ratio equals 1.

CONCLUSION

Overall, the results of the Wald and the variance ratio tests reject the validity

of the EMH in the formation of newbuilding and second -hand prices.

Nevertheless, some inconclusive results are found in the case of

"newbuilding/second-hand" and "second-hand/scrap" models whereas Wald

tests and variance tests seem to diverge.

It should also be mentioned here that a further insight to the failure of the

present value model and the EMH in the tanker market can be gained if we

take into consideration the heterogeneous behaviour of investors in this

59


sector. Investors in the shipping industry can have different investment

strategies and horizons. According to this, investors can be divided into two

main categories. The first group of investors are those who participate in the

sale and purchase market and rely mainly on capital gains rather than

operational profits. This group of investors is known as asset players. The

second group of investors is more interested on operational profits rather than

capital gains and they have long-term investment horizons, i.e. they acquire a

vessel and operate it for long period of time. As a result, the fact that investors

in the shipping industry have heterogeneous behaviour may contribute to the

failure of both the present value model and EMH in the formation of vessel

prices.

A very important conclusion is that in the case where we use as terminal

value the scrap price all the tests for market efficiency fail. This provides us

with strong evidence that investors in newbuildings have irrational

expectations and are driven by other incentives, when placing orders for a

new ship. In the contrary the 'asset players' seem to be more efficient and a

significant percentage of the assets fluctuations can be attributed to

information flow. These results are supportive to the 'asset playing strategy'.

The consistent misspricing of newbuildings is additional evidence that other

forces than maximisation of profits drive investors and this persistency is

evidence for strong subjective beliefs and lack of adaptive learning. From the

creditors' point of view, overpricing of the collateral is a very significant issue,

which shall be examined, in a following paper.

Before concluding we should make clear the following point. Although the 'fair'

prices of vessels have been calculated ex ante (as if the shipowner had a

perfect foresight to the prevailing term structure) this is still not the value

implied by the rational expectations hypothesis. The expected cash flows

under the rational expectations hypothesis are discounted under the

equivalent martingale measure (risk neutral measure, see Duffie 1996 or

Adland, 2002) and the ex ante prevailing cash flows are by no means the

discounted expected cash flows. The divergence of the calculated 'fair' prices

form the prevailing market prices is not directly a measure of market efficiency

or inefficiency, but a measure of economic efficiency and it is a close proxy

for Tobin's q-ratio (marginal value of capital). Thus, the real challenge is

60


weather the difference between ex ante discounted cash flows ('fair price')

and market prices is a signal for new building investing activity (equivalently if

Tobin's q-theory is valid in the shipping industry) and if the market is

economically efficient. The first paper on an investment rule application of

the q-theory in shipping is the seminal paper by Marcus et. al. (1992),whereas for the interrelation between market efficiency and economic

efficiency see Dow and Waldman (1997). Our main task in the Part Ill follow

up to this paper will be the testing of the q-theory and the economic efficiency

of the market, based on the difference between fair values and market prices.

The EMH can only then be directly tested, after the issue of the term structure

of charter rates has been addressed. For an excellent discussion on this issue

see Adland (2002).

Table 12: Summary results of Variance Ratio and Wald Tests

VAR Model VR Test Wald Test Overall

Newbuilding/Secon

d-hand

VLCC

Suezmax

Against the

EMH

Against the

EMH

Support of

EMH

Support of

EMH

Inconclusive

Inconclusive

61


Handysize Support of

EMH

Support of

EMH

Support of

EMH

Newbuilding/Scrap

VLCC Against the Against the Against the

EMH EMH EMH

Suezmax Against the Against the Against the

EMH EMH EMH

Handysize Against the Against the Against the

EMH EMH EMH

Second-Hand/Scrap

VLCC Against the Against the Against the

EMH EMH EMH

Suezmax Against the Support ofInconclusive

EMH EMH

Handysize Support of Against theInconclusive

EMH EMH

62


63


3. A Stochastic Model for the Depreciation Curves

In our previous empirical analysis we derived the two sufficient statistics ordecision parameters that affect the formation of prices of vessels in the second handmarket. In this section we shall construct a dynamic model for the evolution of thedepreciation curves and propose two simple structural models for the empiricalresults derived in Chapter 2.

3.1 Introduction and Motivation

There are numerous studies that have addressed the issue of market

efficiency in the shipping industry (Dikos and Papapostolou, 2002) and the

existence of profitable trading strategies (Marcus et. al., 1992). Most of the

studies conclude that the market is inefficient and there exist profitable trading

strategies in this market; namely excess profit and superior strategy

opportunities are present for agents endowed with courage and available

cash. Dikos and Papapostolou (2002) concluded that the new building market

is inefficient; however, the tests for the second hand market were

inconclusive.

In this study we shall adopt a totally different approach and we shall

address the economic efficiency of shipping investment without treating the

new buildings and second hand vessels as different assets. We shall try to

explain the link between economic depreciation and economic rents. To the

knowledge of the authors the first paper that posed the question of the link

between market efficiency and economic efficiency is by Waldman and Dow

(1997). However, economic efficiency does not necessarily imply asset

market efficiency, as pointed out by the same authors and neither is the

opposite implied.

To gain some insight in this argument let us consider the factors that affect

shipping investment. Although investors may allocate their funds efficiently

between new vessels and second hand assets, this does not preclude the

possibility of strategies that result in excess profits. In this sense economic

efficiency is a different concept than market efficiency.

64


In this paper we shall identify the explanatory variables for the spread

between prices of new vessels (capital expenses added) and vessels traded

in the second hand market, which is a proxy for the economic depreciation of

asset. In paragraph 3.2 we shall discuss the intuition behind our approach, in

paragraph 3.3 and 3.4 we shall present our model and empirical results and in

paragraph 3.5 we shall address conclusions and further directions for

research.

65


3.2 The Relation between Renewal Value and Market Value ofShips

James Tobin (1969) introduced the q-theory in investment theory.

According to Tobin's q-Theory when the market value of an asset exceeds its

replacement cost, one should invest and the reverse. Therefore, the ratio of

the market value and the replacement cost was introduced in

macroeconomics as the q-ratio and has been tested extensively in numerous

studies. The theory has not been verified due to the fact that we should use

marginal costs to calculate the ratio, which are unobservable in the markets.

For an excellent treatise see Ross (1981).

However, the q-theory has never been introduced in shipping to

examine the relationship between the new building market (replacement cost)

with the second hand market (market value) of the asset. To the knowledge of

the authors the first paper that introduced a trading strategy between the two

markets was the paper by Marcus et. al. (1992). In this paper we test the

intuition behind the 'Buy Low - Sell High' strategies introduced by Marcus et.

al. as well as the economic factors that explain the spread between the

replacement value of the asset ship, as measured by the prices of the new

building vessels and the market value, as measured by the second hand

market. The shipping industry is a unique example where organised markets

exist and where both replacement cost and market value are traded.

Following the dynamics of the market the spread between the two

values decreases when the returns on the investment are high and increases

when returns are low. We use as a proxy to the economic conditions and the

market value of a vessel the EBITDA/CAPEX ratio that prevails in the market

and as a proxy to the rate of depreciation, which may be considered as an

equivalent q-ratio the following:

CAPEX, = NewBuldingValue, + OtherExpenses

SEC, = SecondHandValue (1)

_ CAPEX - SEC,

D ' AgeofVessel

66


Before proceeding one could argue that the real value of the ship is its

market value in the second hand market and its true value is the net present

value of the discounted payoffs, which can be calculated ex-ante, given the

ship owner had perfect foresight. This analysis is closer to the original q-

theory and is similar to the efficiency tests as introduced by Shiller (1981).

However, this approach is the one followed when the aim is to test market

efficiency. Furthermore, we can argue that having perfect foresight of the

freight rates ex ante is not equivalent to the rational expectations approach.

Therefore, we argue that even if markets have imperfections, the proxy for the

real value of the asset is its market value and for the renewal value is the

value of the new-under construction asset-ship.

At this point one could argue that in order to compare the value in the

second hand market and the value of the new vessel, one should adjust the

value of the second hand ship for the cash flows already received. Instead of

following this approach which would correspond to a direct test of the q-

theory, we follow a different one: We consider the spread between the capital

expenses needed for a new vessel today and we annualise this spread by the

age of the vessel. This number will correspond to the market depreciation of

the asset (Depr, hereafter). Another proxy for the true value of the asset is

the prevailing economic rent, which in our case corresponds to the time

charter contracts in the markets. Instead of using time charter rates directly

we shall use the EBITDA / CAPEX ratio, which can be considered as the

dimensionless economic rent prevailing in the market.

The intuition now becomes clear: The prevailing economic rent has to

be an explanatory variable for the market depreciation of the asset if the

market is economically efficient. Furthermore, in a good market the

convenience yield of holding the asset increases the value of the existing

vessel and the uncertainty about the future decreases the value of the under

construction vessel. In a bad market the opposite occurs: Vessels in the

second hand market depreciate fast due to technical obsolescence and low

productivity, whereas under construction vessels have a competitive

advantage in productivity and cost effectiveness.

67


We now believe that we have made our case for modelling the

relationship between the depreciation ratio and the economic rents prevailing

in the markets using EBITDA/CAPEX as a proxy. Furthermore, if we divide

EBITDA/CAPEX with Depr, this is a proxy for the long-term expected return

of our investment. If the market is economically efficient with no barriers to

entry, a strong functional relation between these two parameters should

prevail and provide us with incentives for further research and analysis of

investment decisions in the industry.

Taking our analysis one step further, not only we do expect

EBITDA/CAPEX to be an explanatory variable for Depr, but we also expect

an inverse relation. An increase in the economic rents results in a higher

convenience yield for possessing the vessel today and passes the uncertainty

to the vessel under construction. However, a negative correlation between

EBITDA/CAPEX and Depreciation, which is in line with Economic Theory,

would also imply some other important relations: It implies that EBITDA

adjusts more quickly than replacement costs and depreciation. This is

supportive to the evidence of sticky prices in investment theory and provides

us with partial explanations to the fact that time charter rates adjust far more

quickly than new building prices (replacement costs).

We shall now construct our model, discuss the data we used and

present our empirical results. In paragraph 4 we shall draw our conclusions

and directions to further research.

68


3.3 Modelling the Evolution of New Building Prices, SecondHand Prices and Time Charter Rates

3.3.1.1 The Model

From our previous discussion we argued that a decrease in economic

rents (or a decrease in the ratio EBITDA/CAPEX) should result to an increase

of Depr. Since the expected cash flows decrease, investors are willing to

sell this asset. Furthermore, investors involved in an asset play are facing the

deal between 'trading on depreciation', i.e. taking advantage of the evolution

of the prices in the second hand market relative to the new building prices and

the 'risk-free' long term charter rate.

In this sense the shipping market possesses a unique characteristic:

the owner of the ship can get rid of the uncertainty associated to his

investment if he accepts a long-term charter contract. (We assume there is no

counterpart risk.) We shall construct the model based on the following

observation: Any strategy in the shipping industry that is risk-free has to

yield the long-term time charter contract, in order to preclude

economically inefficient opportunities in this market. If this is not the

case, an investor can take adverse opportunities in the market for new

buildings and the second hand market that may lead to economic rents

superior to the market.

Let us consider an investor that constructs a portfolio taking a position

on a new building vessel and short or long positions on vessels in the second

hand market. The investor constructs this portfolio continuously changing

positions between positions among new building vessels and second hand

vessels. In this sense the depreciation of the ships can be considered as a

traded asset.

We now introduce the explanatory variable for economic depreciation;

namely EBITDA/CAPEX (r(t) hereafter). We assume that r has the following

dynamics:

dr(t) = yi(t, r(t))dt + c (t,r(t))dW(2)

Furthermore the 'price process' for depreciation is assumed to be of the form:

69


D(t, T) =F(t, r(t), T) (3), T - t is the remaining economic life of the

CX(t ) - SV (t,T )vessel and in continuous time D(t, T) = (4).

CX(t)t

CX(t)Denote the Capital Expenses required investing in a new

building at each time tand SV(t,T)denote the value of the vessel in the

second hand market with remaining economic life T - t. In the above setting

an investor can construct portfolios with positions on 'capital expenses' and

positions in the second hand market. Therefore, depreciation can be traded in

the market and we shall argue hereafter about the 'price of depreciation.' The

explanatory variable for the evolution of the price of depreciation and all the

risk is attributed to the EBITDA/CAPEX, based on the prevailing time

charter for the remaining life of the vessel.

Now consider the formation of a portfolio of depreciation prices. If we

are able to form a portfolio that eliminates risk, then this portfolio should yield

the EBITDA/CAPEX or economic return on a vessel that is time-chartered

through its entire economic life. The intuition behind this argument is

simple: if an investor accepts a long-term time charter, all freight rate risk is

eliminated. Equivalently any portfolio that eliminates the sources of risk should

yield an EBITDA/CAPEX ratio that corresponds to the long-term (free of

freight rate risk) time charter. Thus, the value dynamics of portfolio with no

freight rate risk is:

dV(t) = r(t)V(t) (5) Using Ito's lemma depreciation prices have the

following dynamics:

dFT = FT a Tdt + FT Y T dW, (6)3

We are now able to construct a portfolio with depreciation prices withmaturity T and S; namely ships with useful lifetime T - t andS - t respectively. The dynamics of this portfolio are given by:

TdF T dFsdV=V{u +u Fs}(7)

3 F T + AF' +0.5Y 2 FT _F,7

a F ,T F' T ' F '

70


Combining (6) and (7) we can choose the portfolio weights in such a

way that freight rate risk is eliminated and the EBITDA/CAPEX yielded is the

one corresponding to the long-term time charter. Following the analysis in

Biais (1996) we choose the portfolio weights in the following way:

U TT+ sUsC= 0(8)

Given the solution to (8) we end-up with the following dynamics for the V-

portfolio:

dV =V{ aSYT -aT s }dt (9)YT T S

In order to avoid excess performance with no freight rate risk, the process

within the brackets must equal the time charter rate and after some

manipulations:

as-r _a T-rs__ - = X (10)

CS CYT

The above equation is the partial differential equation we are looking for and

we shall denote it the Depreciation Term Structure Equation:

F' +(-X)F T +0.5 2 F,,' - rF (11).

It remains now to determine the boundary condition for the above differential

equation and the function X(t). The boundary condition will be derived based

on our economic intuition; however the process X(t) is determined by the

market. We shall derive the boundary condition:

D(T, T)= lim D(t, T) = lim F(tr(t),T) im CX(T) - SV(T - h'T)t--T t->T h-+O CX(T)(T -h)

d CXT__-_CRAPT_

Therefore: D(T, T) = d (12), d CX(T) - SCRAP(T)T CX(T)

In this context d is the incurred depreciation of the ship with terminal value its

scrap value and obviously (1- d) is the percentage of the scrap value as a

fraction of the value of the new building at time T.

71


Combining (12) with (11) we have the full description of the Depreciation

Term Structure Equation:

FfT +( -a)F +0.5 2F' - rF"

d (14)

TWe would be able to solve the equation for depreciation, which relates

the new building market (replacement cost) with the market in the second

hand market if we knew the process 2d(t). However the process X(t) is

determined by the market and is probably different for each type of ship. It is

determined from the laws of supply and demand and the preferences of the

investors.

3.3.1.2 Economic Interpretation of the Depreciation Curves

At this point we have to note that having used only one explanatory

variable for the depreciation it is implied that all depreciation curves for ships

with different remaining economic are perfectly explained by the long-term

time charter rates. However the above Term Structure Differential Equation

has a very fine interpretation. Using the Feynman - Kac Theorem the

probabilistic representation of the D.E. is the following one:

- Jr(s)d' dD(tT)= E"{ef -} ->

T

CX(t) - SV(t, T) = CX(t)Ex{t } d (15)

t T

-I*r()ds dSV(t, T) = CX(t){1- Ex"{e t-}}

TThe above formula connects the price in the second hand market and

the new building prices. It implies that the value of a ship in the second hand

market is equal to the price of the new building discounted continuously by

72


the long-term time charter rate. The formula evaluated at

t = 0, t = T yields:

SV(0,T) = CX(O)

d (16)SV(T,T)= CX(T){1-Ef{e T }T-} = CX(T){1- d}

T

The terminal conditions are consistent with that we expected. The price in the

second hand market of a new building is equal to the new building and the

price of the asset in the second hand market after the end of its economic life

is equal to the scrap value of the asset. Equation (15) connects the prices of

the new building, the second hand value, the scrap value and the time charter

rate in the shipping industry. To get a better feeling for the derived

depreciation curves let us assume that there is no randomness in the

EBITDA/CAPEX rate and taking this rate constant the above formula is:

SV (tT) _d

= {1- er(t -} We display this equation for r = 0.07 andCX(t) T

d = 0.80,T =25.

Table ILifetime of Vessel ->

5 0 15 20 25

O.8.

SV(tT) 0.6

CX(t) 0.4

0.2

It is now obvious that under this specification the value of the vessel in the

second hand market is fully determined by the value of the new building and

its expected 'scrap ratio' d. Even if we assume a source of randomness in

our specification, given the fact that dr(t) remains positive over time, the

r

-Jr,()dsterm E X't {e t I is an increasing function with respect to t and therefore

73


T

-Jr(s)ds dEf'{e }t-is increasing, too and the depreciation curves are a

Tdecreasing function of t. This implies that independently of the evolution of

the prices of the new building prices, the 'spread' between them and the

second hand prices is a decreasing function of time, given that

dr(t) remains positive. If this is not the case then it is possible that the

spread might increase. This is consistent with the observation that in

deep depressions prices of new buildings deteriorate much faster than

ships in the second hand market.

3.3.1.3 The Form of Depreciation Curves

We would be able to fully determine the form of the depreciation curves

if we knew the process X(t). However this process is determined by the

supply and demand conditions that prevail in the market. We can derive this

process by observing market data and doing an inverse fitting. However, this

is not as straightforward as it sounds: there is only a limited family of

functional forms that can be consistent with the Markov setting for the

EBITDA/CAPEX ratio. In this sense one can argue that it might be able to fit

any data set to a depreciation curve; however, only a limited functional

specification doesn't violate the Markov setting for the explanatory variable.

The functional form consistent to the above setting is namely the

Affine Structure. For an excellent review of the underlying theory of affine

structures (in interest rate theory) one could review Duffie et. al. (2000).

Without getting into the details and the mathematics of this theory we shall

directly use its main results. Being consistent with the above setting in 3.1.1.

Employing the theory of affine processes we assume the following form for

the depreciation curves:A(t,T)-rB(tT)

D(t,r;T)=eA (17)

The above equation implies that depreciation is a decreasing exponential

function of the explanatory variable EBITDA/CAPEX. The above setting is

consistent to our modelling and has a very intuitive mathematical and

74


economical interpretation. We are now able to test our model by testing the

above specification with true market data.

Before proceeding we shall plug equation (17) into the differential

equations of the depreciation term structure:

4(t ) -{1 +B (t, 7) r-(p(tr) -%(t)U(t, r))4t, ) +0.562 (t,r)B '(t)=0

B(T,7)=0 (18)

A(TT)=lnd

We can now go on one step further and model:

p*(t, r) = p(t,r) -k(t)G (t,r)

Then we can derive the functions A(tT),B(t,T)from the observed

depreciation curves and the functions t(t, r),cy (t, r) from the time series

data of EBITDA/CAPEX. Having derived the above functions we can easily

solve for X(t)from equation 18, or we can solve for p'(t,r)directly and

then solve for X(t) from equation (19).

3.4 Empirical Analysis

3.4.1.1 Data Analysis

We are now going to fit the empirical model for the depreciation curves

with true data. We are going to carry out the following program:

For a fixed age t = 5,10,15 and economic life T = 25we are going to fit the

depreciation curves with respect to EBITDA/CAPEX r and for different

categories of ships from the tanker industry and the dry bulk industry. We

have used data from five consulting firms and we have carefully ruled out any

inconsistencies among the different sources. As a proxy for the long term time

charter ('risk free freight rate'), we have used the one year time charter rate

and as operating expenses we have used an estimate from different sources.

With these two inputs we calculated the EBITDA/CAPEX ratio and given the

prices for new buildings and vessels in the second hand market we calculated

75


depreciation. By fixing the age of the ship at t = 5,10,15 years we are able

to collect data from 1993-2002 for the tanker sector and from 1976-2002 for

the dry bulk sector. For each month we observe the prevailing

EBITDA/CAPEX ratio and the depreciation ratio for ships five, ten and fifteen

years old for the ships in different categories.

3.4.1.2 Empirical Reusits

Fitting the observed data into affine depreciation curves, namely:

D(t, r; T) = e ,'1,T)-rB'1,T) , Vt = 5,10,15 is equivalent to fitting the

depreciation function for each type of ship and age with respect to the

prevailing EBITDA/CAPEX ratio. In the case of the tanker industry and

specifically for VLCC's and SUEZMAX this type of exponential fitting has

yielded an R2=90% and the characteristics of the observed depreciation

curves are consistent to our model. The derived curves and the depreciation

curves are plotted in the following graph.

76

Massachusetts Institute of TechnologyThe Four Shipping Markets: An Integrated App m Structure

0.1

0.0.+ VLCC-5a VLCC-10

VLCC-150.08 1 - Expon. (VLCC-5)

- Expon. (VLCC-10)

0.07 --- Expon. (VLCC-15)

0.06

4)0.05-

0.04 y+ 0.0812e-3.3337x

R 2 =0.89480.03

y0= 0.1265e-9 1447x

002 -R 2 = 0.8959

0.01 -- 060e1.5882xy=0.0601e

0 R 2 =0.90880 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18

EC

Table 2

77


Suezmax

0.12

0.1* Suez-5w Suez-10

* - " . . -Suez-15

0.08 -Expon. (Suez-5)- Expon. (Suez-10)

Expon. (Suez-15)C.(D 0.06 -

= 0.1449e

R 2 =0.8612

= 0.0885e-2183x

R 2 =0.87060.02

1.9255= 0.0593e1

0 0.05 0.1 0.15 0.2 0.25

EC

Following the same procedure for the category of SUEZMAX we achieve a fit

of R2 =90% and consistency of our model with market data.

We replicated the same procedure for ships in the dry bulk industry and we

found a very good fit of the proposed exponential family and consistency of

the model to market data. Although the estimation of operating expenses for

the period 1976-2002 was difficult and the proxy used for EBITDA/CAPEX is

not always good for the long term time charter rate, the model has yielded a

very good fit with market data. Furthermore, it manages to capture the inverse

relation between depreciation and EBITDA/CAPEX even for 'extreme' events.

3.5 Summary and Topics for Further Research

We have constructed a model to explain the 'spread' between new

building prices, vessels in the second hand market and long term time charter

rates. We based our model on spanning risk arguments and the fact that a

long term time charter takes away all prevailing freight rate risk and allows the

construction of portfolios with new and old vessels that yield the long term

78


time charter. What will allow us to check furthermore the model is the

consistency between the parameters p (t,r),G (t,r) implied by market

depreciation data and statistical data for EBITDA/CAPEX. Finally, any

inconsistency that could prevail might be attributed due to the unobservable

status of the 'long term time charter rate'. However deriving these parameters

by market data allow us project valuation of Ship Finance projects on implied

market data and the derivation of confidence levels for 'good deal' shipping

investment decisions.

79


4. Integrating the Four Shipping Markets using the ContingentClaims Approach

4.1 A Structural Model for the Second Hand Prices

In their seminal paper Marcus et. al. (1992) identified the link between

prices of vessels in the second hand market, prices of newbuildings and time

charter rates, and identified these two risk factors as the main 'sufficient

statistics' for shipping investment considerations in the shipping asset play. In

their excellent paper, Haralambides et. al. (2002) conducted an econometric

analysis of the prices of vessels in the second hand market and concluded to

the same results regarding the significance of time charter rates and

newbuildings. In a similar econometric analysis Dikos et. al. (2002) concluded

that newbuilding prices and EBITDA/CAPEX ratios are the main factors that

drive prices of vessels in the secondary market and proposed a stochastic

model for the depreciation of vessels with respect to these factors.

Maritime economics have based the derivations of the empirical

literature on the interrelation of newbuildings, time charters and second hand

prices on the basis of supply and demand. (Haralambides, 2002) Other

models for the interaction of these markets have been derived on the basis of

Capital Asset Pricing Models and Complete markets. At this point we need to

stress that any approach taken on this basis is de facto misleading: Shipping

Investors do not have quadratic utility functions, since they potentially accept

negative Net Present Values for the potential extreme profits they may gain in

a bullish market. Furthermore, returns are far away from normal and the

market is asymmetric and non-frictionless. Thus, any Capital Asset Pricing

Model approach to Shipping (see Beenstock and Vergottis, 1989) is only an

application of modern corporate finance theory, (which is anyway rejected in

numerous studies for highly integrated and efficient markets) in a very

specialised market. On the other hand, we have significant evidence for a

highly non-linear relation between second hand prices, newbuildings

and time charter rates. This is verified in the excellent study of Haralambides

et. al. (2002), as well as the study of Dikos et. al. In this paper we shall

80


demonstrate that the non-linear pricing relation may be explained by the

real option approach to shipping investment decisions. The paper is as

following: In 4.2 we demonstrate the contingent claim valuation approach to

investment decisions and previous work done in this area (Goncalves, 1992

and Pindyck, 1994). In 4.3 we outlay our model and our empirical findings,

whereas in 4.4 we conclude and propose topics for further research within this

direction.

4.2.1 Risk Factors and Replicating Strategies

In our previous analysis we constructed 'depreciation' portfolios and

introduced EBITDA/CAPEX as a risk factor. Using standard arguments from

bond pricing theory we derived depreciation curves that provided a very good

fit to empirical data. We didn't consider any payoffs from chartering our ships

because our 'depreciation' portfolios cancel out the payoffs from the new

vessel and the second hand vessel. Furthermore we assumed that the one-

year time charter is a good proxy for the 'long term' time charter. We shall

now introduce risk factors and derive the depreciation curves based on little

economics and intuition. Let us consider a one risk factor model and follow

the Dixit - Pindyck (1994) model.

We introduce uncertainty in our model and begin within the simplest

setting following Dixit and Pindyck. Let us assume that the profit flow of a

ship depends on the explanatory variable x. We shall assume that x is a

random process measurable with respect to the filtration 3,,t > 0 on

(Q, 3, P) and namely:

dx = a(x)dt +c (x)dW (1)

where W is a Wiener process on the filtration 3,.

Now we make the assumption that the explanatory variable x can be

traded in financial markets 4. This would be the case if x was oil, which is not a

really bad assumption for the tanker industry, since the demand for

4 X could also stand for the share of a Shipping Company traded in Financial Markets: see recent

successful example Stelmar.

81


transportation is a derived demand from the demand for oil. Oil is a

commodity and it is traded in financial markets, endowed with an associated

derivatives market, which makes it easy for us to estimate the coefficients of

the diffusion. The variablex could also be time charter or spot rates, or even

something more sophisticated like the share of a shipping company traded on

the NYSE. We assume that financial markets span this risk and since we

have one risk factor and one asset (ship values) our market is complete.

Now let us assume that the profit flow for this ship is xT (x, t) and the

value of the ship shall be denoted F(x, t). We shall estimate the value of the

firm using arbitrage arguments in the same lines with Dixit and Pindyck. Let

us consider an investor who decides to invest one dollar in the riskless asset

and also buy n units of the explanatory variable x. Now he holds both assets

for a short period of time dt and in this time he receives a payoff rdt from the

riskless asset and a dividend n6xdt and has a random capital gain of

ndx = na(x)xdt + na (x)xdW. The total return on his investment is:

r + n(a(x)+6 )xdt a (x)nxdW, (2)1+ nx 1+ nx

In the same infinitesimal interval the owner of the asset ship receives a

random capital gain, which using Ito's Lemma is equal to:

1dF= [F, (x, t) +a(x)xF (x t) +-Iy2 (x)x-e F.-,t)1dt+c7(x)xF (xt)dT (3)

2

Then the total return per invested dollar for the owner of the asset ship is

equal to:

1[F,(x 0 +aO (xYF x0t+ aq4Fxt]nxt a(x)xF(xt)2 dt d (4)

FRxt) F (xnt)'

Since our portfolio replicates the risk of the owner of the asset ship:

a (x)xF (x, t) a (x)nxdW,X dW = (5)F(x,t) ' 1+nx

Both holdings must yield the same return in the market or else arbitrage

opportunities would be induced. Thus:

82


1[F(x,t)+a(x)xF(x,t)+-2(x)x2 F(xt)]+n(xt) r + n(a(x)+ )xdt

2 r(6)F(x,t) 1+ nx

Combining (6) and (5) the value of the ship must satisfy the partial differential

equation:

1- 2(x)x 2FL(x,t) + (r -6 )xF(x,t) + F] (x,t) - rF(x,t) + 7u (x,t) = 0(7)2

The terminal condition for (7) is the following:

F(x, T - T) = F(0) = ScrapValue(SV) (8)

The terminal condition implies that at the end of its lifetime (T=25) for a ship

the value of the ship is equal to its scrap value (SV) hereafter.

Now extending the model and following the same arbitrage arguments the

scrap value can be determined as following:

Let y be the price of steel in the commodity markets and let us assume that

y evolves in the following way:

dy = s(y)dt + v(y)dZ, (9)

Then the SV of a ship is equal to the call option to scrap the ship at the end of

its valuable lifetime where the exercise price is the scrapping cost. Thus:

1-v 2 (y)y 2S V (y,t) +rySV(y,t) +SV(y,t) -rSV(y,t) = 02 (10)SV(T) = max[y(T) -D WT- Scrapping6sts,0]

83


Given (7), (8) and (10) we can determine the value of the asset ship for each

price of the explanatory variable oil x and at each point in its lifetime t,

t C- [0,T].

This approach doesn't hold only for ships but for any company whose

value is explained by only one risk factor, that is spanned by financial

markets. However the case of the ships is very interesting due to the simple

form of the payoff function. The above approach integrates the four different

shipping markets (Stopford, 1990) and is therefore intuitively appealing:

At time t = 0, F(x, T) is the value of the new vessel, with remaining lifetime

T.

At time t = T - t, F(x, t) is the value of the vessel with remaining lifetime t

and the scrap value at time t = 0 is the terminal condition of (7). Finally if

x stands for the spot freight rates or for the one year time charter rates, this

continuous time approach integrates the four shipping markets. We can go

one step further by modelling the profit flow. Letting x be the one-year time

xcharter rate 71 (x, t) = C(x, t), where C(x, t) is the running cost

365function and the unit for time is days. Assuming that cost increases with time

x F~xtin the following way: C(x, t) = - K( (x, t) Y we have the following

365 F(x,T)

differential equation that characterises the value of a vessel with remaining

lifetime t and current price of the risk factor x:

1 x 2 x T)___0

-&(x)xF(xF)+(r-)xF(x)+(xt)-r(xt) +- -K( -"))" =0 (11)2 365 F(x)

Having solved the above differential equation we have specified the

depreciation curves introduced in the previous paragraph explicitly:

D(t,T,x)=F(x, T) -F(xt) >F(x,t) =F(x,T) {1 -(T-t)D(t, T,x)} (12)F(x, I)(T -t)

Thus, equation (12) is a sufficient characterisation for the family of

depreciation curves.

84


At this point we should comment on the optimisation counterpart of

equation (9). From the Feynman - Kac theorem we know that F(x, t) is the

solution to the following problem:

F(x,t) = E [ je-(T1- (x, t)dt + e-r(T'Scrap Value] (13)

Here the expectation is taken under the martingale Q-measure:

dx =(r -d)dt + (x)dW (14)

The existence of this martingale measure is a consequence of the no

arbitrage assumptions and its uniqueness is due to the completeness of the

market. The optimisation counterpart to the above analysis provides additional

insight: The value of the ship is equal to its discounted payoffs plus the

discounted scrap value at the end of the economic lifetime. The above

formulation is very general and may be applied to all risky payoffs. In most

cases it is very difficult to estimate the profit flow of the asset. However, in the

case of the asset ship the profit flow is fairly straightforward. For an excellent

treatment of the analogies and differences between no arbitrage arguments

and dynamic optimisation see Dixit and Pindyck p.122.

To the knowledge of the author the first who introduced arbitrage

valuation arguments in shipping is Goncalves (1992). He considered as an

underlying instrument the future contracts traded on the Baltic Exchange and

solved problems of optimal decision making under uncertainty. However, he

did not address the issue of valuation. This issue is addressed in the seminal

book of Dixit and Pindyck (1994, Chapter 7), where the 'real options'

approach is applied to the tanker industry.

At this point we might feel a little bit nervous, because we cannot trade

second-hand prices continuously, neither can we 'short' second hand vessels.

However, since shipping companies are listed on integrated financial markets

and since the markets are tending to become locally complete, we can

replicate the value of the second hand ship, by instruments traded in the

market. If this argument doesn't convince the non-financially oriented reader

here is a more intuitive one: If the shipowner could create value from listing

his companies on the market then he would do so. Thus, by assuming that we

may trade continuously on the second hand vessels, we are always on the

85


safe side from a valuation point of view: If value were to be created from

listing shipping companies, managers would do so. By valuing ships as if they

were traded continuously doesn't take away any value from our analysis.

Finally, if we are not convinced by this ad hoc argument we should simply

note the equivalence between the dynamic trading arguments and the

optimisation approach outlined in formula (13). No dynamic trading is

assumed not needed. However the derived differential equation is the same in

both cases. We shall now proceed by choosing the two underlying processes

that will be a sufficient statistic for the value of the second hand vessel.

86


4.3 A two-factor market model

4.3.1 Valuation in an incomplete market

In 3.3 we empirically verified the following form for the depreciation

curves:

D(t, r; T) = eA(t,T)-rB(t,T) Or equivalently the relation between vessels in the

second hand market, prices of new vessels and EBITDNCAPEX:

F(r, t) = CX{1- teA(,')-'rB(' T) '}(15)

Hereafter r will stand for EBITDA / CAPEX and CX will stand for the

price of the new vessels, capital expenses added. We propose the following

model for the evolution and the dynamics of the EBITDA / CAPEX and

CX:

dCX = p (CX ,t)dt +0 (CX ,t)dZc(16)

dr =v (r,t)dt +G (rt)dZ'

ZC, Z' are two independent Brownian motions defined on the standard

filtration. We now assume that the price of the vessels in the second hand

market is a function of these two risk factors, namely:

F(r, CX, t) = Function(r, CX, t)Our empirical findings in 2.1 and 2.2

suggest that the second hand pricing function should have the following form:

F(r, CX, t) = X(CX, t) * Y(t, r) (17)

Since the value of the vessel in the second hand market is a function of these

two state variables we may use the multi - dimensional form of Ito's Lemma

and assuming that one can trade continuously in second hand vessels we can

derive the following differential equation:

87


F +0.50 2F +0.5a2 F+( -X0)F+(v-Xc)-rF+rCX=0 (18)

We have made the standard assumptions that the risk free portfolio yields the

EBITDA / CAPEX ratio and that we are allowed to trade continuously

values in the second hand market. Although this assumption may seem

unrealistic due to the huge transaction costs in this industry it should hold for

shares of shipping companies listed on organised markets. Thus there

exist assets that allow us to replicate continuous trading strategies in

the second hand market.

There is one more significant observation related to equation 18:

Having used as state variables the capital expenses to invest in a new

vessel and the EBITDA / CAPEX ratio allows us to model the payoffs

received from chartering a ship continuously, simply as the product of

these two variables.

Finally the two Xk, Xrterms those appear in equation 18 are the market

price of risk and correspond to the Girsanov transformation of the

specification of the two processes with respect to the local martingale

measure. In this setting we have two factors of risk and one asset. The market

is therefore incomplete (see Bjork, 1996) since there are more risk factors

than traded assets and an infinite number of (no-arbitrage) local martingale

measures exist. The prices of risk in the above model are simply determined

by the market.

If we now plug into (18) the empirical form (17) we verified in 3.3 we

derive the following two differential equations:

Y(X, +0.50 2Xc+(- k CO)X, -rX )=0

X(Y +0.5G 2Y,, + (v - kc)Y +r(CX / X)) =0

If we set X(CX, t) = CX we obtain the following equation:

k = - rCX and if the evolution of the prices of new vessels are a0

simple log - Ornstein - Uhlenbeck process the above specification is reduced

to:

88


0 = -and it is sensitive to technological advances that affect0

the mean of the prices of new vessels. Technological advances that affect the

market price of risk may be the explanation for the formation of two patterns of

depreciation curves in the bulk industry for data from 1976 until 2002.

BULK 70000

y 0 1158e-s.3'x

14% R =0.391

12 q

* * *0 Bulk 70K 5 YRS OLD

W 8% .0Bulk 70K 10YRS OLD

=Eupon. (Bulk 70K 10YRS OLD)- 4 -V E pon. (Bulk 70K 5700S OLD)

6%-04+, +y 0.0564e- 9579x

R2 = 0.3258

2%

0% 2% 4% 6% 8% 10% 12% 14% 16% 18%EC

Having specified the market price of risk for a new vessel investment

that is consistent to the specification X(CX, t) = CX we now plug into (18)

and derive the following equation for Y:

(Y +0.5c 2 Y +(v - Xpcy)Y+r)=0

We have now a complete characterization of the second hand price function

and once we specify the terminal conditions of this set of differential equations

we have a theoretical model that integrates prices of new vessels, prices of

vessels in the second hand market, the demolition market and time charter

rates and is consistent to the empirical findings in 3.4. At this point one could

argue that the assumption of continuous trading is fairly abstract; however

having identified the two explanatory variables (factor risks) in the industry we

will be able to extend these results in the non continuous trading case in the

form of good deal versus bad deals and relative pricing.

Before concluding it is worth mentioning that the EBITDA/CAPEX ratio is the

inverse of the expected investment recovery period and is similar to the P/E

ratio which is a common risk factor for shares. EBITDA/CAPEX is specified

89


exogeneously in this industry, due to the competitive nature of the industry.

Although one could argue that the resulting EBITDA/CAPEX is an output of

the equilibrium due to the demand and supply for transportation, as well as

the investment decisions of the players in this market, since bulk is shipping is

an extremely competitive market, this process may be considered as

exogeneously specified. In their seminal paper Hansen et. al (2002) consider

an exogeneously 'dividend ratio' process for robust control in a Ramsey-type

model. Introducing the EBITDA/CAPEX as a sufficient statistic to characterize

the uncertainty of investment decisions in this industry has close links to q-

theory. EBITDA/CAPEX is not only an inverse P/E ratio and an approximate

measure of the required capital recovery period, but an equivalent q-ratio.

EBITDA is a statistic for the market value of the asset, whereas CAPEX is a

proxy for its replacement or construction cost. Since no agent can acquire

sufficient power to control this market, instead of deriving the q-ratio as an

output of a dynamic model we specify it exogeneously.

Finally, the specification of time charter rates as a risk factor has been

a drawback for the understanding of shipping investment dynamics, due to the

fact that it is not invariant to size, type and cost parameterizations, whereas

EBITDA/CAPEX is cost and size invariant. Furthermore, time charter rates are

only a proxy for the market value of the asset and not the renewal value.

Equivalently, given the rent for a real estate property you cannot conclude if

you should invest or not, unless you are given the construction costs at the

specific time period.

4.4 Generalized formulation of the 'Good Deal' Problem

There are several assumptions that may seem strong regarding our

discussion in 4.3. Most of them, such as the assumption of the same interest

rate for borrowing and lending, or of an arbitrage portfolio that yields

instantaneously the one process may be relaxed. Making the setting more

realistic might result in a system of forward - backward differential equations

and in advanced computational complications. However the strongest

90


assumption remains the one of continuous trading that seems unrealistic

especially in a thin and illiquid market such as the market for second hand

vessels. For our good luck we can cut corners to this problem once we have

identified the factors that determine the value of the asset and the payoff it

generates, by introducing the optimisation analogous problem. This problem

is far more general and applies to identifying good and bad deals for the

pricing of risky payoffs. Dixit and Pindyck and Cochrane (2000), in his seminal

paper, have first addressed this problem. Intuitively we are interested in

determining 'good deals' and 'bad deals' for risky payoffs, given we have

identified the factors that determine the payoff and the value of the asset. The

specification in 4.3 allows on the one hand to model as a simple product the

payoff of the asset ship and simultaneously its value as an asset traded in the

second hand market. We shall proceed now with the general setting of the

problem.

In order to be in line with our setting in 4.3 and our empirical findings in

3.4 let us assume that the value of the vessel is determined by the following

two factors:

The one factor is the ratio of EBITDA / CAPEX, which may be

considered as a proxy to the required investment recovery period and is close

to the P/E ratio that is a common factor for stock returns. The reason why

freight rates are not a good factor (to the contrary of the beliefs of shipping

economists) is because it is not scale or type invariant. The second driving

factor is the price of new vessels. This process incorporates new technical

advances as well as the economic conditions (or political conditions, such as

subsidies). For example a productivity improvement will result to a decrease

of the drift term of the process, whereas an increase in political uncertainty will

be reflected on a higher volatility term.

Having specified the two factors the payoffs of a ship investor is simply

the product of these two factors and shall be denoted by

,EBITDAx"= EBJ E CX and the terminal payoff or scrap value shall be

SCAPEX

denoted X4. Then the problem we are interested in solving is stated in

Cochrane (2000) as following:

91


m A ATS = min E' j xcds + E'( X)(22)- A,,T SA A T

The problem is to specify a discount factor process that minimises (22),

namely the discounted value of the payoffs and the scrap value of the vessel.

The expectation is taken under the P-dynamics (statistical dynamics) of the

process. However from the risk neutral valuation theory we can restate (22)

under the equivalent martingale measure (a consequence of the absense of

arbitrage) as following:T

S = min e-( 1)EQ xcds + EQ (x) (23)- 2"2,S=1

This is the equivalent risk neutral formation of the problem: If continuous

trading were possible and the underlying assets were traded then the

martingale measure would be uniquely defined and the market price of risk

processes would be unique. However, since continuous trading is not possible

and the market is incomplete the market prices of risk processes are not

uniquely defined. The above risk neural specification of the problem has the

advantage that if we extend the underlying processes beyond diffusions,

we have analytic specifications for the moment generating function of the

wider class of affine processes. Thus, there are advantages when the

problem is posed under the Q-dynamics, especially when one includes

jumps in the processes. The solution of the above problem for a wider class

of processes than the ones considered by Cochrane (2000) will be the main

research topic of this chapter and it is essential since it allows the valuation of

risky payoffs in incomplete markets, where continuous trading might not be

possible. The extension to the differential characterisation (Cochrane, (2000))

of the 'good deal' bounds for wider processes than Ito diffusions is essential to

the valuation of risky payoffs in incomplete markets.

Before concluding there is an important comment to be made: In our

empirical derivations we stacked pairs of (EBITDA/CAPEX, Depreciation)

observations in a graph. We observed however that at different times

snapshots for the same EBITDA/CAPEX different depreciation values were

documented. This implies strong evidence for a time varying market price of

risk. Unfortunately, if we do not make some assumptions about the nature of

92


the market price of risk we cannot find the closed form solution to the

depreciation curves and we cannot extract the time varying risk from market

data. We are faced with an open loop problem: If we do not specify some

characteristics for the market price of risk, we cannot extract it. This implies

that we are not only questioning our assumptions about the model but also

about the market price of risk. An alternative approach to this philosophical

problem that limits substantially our ability to make any inferences on the time

varying prices of risk can be overcome in a robust control setting, as the

one introduced in the seminal work of Hansen et. al. (2002).

93


5. Towards a General Equilibrium

5.1 Partial Equilibrium Pricing

There are numerous works that value a ship as a function of uncertain

freight rates and the existence of real options with the most recent being

Tvedt (1997), who applies the no-arbitrage argument and resulting SDE in a

similar fashion as well as many working papers and theses from the early

1990s in Norway (Andersen, Martinussen, Stray etc.). However, none of these

approaches has considered price formation and vessel valuation in the partial

equilibrium economy, as in Chapter 4.

Although this approach seems promising indeed, we should not be so

categorical as to dismiss price formation as a result of the good old supply

and demand relationship. It is only in a complete, standardized, liquid, and

transparent market where one can be reasonably certain that traded assets

are priced as a function of their risky payoffs - which would then happen to be

equal to the 'market' or 'equilibrium' price. Stock options are still priced as a

result of supply and demand even after Black and Scholes. It just happens

that practitioners now have a better idea of the factors that influence the price,

and still the market price is typically not equal to the B&S price. The shipping

markets do not adhere very well to such ideal trading conditions, and so we

would argue that prices of second-hand vessels are still very much based on

the supply and demand from owners. However, we can hope that this partial

equilibrium price is strongly related to the 'theoretically correct' price based on

risky payoffs. Similarly, the statement that the S&P market ideally 'should not

exist' appears too strong. While the 'no trade' argument in financial economics

perhaps has some theoretical interest, it results from the assumption of

homogeneous expectations (or a 'representative agent'), which evidently does

not hold in practice in any market. People still trade in stocks even though

that market should be fairly efficiently priced. In a presumably less 'efficient'

market such as that for second hand vessels, there is even more reason to

trade.

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Although ideally the S&P market should not exist, it accounts for one of

the most liquid market in this industry. However, we have still not yet

examined issues of 'volume' in this market. Even if the proposed real option

approach is under question, it still remains interesting to examine and

understand the factors that result in divergence of market observed values

from true values. In the following paragraph we shall address some

microstructure effects that may account for the 'extremal values' in this

industry.

In this sense, the term 'real options' in this context is not restricted to asset

play (i.e. sale and purchase timing). Real options in shipping include the

option to lay-up, scrap, wait to fix, and wait to S&P etc.

Another fine point is the difference between replacement cost ( related

to newbuilding prices) and second-hand values and the assertion that the

former is an important statistic (one out of two) for the determination of the

latter. But, if one really believes that the markets are integrated and that all

vessel prices are a result of discounting expected risk-adjusted payoffs, then

the newbuilding price is a superfluous variable in this context. This is

because a newbuilding contract merely is a forward contract on an age-zero

vessel with delivery in, say, two years (the construction lag). Accordingly, the

only difference between the value of a newly delivered vessel and a

newbuilding contract is the value of the postponed earnings (ignoring

operating and technical risk). This is related to the criticism of Brennan and

Schwartz' (1979) two-factor interest rate model (and Black's consol rate

conjecture), where it was argued that using the long-term rate as a second

factor is not necessary, as the long-term rate is determined by the short rate.

This is actually an important point as, by using the newbuilding price

separately (or derivations thereof such as CX), it is implied that the freight

market and the newbuilding market are not integrated. That's an interesting

and possibly necessary extension of the literature in itself, but it still needs to

be tested empirically. In theory, of course, the long end of the term structure

of freight rates would be directly related to the newbuilding price, which would

again be directly related to the 'new' end of the 'term structure' of second-

hand vessel prices.

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There is another important issue of whether the payoff from a vessel

investment can actually be replicated by existing traded assets crucial for this

analysis, and it would be an important contribution if we could show that it is

(in all likelihood) possible in practice. This may be a suggestion for further

research. We could analyze the stock prices of 'pure' shipping companies

such as Frontline and Teekay and investigate to which degree it is possible to

find a dynamic 'hedging' portfolio for a physical VLCC and Aframax,

respectively, made up of their shipping stocks and (U.S. sovereign) bonds. It

would certainly be challenging to replicate the vessel payoffs exactly, and that

could pose a sufficient problem for the use of a 'no arbitrage' argument in this

context. In particular, it is questionable if we could find two traded assets that

could replicate both the freight earnings (dividends) and the residual value

(future resale value or scrap value, depending on horizon).

5.2 Market Microstructure and Open Problems

Although our previous both empirical as well as theoretical analysis has

produced some very promising results regarding the prices of second hand

vessels, there are still many issues that remain unresolved from this

approach. The main issue is that the process for prices of new vessels as well

as the process for the time charter rates has been specified exogeneously.

Although this may be a convenient statistical approximation for our analysis, it

cannot be the case. Supply and demand for transportation should affect both

the prices of new vessels as well as time charter rates. Furthermore, the

number of vessels in the market and the existing book of orders should

interact with these processes. In this sense the above model is simply a

partial equilibrium for second hand prices and doesn't attempt to explain all

the dynamics of the prices in the shipping markets.

Such a task would be far more complicated and could be either

approached based on aggregate data in the framework of an asset pricing

model or by using the 'bottom down approach' (Rust, 1987), namely by using

investment decisions of a specific manager and try to solve out the inverse

Dynamic Programming Algorithm. Even as a partial equilibrium our analysis

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still remains relevant. Once we have identified the dynamics of prices for new

vessels and the dynamics of time charter rates, we can immediately apply the

pricing of second hand vessels contingent on these two sufficient statistics, as

developed in Chapters 2, 3 and 4. Thus, once we have identified an efficient

model for the specification of these two processes, the second hand pricing

approach may be used as an independent module.

Even in the framework of a general equilibrium model there are still

many stylised facts in the shipping industry that cannot be easily resolved and

are crucial to the understanding of the interaction between the different

shipping markets. The main question is the identification of the motivating

forces that 'trigger' investment decisions. In a Real Options framework

investment decisions should occur only when investors expect not only

positive NPV returns, but returns above a critical threshold. In most cases this

is not the case in shipping, since there is evidence for 'high beta' - 'low return'

effects in this industry.

If this is the case, then corporate finance issues like borrowing

constraints and liquidity supply should account for a significant part of the

cyclicality in this business. Especially when the main source of shipping

finance comes from bankers, several 'contract theoretical' issues arise. If

there is an asymmetry between the risk perception of the investor and the

banker, then this will clearly be reflected in the spread between second hand

and new vessels. Under this perspective the time variation in depreciation and

its dependence on the market rent (freight rates) suggest that investment

decisions are not only related to market and renewal value considerations, but

also to financing issues. It is well known that prices of new vessels fluctuate

much less than freight rates or second hand prices. Since liquidity supply by

bankers is correlated with high freight rates, this might imply that the lower

depreciation rates in a good market are due to financing constraints.

Another important point that cannot be totally ruled out is that investors

in shipping may belong to agents with a very specific utility function. It might

be the case, that they possess convex utility functions and belong to the class

of risk lovers. Then no equilibrium model can be derived in this setting.

Although such type of investors should potentially get driven out of the

market, economic theory suggests that some of them may eventually perform

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spectacularly. And indeed, this is the case in this industry. A very small

fraction accumulates an enormous amount of wealth, whereas the vast

majority is eventually driven of the market. If investors are risk lovers then

bankers should not finance their plans. However this asymmetry in

preferences between investors and finance suppliers may account for the

observed anomalies in the prices.

Another important issue is asymmetric information. It can be the case

that the data we are analysing are just a crude approximation of the true data

or true deals in this industry. It might be that the 'true data' are only available

of a closed pool, whose one can become a member only after paying an

'entry fee'.

All the above anomalies have to be taken into account when one

evaluates shipping investment decisions and the interaction of the different

shipping markets.

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