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 IN
PARTIAL 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 Technology
All rights reserved
Signature of Author............
............
Department of Ocean Engineering
December 19, 2003
'U
/J
/
-
/
Certified by............
................
Henry Marcus
Professor of Marine Systems
Thesis Supervisor
Accepted by..............................
.i ...... ...............
Arthur Baggeroer
Professor of Ocean Engineering and Electrical Engineering
Chairman, Department Committee on Graduate Studies
MASAoUil
S INSTITUTE
OF TECHNOLOGY
BARKER
JUL 1 5 2003
LIBRARIES
I
........
The Four Shipping Markets: An Integrated
Approach
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 regarding the four shipping markets are addressed. These markets are the
market for new vessels, the second hand market, the scrapping market and
the freight rate market. Using "no arbitrage" arguments, the four markets
are integrated and equilibrium valuation of vessels is derived. Finally, questions of market efficiency and rational expectations are tested empirically,
using modern econometric theory.
Thesis Supervisor: Henry S. Marcus
Title: Professor of Ocean Systems Management
Massachusetts Institute of Technology
The Four Shipping Markets: An Integrated Approach
ACKNOWLEDGMENTS
First of all I would like to thank the Eugenides Foundation, the A. Onassis Public
Benefit 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 old
friendship between our families. I would also like to thank Professor Henry Marcus
for supervising both this thesis and my PhD research. I am also grateful to Professor
Nick Patrikalakis and Professor Jerry Hausman. Thanks also go to my co-authors
Professor Henry Marcus and Nick Papapostolou for allowing me to use parts of our
joint work from the following working papers: 'Market Efficiency in the Shipping
Sector', 'Second Hand Prices, New Buildings and Time Charter Rates' and
'Integrating the Four Shipping Markets: The End of the Puzzle'. Thanks also go to
Vassilis Papakonstantinou and Mr. N. Teleionis.
I dedicate this thesis to my parents, with all my love.
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Massachusetts Institute of Technology
The Four Shipping Markets: An Integrated Approach
TABLE OF CONTENTS
1. The Four Shipping Markets: Towards an Integrated Approach................ 4
1.1 Introduction and Motivation......................................................................4
7
2. Empirical Analysis of Second Hand Prices ...............................................
2.1 EBITDA/CAPEX as a leading indicator for depreciation ........................ 7
2.1.1 Testing the Hypotheses......................................................................................................
2.1.2 H ypothesis Testing ................................................................................................................
2.1.3 R esults ...................................................................................................................................
9
10
11
16
2.2 Specification of the Depreciation Curves .............................................
Testing....................................22
Benchmark
and
Testing
of
Sample
2.3 Out
23
2.3.1 R esidual D iagram ..................................................................................................................
25
2.3.2 Structural Analysis of our Empirical Findings ..................................................................
2.4 Econometric Analysis of the Second Hand Price and New Vessel Price Dyanmics ................ 31
THE COST OF RUNNING VESSELS.........................................................................................
H andysize .......................................................................................................................................
Table 2: Summary Statistics Of Price & Profit Series..............................................................
ESTIMATION RESULTS .................................................................................................................
Table 3: Summary Statistics of the Excess Returns in the Four Tanker Carriers......................
Table 4: Predictability of Excess Returns on Shipping Investments ..........................................
COINTEGRATION TESTS...............................................................................................................44
Table 5:Cointegration Test For Prices and Operational Profits.................................................
Table 6: Estimated VECM of Handysize Prices & Profits.............................................................48
Table 7: Estimated VECM of Suezmax Prices & Profits ...............................................................
Table 8: Estimated VECM of VLCC Prices & Profits ...................................................................
C ON C LU SION ..................................................................................................................................
33
34
38
40
42
43
45
49
50
59
3. A Stochastic Model for the Depreciation Curves..................64
3.1Introduction and Motivation....................................................................64
3.2 The Relation between Renewal Value and Market Value of Ships..........66
3.3 Modelling the Evolution of New Building Prices, Second Hand Prices and
Time Charter Rates.................................................................................... 69
3.3.1.1 The Model...............................................................................................................................69
3.3.1.2 Economic Interpretationof the DepreciationCurves........................................................
3.3.1.3 The Form ofDepreciation Curves....................................................................................
72
74
3.4 Empirical Analysis.................................................................................75
3.4.1.1 DataA nalysis..........................................................................................................................
3.4.1.2 EmpiricalReuslts....................................................................................................................76
75
. . 77
Ta b le 2 .....................................................................................................
78
3.5 Summary and Topics for Further Research .........................................
4. Integrating the Four Shipping Markets using the Contingent Claims
. 80
A p pro ach ....................................................................................................
4.1 A Structural Model for the Second Hand Prices.......................................................................80
4.2.1 Risk Factors and Replicating Strategies ................................................................................
81
4.3 A two-factor market model .......................................................................
87
4.3.1 Valuation in an incomplete market.......................................................................................
87
4.4 Generalized formulation of the 'Good Deal' Problem ........................... 90
5. Towards a General Equilibrium...............................................................94
5.1 Partial Equilibrium Pricing......................................................................................................
5.2 Market Microstructure and Open Problems..............................................................................96
3
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Massachusetts Institute of Technology
The Four Shipping Markets: An Integrated Approach
1. The Four Shipping Markets:
Approach
Towards
an
Integrated
Historically, the market for new vessels, the market for second hand vessels, the
freight rate dynamics and finally the market for scrap have been considered as
different markets that obey their own laws of supply and demand. The main aim of
this dissertation is to identify the dynamics of second hand prices from a financial
or 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
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Massachusetts Institute of Technology
The Four Shipping Markets: An Integrated Approach
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
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The Four Shipping Markets: An Integrated Approach
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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Massachusetts Institute of Technology
The Four Shipping Markets: An Integrated Approach
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)* DaysEmplagdand
CAPEX
CAPEX stands for the capital expenses associated with investing in a new
vessel. Furthermore, depreciation or Depr will stand for:
Depr(t) =
CAPEX(t) - PriceSH(t)
,
CAPEX
where PriceSH(t) is the price of a
second 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
(EBITDA/CAPEX)/Depreciation
of its replacement
cost.
is a proxy for the long-term return on the
investment compared to its replacement cost and it can be considered as a Qratio equivalent. According to Tobin's Q-Theory when the true value of an
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Massachusetts Institute of Technology
The Four Shipping Markets: An Integrated Approach
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.
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Massachusetts Institute of Technology
The Four Shipping Markets: An Integrated Approach
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 Qratio 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
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Massachusetts Institute of Technology
The Four Shipping Markets: An Integrated Approach
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
ratio and depreciation. We run a linear regression and
EBITDA/CAPEX
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.
a +
p
EBIDA
BD
CAPEX,
+IFt =A CA PEXt-
Hypothesis 1
The second hypotheses we check is the one that underlies our
economic intuition. Namely:
EBIDA
PA CAPEX,
9
+EK = a + ACAPEX,,,_,
Hypothesis2
and
Finally we check the EBITDA/CAPEX ratio for autocorrelation of
10
5th
order:
Massachusetts Institute of Technology
The Four Shipping Markets: An Integrated Approach
P
S1=
J15
AJ(EBIDA )+,
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:
P
2
agel0 + f3agel 5 +
P
EBIDA / CAPEX
4
+
Depr = fage5 +
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
Coefficient
Standard Error
t-ratio
P[ITI>t]
Mean of X
.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
-2486298001
48267514E-01
-5.151
.0000
10342361
Variable
AGE1
EC
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
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Massachusetts Institute of Technology
The Four Shipping Markets: An Integrated Approach
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
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
Variable
Rho =
=
.00005
.39251
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
-.1861053410
.38529597E-01
-4.830
.0000
.20429907E-03
EC
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 tstatistics, which implies that EBITDA/CAPEX
is indeed a leading
indicator and can be used to forecast incurred depreciation.
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Massachusetts Institute of Technology
The Four Shipping Markets: An Integrated Approach
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 = none
Dep. Var. = DEPR
Model size: Observations = 108
Residuals: Sum of squares=.1602804337E-01
Fit: R-squared=.206094
Model test: F[ 3, 104] = 9.00
Diagnostic: Log-L = 322.7942
LogAmemiyaPrCrt.= -8.741
Autocorrel: Durbin-Watson Statistic = .21900
Autocorrelation consistent covariance matrix for
Variable
AGE1
AGE2
AGE3
EC
Coefficient
.7283863620E-01
.7463808064E-01
.7299502509E-01
-.2486298001
Mean= .4777638889E-01
Parameters = 4
Std.Dev.= 01241
Adjusted R-squared = .18319
Prob value = .00002
Restricted(b=0) Log-L = 310.3315
Akaike Info. Crt.= -5.904
Rho = .89050
lags of6 periods
Standard Error
.94738787E-02
.91076161E-02
.79729283E-02
.77457980E-01
t-ratio
7.688
8.195
9.155
-3.210
S.D.=1373611057E-01
Deg.Fr.=104
P[ITI>t]
.0000
.0000
.0000
.0018
Mean of X
.33333333
.33333333
.33333333
.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.
13
Massachusetts Institute of Technology
The Four Shipping Markets: An Integrated Approach
The VLCC Case
Following
the
same
steps we
now
run
the
Depreciation
on
the
EBITDA/CAPEX ratio for the VLCC, accounting for size:
Ordinary
least squares regression
Dep. var. = DEPR
Model size: Observations = 108
Residuals: Sum of squares= .3903941156E-
Weighting variable = none
Mean= .5963129630E-01
Parameters = 4
Std.Dev.= .01937
S.D.= .1362702442E-01
Deg.Fr.= 104
01
Fit: R-squared= -. 964796
Diagnostic: Log-L = 274.7216
LogAmemiyaPrCrt.= -7.851
Autocorrel: Durbin-Watson Statistic = .38163
Adjusted R-squared = -1.02147
Restricted (b=0) Log-L = 311.1926
Akaike Info. Crt.= -5.013
Rho = .80918
Results Corrected for heteroskedasticity
Breusch - Pagan chi-squared = 162.7924 with
Variable
AGE1
AGE2
AGE3
EC
3 degrees of freedom
Coefficient
Standard Error
t-ratio
P[ITI>t
Mean of X
.6997216916E-01
.6727099467E-01
.6678394635E-01
.80811075E-02
.72206230E-02
.46288619E-02
8.659
9.317
14.428
.0000
.0000
.0000
.33333333
.37037037
.33333333
-.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 = none
Dep. var. = DEPR
Model size: Observations = 108
Residuals: Sum of squares= .3903941156E-01
Fit: R-squared= -. 964796
Diagnostic: Log-L = 274.7216
Mean= .5963129630E-01
Parameters = 4
Std.Dev.= .01937
Adjusted R-squared = -1.02147
Restricted (b=0) Log-L = 311.1926
LogAmemiyaPrCrt.= -7.851
Akaike Info. Crt.= -5.013
Autocorrel: Durbin-Watson Statistic = .38163
Rho = .80918
S.D.= .1362702442E-01
Deg.Fr.= 104
Autocorrelation consistent covariance matrix for lags of 6 periods
Variable
Coefficient
Standard Error
t-ratio
P[ITI>t
Mean of X
AGE1
.6997216916E-01
.14813474E-01
4.724
.0000
.33333333
AGE2
AGE3
.6727099467E-01
.6678394635E-01
.10572965E-01
.62887299E-02
6.363
10.620
.0000
.0000
.37037037
.33333333
EC
-.1704179991
.76954789E-01
-2.215
.0290
.81344444E-01
14
Massachusetts Institute of Technology
The Four Shipping Markets: An Integrated Approach
The relationship remains statistically strong having corrected for six period's
lags.
15
Massachusetts Institute of Technology
The Four Shipping Markets: An Integrated Approach
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 timeseries 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
Massachusetts Institute of Technology
The Four Shipping Markets: An Integrated Approach
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
Massachusetts Institute of Technology
The Four Shipping Markets: An Integrated Approach
Joint AFRAMAX and VLCC Results - Specification
Ordinary least squares regression - Weighting variable = none
S.D.=.148867641 1E-01
Deg.Fr.= 209
Mean=.5370384259E-01
Parameters = 7
Std.Dev.= .00889
Adjusted R-squared =.64328
Prob value =.00000
Restricted(b=0) Log-L =602.7835
Akaike Info. Crt.= -6.576
Rho =.84712
Dep. var. = DEPR
Model size: Observations = 216
Residuals: Sum of squares=.1652254741E-01
Fit: IR-squared= .69323
Model test: F[6, 209] = 65.62
Diagnostic: Log-L = 717.1665
LogAmemiyaPrCrt.= -9.413,
Autocorrel: Durbin-Watson Statistic =.30577
Variable
Coefficient
Standard Error
t-ratio
P[ITI>t
Mean of X
AGE
VLCC
AFRA
EC
EA
AA
EE
-.2319671183E-02
.1253398320
.1202226475
-.8855295396
.4478081079E-01
-.1171356135E-03
.8564916386
.11188717E-02
.74237274E-02
.77673709E-02
.10003614
.45390247E-02
.51333956E-04
.42653632
-2.073
16.884
15.478
-8.852
9.866
-2.282
2.008
.0394
.0000
.0000
.0000
.0000
.0235
.0459
10.000000
.50000000
.50000000
.92384028E-01
.92384773
116.66667
.96011111E-02
Predicted Values
(* => observation was not in estimating sample.)
Predicted Y
Observation Observed Y
.53132E-01
.82130E-01
1
.50228E-01
2
.81280E-01
.47253E-01
3
.80500E-01
.45531E-01
.78410E-01
4
.43548E-01
.68360E-01
5
.43135E-01
.61330E-01
6
.41381E-01
7
.58610E-01
.38479E-01
8
.56290E-01
.60432E-01
9
.59060E-01
.56894E-01
10
.62980E-01
.56732E-01
.63980E-01
11
.55916E-01
.56930E-01
12
.54892E-01
.43510E-01
13
.53923E-01
.35080E-01
14
.53526E-01
.35080E-01
15
.51201E-01
.30980E-01
16
.47843E-01
17
.22780E-01
.47670E-01
.25000E-01
18
.45208E-01
19
.24830E-01
.45830E-01
20
.26970E-01
.42796E-01
.20400E-01
21
.44441E-01
.23900E-01
22
.47615E-01
.45870E-01
23
.52875E-01
24
.64060E-01
.52436E-01
25
.68740E-01
.60538E-01
.66810E-01
26
.66143E-01
27
.66810E-01
.67725E-01
28
.59920E-01
.54457E-01
29
.52940E-01
.41362E-01
.43670E-01
30
.32845E-01
31
.31720E-01
.19435E-01
.16220E-01
32
.15735E-01
33
.13720E-01
.22403E-01
34
.16040E-01
.34628E-01
35
.17610E-01
.42192E-01
36
.33960E-01
.52883E-01
37
.69680E-01
.51268E-01
38
.68620E-01
.49648E-01
39
.66460E-01
.48722E-01
.63310E-01
40
.47669E-01
.59410E-01
41
.47451E-01
.55670E-01
42
.46534E-01
.54800E-01
43
.45041E-01
.52480E-01
44
.57037E-01
.51130E-01
45
.55003E-01
46
.50580E-01
.54911E-01
.50640E-01
47
.54447E-01
48
.49700E-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
.0163
.0063
.0007
-.
0078
-. 0015
.0023
-. 0011
-.
-.
-.
-.
-.
0032
0020
0064
0170
0082
.0168
.0174
.0168
.0146
.0117
.0082
.0083
.0074
-.
-.
-.
0059
0044
0043
-. 0047
95% Forecast Interval
.0708
.0354
.0679
.0325
.0296
.0650
.0278
.0632
.0613
.0258
.0609
.0254
.0237
.0591
.0207
.0562
.0782
.0427
.0392
.0746
.0744
.0390
.0736
.0382
.0726
.0372
.0716
.0362
.0712
.0358
.0689
.0335
.0655
.0301
.0654
.0300
.0629
.0275
.0635
.0281
.0605
.0251
.0622
.0267
.0653
.0299
.0706
.0352
.0347
.0428
.0483
.0499
.0368
.0236
.0701
.0150
.0010
-. 0030
.0507
.0042
.0168
.0245
.0352
.0336
.0320
.0310
.0300
.0298
.0288
.0273
.0393
.0373
.0372
.0367
.0783
.0839
.0856
.0722
.0591
.0378
.0345
.0406
.0524
.0599
.0706
.0690
.0673
.0664
.0654
.0651
.0642
.0627
.0748
.0727
.0726
.0722
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HH
Massachusetts Institute of Technology
The Four Shipping Markets: An Integrated Approach
We have included the following variables:
-
Age
-
Type
-
EBIDTA/CAPEX
-
The product of EC with Age
-
Age 2
-
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
Massachusetts Institute of Technology
The Four Shipping Markets: An Integrated Approach
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$1 625)+$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
Massachusetts Institute of Technology
The Four Shipping Markets: An Integrated Approach
(D(EBITDA/CAPEX (a + 0 * age) + y +
*age)
+
DeprLnKai=
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.
AFRAMAXVLCC Observations
o 14
0.12
0.1
0 0.08
0 D8
'I.
CL
a)
0.04
0.02
0
-0.02
Observations
23
Massachusetts Institute of Technology
The Four Shipping Markets: An Integrated Approach
VLCC
2
y = 0.8565x -
0.12
0.2137x + 0.0642
0.1
0.08+ MIT-5
0 MIT-10
.0
0.06
4
."..~.4-4MIT-15
----
-(
0.04-
0.02
0
0.02
0.04
0.06
0.08
0.12
0.1
0.14
0.16
EBITDA-CAPEX
Fitted Curves for VLCC vessels with age 5, 10 and 15 years
24
0.18
0.2
Massachusetts Institute of Technology
The Four Shipping Markets: An Integrated Approach
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
Massachusetts Institute of Technology
The Four Shipping Markets: An Integrated Approach
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 = none
Dep. var. = DEPR
Model size: Observations = 323
Residuals: Sum of squares= .2237366571E-01
Fit: R-squared= .721246
Model test: F[ 7, 315] = 116.43
Diagnostic: Log-L = 1088.4528
LogAmemiyaPrCrt.= -9.528
Autocorrel: Durbin-Watson Statistic = .35024
Variable
AGE
SUEZ
VLCC
AFRA
EC
EA
AA
S.D.= .1578811278E-01
Deg.Fr.= 315
Std.Dev.= .00843
Adjusted R-squared = .71505
Prob value =.00000
Restricted (b=0) Log-L = 882.1485
Akaike Info. Crt.= -6.690
Rho = .82488
coefficient
Standard Error
t-ratio
P[ITI>t]
Mean of X
-.3431757693E-02
.1366533138
.1405608564
-1.086932388
.4536886420E-01
1.579992417
.85803367E-03
.55342457E-02
.54618293E-02
.57097227E-02
.66560000E-01
.32199621E-02
.25874240
-4.000
24.692
25.735
24.045
-16.330
14.090
6.106
.0001
.0000
.0000
.0000
.0000
.0000
.0000
9.9845201
.33126935
.33436533
.33436533
.93676594E-01
.93524467
.10048235E-01
-. 6489909736E-04
.39760161E-04
-1.632
.1036
116.33127
.1372882790
EE
Mean= .5284492260E-01
Parameters = 8
We now compare the 2-industry case coefficients with the3- industry case:
Coefficients
2by2
-0.0023
3by3
-0.00343
Suez
VLCC
AFRA
E/C
0.1253
0.1202
-0.8855
0.1366
0.1405
0.1372
-1.0869
AGE*E/C
0.04478
0.04536
Age
ECA2
AGEA2
0.856
1.5799
-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
Massachusetts Institute of Technology
The Four Shipping Markets: An Integrated Approach
squared becomes even higher
linear effect); however, EBITDA/CAPEX
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 Model
Predicted Values
(* => observation was not in estimating sample.)
Observation
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
Observed Y
.82130E-01
.81280E-01
.80500E-01
.78410E-01
.68360E-01
.61330E-01
.58610E-01
.56290E-01
.59060E-01
.62980E-01
.63980E-01
.56930E-01
.43510E-01
.35080E-01
.35080E-01
.30980E-01
.22780E-01
.25000E-01
.24830E-01
.26970E-01
.20400E-01
.23900E-01
.45870E-01
.64060E-01
.68740E-01
.66810E-01
.66810E-01
.59920E-01
.52940E-01
.43670E-01
.31720E-01
.16220E-01
.13720E-01
.16040E-01
.17610E-01
.33960E-01
.69680E-01
.68620E-01
.66460E-01
.63310E-01
.59410E-01
.55670E-01
.54800E-01
.52480E-01
.51130E-01
.50580E-01
.50640E-01
.49700E-01
Residual
.0282
.0306
.0331
.0329
.0251
.0185
.0176
Predicted Y
.53951E-01
.50671E-01
.47363E-01
.45470E-01
.43307E-01
.42859E-01
.40970E-01
.37883E-01
.62353E-01
.0184
-. 0033
.0047
.58248E-01
.58061E-01
.0059
-.
-.
.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
-.
-.
-.
-.
-.
-.
-.
0002
0124
0198
0193
0208
0252
0228
0203
0188
0221
0204
0019
.0104
.0156
.0043
0023
-. 0110
-. 0025
.62478E-01
.69082E-01
.70966E-01
.55453E-01
.40951E-01
.32057E-01
.19240E-01
.16039E-01
-.
.0027
-.
0003
-. 0030
0023
.21931E-01
-.
-.
.33876E-01
-. 0163
.41842E-01
-.
.52323E-01
.50349E-01
.48414E-01
.47327E-01
0059
0079
.0174
.0183
.0180
.0160
.0133
.0098
.46107E-01
.45856E-01
.44815E-01
.43156E-01
.57539E-01
.54957E-01
.54841E-01
.54264E-01
.0100
-.
-.
-.
-.
27
.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
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en m N N N N N N N m e e C H 0 H
H e L LAH L LA
0 0 0 (000000000000000000000000000000000000
0
a) N 0) o
r
LA LA H
00 H
- - N
HHHHHHHHHHHH
CH
W
LAmaNLALA
mLno
a
enenNNeNeNeNNenenennenNnenenenNNNLAANNNNNNNNNALAALANNALALLALNA
nnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnneeeeeeeeeeeeeeeeeeC)"C)nn"eeeC)"C)"eeeeeeeeeee
Massachusetts Institute of Technology
The Four Shipping Markets: An Integrated Approach
310
311
312
313
314
315
316
317
318
319
320
321
322
323
.44820E-01
.47730E-01
.50560E-01
.51830E-01
.51660E-01
.52040E-01
.48780E-01
.47440E-01
.44050E-01
.44590E-01
.42920E-01
.42280E-01
.42140E-01
.43400E-01
.0002
.0029
.0051
.0053
.0043
.0045
.0018
.0020
-. 0004
-. 0018
-. 0112
-. 0118
-. 0046
-. 0013
.44601E-01
.44865E-01
.45458E-01
.46531E-01
.47318E-01
.47561E-01
.46951E-01
.45464E-01
.44459E-01
.46376E-01
.54099E-01
.54077E-01
.46715E-01
.44668E-01
.0279
.0282
.0288
.0299
.0307
.0309
.0303
.0288
.0278
.0295
.0363
.0363
.0298
.0279
.0613
.0615
.0621
.0632
.0639
.0642
.0636
.0621
.0611
.0633
.0719
.0719
.0636
.0614
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
Massachusetts Institute of Technology
The Four Shipping Markets: An Integrated Approach
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, secondhand and scrap prices are quoted in million dollars for each size and
represent the average value of the vessel in any particular month. Timecharter 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
Massachusetts Institute of Technology
The Four Shipping Markets: An Integrated Approach
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
33
run supply curve.
Massachusetts Institute of Technology
The Four Shipping Markets: An Integrated Approach
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.
-2
More 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,
A
VLCC
Suezmax
Handysize
80332.6
8
(1446.863)
[65.033]
[6.3]
86041.6
(1376.958)
(4683
8
(1795)[834
0.00239
(0.0000807
[29,684]
0.00375
(0.0000752
6
)
2
)
0.88
2
Sample Period 1990:1 to 2001:8.
.
Figures
(.)
90141.6
(2981.797
[31.
[49.8761
0.00516
0.000160)
[32.
556]
6
and [.1 are standard
respectively.
34
371]
0.81
0.95
*
in
[68.334]
errors
and t-statistics,
Massachusetts Institute of Technology
The 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
t)
(40,00Dw
180000
160000
c
140000
0
120000
oa
100000
80000
60000,
82
84
86
88
90
FITTED
-
PANEL
C
-
92
OC -
94
96
ACTUAL
00
98
OC
S UEZM AX (140,00ODwt)
250 000
0
1500 00
-
.
200 000
4)
100 0 00.
50000
A
,
CLt
8 2
84
86
-
88
96
90
9 2
94
O
-
ACT U A L
FITT ED
35
C
0 0
98
0 C
I
Massachusetts Institute of Technology
The Four Shipoing Markets: An Integrated Approach
PANEL
D
-
(250,00ODw
VLCC
t)
0
4Lf-
82
84
8 6
--
88
90
O
FITT ED
C
92
94
--
A C T U A L
96
' 98
00
OC
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
Massachusetts Institute of Technology
The Four Shipping Markets: An Integrated Approach
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
1 st
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
and
12 th
1 st
order ARCH effects indicate the existence of autoregressive
conditional heteroscedasticity in all price and profit series.
37
Massachusetts Institute of Technology
The Four Shipping Markets: An Integrated Approach
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, secondhand, 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
Newbuilding
PNB
N
Mean
Var.
248
25.72
47.61
Skew.
-0.62
Kurtosis
1.95
Q0(1)
Q(12)
ARCH(1)
ARCH(12
27.14
249.03
2799.5
241.30
230.79
[0.00]
[0.00]
[0.00]
[0.00]
[0.00]
8.29
244.83
2347.4
223.35
215.25
[0.01]
[0.00]
[0.00]
[0.00]
[0.00]
23.60
230.18
2053.9
183.94
182.80
[0.00]
[0.00]
[0.00]
[0.00]
[0.00]
6.45
241.19
2092.3
228.05
221.42
[0.02]
[0.00]
[0.00]
[0.00]
[0.00]
8.71
248.35
2704.2
237.37
227.30
[0.01]
[0.00]
[0.00]
[0.00]
[0.00]
27.48
247.98
2627.2
240.82
231.42
[0.00]
[0.00]
[0.00]
[0.00]
[0.00]
22.44
240.94
2150.7
230.31
221.26
[0.00]
[0.00]
[0.00]
[0.00]
[0.00]
9.88
244.19
2011.8
215.34
212.81
[0.00]
[0.00]
[0.00]
[0.00]
[0.00]
J-B
Prices
Second-Hand
pSH
248
16.21
22.47
-0.19
2.19
Prices
Scrap Prices
Operating Profits
PsC
n
248
248
1.40
0.140
0.14
0.0049
0.75
-0.25
2.76
2.39
Suezmax
Newbuilding
PNB
248
46.76
141.37
-0.09
2.10
Prices
Second-Hand
pSH
248
29.79
178.49
-0.54
1.77
Prices
Scrap Prices
Operating Profits
PSc
n
248
248
3.95
0.250
1.12
0.0289
0.72
0.48
2.72
2.93
38
Massachusetts Institute of Technology
The Four Shipping Markets: An Integrated Approach
NB
VLCC
Newbuilding
Prices
Second-Hand
Prices
Scrap Prices
Operating Profits
PNB
pSH
PSC
r
248
248
248
248
71.52
43.21
5.60
0.347
327.25
492.40
2.30
-0.41
-0.57
0.76
0.0361
0.63
2.29
1.77
2.81
3.28
12.05
248.12
2741.9
236.31
226.22
[0.00]
[0.00]
[0.00]
[0.00]
[0.00]
29.24
247.87
2672.8
242.48
232.62
[0.00]
[0.00]
[0.00]
(0.00]
[0.00]
24.02
242.93
2198.2
232.42
223.38
[0.00]
[0.00]
[0.00]
[0.00]
[0.00]
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
Handysize
Suezmax
VLCC
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) Qstatistics on the 1 st and
1 2 th
order sample autocorrelation of the
series. These tests are distributed as X 2 (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
Massachusetts Institute of Technology
The Four Shipping Markets: An Integrated Approach
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 3month 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
12 th
order autocorrelation, the Engle (1982) test for 1 st and
1 2 th
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
Massachusetts Institute of Technology
The Four Shipping Markets: An Integrated Approach
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
Massachusetts Institute of Technology
The Four Shipping Markets: An Integrated Approach
Table 3: Summary Statistics of the Excess Returns in the Four Tanker Carriers
N
Mean
Var.
Skew.
Kurtosis
J-B
Autocorrelation
Q(1)
Q(12)
ARCH(1)
ARCH(12)
56.16733
125.72
174.11
90.96
114.26
[0.00]
[0.001
[0.00]
[0.00]
[0.01]
20.24302
173.30
380.22
122.63
135.45
[0.00]
[0.00]
[0.00]
[0.00]
[0.00]
4.018787
135.11
191.80
86.84
100.72
[0.13]
[0.00]
[0.00]
[0.00]
[0.00]
14.73698
182.72
421.35
135.84
147.16
[0.00]
[0.00]
[0.00]
[0.00]
[0.00]
41.58357
127.11
229.38
50.66
95.94
[0.00]
[0.00]
[0.00]
[0.00]
[0.00]
19.45147
185.55
554.82
147.02
160.63
[0.00]
[0.00]
[0.00]
[0.00]
[0.00]
Handysize
3-Month
exr3
245
0.00491
0.0187
-0.472489
5.146887
[0.57]
6-Month
exr6
242
0.01004
0.0412
-0.324835
4.259166
ARCH
[0.44]
Suezmax
3-Month
exr3
245
0.01252
0.0148
0.202677
3.478921
[0.111
6-Month
exr6
242
0.02622
0.0342
0.431222
3.847178
[0.02]
VLCC
3-Month
exr3
245
0.02544
0.0210
0.201585
4.977612
[0.00]
6-Month
exr6
242
0.04967
0.0524
0.532731
3.890990
[0.00]
Philips-Perron Unit Root Tests
Levels
First Diff.
Levels
First Diff.
exr3
-6.51
-
-5.37
-
-6.19
-
First Diff.
3-Month
6-Month
exr6
-5.15
-
-3.94
-
-4.28
-
Levels
VLCC
Suezmax
Handysize
*
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)
and J(i
*
respectively;
their
asymptotic
distributions
under
the
null
I&
are
-.
3~
N(0,6)
4 - 3)- N(0,24).
2
J-B is the Jarque-Bera (1980) test for normality; the statistic is X (2) distributed.
0(1) and
Q
Q(12)
are the Ljung-Box (1978) Q-statistics on the
2
1
s and 1 2 "
order sample autocorrelation
2
of the series. These tests are distributed as X (1) and X (12), respectively.
*
2
ARCH(1) and ARCH(12) is the Engle (1982) test for ARCH effects. The statistic is X distributed with 1
and 12 degrees of freedom, respectively.
*
The lag length for the Philips-Perron test is set at 12.
42
Massachusetts Institute of Technology
The Four Shipping Markets: An Integrated Approach
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
q
p
exr, =a 0 + aexr,+2fs, +c, ,
,~ -iid(,a2)
i=I :1=1
al
6-month
3-month
6-month
3-month
-0.0018
0.0203
0.0020
0.0202
0.0058
0.0457
(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
(0.0678)
(0.0734)
(0.0654)
(0.0690)
(0.0651)
(0.0709)
[0.0490]
[0.0143]
[0.0210]
[0.0786]
[0.0758]
[0.0000]
a3
-
-
(0.0742)
0.2250
0.0145
-0.0690
a2
(0.0650)
-
-
[0.0529]
[0.0118]
0.1310
0.1619
0.2164
(0.0754)
(0.0691)
-
-
(0.0773)
-0.3439
-
-
-
-
-
-
1
p2
-
-
0.9603
0.0861
1.0148
1.0315
1.0048
0.4717
(0.0244)
[0.0000]
(0.0361)
[0.0000]
(0.0049)
[0.0000]
(0.0285)
[0.0000]
(0.0062)
[0.0000]
(0.0457)
[0.0000]
0.9374
0.9697
0.9799
0.9562
1.0071
0.3569
(0.0230)
[0.0000]
(0.0294)
[0.0000]
(0.0001)
[0.0000]
(0.0277)
[0.0000]
(0.0086)
[0.0000]
(0.0586)
[0.0000]
-
(0.0418)
[0.0000]
(0.0247)
-
0.9041
p4
p3s
-
-
(0.0348)
R
0.66
0.4858
0.8293
0.8704
(0.0277)
0.84
-
0.70
0.87
43
(0.0474)
[0.0000]
0.4638
-
(0.0588)
[0.0000]
[0.0000]
[0.0000]
-2
[0.0081]
[0.0000]
-
(0.0406)
0.8482
(0.0288)
-
-
[0.0000]
[0.0000]
(0.0294)
-0.1085
0.8634
0.8312
3
(0.0683)
[0.0000]
[0.0817]
a5
(0.0900)
[0.0171]
[0.0201]
-0.0178
-
(0.0886)
[0.0349]
[0.0717]
a4
6-month
3-month
-
ao
VLCC
Suezmax
Handysize
0.68
0.83
Massachusetts Institute of Technology
The Four Shipping Markets: An Integrated Approach
0.2753 [0.0001
Q(1)
0.1548 [0.000]
0.1144 [0.000]
0.1745 [0.000]
0.0205 [0.000]
1.5362 [0.000]
39.751 [0.000]
Q(12)
9.3866 [0.000]
38.586 [0.000]
7.2272 [0.512]
4.6193 [0.099]
12.181 [0.143]
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(1) and Q(12) are Ljung-Box tests for 1st and 12th order serial correlation in the residuals.
Q
*
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
Massachusetts Institute of Technology
The Four Shipping Markets: An Integrated Approach
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
Ap,=
q
aj,6p,_,
y(p_+0
b-1_
+00)+61-,
q
f=1
=
La
Normalised
Cointegrating
Xtrace
Paro
Parae
Variables
gs
Vector
HA
H
y 2 (Pt-1 + 0 7y1-
Ltrace
Likelihoo
o
0 0 )+F 2
,,
q
An,~=Zc,4O, +ZdjA~c,
Xtrace
Xtrace
90
90%
95
95%
9%
99%
CV's
CV's
CV's
26.04
1.41
17.88
7.53
19.96
24.60
9.24
12.97
21.66
2.20
17.88
7.53
19.96
24.60
9.24
12.97
13.54
3.35
17.88
19.96
24.60
7.53
9.24
12.97
Handysize
369
4.070]
pNB
r=1
r 1
r=2
pSH and c
q=2
[1 -0.322 3.487]
r=0
r=1
r 1
r=2
pSC and n
q=4
[1 -0.257 0.889]
r=0
r=1
r 1
r=2
Suezmax
45
Massachusetts Institute of Technology
The Four Shipping Markets: An Integrated Approach
ppNB
N and n
[1 -0.296
r0O
20.00
17.88
19.96
24.60
4.353]
r=1
1.11
7.53
9.24
12.97
r=0
40.15
17.88
19.96
24.60
r=1
1.71
7.53
9.24
12.97
-
q=3
r 1
r=2
[1 -0.578
4.283]
-
q=2
pSH and t
r 1
r=2
q=3
iT
[1 -0.308
r=0
18.70
17.88
19.96
24.60
1.902]
r=1
4.68
7.53
9.24
12.97
-
pSC and
r 1
r=2
VLCC
[1 -1.024
r0O
11.87
17.88
19.96
24.60
5.415]
r=1
1.74
7.53
9.24
12.97
-
q=3
pNB
r 1
r=2
[1 -2.043
r=0
20.57
17.88
19.96
24.60
5.909]
r=1
1.71
7.53
9.24
12.97
r=0
22.61
17.88
19.96
24.60
r=1
7.55
7.53
9.24
12.97
-
q=3
pSH and n
r 1
r=2
[1 -0.791
q=1
pSC and aT
2.600]
-
r 1
r=2
* The appropriate number of lags in each case is chosen so as to minimise
AIC.
*
trace =
log(1
-T
-
,)
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
Massachusetts Institute of Technology
The Four Shipping Markets: An Integrated Approach
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 EngleGranger 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
Massachusetts Institute of Technology
The Four Shipping Markets: An Integrated Approach
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,_, +0 7t,_ +0 0 )+s 2
11
Newbuilding-price and operating
Second-hand price and
profit equations
operating profit equations
Apt
ECT
1
AnttI
Ant-2
Apt-2
Ant-3
Apt-3
R-bar squared
Apt
Ant,
At
Scrap-price and operating
profit equations
Apt
Air,
-0.0262
0.2743
-0.0524
0.3029
-0.0301
0.3000
(0.0060)
(0.1242)
(0.0127)
(0.1063)
(0.0171)
(0.1149)
-4.3582
2.2075
-4.1048
2.8481
-1.7569
2.6104
0.0042
-0.2340
-0.0103
-0.2066
-0.0007
-0.2690
(0.0035)
(0.0741)
(0.0086)
(0.0715)
(0.0100)
(0.0670)
1.1861
-3.1576
-1.1995
-2.8876
-0.0726
-4.0157
0.1580
0.1330
0.1263
1.0885
-0.1549
-0.7633
(0.0634)
(1.3091)
(0.0653)
(0.5434)
(0.0657)
(0.4402)
2.4908
0.1016
1.9338
2.0031
-2.3567
-1.7340
-0.0027
0.0001
-0.0051
-0.0101
0.0087
-0.0260
(0.0036)
(0.0754)
(0.0080)
(0.0667)
(0.0103)
(0.0692)
-0.7610
0.0016
-0.6478
-0.1523
0.8443
-0.3760
0.0063
-0.5954
0.1312
0.1666
-0.0065
-0.5893
(0.0640)
(1.3226)
(0.0658)
(0.5477)
(0.0644)
(0.4316)
-0.0990
-0.4502
1.9935
0.3043
-0.1020
-1.3653
-0.0045
0.0894
0.0159
0.0657
(0.0035)
(0.0741)
(0.0102)
(0.0689)
-1.2604
1.2075
1.5521
0.9547
0.0430
1.0745
0.1326
-0.2234
(0.0644)
(1.3303)
(0.0645)
(0.4320)
0.8077
2.0558
-0.5171
0.6681
APM
i=1
-0.0030
0.0468
0.0032
0.0471
(0.0033)
(0.0690)
(0.0097)
(0.0653)
-0.9011
0.6785
0.3285
0.7225
0.0587
0.0906
0.0837
0.1312
0.0631
(1.3033)
(0.0639)
(0.4285)
0.9302
0.0695
1.3082
0.3062
0.206
0.114
0.068
0.127
0.096
48
0.137
Massachusetts Institute of Technology
The Four Shipping Markets: An Integrated Approach
LB-Q(1)
0.0040
0.0155
0.1705
0.0114
0.0040
0.0202
[0.949]
[0.901]
[0.680]
[0.915]
[0.9501
[0.887]
LB-Q(12)
4.0354
13.496
12.257
21.761
5.3413
15.328
[0.983]
[0.334]
[0.425]
[0.040]
[0.946]
[0.224]
1.792
0.014
2.149
0.0038
39.280
0.0150
[0.181]
[0.903]
[0.143]
[0.950]
[0.000]
[0.902]
1.040
0.119
2.694
0.1387
3.9598
0.1089
[0.413]
[0.999]
[0.002]
[0.999]
[0.000]
[0.999]
111.1
149653
553.4
136971
4455.4
139745
[0.000]
[0.000]
[0.00]
[0.00]
[0.00]
ARCH(1)
ARCH(12)
J-B
j
-1.86
-3.46
AIC
[0.00]
-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,_,
i=I
1=1
q
q
on~
P,_,+Zd~AEI,_+Y 2( P,-
i=1
Apt-,
Apt.2
Ant-3
Apt-3
+07c,_,+00 )+F-
+07E,_I +00o)+62.,
i=1
Newbuilding-price and operating
Second-hand price and
Scrap-price and operating
profit equations
operating profit equations
profit equations
Apt
ECTtI1
+y ,(p,
,
*
Apt
At
Antt
Apt
At
-0.0121
0.4162
0.0371
0.4138
0.0029
0.3052
(0.0079)
(0.1051)
(0.0093)
(0.0742)
(0.0113)
(0.0815)
-1.5377
3.9598
3.9965
5.5729
0.2620
3.7438
-0.0053
0.0365
0.0137
0.0712
0.0044
0.0163
(0.0083)
(0.0665)
(0.0089)
(0.0639)
0.2556
(0.0048)
(0.0648)
-1.0953
0.5625
1.6528
1.0719
0.4978
0.1430
0.5485
0.2269
-0.2536
0.0467
0.0833
(0.0644)
(0.8554)
(0.0677)
(0.5407)
(0.0634)
(0.4547)
0.1832
2.2203
0.6412
3.3522
-0.4689
0.7361
-0.0014
0.0838
0.0119
0.0909
0.0110
0.0591
(0.0049)
(0.0650)
(0.0081)
(0.0654)
(0.0089)
(0.0639)
-0.2887
1.2885
1.4635
1.3900
1.2407
0.9258
0.0648
0.3602
-0.0093
0.1259
0.0029
-0.5870
(0.0650)
(0.8632)
(0.0670)
(0.5356)
(0.0634)
(0.4543)
-0.1390
0.2351
0.0469
-1.2922
0.9978
0.4173
0.0062
0.1515
0.0065
0.1186
(0.0048)
(0.0649)
(0.0089)
(0.0639)
1.2705
2.3330
0.7352
1.8564
-0.0030
-0.0181
0.6741
0.0947
(0.0644)
(0.8564)
(0.0636)
(0.4556)
-0.2816
0.7871
1.4905
-0.0066
49
Massachusetts Institute of Technology
The Four Shipping Markets: An Integrated Approach
0.049
0.074
0.168
0.138
0.024
0.069
LB-Q(1)
0.0173
0.3001
0.0134
0.0787
0.0006
0.2625
[0.895]
[0.584]
[0.908]
[0.779]
[0.980]
[0.608]
19.020
19.298
17.636
21.967
4.1286
23.668
[0.088]
[0.082]
[0.127]
[0.038]
[0.981]
[0.023]
6.2441
[0.0131]
LB-Q(12)
'
R-bar squared
ARCH(1)
0.1359
6.2026
0.4047
37.607
5.1338
[0.712]
[0.013]
[0.525]
[0.000]
[0.024]
ARCH(12)
0.3042
2.7299
3.2848
8.1329
1.0473
2.8115
[0.988]
[0.001]
[0.002]
[0.000]
[0.4066]
[0.0013]
1853.1
37089
1157.4
20776
78.953
64.097
[0.000]
[0.000]
[0.000]
[0.000]
[0.000]
J-B
AIC
-3.30
[0.000]
-2.05
-2.49
See note in Table 6.
Table 8: Estimated VECM of VLCC Prices & Profits
1=1
i=1
q
p,=XcAp,
+ dAn,_,
+y 2 (P,- 1 +OTIt
i=1
i=1
+0 0 )+e 2
,
q
A
+0t,_, +Oo)+s
,
q
q
Ap, =ZajAp,_, + bAat, +y 1 (p,_
Newbuilding-price and operating
Second-hand price and
Scrap-price and
profit equations
operating profit equations
operating profit
equations
ECTt-1
Apt
Antt
Apt
Antt
Apt
At
-0.0074
0.0479
0.0058
0.0577
0.0180
0.0799
(0.0047)
(0.0185)
(0.0081)
(0.0137)
(0.0098)
(0.0216)
4.2131
1.8309
3.6942
-1.5713
Ant-2
Apt-3
2.5799
0.7176
0.0111
0.1887
0.0587
0.2204
0.0803
0.2005
(0.0164)
(0.0646)
(0.0378)
(0.0636)
(0.0285)
(0.0627)
0.6809
2.9179
1.5503
3.4625
2.8131
3.1962
0.0834
0.1587
0.0601
0.2086
0.0678
-0.1060
(0.0647)
(0.2552)
(0.0655)
(0.1103)
(0.0656)
(0.1442)
1.2883
0.6220
0.9166
1.8912
1.0328
-0.7352
-0.0229
0.0070
0.0739
0.0401
(0.0166)
(0.0655)
(0.0388)
(0.0652)
-1.3807
0.1072
1.9039
0.6152
0.1929
0.6233
0.1313
0.1153
(0.0638)
(0.2515)
(0.0648)
(0.1090)
3.0237
2.4781
2.0267
1.0580
0.0145
0.0183
0.0800
0.0276
(0.0166)
(0.0654)
(0.0388)
(0.0653)
0.8773
0.2799
2.0602
0.4231
0.0136
0.2083
0.0561
0.0164
(0.0655)
(0.2583)
(0.0647)
(0.1089)
0.2080
0.8066
0.8671
0.1509
50
Massachusetts Institute of Technology
The Four Shipping Markets: An Integrated Approach
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]
18.621
11.126
21.816
12.365
3.8960
12.620
[0.098]
[0.518]
[0.040]
[0.417]
[0.985]
[0.397]
0.7737
0.8372
2.3466
1.3952
0.0011
1.2303
[0.379]
[0.361]
[0.126]
[0.238]
[0.972]
[0.268]
0.8342
0.9807
4.6479
1.1234
0.3633
0.9940
[0.615]
[0.468]
[0.000]
[0.342]
[0.974]
[0.455]
13.179
281.57
1320.8
406.81
209.21
297.79
[0.000]
[0.000]
[0.000]
[0.000]
[0.000]
LB-Q(12)
ARCH(1)
ARCH(12)
J-B
[0.000]
AIC
-4.84
-4.33
-5.92
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,
Sscn) (or S(SH,)) to be generated by a
pth
)
(or S,H)), 7rrt and
order trivariate VAR model. The
general VAR model results for the combinations of "newbuilding/secondhand", "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 NeweyWest (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 to
the DPV of operating profits for the next five years plus the DPV of the second-hand price five years later. In the
case of "newbuilding/scrap", the present value model implies that the newbuilding price is equal to the DPV of
operating profits for the entire economic life of the vessel (i.e. 20 years) plus the DPV of her scrap price at the end
of this period. Similarly, for "second-hand/scrap" model, the present value model implies that the second-hand
51
Massachusetts Institute of Technology
The Four Shipping Markets: An Integrated Approach
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
-
t SI"') + 1,1
,
NB,n) B++n
1=1
i=1
5=1
7tr, = p ZTJi" ZPjE,- JPjT 6,
i=1
S(S, aB) ) 2,
t-i3,S H s
i=1
i=I
VLCC
S
NB,n
ar
Suezmax
S(SH,7)
NB,7c)
r
Handysize
S(SH
)
SNB,i
nrt
Sr"0
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.
52
Massachusetts Institute of Technology
The Four Shipping Markets: An Integrated Approach
0.25
0.947
0.20
-0.027
1.184
-0.039 -0.369
5
6
(0.018
9
(0.015
(0.127 (0.101 (0.311
(0.1
(0.0
65)
70)
[0.0
[0.0
00]
00]
-
-
[0.000
76)
I
[0.0
)
)
)
)
(0.0
)
S(NB n
1.26
[0.068 [0.000 [0.693 [0.235
1
1
I
I
-0.345
(0.164)
[0.032]
06]
8
(0.017
(0.0
72)
[0.013
0.395
0.28
0.25
(0.015 (0.126 (0.101
(0.309
7
0
(0.1
(0.0
65)
70)
[0.0
[0.0
83]
00]
0.32
0.24
5
6
-0.204
[0.008 [0.107 [0.706 [0.202
[0.0
01]
]
-0.061
0.15
(0.024
2
)
[0.013
]
75)
[0.0
0.176
-0.016
(0.019 (0.125 (0.101
0.657
(0.0
66)
67)
[0.000 [0.159 [0.867 [0.032 [0.0
[0.0
51]
00]
)
)
(0.305 (0.1
)
(0.0
0.955
)
StsH,n)
0.368
0.038
0.041
)
0.044
0.22
]I
]
1
]
(0.164)
[0.025]
0.583
(0.165)
[0.000]
44]
R-bar
squared
0.932
AIC
1.292
0.105
[0.225]
6.932
6.681
[0.000]
[0.000]
Statistics
DF
p-value
-3782.11
p-value
Statistics
DF
53
0.094
0.093
[1.000]
[1.000]
[1.000]
-4226.43
Wald tests
0.112
0.093
[0.000]
[0.060]
0.795
0.777
7.370
1.741
[0.025]
0.881
0.786
0.933
2.005
ARCH(12)
0.075
-3712.79
Statistics
DF
p-value
Massachusetts Institute of Technology
The Four ShiDpine Markets: An Integrated Approach
[0.157]
5.196
3
3
Var ratio
[0.233]
4.269
Var(as)Nar(ts)
Var(as)Nar(ts)
t-
t-Observed
Observed
tests
[0.072]
3
Var(as)Nar(ts)
t-
Observed
1.432
1.471
0.512
4.11
1.92
-1.72
6.966
* 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 NeweyWest 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
S.E.
and is used for the null hypothesis of the variance
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
Massachusetts Institute of Technology
The Four Shipping Markets: An Integrated Approach
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
Massachusetts Institute of Technology
The Four Shipping Markets: An Integrated Approach
Table 10: Results of the 3 variable VAR model: Newbuildingand Scrap prices
SI NB,.)
NBx)+ l
1=1
i B) 2,I' t-i
1,
Ut
-n
SsH,
)
-
X
3i- iS
(Bx)+X
2 ,i
i=I
1=1
0.983
(0.027
+X
,
3
,
3 ,t
Suezmax
S (SHn)
0.18 -0.043
7
t-
1=1
VLCC
S(NB,T )
,,
3,
=
1=11
5
+
=
s(NBit)
0.963
t
-0.011
Handysize
(SH,
)
-0.029
(0.026 (0.082 (0.143 (0.062
) (0.0
S(NB,I)
[0.000
75)
[0.0
[0.098 [0.000 [0.933 [0.643
]
]
I
13]
-0.005
0.19
0.059
0.005
0.006
0.057
(0.025 (0.083 (0.146 (0.063
70)
[0.848 [0.0
[0.019 [0.952 [0.962 [0.366
05]
)
)
)
)
6
(0.026 (0.0
I
]
]
]
S(SHnF)
s NBiE
3
9
(0.0
48)
(0.0
[0.0
00]
[0.0
01]
0.048
0.02
0.25
(0.048)
4
(0.0~yJ (.
(0.0
[0.319]
4
49)
79)
[0.6
[0.0
12]
01]
-
)
S(sH,)
[0.460
]
(0.0
79)
[0.2
(0.025 (0.083 (0.150 (0.062
1
(0.0
)
6
0.02
-0.004 -0.001
)
(0.026
0.945
0.948
)
0.09
)
0.019
[0.000 [0.960 [0.989 [0.000
I
I
I
I
squared
0.923
[0.6
0.25
0.945
0.25
(0.050)
2
[0.000]
(0.0
5)72)
[0.0
80]
25]
R-bar
(0.047)
[0.591]
78)
- -----------------. t
----------
-0.025
0.94 0.25
0.065
0.019
0.871
0.882
0.926
56
0.791
0.098
0.816
Massachusetts Institute of Technology
The Four Shipping Markets: An Integrated Approach
0.839
1.577
ARCH(12)
[0.100]
[0.611]
[0.001]
[0.001]
[1.000]
[1.000]
[0.002]
[1.000]
-4386.04
-3651.38
-3583.21
p-value
Statistics
Statistics
p-value
p-value
Statistics
DF
[0.014]
11.02
DF
DF
[0.04]
10.47
Var(as)Nar(ts)
t-
Var(as)Nar(ts)
Observed
1.142
0.912
0.737
-1.52
-2.98
Var(as)Nar(ts)
t-Observed
Observed
[0.011]
3
3
3
tests
0.109
[0.462]
7.841
Var ratio
0.100
0.102
2.739
0.988
AIC
Wald tests
2.845
2.857
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
spread series, respectively. T-observed is the given by
t -observed=
Var(as)/Var(ts) -1
S.E
and is used for the null hypothesis of the variance
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
t-
Massachusetts Institute of Technology
The Four Shipping Markets: An Integrated Approach
Table 11: Results of the 3 variable VAR model: Second-hand and Scrap Prices
N
S NBn)
1=
X1[s
)
S
sLC
CB)
i=
1
=1
i=1
l
0.95 1
0.12
(0.01 9
5
(0.0
S(NB,.)
[0.00 0
73)
I
[0.0
1
=1
e2,ia-i d3,iySHs e,
Suezmax
,i
SSH
)
-0.050
SNB,n
Handysize
O( SH ,rl)
)
s
-0.031
0.635
0.182
(0.020 (0.323 (0.090 (0.130
[0.014 [0.050 [0.730 [0.163
1
]
]
0.068
0.399
0.053
-0.195
(0.016 (0.327 (0.091
(0.132
(0.0
)
69)
[0.00 1[0.0
)
7
)
(0.01 5
0.21
)
87]
0.04 9
]
- -------------- ------4 ----------- -----------------. ........
]
]
[0.141
]
-0.372 -0.045
1.181
(0.016
(0.018 (0.330 (0.096 (0.134
[0.029
]
79)
[0.1
)
)
)
(0.0
)
0.953
,s,)
[0.000 [0.260 [0.638 [0.000
I
]
]
]
squared
0.932
0.928
0.23
7
7
(0.0
(0.0
91)
70)
[0.0
00]
[0.0
0.15
2
(0.0
91)
[0.0
96]
0.112
(0.087)
[0.200]
00]
0.24
0.064
4
(0.0
(0.087)
73)
[0.0
[0.456]
01]
0.15
1
0.24
2
(0.0
(0.0
66)
93)
[0.1
[0.0
04]
32]
R-bar
0.78
(SH ,U)
. ......... . ......
- ------ --
-0.035 0.11
)
S
[0.000 [0.224 [0.561
01]
9
s
s( NB,n
)
a
+3,S>
=1
+2
SB")+Z 2,ln3,AS, +
3 Z-
VLCC
S(NB,ic)
n
,
0.112
0.787
0.891
58
0.104
0.775
0.817
1.060
(0.088)
[0.000]
00]
0.104
Massachusetts Institute of Technology
The Four Shipping Markets: An Integrated Approach
1.223
1.532
ARCH(12)
1.382
[0.269]
[0.000]
[0.000]
[0.176]
AIC
Statistics
DF
p-value
11.13
[0.011]
Statistics
4.041
Statistics
DF
[0.256]
22.43
3
t-
Var(as)Nar(ts)
t-Observed
Observed
tests
p-value
DF
Var(as)Nar(ts)
0.75
-2.04
p-value
[0.000]
3
Var(as)Nar(ts)
t-
Observed
1.260
0.744
1.316
[1.000]
-3159.34
-3421.54
3
Var ratio
[1.000]
[1.000]
[0.000]
-3979.01
Wald tests
0.093
0.102
6.349
[0.114]
0.096
6.968
7.561
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
spread series, respectively. T-observed is the given by
t-
observed= Var(as)/Var(ts) -I
S.E
and is used for the null hypothesis of the variance
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
Massachusetts Institute of Technology
The Four Shipping Markets: An Integrated Approach
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
Massachusetts Institute of Technology
The Four Shipping Markets: An Integrated Approach
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
Against the
Support of
EMH
EMH
Against the
Support of
EMH
EMH
Overall
Newbuilding/Secon
d-hand
VLCC
Suezmax
61
Inconclusive
Inconclusive
Massachusetts Institute of Technology
The Four Shipping Markets: An Integrated Approach
Handysize
Support of
Support of
Support of
EMH
EMH
EMH
Against the
Against the
Against the
EMH
EMH
EMH
Against the
Against the
Against the
EMH
EMH
EMH
Against the
Against the
Against the
EMH
EMH
EMH
Against the
Against the
Against the
EMH
EMH
EMH
Against the
Support of
EMH
EMH
Support of
Against the
EMH
EMH
Newbuilding/Scrap
VLCC
Suezmax
Handysize
Second-Hand/Scrap
VLCC
Suezmax
Handysize
62
Inconclusive
Inconclusive
Massachusetts Institute of Technology
The Four Shipping Markets: An Integrated Approach
63
Massachusetts Institute of Technology
The Four Shipping Markets: An Integrated Approach
3. A Stochastic Model for the Depreciation Curves
In our previous empirical analysis we derived the two sufficient statistics or
decision parameters that affect the formation of prices of vessels in the second hand
market. In this section we shall construct a dynamic model for the evolution of the
depreciation curves and propose two simple structural models for the empirical
results 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
Massachusetts Institute of Technology
The Four Shipping Markets: An Integrated Approach
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.
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3.2 The Relation between Renewal Value and Market Value of
Ships
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,
SEC,
=
_
'
D
=
NewBuldingValue, + OtherExpenses
SecondHandValue
(1)
CAPEX - SEC,
AgeofVessel
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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 qtheory 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 qtheory, 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
advantage in productivity and cost effectiveness.
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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.
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3.3 Modelling the Evolution of New Building Prices, Second
Hand 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:
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D(t, T) =F(t,r(t), T) (3), T - t is the remaining economic life of the
-
SV (t,T
)
CX(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 aTdt + FT Y TdW, (6)3
We are now able to construct a portfolio with depreciation prices with
maturity T and S; namely ships with useful lifetime T - t and
S - t respectively. The dynamics of this portfolio are given by:
aT
FT
+
AF'F+0.5Y
F'T
+u
dFs
Fs}(7)
2 FT
_F,7
F
'
70
'
3
TdF T
,
dV=V{u
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The Four Shipping Markets: An Integrated Approach
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
sUsC= 0(8)
TT+
Given the solution to (8) we end-up with the following dynamics for the Vportfolio:
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
s__
_a T-r
-
CS
=X
(10)
CYT
The above equation is the partial differential equation we are looking for and
we shall denote it the Depreciation Term Structure Equation:
T
F' +(-X)F
+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)
d
Therefore: D(T, T) = d (12), d
T
In this context
h-+O
t->T
t--T
d is the incurred
scrap value and obviously (1-
CXT__-_CRAPT_
CX(T)
-
-
SV(T
-
h'T)
CX(T)(T -h)
SCRAP(T)
CX(T)
depreciation of the ship with terminal value its
d) is the
percentage of the scrap value as a
fraction of the value of the new building at time T.
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The Four Shipping Markets: An Integrated Approach
Combining (12) with (11) we have the full description of the Depreciation
Term Structure Equation:
FfT +(
-a)F
+0.5
2F' -
rF"
(14)
d
T
We 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'
D(tT)= E"{ef
d
-} ->
T
t
CX(t) - SV(t, T) = CX(t)Ex{
d (15)}
T
t
-I*r()ds
SV(t, T) = CX(t){1- Ex"{e
d
t-}}
T
The 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
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The Four Shipping Markets: An Integrated Approach
the
charter
time
long-term
rate.
The
formula
evaluated
at
t = 0, t = T yields:
SV(0,T) = CX(O)
SV(T,T)= CX(T){1-Ef{e
T
d
(16)
}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)
= {1- er(t
_d
CX(t)
-} We display this equation for r = 0.07 and
T
d = 0.80,T =25.
Table I
Lifetime of Vessel
->
0
5
15
25
20
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
term E X't {e t
-Jr,()ds
I is an increasing function with respect to t and therefore
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The Four Shipping Markets: An Integrated Approach
T
-Jr(s)ds
Ef'{e
d
}t-is increasing, too and the depreciation curves are a
T
decreasing 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
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The Four Shipping Markets: An Integrated Approach
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
depreciation curves and the functions
A(tT),B(t,T)from
the observed
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
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The Four Shipping Markets: An Integrated Approach
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
, Vt = 5,10,15 is
,'1,T)-rB'1,T)
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.
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m Structure
The Four Shipping Markets: An Integrated App
0.1
VLCC-5
a VLCC-10
VLCC-15
Expon. (VLCC-5)
- Expon. (VLCC-10)
0.0.+
0.08
1
0.07
---
Expon. (VLCC-15)
0.06
4)0.05-
y+ 0.0812e-3.3337x
0.04
R 2 =0.8948
0.03
y0= 0.1265e002
0.01
2
-R
9 1447x
= 0.8959
060e1.5882x
--
y=0.0601e
R 2 =0.9088
0
0
0.02
0.04
0.06
0.1
0.08
EC
Table 2
77
0.12
0.14
0.16
0.18
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The Four Shipping Markets: An Integrated Approach
Suezmax
0.12
0.1
* Suez-5
w Suez-10
*
-
0.08
(D
0.06
.
-Suez-15
.
-Expon. (Suez-5)
Expon. (Suez-10)
Expon. (Suez-15)
-
C.
"
= 0.1449e
R 2 =0.8612
= 0.0885e- 2 1 83 x
R 2 =0.8706
0.02
1.9255
= 0.0593e1
0
0.05
0.15
0.1
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
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The Four Shipping Markets: An Integrated Approach
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.
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4. Integrating the Four Shipping Markets using the Contingent
Claims 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
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The Four Shipping Markets: An Integrated Approach
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 oneyear 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
(Q, 3, P)and
3,,t
> 0 on
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.
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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
1+ nx
a (x)nxdW,
1+ nx
(2)
In the same infinitesimal interval the owner of the asset ship receives a
random capital gain, which using Ito's Lemma is equal to:
1
dF= [F,(x, t) +a(x)xF(x t) +-Iy2 (x)x-e F.-,t)1dt+c7(x)xF(xt)dT
2
(3)
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
2
dt a(x)xF(xt) d
F(xnt)'
FRxt)
(4)
Since our portfolio replicates the risk of the owner of the asset ship:
a (x)xF (x, t)
X dW =a (x)nxdW,
F(x,t)
'
(5)
1+nx
Both holdings must yield the same return in the market or else arbitrage
opportunities would be induced. Thus:
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The Four Shipping Markets: An Integrated Approach
1
[F(x,t)+a(x)xF(x,t)+-2(x)x2 F(xt)]+n(xt)
2
F(x,t)
r + n(a(x)+ )xdt
r(6)
1+ nx
Combining (6) and (5) the value of the ship must satisfy the partial differential
equation:
1
2
-
2 (x)x 2FL(x,t) + (r -6
)xF(x,t) + F] (x,t) - rF(x,t) + 7u(x,t) = 0(7)
The terminal condition for (7) is the following:
(8)
F(x, T - T) = F(0) = ScrapValue(SV)
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)
2
SV(T)
= max[y(T)
-D WT- Scrapping6sts,0]
83
=
0
(10)
2 x
T)___0
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The Four Shipping Markets: An Integrated Approach
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
charter rate 71 (x, t) =
x
365
C(x, t),
where C(x, t) is the running cost
function and the unit for time is days. Assuming that cost increases with time
in the following way:
C(x, t)
=
x
365
K(
F~xt
(x, t) Y
F(x,T)
we have the following
differential equation that characterises the value of a vessel with remaining
lifetime t and current price of the risk factor x:
1
-&(x)xF(xF)+(r-)xF(x)+(xt)-r(xt)+- -K( -"))"=0 (11)
2
365 F(x)
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)}
F(x, I)(T -t)
Thus, equation (12)
(12)
is a sufficient characterisation for the family of
depreciation curves.
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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 +
(14)
(x)dW
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
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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.
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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
dr =v (r,t)dt +G (rt)dZ'
(16)
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:
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The Four Shipping Markets: An Integrated Approach
F +0.50 2F +0.5a 2 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 a
0
simple log - Ornstein - Uhlenbeck process the above specification is reduced
to:
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The Four Shipping Markets: An Integrated Approach
=aitnd is sensitive to technological advances that affect
-
0
0
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
12
0
1158e-s.3'x
R
14%
=0.391
q
*
W
Bulk 70K 5 YRS OLD
.0Bulk 70K 10YRS OLD
=Eupon. (Bulk 70K 10YRS OLD)
E pon. (Bulk 70K 5700S OLD)
*0
*
8%
-V
4
-
6%04+,
0.0564e-
+y
R2 =
9579x
0.3258
2%
2%
0%
4%
6%
10%
8%
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
2Y
+(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
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The Four Shipping Markets: An Integrated Approach
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 qtheory. 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.
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The Four Shipping Markets: An Integrated Approach
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
,EBITDA
x"= EBJ
E
SCAPEX
these
two
factors
and
shall
be
denoted
by
CX and the terminal payoff or scrap value shall be
denoted X4. Then the problem we are interested in solving is stated in
Cochrane (2000) as following:
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The Four Shipping Markets: An Integrated Approach
mA
S = min E' j
-
A,,T
xcds + E'(
AT
SA
A
X)(22)
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
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The Four Shipping Markets: An Integrated Approach
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).
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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
Real options in shipping include the
play (i.e. sale and purchase timing).
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 secondhand 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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The Four Shipping Markets: An Integrated Approach
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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[1] Biais, B., Bjork, T., Cvitanic, J., El Karoui, N., Jouini, E., Rochet, J.C.,
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[14] Stopford, M. Maritime Economics, 1996.
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[15] Tobin, J., A general Equilibrium Approach to Monetary Theory, Journal of
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[16] Zannetos, Z., The Theory of Oil Tanker Ship Rates, MIT Press 1966.
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Massachusetts Institute of Technology
The Four Shipping Markets: An Integrated Approach
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