1 Kavussanos, M.G.*, ‘Time varying risks among segments of the tanker freight markets’, Maritime Economics and Logistics, Vol. V, No 3, 227-250, 2003. *Athens University of Economics and Business, 76 Patission St, 10434, Athens, Greece. Tel: +30 210 8203167, Fax: +30 210 8228816, Email: [email protected]. Abstract The aim of this paper is to investigate the relative risks involved in owning and operating tanker vessels of different sizes in world spot and time-charter markets. Cointegrating Error Correction ARCH models are used to model spot and time- charter rates for each size ship and the associated time varying risks involved. The advantage of using this class of models for analysis is that the error correction term can capture the short run dynamic behaviour of rates, while the estimation of time varying volatilities allows for the explicit comparison of risks at each point in time. Indeed, levels and patterns of freight risk are shown to vary over time. Broadly, comparison of these risks across markets point to time charter rates having lower volatilities in comparison to the spot rates, and freight rates of larger vessels having higher volatilities compared to the freight volatilities of smaller vessels. Thus, for risk averse owners, wishing to reduce risks, results suggest operating tanker ships in time- charter rather than spot markets, and using smaller size vessels to diversify the higher risks involved in owning and operating larger size vessels. Keywords: Tanker freight markets, Shipping, ARCH, Error Correction models Acknowledgement: An earlier version of this paper was presented at the IAME conference in Vancouver, Canada, June 1996, and has appeared during the same year as a working paper at City University, London, UK. The paper has benefited from the comments of an anonymous referee.
Transcript
1
Kavussanos, M.G.*, ‘Time varying risks among segments of the tanker freight
markets’, Maritime Economics and Logistics, Vol. V, No 3, 227-250, 2003.
*Athens University of Economics and Business, 76 Patission St, 10434, Athens, Greece. Tel: +30 210 8203167, Fax: +30 210 8228816, Email: [email protected].
Abstract The aim of this paper is to investigate the relative risks involved in owning and operating tanker vessels of different sizes in world spot and time-charter markets. Cointegrating Error Correction ARCH models are used to model spot and time-charter rates for each size ship and the associated time varying risks involved. The advantage of using this class of models for analysis is that the error correction term can capture the short run dynamic behaviour of rates, while the estimation of time varying volatilities allows for the explicit comparison of risks at each point in time. Indeed, levels and patterns of freight risk are shown to vary over time. Broadly, comparison of these risks across markets point to time charter rates having lower volatilities in comparison to the spot rates, and freight rates of larger vessels having higher volatilities compared to the freight volatilities of smaller vessels. Thus, for risk averse owners, wishing to reduce risks, results suggest operating tanker ships in time-charter rather than spot markets, and using smaller size vessels to diversify the higher risks involved in owning and operating larger size vessels. Keywords: Tanker freight markets, Shipping, ARCH, Error Correction models Acknowledgement: An earlier version of this paper was presented at the IAME conference in Vancouver, Canada, June 1996, and has appeared during the same year as a working paper at City University, London, UK. The paper has benefited from the comments of an anonymous referee.
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1. Introduction
Uncertainty is central to business decision making. Not least so in world shipping
markets where companies have collapsed overnight due to disastrous miscalculations
of the risks involved. It is therefore of outmost importance to be able to calculate
risks, and possibly try to minimise them through some diversified portfolio of
(shipping) assets. If one considers shipowners as profit maximizing `agents' which
hold portfolios of shipping assets, then measures of risk in conjunction with returns
must be considered when selecting the type of assets to include in their portfolio (see
for e.g. Markowitz(1952)).
However, this methodology, despite its promising results elsewhere, has not been
applied before in shipping markets, with the exception of Kavussanos(1996a, 1996b,
1997, 2002). The aim of this paper is to extent the ARCH class of models to
investigate volatility in the spot and time charter markets of tanker vessels. In
particular, it tries to answer the following two questions which are of extreme
importance to `agents' involved in the shipping industry: a) `Is volatility higher in the
spot or in the time-charter market?', and b) `Are these markets riskier for smaller size
or larger size vessels?'.
Thus, shipowners for example that operate in tanker trades are faced with the
decision of whether to employ their vessels in the spot or time charter market, and
also in what size ships to invest on. Broadly, three weight categories of tanker ships
carry the bulk of crude oil trades. Aframax (80,000 dwt), Suezmax (140,000 dwt) and
VLCC/ULCC (250,000 dwt), and clean(oil) products are carried mainly by the
Handymax (40,000 dwt) category. Suezmax and VLCC vessels transport mainly
crude oil, while part of the Aframax fleet is used in clean products transportation.
Furthermore, each size ship is used in different routes. VLCC's trade in 4 major
routes, Suezmax can use the Suez canal, and are in that sense more flexible for
employment, while Aframax can approach even more ports since they face less draft
restrictions than the other two sizes. Finally Handymax have very few draft
restrictions and operate in specific 'pockets' of the world, such as the Caribbean,
Pacific basin etc. All the above is summarised in table 1.1. Shipowners then will
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typically consider the risk/return trade-off in different weight categories and also in
the spot vs time-charter markets and invest or speculate accordingly.
The importance of risk in finance is embedded in theories such as asset pricing,
option pricing and the construction of hedge portfolios just to mention a few. While it
was recognized early enough that uncertainty in prices, as measured by their
variances and covariances, are not constant through time (see for e.g. Fama(1965)), it
is not until recently that the technical statistical tools have been developed to deal
with the problem.
Since the seminal article of Engle(1982) who introduced the class of Autoregressive
Conditional Heteroskedasticity (ARCH) models, several extensions and variations of
it have appeared in the literature (see for e.g. the excellent surveys by Engle(1993)
and Bollerslev et al(1992)). An abundance of empirical work has employed this
methodology to model stock return data, interest rates, foreign exchange rates, price
inflation rates etc. It is found that, apart from allowing one to estimate variability of
prices over time, estimation results are improved by using ARCH models over the
simple assumption of constant variance throughout the estimation period employed by
OLS.
This paper extends the class of ARCH models to the shipping industry in order to
measure and compare time varying risks in the world tanker freight and time-charter
markets for different size vessels. In particular, spot freight rates and time-charter
rates on Handysize, Aframax, Suezmax and VLCC vessels, and the time varying
volatilities of the return on each is measured and compared between spot and time
charters and between sizes. Furthermore, the class of ARCH models are combined
with the cointegration approach to modelling the conditional means of variables.
The paper is in six main sections apart from this one. The theoretical framework for
determining the conditional means of freight and time charter rates is set out in the
next section. Section 3 discusses the methodology of determining jointly the
conditional means and variances of the above variables in an error correction-ARCH
4
framework. Section 4 looks at the data, section 5 presents the results, section 6
provides a discussion of the results, while section 7 concludes.
2. The theoretical models of freight and time charter markets.
2.1. The spot freight rate market
Examples of past efforts to model the freight market may be found amongst others in
the works of Koopmans(1939), Zannetos(1966), Hawdon(1978) and Beenstock and
Vergottis(1993). In all these studies there is universal support to the notion of a
perfectly competitive freight market in the tanker sector. Market clearing spot freight
rates, FR, are in that sense moving quickly to bring a perfectly inelastic demand for
freight services into equilibrium with supply. The spot rate then varies directly with
the demand for shipping services Q, and with the price of bunkers Pb (since higher
transportation costs will be passed on partially or on the whole to freight rates), and
inversely with the size of the fleet K (since an over-supply of freight services will
exert negative pressures on freight rates).
)1.2(),,(
KPbQfFR
Equation (2.1) expresses the above mathematically, where signs on top of variables
are partial derivatives, indicating how each of the variables on the right hand side of
the equation, ceteris paribus, affects the dependent variable. It is a reduced form
equation for the freight rate with all the right hand side variables being exogenous.
2.2. The time charter market
Under a time charter agreement the shipowner does not pay bunker costs. He has the
option to let the vessel either on the spot or the time charter market. His choice of
alternative depends on the relative profitabilities of the two options. Time charter
5
rates(TC) thus reflect expectations of future profitability in the spot freight market,
which in turn depends positively on expected freight rates Et (FRt+1 ) and negatively
on expected bunker prices Et (Pbt+1) – see Beenstock and Vergottis(1993), amongst
others for this. Assuming one period horizon one can write:1
)2.2(])(,)([( 11
ttttTC
t PbEFREfTC
It is assumed that expectations of future freight and bunker prices are rational in the
sense of Muth(1961). That is, agents base their expectations on the best available
information.
3. Methodology
Equations (2.1) and (2.2) above can be written as:
yt = x't b + t ; t ~ IN(0, h), (3.1)
LL = -(T/2)lnh - (1/2h) t
2t
where t is a white noise error term with the usual classical properties2, xt is the matrix
of right hand side variables, b the associated vector of coefficients and LL is the
corresponding log-likelihood function after omitting the irrelevant constant, with T
representing the sample size.
Building an ARCH model to describe a stochastic variable of interest, may be
summarized in three steps: i) Specify the conditional mean of the variable of interest,
ii) Specify the conditional variance of the variable, iii) Specify the conditional density
of the error term in the model. Consider each step.
3.1. Cointegration and Error Correction Models
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For step i of the problem, the theoretical specification of the conditional mean of
freight and time-charter rates is established in equations (2.1) and (2.2), and
summarized in equation (3.1).
Following the results of amongst others Engle and Granger(1987) and
Johansen(1988), estimating meaningful long run relationships, such as those specified
in equations (2.1) and (2.2), requires some further terminology. A stochastic variable
yt is said to be integrated of order d, denoted yt ~I(d), if it needs to be differenced d
times in order to become stationary 3. Most economic variables follow I(1) processes;
that is, yt( =yt - yt-1 )~I(0), and the series are said to have a unit root.
For a time series regression model to be fitted to a set of I(1) variables (and an I(0)
variable), the variables must be of the same order of integration. In general, a linear
combination of a set of I(1) variables, say (yt -xt'b)=t, will be I(1). In the special case
when this linear combination, t, is an I(0) variable, it is said that the variables are
cointegrated, denoted CI(1,0) with a cointegrating vector (1,-b); that is, there is a long
run relationship between the variables, in the sense that following a shock, the system
will eventually return to equilibrium.
The implications of this are two fold. First, the regression variables are related
through some long run `economic' relationship which keeps (attracts) them together in
the long run. Any correlation between the variables is not spurious, a result of each of
them having unit roots (see for example Engle and Granger(1987)), and it makes
sense to run the regression. Second, the classical distribution theory may be used to
make inferences in cointegrated systems, regarding linear restrictions on the
parameters (see for example Johansen and Juselius(1990), Johansen(1991) and
Phillips(1991)).
Furthermore, following the Granger representation theorem an Error Correction
Model (ECM) may be estimated for a set of cointegrated variables and visa-versa.
That is (3.1) may be written as:
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yt = ao + a1 (yt-1-x't-1b ) +
m
iity
1i c +
m
iitx
1i d + t ; t ~ IN(0,h) (3.1.1)
All the variables in the above equation are I(0) and as a result inference in this
equation is valid. The ECM specification captures both the short and long run
dynamics in the relationships. The coefficient a1 of the error correction term
represents short run adjustments of deviations from equilibrium.
3.2. Tests for non-stationarity (unit roots) and cointegration
To test for the presence of a single unit root in a series yt against the alternative of
stationarity around a deterministic linear time trend t, the following Augmented
Dickey Fuller(1981) (ADF) regression may be used:
yt = ao+ a1t + 0 yt-1 +
p
1i
i y t-i + i ; t ~ IN(0,h) (3.2.1)
Where the Null of a unit root is H0 : 0 = 0, and sufficient lags of yt are included to
make the stochastic term white noise. When p=0 the test is the simple Dickey-Fuller
test(DF). Evans and Savin(1984) suggest the inclusion of a linear time trend to make
the distribution of 0 and its pseudo t-statistic independent of the unknown intercept
a0. This is true even if a1 is insignificant. Critical values of the empirical distribution
of 0 are derived in MacKinnon(1991).
If the null of a single unit root is rejected the series in levels is declared I(0). If the
null is not rejected, then one should test whether yt has a unit root (that is of the
existence of two unit roots in yt ). The procedure is the same as before, only that yt-1
becomes yt-1 and yt become yt in equation (3.2.1). If the null of a unit root in
yt is rejected then yt ~I(1), equivalently yt ~I(0). If the null is not rejected similar
tests should be conducted for a third unit root and so on.
8
Dickey, Fuller and Pantula(1987) show that use of the ADF test for a single unit root
makes the asymptotic pseudo t distributions of 0 sensitive to the number of unit roots
in the data, with the null of a single unit root rejected too often. To avoid the problem
they recommend a sequential testing procedure as a complementary test, under which
tests are performed for three unit roots, then for two, then for one unit root in the data.
This is the approach used in this paper.
Once it is established that the variables are integrated of the same order, tests of
cointegration may be performed to see if there exists a long run relationship between
the variables, such as those specified in (2.1) and (2.2).
Engle and Granger(1987) propose that testing for a unit root in the residuals of
equation (3.1) determines the absence or presence of cointegration. The ADF
regression (3.2.1) may be used to test the null of no cointegration, that is of a unit root
in the estimated residuals.4
3.3. Error Correction Models and ARCH specifications
Once an error correction model of cointegrated variables is obtained, Ordinary Least
Squares(OLS) or Maximum Likelihood Estimation(MLE) yield the BLUE of the
parameters of interest a0, a1, ci, di and h in equation (3.1.1). However, when the
assumption of constant variance of t (or equivalently of yt ), h, fails, then even
though the estimated parameters remain unbiased and consistent, they are inefficient
(their variance does not reach the Cramer-Rao lower bound). In addition, the
estimated variances of the estimated parameters will be biased estimators of the true
variances of the estimated parameters (see for e.g. Pindyck and Rubinfeld(1991)).
These difficulties can be overcome by using models of conditional variances, such as
ARCH, Generalised ARCH (GARCH) etc (for a survey see Engle(1993)). Thus, in
the 2nd step of the problem of ARCH specification the variance is conditioned on the
available information set, in conjunction with the conditional mean.
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GARCH formulations capture the tendency for volatility clustering, i.e. the tendency
for large (small) swings in prices to be followed by large (small) swings of random
direction. An important consequence of GARCH models is that their parameters can
be estimated from historical data and used to model and forecast future patterns of
volatility. Milhoj(1984) shows that ARCH processes are `fat-tailed' compared to
normal distributions and that makes ARCH models suitable for modelling asset
returns.
An empirically successful parameterisation for ht is the GARCH(p,q) model of
Bollerslev(1986). In this model ht is expressed as a linear function of p values of
past squared errors, and q past values of the conditional variances ht:
yt = a0 + a1 (yt-1 - x't-1 b) +
m
iity
1i c +
m
iitx
1i d + t ; t ~ IN(0, ht)
ht = 0 +
p
1i
i 2t-i +
q
1j
βj ht-j
LL = - (T/2) lnh t - (1/2h t) t
2t
where αo > 0, αi , j 0 for non negativity of the variance. Nelson and Cao(1992)
have shown that although these conditions are sufficient to ensure non-negativity,
weaker sufficient conditions may be found for GARCH models with order of p or q
higher than 1. For example, in a GARCH(2,1) model 2 may become negative. Also
for stationarity of ht, (
p
1i
i +
q
1j
j ) 1.
MLE of the GARCH parameters ai , ci , di, i and j are asymptotically superior to
performing OLS on the GARCH model, in terms of efficiency, since the latter do not
achieve the Cramer-Rao lower bound, as demonstrated by Engle(1982). MLE
estimation is nonlinear and may be achieved by solving the first order conditions with
respect to the parameters i, j, ai , ci and di , using some numerical optimization
method.5
10
The procedure of specifying the conditional variance of the ARCH model is an
extension of the Box-Jenkins approach of specifying the conditional mean.
Identification of the correct ARCH process may be achieved by examining the
autocorrelation function of the squared residuals of the estimated error correction
model (see Weiss(1984) and Bollerslev(1986)). In practice, the appropriate lag
structure for the conditional variance is decided both by examination of the
autocorrelation function of the squared residuals, and by likelihood ratio tests in a
series of nested ARCH/GARCH models.
The GARCH(p,q) model is only one in a series of ARCH models, with `exotic' names
such as ARCH and GARCH in Mean, Exponential, Augmented, Asymmetric,
Modified, Multiplicative, Nonlinear, Threshold ARCH, etc (see Engle(1993)). Each
of these have advantages over the original ARCH (under which q=0 in equation
(3.3.1)) in fitting particular time series. However, most investigators have found that
the GARCH(1,1) is a generally excellent model for a wide range of financial data (see
for e.g. Bollerslev(1986), Engle and Bollerslev(1986)) and Engle(1993)).
The third step in ARCH modelling refers to diagnostic checking, to ensure that the
chosen model is well specified. The following diagnostic tests on the standardized
ARCH residuals, et / h t (denoted eh), and standardized squared ARCH et2 /ht
residuals are used to evaluate the models.
i) The Durbin-Watson statistic (DW) testing for first order serial correlation in the
residuals (see Pindyck and Rubinfeld(1991).
ii) The Ljung-Box(1978) Q portmanteau statistic (Q(12)) on the first 12 lags of the
autocorrelation function, distributed as chi-squared with 12 degrees of freedom; that
is testing for high order serial correlation.
ii) The Ljung-Box test on the first 12 lags of the autocorrelation function of the
squared standardized ARCH residuals (denoted Q2(12)); that is testing for high order
heteroskedasticity.
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iv) Finally, coefficients of skewness and kurtosis denoted respectively SK(.) and
KU(.) are calculated for the standardized ARCH residuals.
Standard errors (se) and R-Bar square values (RBSQ) are also reported as measures of
goodness of fit of the equations.
4. Data
Monthly data for one year time-charter rates in $/day for Handymax(40,000) denoted
TCH, Aframax(80,000 dwt) TCA, Suezmax(140,000 dwt) TCS and VLCC(250,000
dwt) TCV, vessels in the tanker sector come from Clarkson Research Studies Ltd.
Lloyds ship manager spot freight rate indices in worldscale=100 for the same
categories vessels(denoted FRH, FRA, FRS and FRV) are published in the Institute of
Shipping Economics and Logistics'(Bremen) yearbook. Bunker prices in $/ton of
heavy fuel oil PB, demand (QH, QA, QS, QV) and supply (KH, KA, KS, KV) for
shipping services in million dwt for 10-40K, 40-150K and 150K plus dwt come from
the Lloyds shipping economist. Due to lack of sufficient disaggregation of the
demand and supply data, the 40-150K series of the latter are used both in the Aframax
and Suezmax categories when modelling freight rates. Aggregate freight and time-
charter series (FRAGR and TCAGR) for the tanker sector are constructed as weighted
averages of the individual series, where the weights used are the fleet size for each
category. The longest period covered with the available series is 1979:1 to 1994:3.
Summary statistics of first differences in the logs of spot and time charter rates for
Handymax, Aframax, Suezmax, VLCC and aggregate series denoted DLFRH,
DLFRA, DLFRS, DLFRV, DLTCH, DLTCA, DLTCS, DLTCV, DLFRAGR and
DLTCAGR are calculated over the period 1980:2 to 1993:12. The results are shown
in table 4.1.
The leptokurtic property of the sample distributions of monthly returns in spot and
time-charter markets is evident in the data. The coefficients of skewness and kurtosis
particularly, indicate significant excess skewness and kurtosis across the data apart
12
from the Handy, Suez and VLCC coefficients of skewness and the kurtosis coefficient
of VLCC in the spot market 6. Leptokurtosis seems to be substantially higher in time-
charter markets.
Preliminary comparisons of unconditional volatilities between pairs of spot versus
time charters for different size vessels and the aggregates, and between sizes for both
the spot and time-charter market over the whole period are made using the F-statistic
F=S12 / S2
2 ~ F (n-1,m-1); where S12 , S2
2 are the variances of changes in logs of
freight rates of, say, two different size vessels, with S12 greater than S2
2 , and n-1, m-
1 referring to the degrees of freedom of the samples that S12 and S2
2 come from
respectively.
Results in table 4.2 show that variances of spot rates(FR) are significantly above the
corresponding time-charter rates(TC) for the aggregate tanker sector and for each
category of vessels (except for Aframax). The results are not so clear cut when
comparing variances in time-charter and spot rates across sizes, in table 4.3. Thus, in
the spot market, the VLCC volatility is significantly above those of the other sizes.
The Handy is below the Aframax and Suezmax, however the Aframax is
insignificantly higher than the Suez. In the time-charter market, again the VLCC
variance is significantly above the other sizes apart from the Aframax one. The
Handymax is significantly below the other sizes except for Suez(however
insignificant), and somewhat 'strangely' the Aframax volatility is significantly higher
than the Suez one.
However, if one wants to have a closer look at the patterns and relative levels of these
volatilities for individual size vessels, at each point in time, one needs to model the
latter using the class of ARCH models.
In order to fit a meaningful model to a set of random variables, these variables should
be of the same order of integration and they must be cointegrated. Tables 4.4 and 4.5
present Augmented-Dickey-Fuller(ADF) tests (see Dickey and Fuller(1981)) on the
logarithms and the logarithmic first differences of each variable respectively, utilizing
equation (3.2.1). The results indicate that the former set of variables are I(1), while
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the latter are I(0). Engle-Granger cointegration tests performed for each equation in
table 4.6, indicate the existence of a long run relationship in each case. As a result an
error correction model(ECM) as proposed in equation (3.1.1) may be estimated in
each market.
5. Results
The discussion in this section is focused on the final ECM-ARCH selected models,
since conclusions regarding volatilities are based on these specifications. Thus, once
specification of the conditional mean as an ECM takes place, the Berndt, Hall, Hall
and Hausman(1974) algorithm is used to estimate the ARCH models for DLFRH,
DLFRA, DLFRS, DLFRV, DLTCH, DLTCA, DLTCS, DLTCV, DLFRAGR and
DLTCAGR. The results are in tables 5.1 and 5.2.
Likelihood ratio tests lead to selection of ARCH(1) models for individual categories
in the spot market and a GARCH(1,1) model for the corresponding aggregate, while
in the time-charter markets an ARCH(1) for Handy and Suez, an ARCH(3) for
Aframax, a GARCH(1,1) for VLCC and a GARCH(1,2) specification for the
aggregate tanker sector are appropriate. April(m4), May(m5), July(m7), August(m8)
seasonals in the Handy volatility and January(m1), February(m2), April(m4) and
July(m7) seasonals in the Aframax volatility in these time-charter markets are also
found significant.
In the specifications of the individual conditional means every error correction
term(ECT) is significant - negative, as expected from variables in a long run
relationship. These ECT's, summarized in table 5.3, indicate the short run adjustment
to long-run equilibrium, and as can be seen they are substantially higher in the spot as
compared to the time-charter market. The implication is that the spot markets react
more swiftly to return to long run equilibrium, indicating higher levels of risk.
Comparison of ECT's between vessel sizes reveals that the magnitude of the short run
disequilibrium increases with size in the time-charter markets. In the spot markets the
14
ranking by size is preserved, apart from the Suezmax ECT which is the lowest. The
results are consistent with the earlier rankings of risk based on the variance statistics.
In table 5.1 the conditional means for spot-freight markets indicate significance of:
the first and second period lag values of bunker prices in the Handy market, the
demand for freight services in the Aframax market while supply for freight services is
not significant in any market. A dummy variable, d, taking the value of 0 up to 1986:3
and 1 thereafter (to account for these differing periods of the shipping industry) is
required in the Handy market. Specification of the conditional means of time-charter
markets, in table 5.2 shows significance of various order lags of the dependent
variable in markets, indicating the dynamic nature and the expectations involved in
time-charters. Some seasonality is also observed in the Suemax and VLCC markets –
see Kavussanos and Alizadeh (2002) for a more formal analysis of the issue.
The diagnostics of the estimated systems, presented at the end of tables 5.1and 5.2,
show that the equations are well specified, with no evidence of serial correlation or
heteroskedasticity as indicated by the DW, LJBQ(12) and LJBQS(12) statistics.
Goodness of fit is satisfactory with se's ranging from 0.04 for DLTCS to 0.17 for
DLFRV.
There is evidence of persistence in variance for time-charter VLCC and aggregate
series as indicated by the sum of the ARCH coefficients being greater than one.7
Current information remains thus important for the forecasts of conditional variances
for all horizons. This class of models is known as Integrated GARCH, IGARCH, after
Engle and Bollerslev(1986). The result is a common finding across much of the
literature using high frequency financial data, see Bollerslev et al(1992). However,
Nelson(1990) and Bougerol and Picard(1992) show that IGARCH models are strictly
stationary and ergodic, though not covariance stationary, and Lumsdaine(1991) shows
that standard asymptotic inference procedures are valid in IGARCH models.
Having modelled the conditional standard deviation in each market, these time-
varying measures of risk are extracted, and their behaviour examined over time and
compared across markets in figures 1 to 7.
15
6. Discussion of the results
Risks in the freight and time-charter tanker markets are not constant over time, as
manifested by the need for ARCH modelling of the conditional variances. Such time
varying risks are a combination of industry-market risk and `idiosyncratic' risk
(relating for example to the individual vessel size). As long as one is faced with more
than one options over choices, then idiosyncratic risk may be diversified. The
shipowner, for example, may choose to use the spot instead of the time-charter
market, or may decide on alternative size ships to invest upon.
Consider first how the industry has been affected across markets, by examining
figures 1, 2 and 7. A clear tendency for volatility clustering is observed. That is, large
changes in volatilities tend to occur around certain periods of time, which are then
followed (preceded) by small changes in volatility. Volatility is high during and just
after periods of large shocks and imbalances in the industry. For example the 1980-81
oil crises, coupled with the decline in the demand for shipping services, due to the
lower than expected growth in world demand following the second oil shock, the
supply of oil restrictions imposed by the OPEC production ceiling in 1982/83, the
targeting of ships in the Gulf in 1984, the sharp decline in oil prices in 1986 with its
lasting effect and the 1990-91 period of the Gulf-war are particularly visible.
The above incidents are manifested in patterns of risk which are different between
sizes and between the spot and time-charter markets. Thus, figure 7 for example
reveals that the fluctuations of risk in the spot market are relatively smoother as
compared to the time-charter market. Responses of the latter are strikingly sharper as
expectations are built into this market. Time-charter risk is particularly sensitive in
the pre-1987 depression era, while it is much smoother once the upturn takes place.
Furthermore, there is a downward trend in this index, reflecting the less risky, more
steady environment faced by the industry after 1987.
16
Going back to figure 1 it may be seen that the fluctuations in the aggregate time-
charter index may be attributed mainly to the VLCC and Aframax sectors. In
particular, VLCC vessels trade in four routes only (since there are draft restrictions in
them approaching certain ports of the world) all lifting oil from the Gulf, which were
severely disrupted in periods of crises; as a result volatility for this category is the
highest (in the spot market also, as seen in figure 2) and fluctuations are a lot sharper
than any of the other sizes.
The Handymax volatility is the lowest in both the spot and time charter markets
reflecting the steady trades this type of ships are involved in. The Suezmax and
Aframax volatilities fluctuate between the Handymax and VLCC. In the spot market
the levels of these volatilities are interchanged with neither being significantly above
the other, however in the time charter market the Aframax volatility is clearly above
the Suezmax one. This somewhat peculiar result calls for further examination of the
Aframax and Suezmax sectors, perhaps in a separate study.
Overall it may be said that the shipping markets tend to respond together to external
shocks, and yet quite differently implying market segregation between different size
ships. That is, there are some common driving forces of volatilities in different size
vessels, and yet there are idiosyncratic factors to each market that make each size-ship
volatility move at its own level and in its own way. These idiosyncratic factors relate
to the type and number of routes each size ship is engaged in. Thus, the VLCC
volatility is the highest and is very sensitive to its thin market conditions as revealed
by its hikes, while that for the Handy vessels is the lowest, in both the spot and time-
charter markets.
The results suggest that risks in the larger VLCC sector may be mitigated by holding
Suezmax, Aframax and especially Handymax vessels. Hence, risk averse investors in
shipping can diversify risks in their portfolios by heavier weighting towards smaller
size vessels. Similar opportunities for diversification may also arise by positioning
vessels of each category in specific routes – however, this is a matter of further
investigation and requires a different dataset to the one used in this paper.
17
With respect to the choice between spot and futures markets, volatilities are compared
in figures 3-7 between time-charter and spot freight rates for each size vessel and the
aggregate tanker sector. Figures 3 and 5 reveal that the volatility of spot-freight rates
in the Handymax and Suezmax sectors are clearly above the corresponding time
charter ones over the whole period.
The results are not so neat for the Aframax and VLCC markets. Figure 4 shows that
before 1987 the Aframax time charter volatility was mostly at a higher level than the
spot one, with the reverse occurring once the market recovered. The fluctuations of
time charter risk in the early period are sharp and in wider bands as compared to the
post-87 period, forcing the average in table 4.2 to be insignificantly above the spot
rate. The story is similar in the VLCC sector. The downward trend in time charter risk
lying constantly below the spot rate level of risk from 1988 onwards is particularly
noticeable.
Comparison of risks in the aggregate tanker sector in figure 7 shows similar patterns
as those observed in the VLCC sector. This is not surprising since the bulk of the
tanker fleet in dwt is in this sector, 3/5 of the fleet in 1994. For research purposes it
points to the fact that using disaggregated data to compare risks between spot and
time charter markets can enlighten significantly one's results, eliminating the likely
distortions that emanate from the use of aggregate figures. As a consequence, policy
implications may also be spared from mistakes.
Policy implications for risk averse shipowners with a choice of employing ships
between the spot and time charter markets, point to preferring the lower risk time
charter market over the spot market in general. However, in prolonged 'bad' periods
for the industry, time charter risk in the Aframax and VLCC sectors may rise above
the corresponding spot market risk.
7. Conclusions
18
In sum, the level and patterns of risk between spot and time-charter freight markets
and between different size vessels in the tanker industry vary with time and market.
Industry risks seem to be lower in the relatively calm post-1987 period compared to
the early part of the 1980's. The message for prospective investors is that the tanker
shipping industry is becoming safer to invest. However, comparison of risk with other
industries should enhance the information set of such investors. For existing risk-
averse investors in the tanker industry, the results point to: a) using the lower risk
time-charter markets but beware of the possible escalation of these, particularly for
VLCC and Aframax, above the spot market risk in turbulent periods, b) use smaller
size vessels to diversify the inherent risks in the 'thin' markets VLCC ships operate
on.
19
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20
Kavussanos, M. G. (2002), ‘Business Risk Measurement and Management in the Cargo Carrying Sector of the Shipping Industry’, in Eds. Grammenos, C. (2002), ‘The Handbook of Maritime Economics and Business’, Lloyds of London Press, Chapter 30, pp 661-692. Kavussanos, M. G. and Alizadeh, A., (2002), ‘Seasonality patterns in tanker shipping freight markets’, Economic Modelling, Vol. 19, Issue 5, p 747–782, Nov. 2002. Koopmans, T. C. (1939), `Tanker freight rates and tankship building', Haarlem, Holland. Ljung, G. M. and Box, G. E. P., (1978), `On a measure of lack of fit in time series models', Biometrika, 65, pp. 297-303. Lumsdaine, R.L. (1991), `Asymptotic properties of the maximum likelihood estimator in GARCH(1,1) and IGARCH(1,1) models', Unpublished manuscript, Dept. of Economics, Princeton University. MacKinnon, J. G.(1991), `Critical values for cointegration tests', in Engle, R. F. and Granger, C. W. J. (eds), `Long-run economic relationships: Readings in cointegration', Oxford University press, p. 267-76. Markowitz, H. (1952), `Portfolio selection', Journal of Finance, Vol. 7, March, pp. 77-91. Milhoj, A. (1984), `The moment structure of ARCH processes', Research report 94, Institute of Statistics, University of Copenhagen, Copenhagen. Muth, J. (1961), Rational expectations and the theory of price movements', Econometrica, Vol. 29, July. Nelson, D. B. (1990), `Stationarity and persistence in the GARCH(1,1) models', Econometric Theory, 6, pp. 318-334. Phillips, P.C.B. (1991), `Optimal inference in cointegrated systems', Econometrica, Vol. 59, No 2, pp. 283-306. Pindyck, R. S. and Rubinfeld, D. L. (1991), `Econometric models and economic forecasts', McGraw-Hill. Weiss, A. A.(1984), `ARMA models with ARCH errors', Journal of Time Series Analysis, Vol. 5, No 2, pp. 129-143. Zannetos, Z. S. (1966), `The theory of oil tankship rates', MIT press, Cambridge, MA.
21
Endnotes: 1 The assumption of one period expectations is for notational convenience. The results do not change for longer horizons. 2 That is, εt is independent normal with mean 0 and variance h. 3 Stationarity of the series refers to the series having constant mean: E(Yt) =, t, constant variance: V(Yt) = E(Yt -)2 = h t, and autocovariances which depend only on lags: C(Yt, Yt-s) = hs , that is lagged covariances do not depend on the time they are observed but only on the gap between the periods t and s. If a stochastic process is stationary, its moments (mean, variance etc.) or more generally it's probability distribution is invariant with time, and as a result the conventional distribution theory may be used for inference. 4 Alternatively, cointegration may be tested for in a multivariate vector autoregressive setting as proposed by Johansen (1988,1991). 5 Virtue of the block diagonality of the information matrix, Engle(1982) and Bollerslev(1986)recommend estimating ai , ci , di by OLS and use the residuals to find efficient estimates of i ,j. Based on these estimates of i, j find efficient estimates of ai, ci, di, and continue the iterations until convergence. The final estimates of i, j and ai, ci, di from this procedure are asymptotically normally distributed. 6 The figures reported in table 4.1 are the estimated centralized third and fourth moments of the data,
denoted ̂ 3 and ( ̂ 4-3), respectively. Their asymptotic distributions under the null are
)6,0(N~ˆT 3 and )24,0(N~)3ˆ(T 4 , where T=167 in this case. 7 For DLTCV this sum is 1.17, while for DLTCAGR the number is 1.07.
22
Table 1.1: Market Segmentation of the Tanker Industry - Vessel sizes, Commodities carried, Routes
1. Logs of spot freight rate indices for Handymax(40,000), Aframax(80,000 dwt), Suezmax(140,000 dwt), VLCC(250,000 dwt) and aggregate over all categories vessels are denoted LFRH, LFRA, LFRS, LFRV and LFRAGR, while logs of time-charter rates for the same sizes are denoted LTCH, LTCA, LTCS, LTCV and LTCAGR, respectively.
2. Critical values of the ADF(4) statistics at the 10% and 5% significance levels with 163 observations are -3.14 and -3.44.
Table 4.5: Stationarity tests for log-differences of spot and time charter rates
1. See notation in table 4.4 for definition of variables 2. Critical values of the ADF(4) statistics at the 10% and 5% significance levels with 162
observations are -3.14 and -3.44. Table 4.6: Engle-Granger cointegration tests for equations in log-levels LFRH LFRA LFRS LFRV LTCH LTCA LTCS LTCV LFRAGR LTCAGR -4.57 -5.52 -5.40 -6.40 -3.16 -5.29 -3.98 -5.27 -5.54 -4.55 Notes:
1. See notation in table 4.4 for definition of variables 2. Critical value of the Engle-Granger statistic with 168 observations, and 4(spot) and 3(time-
charter) variables in the equation, at the 10% level of significance are -4.21 and -3.89. Table 5.3: Error correction terms in the tanker markets VESSEL HANDY AFRAMAX SUEZMAX VLCC AGGREGATE
SPOT -0.20 -0.23 -0.18 -0.34 -0.21 TIME-CHARTERS
-0.06 -0.07 -0.08 -0.17 -0.12
Table 5.1: ECM-GARCH model estimation for spot freight rates (markets)
25
yt = a0+a1 ECTt-1 +dt+1i
c i yt-i +1i
di lnQt-i +1i
ei lnPbt-i + 1i
fi lnKt-i + t
where t ~ IN (0, ht); and ht = 0 +
p
1i
i 2t-i +
q
1j
j ht-j +
11
1i
i mi
Dependent Variable ( yt) Estimated Parameter
DLFRH
DLFRA
DLFRS
DLFRV
DLFRAGR
a0
-.023690 -1.94228 052.
-.654945E-02 -.771966 440.
-.454732E-02 -.550694 582.
.771348E-03
.059219 953.
.526948E-03
.072462 942.
.032969 2.12925 * 033.
a1
-.200764 -6.07213 ** 000.
-.226417 -4.68925 ** 000.
-.180490 -4.06655 ** 000.
-.335909 -4.66821 ** 000.
-.209860 -4.04247 ** 000.
e1
.138219 2.54381 * 011.
e2
.206526 3.93557 ** 000.
d1
-1.04911 -3.47672 ** 001.
o
.716305E-02 7.12443 ** 000.
.813988E-02 5.03246 ** 000.
.868841E-02 5.86778 ** 000.
.020651 7.11213 ** 000.
.108271E-02 1.48885 137.
1
.304859 1.96825 * 049.
.403790 3.39233 ** 001.
.409573 2.39892 ** 016.
.251099 1.87307 061.
.170587 1.87093 061.
1
.709184 5.71673 ** 000.
Se .10 .12 .12 .17 .10
RBSQ .17 .12 .08 .16 .11
DW 1.84 1.87 1.92 1.93 1.83
LL 149.53 130.93 126.03 66.50 154.44
Q(12) 8.94 6.50 13.8 7.25 10.8
Q2(12) 13.7 6.44 13.3 24.3 11.7
SK 0.10 0.37 0.27 0.27 0.21
KU 0.67 0.16 0.55 0.39 0.01
Notes:
26
(1) See notes in tables 4.4 and 4.5 for definition of variables (2) Demand and supply for shipping services in million dwt are denoted Q and K
respectively, while bunker prices in $/ton of heavy fuel oil are denoted PB. ECT is the estimated Error Correction Term. The dummy variable d, takes the value of 0 up to 1986:3 and 1 thereafter.
(3) Numbers below each estimated coefficient are t-statistics and p-values, se=standard errors, RBSQ=R-Bar squares, DW=Durbin-Watson statistic, LL=Value of Log-likelihood function, Q(12) = Ljung-Box (1978) Q portmanteau statistic on the autocorrelation function of the standardized residuals, Q2(12)=Ljung-Box test on the autocorrelation function of the squared standardized ARCH residuals, SK = coefficient of skewness and KU = coefficient of kurtosis.
(4) **indicate significance at the 1% level, and * indicate significance at the 5%level.
27
Table 5.2: ECM-GARCH model estimation of time-charter markets
SK -0.44 -0.37 -0.09 -0.39 -0.27 KU 1.13 1.81 2.81 4.34 2.55
Notes: (1) See notes in tables 4.4 and 4.5 for definition of variables (2) ECT is the estimated Error Correction Term, and mit i=1,…11 are 11 monthly
dummies for January to November, taking the value of 1 on the specified month and 0 otherwise.
(3) Numbers below each estimated coefficient are t-statistics and p-values, se=Standard errors, RSBQ=R-Bar squares, DW=Durbin-Watson statistic, LL=Value of Log-likelihood function, Q(12)=Ljung Box(1978) Q portmanteau statistic on the autocorrelation function of the standardized residuals, Q2(12)=Ljung-Box test on the autocorrelation function of the squared standardized ARCH residuals, SK=coefficient of skewness and KU=coefficient of kurtosis.
(4) ** indicate significance at the 1% level, and * indicate significance at the 5% level.
29
Figure 1: Time Charter Volatilities by Vessel Size
0
0.1
0.2
0.3
0.4
0.5
0.6A
ug-8
0
Jun-
81
Apr
-82
Feb
-83
Dec
-83
Oct
-84
Aug
-85
Jun-
86
Apr
-87
Feb
-88
Dec
-88
Oct
-89
Aug
-90
Jun-
91
Apr
-92
Feb
-93
Dec
-93
Sta
nd
ard
Dev
iati
on
sHandy T/C Aframax T/C Suezmax T/C VLCC T/C
Figure 2: Spot Freight Rate Volatilities by Vessel Size
00.050.1
0.150.2
0.250.3
0.350.4
Aug
-80
Jun-
81
Apr
-82
Feb
-83
Dec
-83
Oct
-84
Aug
-85
Jun-
86
Apr
-87
Feb
-88
Dec
-88
Oct
-89
Aug
-90
Jun-
91
Apr
-92
Feb
-93
Dec
-93
Sta
nd
ard
Dev
iati
on
s
Handy Spot Aframax Spot Suezmax Spot VLCC Spot
30
Figure 3: SPOT VS TIME CHARTER VOLATILITIES: HANDYMAX
SECTOR
0
0.05
0.1
0.15
0.2
0.25
Aug-8
0
May
-81
Feb-8
2
Nov-8
2
Aug-8
3
May
-84
Feb-8
5
Nov-8
5
Aug-8
6
May
-87
Feb-8
8
Nov-8
8
Aug-8
9
May
-90
Feb-9
1
Nov-9
1
Aug-9
2
May
-93
ST
AN
DA
RD
DE
VIA
TIO
NS
Handy Spot
Handy T/C
Figure 4: SPOT VS TIME-CHARTER VOLATILITIES: AFRAMAX SECTOR
0
0.1
0.2
0.3
0.4
0.5
0.6
Aug-8
0
May
-81
Feb-8
2
Nov-8
2
Aug-8
3
May
-84
Feb-8
5
Nov-8
5
Aug-8
6
May
-87
Feb-8
8
Nov-8
8
Aug-8
9
May
-90
Feb-9
1
Nov-9
1
Aug-9
2
May
-93
ST
AN
DA
RD
DE
VIA
TIO
NS
Aframax Spot
Aframax T/C
31
Figure 5: SPOT VS TIME-CHARTER VOLATILITIES: SUEZMAX
SECTOR
0
0.05
0.1
0.15
0.2
0.25
0.3
Aug-8
0
May
-81
Feb-8
2
Nov-8
2
Aug-8
3
May
-84
Feb-8
5
Nov-8
5
Aug-8
6
May
-87
Feb-8
8
Nov-8
8
Aug-8
9
May
-90
Feb-9
1
Nov-9
1
Aug-9
2
May
-93
ST
AN
DA
RD
DE
VIA
TIO
NS
Suezmax Spot
Suezmax T/C
Figure 6: SPOT VS TIME-CHARTER VOLATILITIES: VLCC SECTOR
0
0.1
0.2
0.3
0.4
0.5
0.6
Aug-8
0
May
-81
Feb-8
2
Nov-8
2
Aug-8
3
May
-84
Feb-8
5
Nov-8
5
Aug-8
6
May
-87
Feb-8
8
Nov-8
8
Aug-8
9
May
-90
Feb-9
1
Nov-9
1
Aug-9
2
May
-93
ST
AN
DA
RD
DE
VIA
TIO
NS
VLCC Spot
VLCC T/C
32
Figure 7: SPOT VS TIME-CHARTER VOLATILITIES: AGGREGATE
