Zenon S Zannetos.

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MAR 8 1965


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Theoretical Factors Affecting the
Long-Term Charter Rate for Tankers in the
Long Run and Suggestions for Measurement

Zenon S. Zannetos


NOV 9 ir.65

Theoretical Factors Affecting the Long-Term Charter Rate for

Tankers in the Long Run and Suggestions for Measurement


Zenon S. Zannetos

I. Introduction; A Model for Long-Term Rates in the Long Run

The purpose of this note is to put forth and analyze the factors that affect
the determination of the long-term tanker rate in the long run and suggest some
methods for measuring the effects of these factors. One of the most important
determinants of the long-term charter rate is, of course, the short-term rate
at the point of the transaction. The reason for this is that the short-term
rate incorporates in it certain fundamental structural relationships between
supply and demand that are valid over time, and are reflected in the operations
of the tankship markets. Since operating in the spot market is a substitute for
operating on a time-charter basis, these two alternatives are naturally related
by marginal rates of substitution. The latter, however, are not independently
determined because both the supply as well as the demand schedules for spot
versus time charters are vitally interdependent. With the exception of a small
percentage of tanker capacity that is used for marginal trades, such as grain,
vegetable oils and molasses, the demand for tonnage on spot is the difference between
the total demand for independent tonnage and the time-charter demand. The same

This is part of a larger project on "The structure of Tankship Rates and
Oil Prices in the Post World-War II Period" that this author is jointly pur-
suing with Professor Morris A. Adelman of the MIT Department of Economics. The
author wishes to acknowledge the aid of the Ford Foundation for granting him
a Faculty Research Fellowship for 1964-65 to pursue part of this research,
and the MIT Sloan School of Management, for granting the necessary computer
time and the research assistance of Milliard Wood.



37 HY ._ 061 _ 4St?f^

'S 13 e^


can be said of the supply side of the market. This circularity, of necessity,
is reflected in the rates. As a result, with the exception of the uncertainty
premiums that we will shortly explain, at any mcnent of time, spot and the long-
term rates are interdependent. As in any other forecasting exercise where
existing data and short-run indicators are used for conditioning expectations
about the future, so are short-term rates used as inputs for decisions on
long-term rates, and the latter for determining the long-term rates in the
long run.

In using the short-term rate in a model for time-charter rates in the long
run, we must therefore divorce the former from any short-run fluctuations that
do not reflect basic structural relationships which are valid over time. Other-
wise, the long-term rate that we will be determining will be a long-term rate
in the short run. Consequently the model that we will propose will include
only "normal" short-term rates.

Two basic models will be tested, a linear-additive and a multiplicative.

The general form of the relationships is :

(1) R, = R' + aX, + bX^ + cX, + dX + fX, + E , and
L s 1 2 3 4 5

= -• x%s\x%x%^,.

s 1 2 3 4 5

(1') R^ = R'_X",S"^X""^X",X\E

where R' and the X, are all some type of a function of time, as we will
s i -"^

shortly indicate in detail, and E is a random error.

In the above formulations R' stands for the "certainty equivalent of


the normal short-run rate" at the time the transaction takes place. This
rate is not equivalent to the empirical market short-run rate because the
market short-run rate may reflect at any moment of time market imperfections.
We are here concerned with a rate that is based on the long-run supply


schedule of the industry. It includes the minimum necessary return to guarantee
replenishment of the required investment and also reflects the normal conditions
of uncertainty of emplojrment. To the extent that no one will be encouraged to
invest unless he expects to earn the minimum necessary return on his invest-
ment, R' may be based on the long-run cost of the marginal block of ves-


sels at the time the transaction takes place. '

The definition of what constitutes the "marginal block" of vessels is not

intuitively obvious. It cannot refer to the class of the smallest vessels

operating in the markets because these vessels are mostly used for special

purposes such as for transporting oil to isolated harbors which are not

equipped to handle larger vessels. Furthermore, vessels operating on time

charters are usually used for transporting crude oil and not refined products.

For the latter, smaller vessels are normally used because of constraints

imposed by the size of markets. As a result, whenever at any moment of time,

we wish to define the "marginal capacity" for time-charter purposes, we must

think of the marginal vessels which normally operate in the crude trade for

major routes and not of the most marginal vessels operating in the most

marginal trade of the most marginal route.

Finally there is another requirement that we must impose on our definition

before we calculate the normal short-term rate. The vessel chosen as marginal

must belong to a class that represents at least 2-3 per cent of the total

tonnage. If not, it will not be very influential in rate setting. Luckily

this requirement can be easily met since tankers are built in sizes that belong

to representative classes.

The impact of any errors in measurement because of the above assumptions

concerning the determination of R' , or any imperfections and bias in the



basic statistic itself, will be corrected by variables X , and X ,

as we will shortly observe. If the model is to be used only for prediction and
given that the partial interrelationships remain constant over time, only
consistency is required in the assumption of a point of departure, because the
model includes self-correcting (or compensating) features. We realize, however,
that if we cannot solve this basic measurement problem to our satisfaction,
the estimated quantitative impact of the various independent variables on
long-term rates will be biased.

A. Two Aspects of Risk; Underemployment and Unemployment

One of the reasons for the difference between the normal spot rate under
uncertainty and the time-charter rate (in both the short run and the long
run) is what one may call the risk premium. Vessels that operate in the
spot market run the risk of underemployment as well as unemployment, con-
sequently R' must include a premium commensurate to these risks. Under
long-term contracts these risks are shifted from the owner to the charterer.

1. The Risk of Underemployment

The risk of underemployment is caused by the inflexibilities of size. A
large vessel reflects potential economies of scale which can only be realized
if the proper co-ordination and information flow is achieved. In order to
avoid costly delays and idle capacities, a careful and sensitive scheduling
process must precede the utilization of facilities. This scheduling activity
is costly and will only be undertaken of course if the benefits from the
reduction of uncertainty surrounding the probable values of the expected output
are greater than the cost of the co-ordinative system.


Another factor affecting underemployment and also entering into the
co-ordinative system relates to the nature of ancillary facilities. In
order that a charterer may utilize effectively tankers of let us say,
100,000 D.W.T., he must make sure that:

(a) The potential loading and unloading ports have berth facilities
for 100,000 D.W.T. tankers. If not, one must must arrange for off-
shore loading and unloading.

(b) The depth of the harbors, rivermouths and canals is sufficient
for the "draft" of the vessel. The alternative here is to reduce
the draft of the vessel by not loading it fully, and losing some of
the economies of size through loss of capacity.

(c) The proper balance between receipts of crude oil and refining
capacity is preserved. A tanker of 100,000 D.W.T. can provide in
one trip enough crude oil for approximately two days of operation
for a refinery of 350,000 barrels per day of throughput capacity,
and for 35 days for a refinery such as the one operating in
Everett, Massachusetts. Since the cost of transportation of
refined products is much greater than that of crude oil, the
location of refineries is influenced extensively by the proximity
and size, of the markets these refineries aim to cater. On-shore
storage facilities can provide some flexibility, and allow the
use of larger tankers. Such flexibility, however, is costly
because of the fixed investment involved and the evaporation
which ensues .

The various technical-technological aspects of the ancillary facilities

and the process of scheduling that we have just mentioned, affect no doubt

the prior distribution surrounding the various degrees of utilization of the

large tankers. The risk of underemployment is a function of the shape, mean,

and variance of this distribution. The expected loss of underemployment

given an information-co-ordinative system, plus the cost of the system itself

(including the cost of additional facilities that it requires) must be no greater
than the part of the efficiency of large tankers that reverts to the charterer.
Otherwise, the charterer will be better off in chartering smaller vessels and
have a "continuous" delivery. In this way the co-ordinative system will be
simpler and less costly, and the need for on-shore storage facilities will be
extensively reduced because the vessels will serve as floating storage depots
"en route" to their destination.

Although the probability of unscheduled delays due to breakdowns, weather, etc.,
and the consequent probability of interruption of the flow of oil to the refineries
may be assumed to be the same for each vessel irrespective of size, and the
probabilities surrounding the causes of these delays as well as the occurrences
of delays per vessel over time, and among vessels may be assumed independent
but not mutually exclusive, yet the expected cost of a given time delay of
larger vessels may be greater. In other words and even if the expected value
of time delays under alternative plans may be the same, yet the incidences
of refinery interruptions will have different time profiles and each incidence
will be of different magnitude. The larger the vessel is, the greater will be
the discontinuity of refinery interruptions, and the longer the duration of
each idleness under the assumptions postulated above. Consequently the
expected costs may be different, as in the case of the "gambler's ruin".

Variable X represents this risk premium of underemployment. It operates
both on the short term as well as the long-term rate and it obviously refers
to the particularities of the chartered vessel. Since technology changes over
time, we expect X to be a function of the technological changes expected
to occur over the charter duration.

But see the special problems encountered in measuring the underemployment
premium in the short run.


The sign of the coefficient of X is expected to be negative in our

formulation because we take as a reference point for R' the "marginal"


vessels. For any submarginal or special purpose vessels the coefficient of
X is thus expected to be positive. There is only one possible exception
that comes to mind. In cases of very depressed market conditions and given
that all the ancillary facilities are scheduled on the assumption that large
vessels will be normally used, the owners of unemployed small vessels may
be willing to conceed a lower rate than that which prevails for larger ves-
sels in order to compensate the charterer for the changes (and possible
concommittant inefficiencies) that are introduced into his scheduling plans.

2. The Risk of Unemployment

Any vessel that operates in the spot market runs the risk of being unemployed

a certain part of the year. This risk is not only due to frictional unemploy-

ment between the completion of contractual commitments but also due to the

particularities of the tanker markets. The particularities are conducive to

fluctuations where periods of surpluses are followed by periods of excess

demand. Most of these factors are explained in detail in The Th eory of Oil

Tankship Rates: An Economic Analysis of Tankship Markets especially In

Chapter VII entitled "Characteristics of the Tankship Markets'.

The common practice is for vessels to enter the market before the expira-
tion of their commitment. Expectations concerning the trend of rates will
determine the exact timing but in general, for vessels trading in the spot
market, the time difference between contract and vessel delivery is an increas-
ing function of the spot rate and ranges between zero and fifty days. Normally,
the vessel will enter the market at the time it leaves the loading point for
the final leg of its trip.

Zannetos, Zenon S., The Theory of Tankship Rates; An Economic Analysis of
Tankship Operation s. MIT, Alfred P. Sloan School of Management, Working Paper 84-64,
363 pp. plus Appendices, September 1, 1964.


The seasonality of the petroleum products accentuates further the risk of
unemployment. In order to meet the requirements of seasons of peak demand,
it is necessary to have over the year approximately 9 per cent more transporta-
tion capacity, than what is necessary tp meet the average demand. In other
words, given the transportation requirements of any particular year, if these
requirements were distributed uniformly over the year, the tonnage required
to meet the demand would have been 91.7 per cent of what is normally necessary
to meet peak demand and this because the demand is not uniformly distributed.
Between the peaks and valleys of demand for transportation capacity of each
year, there is a difference of 13 per cent of the average yearly capacity
requirements. Unfortunately not very much can be done to smooth out ship-
ments because the demand for fuel oil in winter months is not postponable.
Consequently, although the capacity available at any moment of time may be
sufficient to meet average yearly requirements, shortages and surpluses will
appear over certain periods during any one year. Alternatively, if the
industry makes plans for meeting peak demand requirements, at least seven
months out of twelve the tanker markets will have surplus vessels. This is
a piece of information the implications of which some oil companies fail to
appreciate and do not usually consider in their plans, although they know
that it exists. Always they plan on average yearly requirements and thus
generate information that is biased. With the volatility of the tankship
rates, whenever utilization reaches beyond 95 per cent of available capacity,
a severe winter can cause rates to go easily from Intascale minus 55 to plus 50
(a three-fold increase) even though there is enough capacity to meet average
demand. The rate increase may cause a flood of new orders and thus set up
the beginnings of a rate cycle. The moral here of course is that the oil


industry should plan on the basis of the actual profile of demand over the year
and not the average, since the transportation plans cannot be smoothed out.

We have chosen X2 to represent the unemployment risk premium. This
variable, unlike X^ the risk of underemplojrment, operates only on long-
term charters . Its coefficient is expected to be negative, because under
a long-term charter agreement, the risks of unemployment are shifted to the
charterer. The longer the duration of the time charter, the greater the
reduction of the risk of unemplojrment facing the owner of a vessel. Conse-
quently Xy is a function of time.

B. Brokerage Fee Savings

On all transactions no matter whether these are for spot (single voyage),
consecutive voyage or time charters, the brokerage fee is paid by the vessel
owner. This fee is normally 1 1/4 per cent of the total rental involved
(called "hire") times the number of brokers taking part in the transaction.

According to information obtained from industrial sources, most charters
of all types:

(a) Are transacted through brokers, and

(b) Involve two brokers.

There are, of course, certain exceptions to these rules. For instance,
the Japanese shipowners, who only recently entered the universal market, pre-
fer to deal directly with the charterers (oil companies). These agreements,

however, are a very small percentage of the total transactions. Turning now

Our model will still be valid in these cases because of the alternatives
facing the owners. The Japanese practices, however, will tend to understate
the brokerage fee saving and hence reduce the importance of X_ in determining
the long-term rate.


to the number of brokers who enter into the transaction we find that most ship-
owners list their vessels with both London brokers, since London is the central
tankship market, and Norwegian or United States (New York) brokers. As a
result the fee paid is normally 2 1/2 per cent of the charter hire and often
goes as high as 5 per cent.

Given that the fee is a function of the total revenue represented by the
agreement, as long as the percentage is fixed, it makes little difference to
the owner whether he enters the market only once or many times over the life
of his vessel. There are two exceptions that need to be examined, however,
one of which as we will see results in a fee saving. One of these two
considerations is the time-cost of money and the other the special discounts
in the brokerage fee given to the owners of large vessels.

On first glance we observe that the larger the total represented by the
charter agreement (because of the length of the time charter, the size of the
vessel or the level of the rate), the greater is the financial strain imposed
on the owner because of the brokerage fee. And this because the rental is
received monthly while the brokerage refers to the total amount of the con-
tract. Special arrangements are made, however, and the fee if large is spread
over several months if not over the entire duration of the contract. So
this consideration is not important from our point of view.

With the introduction of large tankers of 100,000 DWT and over, and charter
agreements extending over 15-20 years, often special arrangements are made
with the brokers and the fee may be reduced to as low as 3/4 per cent. As a
result we must make provisions in our formulation to reflect the impact of
brokerage fee savings on the long-term rate. Variable X_ is intended to
represent these savings and its coefficient is expected to be negative since
the brokerage fees are paid by the shipowners.


C. Ability to Borrow on Long-Term Charter Agreements

A long-term charter agreement is very valuable for the owner of a vessel

for another reason. It can be mortgaged. The steady income from the charter

is used to liquidate the loan by being pledged as collateral. As a result

the higher the rate and the longer the duration of the charter, the greater

the "mortgageability" of the agreement. To the extent that we are concerned

with the long-term rate in the long run and having taken care of the level of

the rate in R' , we need only be preoccupied here with the impact of the

charter duration on the long-term rate via the ability to borrow on the

Banks have financed the majority of new vessels built subsequent to World
War II on the basis of the security of the long-term charter agreements signed
by the major oil companies. In the United States the normal practice has been
to charge 5 per cent to 5 1/2 per cent for loans ranging from five to seven
years. The maximum loan value of a charter has been usually 90 per cent of
the amount that can be liquidated from the monthly "net hire," the latter
being equal to the gross rental less all the operating costs that fall on the
owner of the vessel. In other words. if one takes the total monthly rent,
subtracts out of it crew wages, stores and supplies, insurance, repairs and
maintenance, takes 90 per cent of what is left and determines how much loan
it can amortize over the life of the charter (present value of an annuity),
then that is the loan value of the time charter.

Because banks are not willing or anxious to commit funds for a period longer
than five to seven years, a new financing scheme has been devised where an insurance
company accepts the mortgage beyond the 5th or 7th year, for a total of 12 years
for the combined plan. Normally the bank will charge 5 per cent interest and
the insurance company 6 per cent. If the charter agreement does not provide


enough for the repayment of 90 per cent of the original cost over 12 years then
the owner is expected to provide a down payment of 20 to 25 per cent of the
fixed investment. A net hire which does not yield a present value equal to
75 per cent of the cost of the vessel over 12 years is normally considered a
bad risk and avoided. Especially if the charter agreement does not include
escalation clauses for the costs that fall on the owner of the vessel. This
does not mean, however, that a smaller loan may not be obtained.

In our formulation X, stands for the mortgageability of the long-term
charters and its coefficient is expected to be negative.

D. Efficiency Premium of Vessels

Even though we are attempting to develop "the long-term rate in the long
run" yet we cannot completely divorce ourselves of the characteristics of
the particular vessels. And this because there is a tremendous difference
between the operating costs of vessels of different sizes and propulsion. These
differences are expected to continue with the continuation of technological
changes. It must be remembered that in our model we took as a point of
departure the normal rate of the marginal block of vessels. As a result, if
we do not provide for the advantages of size, then our estimated long-run
rate will be biased by the cost of the current marginal vessel.

We must therefore recognize that the more efficient a vessel is in terms
of fuel consumption and speed, the greater the rate it will succeed in secur-
ing. . Let us remember that an efficient vessel under a time-charter agreement
benefits also the operator. To the extent that the rental is in the form of a
flat charge per dead-weight-ton (DWT) per month, the faster a vessel is the


greater is its potential capacity, and the lower its fuel consumption the lower
the total cost for the oil carried. Both these factors reduce the cost per
ton of oil delivered, and as a result the time-charter rates for the ef-
ficient and faster vessels must be greater. In this way vessels of the
same size, but of different speed and fuel consumption, by securing different
rates tend to equalize the cost to the charterer per ton of oil delivered.

Because the charterer is not assuming any "risks" or is in any way in-
convenienced if he charters an efficient vessel, we do not expect any part
of the efficiency premium to revert to him. The added carrying capacity
emanating through ef f iciency - reduced space taken by bankers and more trips
per year - although affecting the cost per ton delivered favorably, yet it is
not of such a magnitude as to create inflexibilities of the nature covered by
variable X . The efficiency is normally achieved through additional capital
investment and added maintenance costs, such as those associated with diesel-
engine propulsion, all of which are borne by the owners of chartered vessels.
It is for these reasons that we expect these efficiency premiums to remain
with the owners. Let us repeat again, however, that in terms of a_ spot-rate
equivalent these differentials will be fully accounted for, and other things
equal rates per ton of oil delivered for vessels belonging to the same size
class will be equalized in the market. Consequently the coefficient of X
representing the efficiency premium is expected to be positive, JlI the long-
term rate of our model is given in terms of dollars per DWT per month . If
we translate everything in terms of spot-rate equivalent, however, then we do
not need to provide for X because the spot rate is expressed in dollars

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Online LibraryZenon S ZannetosTheoretical factors affecting the long-term charter rate for tankers in the long run and suggestions for measurement → online text (page 1 of 3)