(Portfolio) Bar-lev Katz 1976

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merican Finance ssociation

A Portfolio Approach to Fossil Fuel Procurement in the Electric Utility IndustryAuthor(s): Dan Bar-Lev and Steven KatzSource: The Journal of Finance, Vol. 31, No. 3 (Jun., 1976), pp. 933-947Published by: Wileyfor the American Finance Association

Stable URL: http://www.jstor.org/stable/2326437.Accessed: 15/03/2014 10:36

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2/16

THE

JOURNAL OF

FINANCE *

VOL. XXXI,

NO.

3 * JUNE

1976

A

PORTFOLIO

APPROACH TO

FOSSIL FUEL

PROCUREMENT IN THE ELECTRIC UTILITY INDUSTRY

DAN

BAR-LEV

ND

STEVEN ATZ*

RISING

COSTS

OFFUEL

nputs have

greatly

affected the

operating

performance

of

the

electric

utility

industry. Fuel is

no longer

cheap

and abundant,

but

has become

a

precious

resource to be

conserved and

efficiently

utilized. The

purpose of

this

study

is to

inject

a novel

approach to

fossil

fuel

procurement, and

to determine

to

what

extent

the utility

industry

has been an

efficient

utilizer of

scarce

resources.

The implications of this study have relevance to the managers of the utility

industry, to

the public

regulatory

commissions

and to

students of the

industry.

Section

I

deals briefly

with some of

the

characteristics

of

the industry

and

indicates the

relationship of

portfolio

theory to fossil

fuel

mix.

Section

II

reviews

the

methodology and

data used in

the

study, while

Section

III

contains

the

empirical

results and an

analysis

of them.

A

theoretical extension

is introduced in

Section IV

where

the

notion of the

Capital Market

Line

as it

applies

to fuel

diversification

is

interpreted. Section

V

contains

a

summary

and

implications

of

the

paper.

I.

CHARACTERISTICS

OF THE

ELECTRIC

UTILITY INDUSTRY

Utilities need

fuel

inputs

to

produce

the

steam which

turns the

turbine-generators.

In

a

conventional fossil

fuel

plant, fuel inputs

are

burned

in

boilers,

while in

a

nuclear

reactor plant, a

nuclear

reactor

substitutes for the

boiler.

Since the

electric

utility

industry is a

price-sensitive fuel

market,

many steam-electric

power plant

boilers are

already equipped to burn

more

than

one

type

of fuel and

can

readily

switch

from

one

to

another as

shifting prices favor their selection.

Furthermore,

most

existing

conventional

steam

plants

can

be

equipped

to

utilize

coal, oil,

and

natural gas either singularly or in various combinations. This ability may be due

either

to

the

original

design of

the boilers or

to

the

installation

of conversion

equipment.

Electric utilities

require an

assured

long-range

supply

of fossil

fuel,

and

therefore,

the electric

utility

companies

generally

sign long-term

contracts

of

10 to

20

years

covering

about

70%

to

80%

of their

expected

needs.

The

rest is

bought

on

a

spot

basis. These

contracts

usually

contain features

allowing price

adjustments

over

the

duration of

the

contract

for

changes

in

production

costs,

transportation

costs,

wage-rate

increases, etc.

The

fuel

quantities

are

generally

flexible,

however,

due to

the contract terms or the ability of the electric utility company to sell a contract to

another

buyer.

*Assistant Vice

President,

International

Division,

Tadiran

Ltd.,

Haifa,

Israel,

and

Assistant

Professor

of

Economics

and

Finance,

Baruch

College,

CUNY, respectively.

Our

thanks to

Professors Paul

Grier

and

Roger

Mesznik

of

Baruch

College,

and

to

Professor

Myron

J.

Gordon,

University

of

Toronto,

for

their

suggestions

in

improving

the

quality

of

the

paper.

933

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3/16

934

The Journal of Finance

If

the electric utility

companies would

buy all their needed fuel on a spot

basis

and

not contract 70% to 80% of their

required fuel, the

whole problem of fuel

diversification would not exist. The

utilities would buy the

cheapest available fuel

as

defined by as burned costs on a spot

basis and would

switch from one kind

of fuel to another each time there was a relative change in the as burned costs. In

such a situation, the only problem of

the utility company would be to

keep

informed of the

cheapest available fossil fuel. However, since

the utilities do

sign

long-term contracts

for fuels which contain price

adjustment clauses, the com-

panies must estimate

the factors that

might cause the prices of these fuels to go

up

or

down.

This situation brings an uncertainty

factor to the decision making process

of

buying fuels and is

analogous

to

the problem

of selecting risky

securities.

In

buying

risky

securities the

problem is one of

estimating

the

returns,

risks,

and

correlations

of the securities, where the risk is defined as the standard deviation of the expected

return on the portfolio,

and the goal is to maximize the return

of the portfolio for

a

given

risk. Once the

return-risk inputs for the various securities

are determined, one

uses a

quadratic programming approach to determine

the loci of

portfolios

which

would

maximize return

for various levels of risk.'

The

choosing

of

which

portfolio

to

invest

in

is then a matter of personal

preference where

the trade-off is greater

risk

for

greater return. Similarly, in

buying fossil fuels, the goal

would

be to

minimize both

the expected cost of the

fuel and its standard

deviation, namely, the

risk.

By using Markowitz diversification, an efficient frontier of fuel mixes would be

generated

for

various combinations

of cost

and

risk.

The

utility's management

would

then

choose

that

point

on

the frontier

which

minimizes its

utility, trading

off

cost for

risk. In

dealing

with the

problem

of

fuel

diversification,

we will

assume

that

the electric

utility

sector is

composed

of

risk

averting companies

and

that the

utility

companies

have loci of indifference curves between combination of risk and

expected

return.

II.

METHODOLOGY AND

DATA

In

order to apply the Markowitz

technique, expectations

must

be

formed

for the

following components.

1.

E(r,)= expected cost of fuel i, i

=

1,.

..,n

2.

vii

=

the

variance

of cost

ri,

i

=

I,.,

n

3.

ayj,

ij =the

covariance

of costs

between

ri

and

rj

for

all

pairs

of

fuels,

i=

Il,...,In,j

l.,n

Once the

parameters

have

been obtained the efficient

frontier can be

determined

for various levels of costs, E*, by minimizing the Lagrangean function Z, where

n

n n n

Z

=

?E

wiwjw

+

XI

E wiE(ri)-E*

+

X2 ?E

Wi)

and

w

=percentage

of

portfolio

in

fossil fuel

i.

1. Harry Markowitz in a pioneering

work (13) developed this approach to portfolio

construction.



4/16

Fuel Procurement

n the

Electric

Utility Industry

935

The cost

inputs

used

in

our

study

are the as

burned costs

incurred

in

bringing

the

fuel

to

its

point

of use.

Included in the

as

burned costs

are

additional

overheads

resulting from

transportation

expenses, the

heating of oil

lines

to

improve

atomization and

flow

characteristics,

stock

cleaning and

fuel handling

facilities

for coal,

fuel storage

and

inventory costs

for

both coal and

oil, and

maintenance.

These

costs are not

readily

identifiable

and may vary

among

users.

However, they are

reported

by the utilities,

and are

published

by the

National Coal

Association on

the

basis of an

average

cost per million

BTU (14). It

is

necessary to

consider

these

additional

expenses

incurred

in

the use of

each fuel

in

order

to

determine the

relative

costs to the

users

on a common

basis.

For

example,

the cost of

fuel at

the point of

use is

greatly

influenced by the

distance

that it has to

be

transported. In

the United

States

in

1969

average

transportation

costs

of

natural

gas delivered

to

distributors

in

Boston

represented

95%of total expenses, while for New York they represented 60%(14). Because of

the

disparity

of as

burned costs

for

the same fossil

fuel

in

different sections of

the

United

States

the

country

was divided into

nine

regions

where within

each

region

the as

burned cost

experience is similar.2

The nine

geographical regions

are:

1)

New

England 2)

Middle Atlantic

3) East

Coast

Central

4)

West

South Central

5)

South

Atlantic 6) East

South

Central 7)

West South Central

8)

Mountain and

9)

Pacific. (See

Appendix I.)

Seventeen annual

as

burned

costs

C,

for

coal, oil,

and

gas

for

the

1952-1968

period for the

nine different

regions

are

determined,

and

transformed

to l/cx

1000.3

The average of the actual 1969 and 1970 as burned costs were used as the

expected

1969

fuel costs.

The minimum

risk

portfolios

can now

be

determined

for

various levels

of

transformed

reciprocal

as

burned

costs E*

through

solving

the

following Lagrangian

objective

function.

Z=

Ewiwjy+1(X

EwiE(r)-E*)

+X

2(wi-)

where

aii

=

covariance

(variance,

if

i

=j)

between fuels

i

and

j.

E*

=

a specific

level of return

wi=percentage

of

portfolio in

fossil fuel i

E(r1)=

expected value of

reciprocal of as

burned cost

for fuel

i.

The

efficient

frontier for

1969 was

then

constructed

for each

region, and

compared

to

the

actual

performance

of the

regional utilities to

determine

whether

the

actual fuel

diversification

for

each

of

the

nine

regions

was near or

on the

efficient

frontier,

or below it

indicating that a

better fuel

diversification

could have

been

obtained

by

the

utility

companies.

Limitations

of Data

It should

be

understood

that the

analysis is

based on

aggregate

data for each

region.

Therefore,

if the

actual

fuel

diversification

of

a

specific

region

is in

2.

We

have

used

the

regionalbreakdown

etermined

y theNational

Coal

Association

which

s based

on

homogeneity

of

as burned costs.

Appendix

II

contains the data

inputs

used

in

determining he

efficient

frontier.

3.

The

transformation

n(l/c)

was

investigated

but we found that

l/c more

closely resembles

he

normaldistribution.



5/16

936

The

Journal

of Finance

compliance

with the calculated

efficient

frontier, this does not

necessarily

mean

that

all the

companies

in

that region

optimized their fuel mix

in

accordance with

the portfolio

approach.

Similarly, if a region is

inefficiently

diversified, it is

still

possible that

one or two of

the utilities

servicing that region

had an efficient

fuel

mix. It should also be noted that because of possible imperfect supply markets,

problems might exist in

obtaining

all the fuel one wants

at the prevailing

prices.

Furthermore,

existing contracts of

various maturities

have been left

out of the

analysis.

In

fact, an

extension of this

study might be the

evaluation

of marginal

decisions given

the

existing

contracts.

In

fairness to the

utilities,

it must

be

recognized that

they operate under

a

number of

legal,

environmental,

and

political restraints

which

could

obviate the

achievement of

efficient

fuel

diversification from a Markowitz

standpoint.

Even

though

costs

of fuel constitute

approximately 80%

of their

production

expenses,

management may have, out of necessity, additional objectives beyond simply

minimizing fuel

costs subject to a specific level

of

risk.

To

dampen

the

effect of

these

secondary objectives

and

constraints,

we

analyze

the

performance

of

utilities

in

1969

before many of

the

problems which

now beset

them

became

important

considerations.

III.

EMPIRICAL

RESULTS

Figures

1

through 9 show

the efficient frontiers

that could have

been attained

in

1969 for the nine different regions and the actual portfolio mix of fuels (A)

achieved

by the

regional

utilities.

t1

C)P

29.01

28.01

27.01,

26.04

A

25.5e

1.6

1.7

1.8

2.5

FIGURE

1-New

England

percent

accounted for

by:

portfolio

coal oil

gas

Actual

30.6 69.3

0.1

I

-

-

100.0

II

17.7

82.3

III

29.8

70.2



6/16

(

/C)

p

30.5

30.0

/

A

29.5

29.0

II

1.5

1.7

1.9

2.1

FIGURE

2-Middle

Atlantic

Region

percent

accounted for

by:

portfolio coal

oil

gas

Actual

57.0 34.0

9.0

I

100.0

II

63.4

36.6

III

62.0 38.0

12

(1/C)P1

35,

30

25

20

1.2

1.4

1.6

1.8

FIGURE

3-East North Central

percent

accounted

for

by:

portfolio

coal

oil

gas

Actual 93.0 7.0

I

100.0

II

79.0

-

21.0

III 25.4

74.6

937



7/16

(

/C)p

A

40.0

39.0

38.0

*A

37.0

0.5 1.0 1.5 2.0

2.5 3.0

FIGURE

4

-West

North

Central

percent

accounted for

by:

portfolio

coal oil

gas

Actual 54.7 2.0

43.3

I

100.0

II

62.6 37.4

III

63.2 36.8

(1

/C)p,

\

32.2

31.9

31.6

31.3

I

1.0 1.5

2.0 2.5

FIGURE

5-South Atlantic

percent

accounted for

by:

portfolio

coal

oil

gas

Actual

71.3

15.7 13.0

I

-

100.0

-

II

17.7

82.3

III 88.0 12.0

938



8/16

(

/C)

pi

45

44

i.

42

40

38

1.35 1.45 1.55 1.65

FIGURE 6-East South Central

percent accounted for by:

portfolio coal oil

gas

Actual 88.3

11.7

I

100.0

II

96.9 3.1

III

76.7 23.3

(1/C)p

/\

50

45

*A

40

35

30

25

ii

.

,

P

1

5

10

15

20

FIGURE

7-West

South Central

percent

accounted

for

by:

portfolio coal

oil

gas

Actual

-

100.0

I

- -

100.0

II

-

99.0 1.0

III

-

100.0

-

939



9/16

(

/C)p

/

48,

46

44

42

404

0.5

1.0 2.0

3.0

4.0

FIGURE

8-Mountain

Region

percent accounted for by:

portfolio

coal

oil

gas

Actual

44.0 3.5 52.5

I

100.0

II

79.7 20.3

III 29.3 70.7

(_/c

_)

31

A

30

29

28

3.5 4.5

5.5

6.5

>

FIGURE

9-Pacific

percent accounted for

by:

portolio

coal oil

gas

Actual 18.4 81.6

I

-

-

100.0

II

-

91.2 8.8

III

-

100.0

940



10/16

Fuel Procurement

n

the Electric

Utility Industry

941

In three

of the

nine

regions

(South Atlantic,

West South Central

and Pacific),

the

actual

fuel

mix

lies

on the efficient frontier.

The other

six regions fall below

their

respective

efficient

frontiers,

but

to determine

the

extent

of the shortfall

we apply

a

measure

to

the

results

similar

to

Sharpe's

(16) ex-post

measure

of

performance.

Y-RF

where

Y=

average

realized

yield

over

n prior

periods

RF=

Return of

risk-free

investment

cy

=

Standard

deviation

of realized

yield

over

prior

periods.

However,

in the fuel

diversification

case,

we assume

that

RF=

0

and

our

measure

of

performance

will be

(1/IC)1

i=(l/C)1

i

,.,

where

1/C is

the

reciprocal

of

the as

burned

cost

and

al/c

is the standard

deviation

of

1/

C.

For

each

one

of

the nine

geographical

regions,

we

calculate

three

values:

one for

point

A,

the actual

fuel

diversification

of 1969;

one for point

B which is a

vertical

point

on

the efficient

frontier

that

lies

above

point

A, and

one for point C,

which

is

a

horizontal point

on

the efficient

frontier

that

lies

to the

left of

point

A. The

illustration of these points is presented in Figure 10.

After

calculating

the

Zi

values

for

the A,

B

and

C fuel

portfolios,

we have

to

calculate

two ratios

for

each region.

The

first one

is

ZA (1/ C)A

CB

(1/C)A

qa=

=

.

q

ZB

AA

(1/C)B

(/C)B

where

0< q

(Portfolio) Bar-lev Katz 1976

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