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ALFRED
P.
WORKING PAPER
SLOAN SCHOOL OF MANAGEMENT
Risk Analysis:
To Exploration
From Prospect
Portfolio
and Back
by
Gordon M. Kaufman
MIT
Sloan School Working Paper 3639
December 1993
MASSACHUSETTS
INSTITUTE OF TECHNOLOGY
50 MEMORIAL DRIVE
CAMBRIDGE, MASSACHUSETTS 02139
Risk Analysis:
To Exploration
From
Portfolio
Prospect
and Back
by
Gordon M. Kaufman
MIT
Sloan School Working Paper 3639
December 1993
RISK ANALYSIS:
FROM PROSPECT
TO EXPLORATION PORTFOLIO AND BACK*
Gordon M. Kaufman
Sloan School of Management,
MIT
International Petroleum Resource Conference
Stavanger,
December
*
I
Norway
6-8,
1993
wish to thank James Smith and L. James Valverde A.,
Brant Liddle
assistance.
for
Jr. for
valuable discussions,
computing options valuation examples and John MagUo
for
programming
INTRODUCTION
In a 1962 visit to the offices of General Petroleum in Los Angeles, the corporate exploration
manager proudly informed Jack Grayson and me
that, starting with the
company's
next aimual exploration budget allocation meeting, a geologist must assign a "dry hole"
probability to each prospect that he promotes. This was the company's
the world of quantitative risk assessment.
Few companies went
first
venture into
so far at the time.
have come along way in thirty-one years. The sophistication of probabilistic,
and economic aids
to oil
geophysical, geochemical
precise
and gas exploration has developed
and geological techniques that
and more accurate data.
It is
mation systems that integrate large
mapping protocols and economic
ciding
how much
to spend
routine for
oil
tandem with advances
and gas firms
it
more
infor-
and geophysical data
bases,
management
in de-
and where
it
to
should be spent.
frameworks constructed from a blend of geo-
geochemical and engineering theory and practice, probabihstic and
statistical analysis of earth science
maximizing behavior of firms
and economic data and micro-economic theory of
in the presence of large project risks.
profit
The papers presented
at this meeting illustrate the broad ramge of systems that can be constructed
mon
in
employ
decision maJcing paradigms to assist
intellectual
statistical
yield descriptively richer,
geological, geochemical
on exploration, when to spend
These systems are shaped by
logical, geophysical,
now
in
We
from a com-
core of ideas and they give us a view of techniques for exploration and development
uncertainty and risk analysis at the cutting edge of current knowledge.
My
comments hinge on
accounting correctly
four basic themes:
for covariation of
the
first
theme
uncertain quantities at
is
the importance of
all levels
prospect, play, basin, and exploration portfolio. Omission of dependencies
of aggregation-
among
uncertain
quantities can lead to seriously distorted estimates. Covariability plays different roles as
analysis steps
up the ladder
for covariation of
of aggregation. Statistical analogy can be employed to account
uncertain quantities in
analogy to provide a benchmark
The second theme
ration effort
among
is
for
much
among
plays and
first:
among
Decisions about allocation of explo-
prospects within plays should account
for covariabiUty of returns to exploration effort introduced
by price and cost uncertainties
and, in particular, should distinguish between systematic and imsystematic
variance portfoho analysis and
When
its
geological
understanding geological features of frontier areas.
closely related to the
basins,
same way that we employ
the
risk.
Mean-
generaUzations can be employed to this end.
exploratory risk analysis
is
based on personal assessments of uncertainties by
one or more technical experts, post mortems aimed at measuring the ex post quality of
such assessments
is
direct eUcitation of
always
difficult
much
talked about, but unfortunately too httle done.
judgements about dependencies among uncertain quantities
and often
infeasible.
final
theme
frequently used
Ls
method
is
almost
Ignoring even modest correlations can distort both
the accuracy aoid precision of assessments of
The
In addition,
field size.
the importance of correctly valuing project
of project valuation
distribution of project net present value
is
to base
computed
it
flexibility.
The most
on properties of the probabifity
at a pre-assigned discount rate.
This
method
is
appropriate when, once the project
future course. If however,
is
under way, management cannot
management can expand,
contract, or
alter its
abandon the project
as
the future unfolds then unfortunately, the method does not correctly account for project
Possession of a lease to explore a tract and then to develop
value.
found
in
commercial quantities
or not depending
is
just such
an option. In
on the outcome of exploratory
Modern
or not before lease expiration.
fact,
it is
drilling) within
it
or gas
if oil
an option
(to develop
an option to explore
methods
finance theory offers option valuation
that correctly account for fiexibihty in the timing of exploration and development.
illustrative
A
example
is
given in section
is
simple taxonomy of types of risk faced by
self-explanatory.
systematic risk
is
[Table
1
here].
An
4.
stage for our discussion of uncertainty and
1
is
The
risk.
oil
and gas explorationists.
The
classification
It
sets the
appearing in Table
and non-
distinction between systematic risk
Non-systematic risks axe those that can be reduced by
fundamental:
geographic and geological diversification of exploration and development activities, whereas
systematic risks axe those risks that carmot be so reduced.
systematic. Economic returns to
all oil axid
Oil
emd gas price
risks are
gas projects, like boats on a rising and falling
We
show
tide,
move up and down
how
the aggregate risk of an exploration prospect portfoUo can be spUt into systematic
and non-systematic
A
together with rising and falling
The
and gas
prices.
later
parts.
Umited but powerful battery of
2 here].
oil
state of the art
is
tools with
which to reduce
risk are available:
[Table
well illustrated by the presentations given at this confer-
They range
ence.
widely:
Burrow-Newton and colleagues focus on a modern approach
processing eind presenting subsurface spatial uncertainty, and in the same
to
Grant.
spirit,
Milton and Thompson develop the concept of play uncertainty maps and play risk maps.
Dahl and Meisingset show how state of the
art
menu
driven basin modelling software
can yield quick basinaJ assessments and projections of accimiulation
and Backer-Owe
treat spatially distributed
Kaxlsen
petroleum inclusions, Knaxud, Ulateig, Gran
and Bjorlykke predict reservoir quality on a regional
and Sylta show us a method
histories.
scale using log data,
for assessing uncertainties in source
and Krokstad
rock yields and trapped
hydrocarbons.
In their discussion of a model-based approach to evaluation of exploration opportu-
nities.
Duff and Hall suggest a distinctive approach to play defanition and modelling that
emphasizes closure
ation of
style.
They
correctly emphasize the importance of post
model performance as a way of correcting biases and adapting
and tag probability
to
mortem
evalu-
new information
intervals (risk tranches) with specific discriptions of the type of
data
that supports assignment of a geologic event to an interval. Morbey's examination of historical play efficiency
of play successes
Ex
and
throughout the South Atlantic
failures at
rift
an aggregated basinal
system
is,
in effect a post
level.
post analysis of the quality of subjective probabihstic assessments
rationists
is
mortem
made by
explo-
an increasingly attractive way to improve the quahty of risk assessment. Many
companies are riding
this
bandwagon. Some desireable properties of subjective probability
assessments are shown in Table
3.
Without a vigourous
effort to
encode and analyze the
historical performance, expert
Rose
tells
us
how
judgement
to improve the precision
30, 1992 testimony to the
Edwards underground
is
not likely to improve. In a 1987
AAPG
and accuracy of probability judgements. In June
Texas Water Commission on proposed regulations regarding the
river,
Rose
says:
...most technical people have almost
no idea as to their their degree
of uncertainty-they cannot differentiate between 98 percent confidence
and 30 percent confidence\ Moreover, the prevaihng pattern is one of
overconfidence-when asked to make estimates
at, say,
90%
confidence,
they characteristically set predictive ranges that actually reflect about
35-40% accuracy. As Capen says, "people tend to be a lot prouder of
their answers
This bias
empt!)
[i.e.,
is
predictions] than they should be."
nearly universal (scientists and engineers are not ex-
and expresses
by subsequent events
itself specifically in forecasts
(or not
met
at
all).
That
is,
that are exceeded
in their quantitative
predictions, experts usually set their predictive ranges far too narrow.
In qualitative forecasts
rely
,
this bias
is
expressed by a strong tendency to
on only one or two hypotheses-rather than on many-in carrying
out a scientific investigation.
Put simply, most scientists and engineer are overconfident-they
think they know more than they do! So they frequently find themover the past 10 years I
selves surprised by Nature's outcomes
have tested more than 100 technical audiences, totaUing well over 5,000
professional scientists and engineers. The results are always the samethey are significantly overconfident, actually estimating at about 40%
confidence while believing they are estimating at
We
80%
confidence.
...
have found that, with training and practice, scientists and engineers can improve significantly, but even after considerable eS'ort, they
have a hard time consistently setting ranges that really do correspond
to demonstrable uncertainty."
Now
let's
paper,
turn to covariability.
2.
COVARIABILITY-WHEN YOU CAN NEGLECT
IT
AND WHEN YOU CAN'T
Covariability of uncertain physical
ploration risk assessment
all levels
as well.
is
and economic variables underlying
the rule rather than the exception.
of aggregation-prospect, pool, play
This fact leads to a small paradox:
Some
oil
and gas
ex-
variables covary at
and basin levels-and may covary
spatially
while sophisticated multivariate statistical
techniques specifically designed to parse vector valued observations of geological, geo-
chemical and geophysical phenomena into probabilistically independent components are
now widely employed,
decision
probabilistic dependencies at other levels in the chain of analysis for
making axe not often treated with
should not be omitted.
Many
precision
and are sometimes omitted when they
of the studies presented at this conference alert us to the
importance of probabilistic dependencies among geological, geochemical and engineering
variables. Hvoslef, Christie, Sassen,
Kennicut and Requejo's description of use of principal
component analysis of geochemical data to
establish the presence or absence of hydro-
carbon charge and to motivate a new concept-thematic surface geochemistry maps-is an
example of sophisticated multivariate
statistical analysis
aimed
at splitting a covaxiance
structure into orthogonal components. Several presenters call attention to the importance
of proper modeling of probabiUstic dependencies:
Grant, Milton and
the distinction between prospect specific emd play
analysis in the
risk,
Thompson highUght
Flood's review of prospect risk
North Sea emphasizes the importance of proper accounting
for probabilis-
tic
dependencies in play analysis, and Snow, Dore and Dorn-Lopez model risks generated
by a portfolio of prospects.
The
introduction of play level uncertainties can introduce probabilistic dependencies
that do not vanish even after drilling has confirmed the play's existence.
case for discovery process models based on the idea that discovery
a
finite
model
is
population of deposits without replacement and proportional to
for the total
dependence
in the
number
of discoveries that can be
made
in
This
is
the
akin to sampling
size.
Damsleth's
an area incorporates prospect
form of expert judgement about pairwise dependence of prospects within
a cluster of prospects that share the same marginal probabilities and pairwise
probabilities of success. Sinding-Laxsen
(joint)
and Chen's integration of discovery process models
and volumetric accumulation models automatically incorporates dependencies among
sizes
of fields remaining to be discovered.
It is
well understood that geologic play risk
logical events
rock and
is
sensitive to dependencies
among
geo-
such as timing, presence or absence of migration paths, existence of reservoir
seal.
Hermanrud, Abrahamsen, Helgoy and
North Sea economic
risks to vEu-iations in levels of,
events and to variations in infrastructure,
field size
Vollset highhght the sensitivity of
and dependencies among such geologic
and water depth.
It is less well
under-
stood that even mild correlations among the primary physical variables that determine
field
size-area of closure, average feet of pay and yield per acre foot, for example-can induce
large differences in properties of a field size distribution relative to a field size distribution
that does not.
The Lloydminster
play
is
an excellent example.
The Lloydminster
ways. First,
play
down
Figure
1 is
play in Canada's Western Sedimentary Basin
McCallum and Stewart measured
Normal probability
of oil in place correspond to a
as a straight line.
reasonable (See
appear
large
Normal
The assumption
Kaufman
in
1
here].
constructed so that
distribution, then the
that
oil in
place
is
if
The
None
fractiles of the
graph of the ecdf
is
in
logarithm
will
approximately Lognormal
is
appear
clearly
Lloydminster play
here].
of deposits in this play enable us to pin
down with
precision the
Table 4b displays
[Table 4b
of the pairwise correlations are large.
oil in
place in a deposit
the working assumption that
compute properties
Table 5
oil in
horizontal scale
(1993) for further discussion of this play).
Table 4a. [Table 4a
number
is
scale [Figure
covariance and correlation matrices for the logarithms of area, pay and yield.
Since
two
deposits in this well explored
covariance structure of deposit area, net pay and yield per acre-foot.
here].
in
the empirical cumulative distribution function (ecdf ) of the logarithm of
logarithmic units and the vertical scale
The
all
unusual
to single well deposits using a uniform protocol. Second, there are 2509 deposits.
place plotted against a
statistics
features of
is
oflFers
all
is
the product of these three variables,
a comparison of properties of the distribution of
oil
we adopt
we can
easily
pay and
yield.
three variables are jointly Lognormal, then
of the distribution of oil in place as a function of area,
if
and place assuming
independence of log area, log pay and log yield with the distribution that arises
account for empirically derived correlations (those of Table 4b).
correlations are small, ignoring
them
if
we
Even though pairwise
substantially distorts estimates of the mean,
mode
and standard deviation of
oil in
place specifically, the
by about 21%, the standard deviation by about
A 21%
about 30%.
underestimate of
about 3 X 10^ barrels of
a scale of
oil in place,
When
that
size,
is
the
mode
is
underestimated
is
overestimated bv
deposit size results in an underestimate of
positively
skewed
that,
on
they are virtually indistinguishable. [Figure 2 here].
is
computed from assessments of individual compo-
component correlation structure can
components are independent
pendence
47% and
deposit size
Both distributions are so
oil in place!
a deposit size distribution
nents of deposit
mean
mean
is
be ignored only if the
absolutely convincing.
When
the
assumption
assumption of inde-
not warranted, import the covariance structure of a good geologic analogy
you can, rather than ignore covariation.
if
3.
EXPLORATION, DEVELOPMENT AND RISK-RETURN TRADEOFFS
Further up the ladder of aggregation,
the
poration's exploration and development portfolio
variabilities
of geological,
price risk.
The
among
plays
engineering
and cost
aggregate economic
may be
risks
within
basin
a
of a
is
is
always
allocated
influenced
among
earlier,
by
basins,
and among prospects within a play determines an
exploration portfoho's relative exposure to systematic and to non-systematic
As stated
cor-
strongly influenced by co-
and
fashion in which an exploration budget
risk
the distinction between these two types of risk
is
risks.
fundamental:
NON-SYSTEMATIC RISK = DIVERSIFIABLE RISK
SYSTEMATIC RISK = NON-DIVERSIFIABLE RISK
By
appropriate spreading of the investment budget within
and development opportunity
set,
(ROR)
diversifying
that depends on geological and enguaeering
bottom hole contributions and syndication of
fainihaj devices for sharing risks. However, cost
in this fashion.
and price
Price risk can be reduced by hedging in
away from
oil
negative correlation with
and gas exploration
a corporation can reduce the component of dispersion
(variabihty) of investment rate of return
uncertainties. Farmouts,
its oil
and gas markets
oil eind
(e.g.,
risks
oil
lease bids are other
caimot be diversified away
price futiures markets or by
buy airhne company stocks to introduce
gas exploration and development
ROR), but our
interest
here centers on those risks associated with exploration and development management.
It is
possible to measure the relative contributions of systematic
risks to overall risk
and non-systematic
by appropriate appUcation of financial portfoUo theory. The principal
10
aim
of this theory
is
to identify allocations of a fixed investment budget that, subject to a
budget constraint and to activity constraints, minimizes dispersion or variability of
ROR. Table
while achieving a target expected
6 outlines inputs
ROR
and outputs of such an
analysis restricted to an exploration prospect opportunity set. [Table 6 here]. Associated
with each target expected
ROR
is
a
minimum
variance portfoho.
The graph
describing
ROR
how the standard
deviation of such portfolios varies as a function of target expected
and budget
a valuable display of available risk-return tradeoffs and we shall discuss
size
is
an example. Before doing
By
ration
so,
however, we note an important property of portfolio variance.
use of a formula well
known
to statisticians, the variance of
and development portfoho can be spht
the other non-systematic.
into a
sum
ROR
for
any explo-
of two pieces, one systematic
[Table 7 here]. Total portfoho variance
is
seen to be the
ROR
of the expectation with respect to uncertain future prices of the variance of
and
sum
condi-
—and the variance with respect to
future prices of the expectation of ROR conditional on future prices— the non-diversifiable
tionaJ
on future
component.
—the
prices
diversifiable
component
Price variabihty introduces positive correlation of the
RORs
of individual
prospects and the contribution to overall variabihty due to these correlations
large.
The formula
tion of geological
in
Table 7 enables us to see why even the most extreme
and engineering
risks leaves price risk intact.
is
generally
diversifica-
Consider a portfoho of
A'^
prospects with a fraction 1/iV of the exploration budget (scaled to equal one) allocated to
each.
Suppose that the
that, given
known
risk characteristics of
each prospect are identical and in addition
future prices, the outcomes of drilMng these prospects are uncorrelated.
11
Denote the variance of
let
E{ROR\P)
ROR of a generic prospect
be the expected
expectation with respect to
P
ROR of a generic
of
V/N
larger,
is
the variance of a single
drilling
ROR variance
E{ROR\P)
P
by
V{ROR\P) and
prospect given P. In turn
V{ROR\P). Because
be uncorrelated, the unsystematic component of
component
given future prices
let
V equal
the
outcomes are assumed to
is
V/N and
with respect to P. As
the systematic
N gets larger and
approaches zero, while the systematic component, the variance of E{ROR\P),
remains unchanged.
To
illustrate these ideas,
mean-variance tradeoffs
available to a U. S. independent are
gas prospects. Since this
measured
tional
is
is
an
shown
on success, production
constrained to be
less
and
an exploration opportunity
4.
The set
MCF
and
are uncorrelated
in
consists of sixty U. S.
in addition that condi-
and known. Working
profiles are fixed
interest in a prospect
than or equal to 100% (the allocation cannot oversubscribe de-
sireable prospects), but fractions of working interest axe allowable.
denominated
set
example, we have assumed that drilling outcomes
illustrative
in recoverable gas equivalent
in Figures 3
for
Price uncertainty
is
terms of a single uncertain price that scales a future price vector. At the
time that these prospects were in contention, the relevant unregulated price was about
$6.15/MCF because
1978.
of
market distortions introduced by the Natural Gas Policy Act of
For each choice of exploration budget
ing of the set of pairs of target expected
teirget.
Associated with each such pair
is
3 displays efficient frontiers conditioned
level there is
ROR
an
an
and minimiun variance of
etllocation of the
on a
fixed price of
12
"efficient frontier" consist-
ROR given
this
budget to prospects. Figure
$6.15/MCF. Figure 4 displays
efficient frontiers
assuming price uncertainty and price
volatility of
70%
(standard devia-
tion of percent change in price from one period to the next). Price volatiUty introduces a
risky shift of efficient frontiers. Systematic risk as a percent of total risk varies with target
ROR
and budget
size as
shown
in Figiu-e 5.
Unregulated wellhead prices up to
Anadaxko Basin (Fletcher
high as $6.15/MCF
it is
Field) deep gas wellhead price
possible to achieve target
fraction of allocated budget.
budget, here
is
how
Thus with
target
ROR
set, increases,
is
is
RORS
at the time of this example;
a case in point. At prices as
of
20-50% by investing only a
price volatility of .707
and a 50 miUion
the fraction of budget invested varies with target
20%
.190
30%
.343
40%
.440
held fixed, as the
amount invested
ROR.
in this fixed prospect opportunity
systematic risk increases as a proportion of total
increases with the budget fixed, this proportion decreases.
An
risk.
As the
target
example.
the expected
ROR
on three features of the structure of the portfoUo model adopted
First, price uncertainty is represented
NPV
of each prospect.
ROR
intuitive explanation for
the decrease in systematic risk divided by total risk for a fixed budget as target
creases, rests
dollar
BUDGET FRACTION INVESTED
TARGET ROR
If
$10/MCF appeared
in-
for this
by a single price that linearly scales
Second, the large value of current price relative
to the variance of price even in the presence of substsLntied volatifity of .707 leads to
13
Var {Price) /[CurrentPrice]^ =
The non-systematic
1.5.
risk
.5
and Expectation{PriceSquared)/[CurrentPrice]^
component
the systematic component of risk by
ROR
is
increased, effort
is
.5.
of portfolio variance
Third,
if
the budget
is
treats upside
1.5)
As
this
happens,
than systematic
object to the choice of
and downside variations
in
minimum
risk
ROR
vaxiance as a criterion because
symmetrically.
They
decomposition of both the expectation of downside
risk into systematic
is
a story
for
and non-systematic
another day!
14
risk of
risk
it
prefer to minimize
the expectation of downside risk subject to achieving a benchmark expected
can be done
and
.5).
Some managers
downside
1.5
held fixed and target
increasingly allocated to riskier prospects.
non-systematic risk increases more rapidly (roughly with weight
(with weight
weighted by
is
=
ROR. A
a portfolio and the variance of
components
is
possible.
How
this
LOOKING FORWARD: OPTIONS, EXPLORATION
4.
AND DEVELOPMENT
We
are
familiar with the explosion of stock
all
activity that built
Scholes) of a
on the 1973 development by three
compelhng theory of stock option
and commodity market investment
MIT
professors (Black,
Merton and
work aimed
at extending
valuation. Recent
the theory to provide correct valuation of exploration and development projects should be
of particular interest to exploration managers.
It
has long been recognized that possessing the right to explore a tract
period of time
stock.
an operating option that
is
The analogy
is
sketched in Table
8.
for
a specific
informally equivalent to a call option on a
is
[Table 8 here]. All explorationists appreciate
the option value of pre-emption-get into a highly prospective frontier area before the
competition in order to maximize exploration
fields.
If
a discovery
is
made, another option
flexibility
arises:
or not develop at aU. This development option
at
some point
manager
compound
easily explainable
is
method
this
option.
Only
for valuing
method?
off the
most promising
develop now, postpone development
imbedded within the option
in time prior to expiration of the lease.
faces a
Just what
is
and to pick
to explore
Thxis, ex ante, the exploration
recently, however, has a conceptually
sound and
such options been in place.
Trigeoris
and Mason (1987) point out that extensions of
stock market option theory to embrace valuation of project flexibihty axe a special, market
adjusted version of decision tree analysis that expUcitly prices out the value of operating
flexibihty.
Why
is
this
important?
Because, acccording to
15
all
published accounts, the
method overcomes inadequacies
of approaches to project
of a single risk adjusted discounted rate of return to
management that
rest
on choice
compute the probabihty distribution
(NPV):
of project net present value
NPV methods do not properly capture the value of a manager's
modify a project as uncertainty is resolved.
• Traditional
to
•
•
As uncertainty unfolds and
risk increases or decreases, so
adjusted discount rate;
no single discount rate may be appropriate.
The
i.e.
ability
does the "correct" risk
adapt the operation of a project to future contingencies introduces
asymmetries in future project value resulting in an overall increase in value, relability to
NPV
ative to static
analysis.
According to Pickles and Smith (1993),
"DCF
analysis typically ignores the
value brought to the project through management's ability to
during the
life
of the project
they change over time"
.
and to adjust the investment
make operating
added
decisions
to existing market conditions as
Options or contingent claims methods of valuing project
flexibility
have advantages:
no need to forecast the mean path of future
•
There
•
The appropriate
is
discount rate,
is
the risk free rate;
a risk adjusted discount rate as risk axijustment
These methods do depend on an estimate of price
sumption that the relevant
oil
and gas market
is
is
prices.
i.e.
no need to pick
to the method.
there
intrinsic
is
volatility (price variance)
and the
as-
in equilibrium.
Paddock, Siegel and Smith (1988) document the practical importeince of option valuation:
"The government uses valuations to establish presale reservation prices
and to study the effect of policy changes on revenues it expects to receive
from lease sales. Because the bidding process involves billions of dollars,
16
to obtain accurate valuations.
[As of 1988]
to underestimate industry bids. Using the
Government valuations have tended
same geological and cost data as the
government, our option valuations are closer to industry bids."
The
analysis of stock option value done by Merton, Black and Scholes requires an
understanding of advanced mathematical concepts
partial differential equations with
moving boundaries). Paddock,
and Jacoby and Laughton (1992) show how
inators'
to value
mathematical approach to the problem.
traditional
NPV
Pickles
how
is
orig-
is
made
distinct types of operat-
concrete with an excellent
operating flexibility cheinges the value of a North Sea
and Smith (1993) adapt a
and Smith (1988)
Bjerksvmd and Ekern (1990) compare
Their theoretical analysis
oil field.
simplified approach to option valuation developed
by Cox, IngersoU and Rubenstein (1977) to
approach
Siegel
and parabolic
an exploration option using the
methods and option valuation and show how
ing flexibiUty aifect value.
discussion of
(Ito's stochastic calculus
oil
and gas development options. This
latter
based on an easily understood binomial model of price variation that, as
the time span between periods of price change approaches zero, converges to the same
continuous time distribution of price changes employed by Merton et
limiting valuation formula
and Smith's approach
to improve upon.
of a North Sea
A friendly
of real
is
is
by
identical to the continuous time formula.
far the easiest to
They provide
I
aJ.
In addition, the
beheve that Pickles
understand eind their explanation
several examples, one of which
is
is difficult
a prototypical valuation
oil field.
toy example of a development option will help set the stage for a discussion
compoimd
options.
You own a 100
million barrel field that will cost $500 million to
17
Once developed, you
develop.
sale time, the
and
is
fall
will
market price per barrel
to $4.68 with probabihty
$47.2 million. This calculation
here].
A
immediately
ground
field.
shown
However, between now and
will rise to $7.32
Thus the expected value
.7.
is
in the
the
sell
of developing the field
in the top decision tree of Figure 6.
clairvoyant claims that she has perfect foresight. She can
whether the price/barrel
will
with probability
tell
.3
now
[Figure 6
you with certainty
be $7.32 or $4.68, but has not yet done
so.
What
is
the
value of being able to postpone choice until the clairvoyant has spoken? (She will speak
in
time
The
you to decide whether or not to develop
for
clairvoyant flips the decision tree for you! Choice
This tree
shown
is
at the
bottom of Figure
postpone choice until price
is
revealed
is
5.
The
at each possible price just cited.)
is
postponed
prior expected value of the option to
a gain of $22.4 milUon over and above the value
of the best (static with respect to price) choice in the top tree.
introduced at choice nodes:
to -$32 miUion
if
choice
is
If price
to be
until price is revealed.
Notice the asymmetry
turns out to be $4.68, the value
made without
clairvoyance).
Any
is
zero (in contrast
operating option, no
matter how compUcated, possesses these features.
Additional work on valuation of exploration and development as a
remains to be done.
Paddock
et al.
decision to undertake development
is
assiune that
made
at the
if
exploration
same time
is
compound option
successful, then the
as the decision to explore.
This ignores the value of development delay. Pickles and Smith assume that the decision
to explore
is
taJcen immediately,
but that the option exists to delay development.
ignores the value of exploration delay. Valuation of the
18
compound option
via Pickles
This
and
Smith's representation of the development option can be done by interfacing a decision
tree representing the complete choice set
lattice of
and layered spread
development option value as a function of
sheets,
field size.
one
for
each binomial
The appendix
presents key
steps in such an analysis.
A
student of mine, Brant Liddle, calculated the
period option. Exploration
compound option
allowed to take place up to and including the third period
is
and development can be delayed up to and including the fourth
chosen are based on Pickles and Smith's (1993) Figure
with tax and delay. [Shown here as Figure
that
if
a discovery
is
value of a four
7]
5,
period.
The parameters
a 25 period development option
[Table 9 here]. For simplicity,
made, 100 million developable barrels
will
it is
be discovered.
8 presents development option values given discovery of 100 miUion barrels.
10,
and
11 present binomial lattice values of exploration rights with
how
corollary flexibiUty gains.
values at
t
=
Figiire
Figures
Table 10 and
change with exploration cost and presents
Even though the value
of exploring
and developing a
negative at the current time, the value of the option to explore
may be
tract
negative, but the
The
reader
appendix.
A
is
(compound option) value
of exploration rights
is
structed (a fom: period tree
is
i
=
positive.
encouraged to examine the schematic outUne of analysis given
decision tree for a three period exploration
is
At an
positive.
exploration cost of $.2 per barrel hi our example, the expected value of exploring at
is
9,
development timing
flexibiUty built in, eax;h at different choice of exploration cost per barrel.
Figure 12 summaxizes
assumed
and development option
in the
is
con-
too large to display conveniently), and evaluated by backward
19
induction.
"Explore
The
value at
f
=
Now" (EXERCISE)
of "Wait
and See" (HOLD)
is
compared with the value
of
unconditionally as regards an optimal development strategy.
Straightforward extension of this scheme by partitioning more finely the binomial
lattice
and by accounting
for uncertainty
about discovery
will yield a practical tool for valuation of gains
size prior to exploratory drilling
from the abiUty to delay independently
exploration and development.
20
I
CONCLUSION
5.
Our
focus on the role of covariability of geological, engineering and economic variables
and gas
in oil
risk assessment led us
from prospect
risks to field size distributions,
up the
ladder of aggregation to prospect portfolio risk via mean-variance portfolio analysis and
back down to valuation of operating flexibiUty at the prospect
The
risk
management messages
level.
that emerged axe as follows:
Expert judgement and risk reduction:
•
Requires consistent monitoring
•
Evaluate and calibrate because the payoff
effort
is
large.
Covariability of geologic variables:
•
If present, neglect at
•
Import
your
peril!
statistical analogies.
Covariability of project returns
and
efficient allocation of exploration effort:
•
Use Mean- Variance portfoUo analysis or
•
Separate systematic aind non-systematic risk and measure both
its
generalizations
Value project flexibility correctly:
•
Avoid under-estimation of project value
•
Eliminate need to forecast
mean path
of future-prices
21
REFERENCES
Bjerksund,
P.,
and
Uncertainty:
S.
"'Managing Investment Opportunities Under Price
Ekern (1990).
From Last Chance
to
Wait and See Strategies." Financial Management
19(3): 65-83.
Cox, John
C, Stephen
A. Ross, and
Mark Rubenstein (October
a Simplified Approach." Journal of Financial Economics
7,
"Option Pricing:
1979).
229-264.
Jacoby, Henry D., and David G. Laughton (1992). "Project Evaluation:
A
Practical Asset
Pricing Method." The Energy Journal 13(2): 19-47.
Kaufman. Gordon, M. (1993). "Statistical Issues in the Assessment of Undiscovered Oil
and Gas Resources". The Energy Journal 14(1), 183-215.
Paddock, James L., Daniel R. Siegel, and James L. Smith (1988). "Option Valuation
of Claims on Real Assets: The Case of OfTshore Petroleum Leases." The Quarterly
Journal of Economics, 479-508
Smith (1993). "Petroleum Property Valuation:
Lattice Implementation of Option Pricing Theory." The Energy Journal
Pickles, Eric
and James
Rose, Peter R. (1987).
We
A
L.
,
"Dealing with Risk and Uncertainty in Exploration:
Binomial
14(2), 1-26.
How Can
Improve?" The American Association of Petroleum Geologists Bulletin, 71(1), pp.
1-16.
Trigeoris
and Mason (Spring
Finance Journal.
1987). "Valuing Meinagerial FlexibiUty."
5(1), pp. 14-21.
22
Midland Corporate
APPENDIX
Vcduation Schematic for Exploration
as a Compound Option
and Development
23
ACTS AVAILABLE
t
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+
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EgLp max {qp^ V (B, uP^)
+
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TABLE 9
ASSUMPTIONS
Have
to
[Pickles and Smith (1993) 25-period
model with tax and
develop by the fourth period and have to explore by the end of the
third period.
Upward
price change in one time period
Downward
=
price change in one time period
Probability of
upward change p = .3840
Probability of
downward change
Discount per period
(1-p)
1
1.38%
= 10.22%
= .6160
at after-tax risk-free rate
d = .9954
Present value of after tax cost of development
Present value of price $3,293
Probability of discovery q
If discovery, field size is
=
= Current
D = $2,528
Price
.2
lOOM
barrels
AVAILABLE ACTS
Initial
delay.]
TABLE
10
EXPLORATION OPTIONS
Exp cost^bl *
Value of
Exploration Rig hts
Flexibility
Gains
10
.0532
.0135
.15
.0323
.0323
.20
.0161
.0161
FLEXIBILITY GAINS
EXPL COST/BBL
*With LOW exploration cost^bl, the inflexible option "E
now, D one period later" has positive E. V. With HIGH
exploration cost/bbl the inflexible option has negative E.V.
See Table 9 for assumptions
HGURE
1
LLOYDMINSTER OIL IN PLACE
(BBLS)
LJJ
_l
Q
UJ
h-
O
LU
a.
X
LU
LOGOIP
nGURE2
LLOYDMINSTER
CL
0.2
-
OIP:
Var=3,221
HGURES
MV ANALYSIS— FIXED
70
o
60
1
Z
O
H
<
>
Q
Q
<
Q
Z
<
H
50
1
1-^
c:/5
40
1
30
1
20
1
10 1
PRICE
nGURE4
MV ANALYSIS— PRICE VOLATIUTY=.707
1
o
100
-
60
-
o
<
>
l-H
<
CO
nGURE5
SYSTEMATIC RISK/TOTAL RISK— HIGH VOLATILITY
0.31
O
H
O
O
IQ
o
>
>
Q
O
<N
CO
on
H
O
u
a:
o
a
w
<
HGURE?
Figure
5.
Introduction of
Tax and Delay with a 25-Period Model
WITH DEVELOPMENT DELAY AND TAX-RELATED PARAMETERS
Tim«
to •xpirv ft'*
Ltr>gT^ of Oina
T
I
p«nod
lyrt
I
Votatilny lannualutdl
RmI
ntk-fr«« imaratt rata
PlVOid rata
Pnca
it
oma
laro.par
bM
Exarciaa pnca. par bbt
Marginal
u«
rata
coau axoartaad
Davatapmam dalay lyrt.)
Parcant of
Praaant vakja of Prica
PV
(SI
Praaant valua of Exarciaa pnca
(Atiar-ta«)
Calculatad Option Valua
PV
fX)
OV
.
HGURES
VALUE OF THE DEVELOPMENT OPTION GIVEN DISCOVERY
Initial
p
=
1^1
T=2
T=3
T=4
nGURE9
Exploration Option with q =
.2
Exploration Cost = 0.1
Initial
T=1
T=2
T=3
FIGURE
10
Exploration Option with q =
.2
Exploration Cost = 0.15
Initial
T=1
T=2
0.1443
0.1284
0.1443
explore
0,0628
0.0699
0.0699
HOLD
Exercise value
Hold value
Option value
Exercise ?
0.0323
0.0323
HOLD
0.0092
0.0092
HOLD
0.384
FIGURE
I
11
Exploration Option with q =
.2
Exploration Cost = 0.2
Initial
Exercise value
Hold value
Option value
Exercise ?
0.384
T=1
T=2
T=3
fs
D
O
E
o
0)
MIT tIRRARIES
3
=1080
OOflSbbbT
M
;
Date Due
££6
i
2005