Transcript Real Options and Investment under Uncertainty in E&P

. Investment in Information in Petroleum,
Real Options and Revelation
Workshop on Real Options
in Petroleum and Energy
September 19-20, 2002, Mexico City
By: Marco Antonio Guimarães Dias
- Internal Consultant by Petrobras, Brazil
- Doctoral Candidate by PUC-Rio
http://www.puc-rio.br/marco.ind/
E&P As Real Options Process
Oil/Gas Success
Probability = p
Expected Volume
of Reserves = B
Revised
Volume = B’


Drill the wildcat (pioneer)? Wait and See?
Technical uncertainty model is required
 Appraisal
phase: delineation of reserves
 Invest in additional information?

Delineated but undeveloped reserves
 Develop? “Wait and See” for better
conditions?

Developed reserves

Possible but not included: Options to expand
the production, stop temporally, and abandon
A Simple Equation for the Development NPV

Let us use a simple equation for the net present value (NPV) in
our examples. We can write NPV = V – D, where:



Given a long-run expectation on oil-prices, how much we shall
pay per barrel of developed reserve?



V = value of the developed reserve (PV of revenues net of OPEX & taxes)
D = development investment (also in PV, is the exercise price of the option)
The value of one barrel of reserve depends of many variables (permoporosity quality, discount rate, reserve location, etc.)
The relation between the value for one barrel of (sub-surface) developed
reserve v and the (surface) oil price barrel P is named the economic quality
of that reserve q (because higher q means higher reserve value v)
Value of one barrel of reserve = v = q . P



Where q = economic quality of the developed reserve
The developed reserve value V is v times the reserve volume (B)
So, let us use the equation:
NPV = V - D = q P B - D
Intuition (1): Timing Option and Waiting Value

Assume that simple equation for the oilfield development NPV.
What is the best decision: develop now or “wait and see”?


NPV = q B P - D = 0.2 x 500 x 18 – 1750 = + 50 million $
Discount rate = 10%
t=1
E[P+] = 19  NPV+ = + 150 million $
50%
t=0
E[P] = 18 /bbl
NPV(t=0) = + 50 million $
50%
E[P-] = 17  NPV - = - 50 million $
Rational manager will not exercise
this option  Max (NPV-, 0) = zero
Hence, at t = 1, the project NPV is: (50% x 150) + (50% x 0) = + 75 million $
The present value is: NPVwait(t=0) = 75/1.1 = 68.2 > 50
Hence is better to wait and see, exercising the option only in favorable scenario
Intuition (2): Deep-in-the-Money Real Option
 Suppose



the same case but with a higher NPV.
What is better: develop now or “wait and see”?
NPV = q B P - D = 0.22 x 500 x 18 – 1750 = + 230 million $
Discount rate = 10%
t=1
E[P+] = 19  NPV = 340 million $
50%
t=0
E[P] = 18 /bbl
NPV(t=0) = 230 million $
50%
E[P-] = 17  NPV = 120 million $
Hence, at t = 1, the project NPV is: (50% x 340) + (50% x 120) = 230 million $
The present value is: NPVwait(t=0) = 230/1.1 = 209.1 < 230
Immediate exercise is optimal because this project is deep-in-the-money (high NPV)
There is a NPV between 50 and 230 that value of wait = exercise now (threshold)
Threshold Curve: The Optimal Development Rule
 In
general we have a threshold curve along the time

We can work with threshold V* or P* (figure below) or (V/D)*
 At or above the threshold line, is optimal the immediate
development. Below the line: “wait, see and learn”
Invest Now Region
Wait and See Region
Expiration
Investment in Information: Motivation
 Motivation: Answer the questions below related to an
undeveloped oilfield, with remaining technical uncertainties
about the reserve size and the reserve quality
 Is better to invest in information, or to develop, or to wait?
 What is the best alternative to invest in information?
Revealed Scenarios
Investment in
Information
Expected Value of Project
(before the investment
in information)
E[V]
E[V | good news]
E[V | neutral news]
E[V | bad news]
 What
are the properties of the distribution of scenarios
revealed after the new information (revelation distribution)?
Technical Uncertainty Modeling: Revelation
 Investments
in information permit both a reduction of the
technical uncertainty and a revision of our expectations.



Firms use expectations to calculate the NPV or the real options exercise
payoff. These expectations are conditional to the available information.
When we are evaluating the investment in information, the conditional
expectation of the parameter X is itself a random variable E[X | I]
The process of accumulating data about a technical parameter is a
learning process towards the “truth” about this parameter
 This

suggest the names information revelation and revelation distribution
A similar but not equal concept is the “revelation principle” in
Bayesian games that addresses the truth on a type of player.
Here

the aim is revelation of the truth on a technical parameter value
The distribution of conditional expectations E[X | I] is named here
revelation distribution, that is, the distribution of RX = E[X | I]
We
will use the revelation distribution in a Monte Carlo simulation
Conditional Expectations and Revelation

The concept of conditional expectation is also theoretically sound
We
want to estimate X by observing I, using a function g( I ).
The most frequent measure of quality of a predictor g( I ) is its mean
square error defined by MSE(g) = E[X - g( I )]2 .
The choice of g* that minimizes the error measure MSE(g), called
the optimal predictor, is exactly the conditional expectation E[X | I ]
This is a very known property used in econometrics

Full revelation definition: when new information reveal all the
truth about the technical parameter, we have full revelation




Full revelation is important as the limit goal for any investment in
information process, but much more common is the partial revelation
In general we need consider alternatives of investment in information
with different revelation powers (different partial revelations). How?
The revelation power is related with the capacity of an alternative to
reduce the technical uncertainty (percentage of variance reduction)
We need the nice properties of the revelation distribution in
order to compare alternatives with different revelation powers
The Revelation Distribution Properties

The revelation distributions RX (or distributions of conditional
expectations, where conditioning is the new information) have
at least 4 nice properties for the real options practitioner:


Proposition 1: for the full revelation case, the distribution of revelation
RX is equal to the prior (unconditional) distribution of X
Proposition 2: The expected value for the revelation distribution is
equal the expected value of the prior (unconditional) distribution for
the technical parameter X


E[E[X | I ]] = E[RX] = E[X] (known as law of iterated expectations)
Proposition 3: the variance of the revelation distribution is equal to the
expected variance reduction induced by the new information
| I ]] = Var[RX] = Var[X] - E[Var[X | I ]] = Expected Variance
Reduction (this property reports the revelation power of an alternative)
 Var[E[X

Proposition 4: In a sequential investment in information process, the
the sequence {RX,1, RX,2, RX,3, …} is an event-driven martingale
 In
short, ex-ante these random variables have the same mean
Investment in Information & Revelation Propositions
 Suppose
the following stylized case of investment in
information in order to get intuition on the propositions

Only one well was drilled, proving 100 million bbl
Area A: proved
BA = 100 million bbl
A
B
Area B: possible
50% chances of
BB = 100 million bbl
& 50% of nothing
Area C: possible
50% chances of
BC = 100 million bbl
& 50% of nothing
C
D
Area D: possible
50% chances of
BD = 100 million bbl
& 50% of nothing

Suppose there are three alternatives of investment in information
(with different revelation powers): (1) drill one well (area B);
(2) drill two wells (areas B + C); (3) drill three wells (B + C + D)
Alternative 0 and the Total Technical Uncertainty
 Alternative


Zero: Not invest in information
Here there is only a single expectation, the current expectation
So, we run economics with the expected value for the reserve B:
E(B) = 100 + (0.5 x 100) + (0.5 x 100) + (0.5 x 100)
E(B) = 250 million bbl
 But
the true value of B can be as low as 100 and as higher
as 400 million bbl. So, the total (prior) uncertainty is large

Without learning, after the development you find one of the values:
 100 million bbl with 12.5 % chances (= 0.5 3 )



200 million bbl with 37,5 % chances (= 3 x 0.5 3)
300 million bbl with 37,5 % chances
400 million bbl with 12,5 % chances
 The
variance of this prior distribution is 7500 (million bbl)2
Alternative 1: Invest in Information with Only One Well
 Suppose that we drill only one well (Alternative 1 = A1)


This case generated 2 scenarios, because this well results can be
either dry (50% chances) or success proving more 100 million bbl
In case of positive revelation (50% chances) the expected value is:
E1[B|A1] = 100 + 100 + (0.5 x 100) + (0.5 x 100) = 300 million bbl

In case of negative revelation (50% chances) the expected value is:
E2[B|A1] = 100 + 0 + (0.5 x 100) + (0.5 x 100) = 200 million bbl


Note that with the alternative 1 is impossible to reach extreme scenarios
like 100 or 400 millions bbl (its revelation power is not sufficient)
So, the expected value of the revelation distribution of B is:

EA1[RB] = 50% x E1(B|A1) + 50% x E2(B|A1) = 250 million bbl = E[B]
 As

expected by Proposition 2
And the variance of the revealed scenarios is:

VarA1[RB] = 50% x (300 - 250)2 + 50% x (200 - 250)2 = 2500 (million bbl)2
 Let
us check if the Proposition 3 was satisfied
Alternative 1: Invest in Information with Only One Well
 In
order to check the Proposition 3, we need to calculated
the expected variance reduction with the alternative A1
 The prior variance was calculated before (7500).
 The posterior variance has two cases from this well outcome:

In case of success, the residual uncertainty (posterior distribution) is:
 200 million bbl with 25 % chances (in case of no oil in C and D)
 300 million bbl with 50 % chances (in case of oil in C or D)
 400 million bbl with 25 % chances (in case of oil in C and D)
 For the negative revelation case, the other posterior distribution is 100
million bbl (25%); 200 million bbl (50%); and 300 million bbl (25%)
 The residual variance in both scenarios are 5000 (million bbl)2
 So, the expected variance of posterior distributions is also 5000
 So, the expected reduction of uncertainty with the alternative A1 is:
Var(prior) - E[Var(posterior)] = 7500 – 5000 = 2500 (million bbl)2

Equal variance of revelation distribution(!), as expected by Proposition 3
Visualization of Revealed Scenarios: Revelation Distributions
All the revelation distributions have the same mean (maringale): Prop. 4 OK!
This is exactly the prior distribution of B (Prop. 1 OK!)
Posterior Distribution x Revelation Distribution

Higher volatility, higher option value. Why invest to reduce uncertainty?
Why learn?
Reduction
of technical
uncertainty

(distributions
of conditional
expectations)
Increase the
variance of
revelation
distribution
(and so the
option value)
Oilfield Development Option and the NPV Equation
 Let
us see an example. When development option is
exercised, the payoff is the net present value (NPV)
given by the simplified equation:
NPV = V - D = q P B - D
q
= economic quality of the reserve, which has technical
uncertainty (modeled with the revelation distribution);
 P(t) is the oil price ($/bbl) source of the market uncertainty,
modeled with the risk neutral Geometric Brownian motion;
 B = reserve size (million barrels), which has technical uncertainty;
 D = oilfield development cost, function of the reserve size B (and
possibly following also a correlated geometric Brownian motion)
Real x Risk-Neutral GBM Simulation
In the simulation paths we use the risk-neutral measure, which
suppresses a risk-premium p from the real drift. That is:
Real
Simulations
 The real drift =
a ,Versus
and theRisk-Neutral
risk-neutral
drift = a - p
45
Real Simulation
40
Risk-Neutral Simulation
35
30
25
20
15
10
5
Time (Years)
6.
0
5.
8
5.
5
5.
3
5.
0
4.
8
4.
5
4.
3
4.
0
3.
8
3.
5
3.
3
3.
0
2.
8
2.
5
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2.
0
1.
8
1.
5
1.
3
1.
0
0.
8
0.
5
0.
3
0
0.
0
Oil Price ($/bbl)

Development Investment and Reserve Size
Revealed Scenarios
Investment in
Information
E[B | good news]
Development Decision
 Large Platform
(large D)
E[B | neutral news]  Small Platform
(small D)
E[B]
Expected Reserve Size
(before the investment
in information)
E[B | bad news]
No Development

(D = 0)
 For specific
ranges of water depths, the linear relation
between D and B fitted well with the portfolio data:
D(B) = Fixed Cost + Variable Cost x B
 So, the option exercise price D changes after the information revelation on B
Sub-Optimal Capacity and the Penalty Factor

Without full information, if the reserve is larger (and/or more
productive) than expected, with the limited processing plant capacity
the reserves will be produced slowly than in case of full information.

A penalty factor g can be estimated by running a reservoir simulation
with limited process capacity and calculating the present value of V.
The NPV with technical uncertainty is
penalized using a Monte Carlo
simulation and the equations:
NPV = q P B - D(B)
if q B = E[q B]
NPV = E[V] + gup (Vu, i - E[V]) - D(B) if q B > E[q B]
NPV = q P B - D(B)
if q B < E[q B]
Here is assumed gdown = 1 and 0 < gup < 1
OBS: Vu = gup Vu, i + (1 - gup) E[V]
Dynamic Value of Information
 Value
of Information has been studied by decision
analysis theory. I extend this view with real options tools
 I call dynamic value of information. Why dynamic?

Because the model takes into account the factor time:
Time
to expiration for the rights to commit the development plan;
Time to learn: the learning process takes time to gather and process
data, revealing new expectations on technical parameters; and
Continuous-time process for the market uncertainties (P and in D)
interacting with the expectations on technical parameters
 When
analysing a set of alternatives of investment in
information, are considered also the learning cost and
the revelation power for each alternative

The revelation power is the capacity to reduce the variance of technical
uncertainty (= variance of revelation distribution by the Proposition 3)
Best Alternative of Investment in Information

Given the set k = {0, 1, 2… K} of alternatives (k = 0 means not
invest in information) the best k* is the one that maximizes Wk
 Where Wk
is the value of real option included the
cost/benefit from the investment in information with the
alternative k (learning cost Ck, time to learn tk), given by:

Where EQ is the expectation under risk-neutral measure,
which is evaluated with Monte Carlo simulation, and t* is the
optimal exercise time (stopping time). For the path i:
Combination of Uncertainties in Real Options

The simulated sample paths are checked with the threshold (V/D)*
Vt/Dt = (q Pt B)/Dt
A
B
F(t = 0) =
= F(t=1) * exp (- r t)
Present Value (t = 0)
Option F(t = 1) = V - D
F(t = 2) = 0
Expired
Worthless
Model Results Examples (Paper)
 In
the paper are analyzed two alternatives of investment in
information, with different costs and revelation powers:



Alternative 1 (vertical well) has learning cost of $ 10 million and time to
learn of 45 days. Reduction of uncertainties of 50% for B and 40% for q
Alternative 2 (horizontal well) has learning cost of $ 15 million and time
to learn of 60 d. Reduction of uncertainties of 75% for B and 60% for q
The table below shows that Alternative 2 is better in this case:
 The
Conclusions
paper main contribution is to help fill the gap in the
real options literature on technical uncertainty modeling

Revelation distribution (distribution of conditional expectations)
and its 4 propositions, have sound theoretical and practical basis
 The
propositions allow a practical way to select the best
alternative of investment in information from a set of
alternatives with different revelation powers

We need ask the experts only two questions: (1) What is the total
technical uncertainty (prior distribution); and (2) for each alternative
of investment in information what is the expected variance reduction
 We
saw a dynamic model of value of information
combining technical with market uncertainties

Used a Monte Carlo simulation combining the risk-neutral
simulation for market uncertainties with the jumps at the
revelation time (jump-size drawn from the revelation distributions)
Anexos
APPENDIX
SUPPORT SLIDES

See more on real options in the first website on real options at:
http://www.puc-rio.br/marco.ind/
Technical Uncertainty and Risk Reduction
 Technical
uncertainty decreases when efficient investments
in information are performed (learning process).
 Suppose a new basin with large geological uncertainty. It is
reduced by the exploratory investment of the whole industry

The “cone of uncertainty” (Amram & Kulatilaka) can be adapted to
understand the technical uncertainty:
Expected
Value
confidence
interval
Higher
Risk
Current
project
evaluation
(t=0)
Lower
Risk
Lack of Knowledge Trunk of Cone
Risk reduction by the
investment in information
of all firms in the basin
(driver is the investment, not
the passage of time directly)
Expected
Value
Project
evaluation
with additional
information
(t = T)
Technical Uncertainty and Revelation

But in addition to the risk reduction process, there is another
important issue: revision of expectations (revelation process)

The expected value after the investment in information (conditional
expectation) can be very different of the initial estimative

Investments in information can reveal good or bad news
t=T
Value with
good revelation
Value with
neutral revelation
E[V]
Value with
bad revelation
Current project
evaluation (t=0)
Investment in
Information
Project value
after investment
Geometric Brownian Motion Simulation

The real simulation of a GBM uses the real drift a. The price P
at future time (t + 1), given the current value Pt is given by:
Pt+1 = Pt exp{ (a - 0.5 s2) Dt + s N(0, 1) Dt }


The risk-neutral simulation of a GBM uses the risk-neutral
drift a’ = r - d . Why? Because by supressing a risk-premium
from the real drift a we get r - d. Proof:




But for a derivative F(P) like the real option to develop an oilfiled,
we need the risk-neutral simulation (assume the market is complete)
Total return r = r + p (where p is the risk-premium, given by CAPM)
But total return is also capital gain rate plus dividend yield: r = a + d
Hence, a + d = r + p  a - p = r - d
So, we use the risk-neutral equation below to simulate P
Pt+1 = Pt exp{ (r - d - 0.5 s2) Dt + s N(0, 1) Dt }

Oil Price Process x Revelation Process
What are the differences between these two types of uncertainties?
 Oil price (and other market uncertainties) evolves continually along
the time and it is non-controllable by oil companies (non-OPEC)
 Revelation distributions occur as result of events (investment in
information) in discrete points along the time
 For exploration
of new basins sometimes the revelation of information from
other firms can be relevant (free-rider), but it also occurs in discrete-time
 In many cases (appraisal phase) only our investment in information is
relevant and it is totally controllable by us (activated by management)

In short, every day the oil prices changes, but our expectation about
the reserve size will change only when an investment in information
is performed  so the expectation can remain the same for months!
P
Inv
E[B]
Inv
Economic Quality of the Developed Reserve
 Imagine
that you want to buy 100 million barrels of developed
oil reserves. Suppose a long run oil price is 20 US$/bbl.

How much you shall pay for the barrel of developed reserve?
 One
reserve in the same country, water depth, oil quality,
OPEX, etc., is more valuable than other if is possible to extract
faster (higher productivity index, higher quantity of wells)
 A reserve
located in a country with lower fiscal charge and
lower risk, is more valuable (eg., USA x Angola)
 As higher is the percentual value for the reserve barrel in
relation to the barrel oil price (on the surface), higher is the
economic quality: value of one barrel of reserve = v = q . P

Where q = economic quality of the developed reserve
 The value of the developed reserve is v times the reserve size (B)
NPV (million $)
NPV x P Chart and the Quality of Reserve
Linear Equation for the NPV:
NPV = q P B - D
NPV in function of P
spreadsheet value
tangent q = q . B
P ($/bbl)
-D
The quality of reserve (q) is related
with the inclination of the NPV line

Overall x Phased Development
Consider two oilfield development alternatives:



Overall development has higher NPV due to the gain of scale
Phased development has higher capacity to use the information along
the time, but lower NPV
With the information revelation from Phase 1, we can
optimize the project for the Phase 2


In addition, depending of the oil price scenario and other market and
technical conditions, we can choose not exercise the Phase 2 option
The oil prices can change the decision for Phased development, but not
for the Overall development alternative
The valuation is similar to
the previously presented
Only by running the
simulations is possible to
compare the higher NPV
versus higher flexibility
Real Options Evaluation by Simulation + Threshold Curve

Before the information revelation, V/D changes due the oil prices P (recall
= qPB and NPV = V – D). With revelation on q and B, the value V jumps.
V
A
B
Present Value (t = 0)
F(t = 0) =
= F(t=5.5) * exp (- r*t)
Option F(t = 5.5) = V - D
F(t = 8) = 0
Expires Worthless
NYMEX-WTI Oil Prices: Spot x Futures
Note that the spot prices reach more extreme values and have more
‘nervous’ movements (more volatile) than the long-term futures prices
WTI Nymex Prices: Spot (First Month) vs. 18 Months
Jul/1996 - Jan/2002
40
WTI Nymex Spot (1st Mth) Close (US$/bbl)
WTI Nymex Mth18 Close (US$/bbl)
35
30
25
20
15
10
1/22/2002
10/22/2001
7/22/2001
4/22/2001
1/22/2001
10/22/2000
7/22/2000
4/22/2000
1/22/2000
10/22/1999
7/22/1999
4/22/1999
1/22/1999
10/22/1998
7/22/1998
4/22/1998
1/22/1998
10/22/1997
7/22/1997
4/22/1997
1/22/1997
10/22/1996
5
7/22/1996
WTI (US$/bbl)

Brent Oil Prices: Spot x Futures
Note that the spot prices reach more extreme values than the longterm futures prices. Futures prices have lower volatility.
Brent Prices: Spot (Dated) vs. IPE 12 Month
Jul/1996 - Jan/2002
40
Brent Platt's Dated Mid (US$/bbl)
Brent IPE Mth12 Close (US$/bbl)
35
30
25
20
15
10
1/22/2002
10/22/2001
7/22/2001
4/22/2001
1/22/2001
10/22/2000
7/22/2000
4/22/2000
1/22/2000
10/22/1999
7/22/1999
4/22/1999
1/22/1999
10/22/1998
7/22/1998
4/22/1998
1/22/1998
10/22/1997
7/22/1997
4/22/1997
1/22/1997
10/22/1996
5
7/22/1996
Brent (US$/bbl)

Other Parameters for the Simulation
 Other important
parameters are the risk-free interest
rate r and the dividend yield d (or convenience yield for
commodities)

Even more important is the difference r - d (the risk-neutral
drift) or the relative value between r and d
 Pickles
& Smith (Energy Journal, 1993) suggest for
long-run analysis (real options) to set r = d

“We suggest that option valuations use, initially, the ‘normal’ value of d,
which seems to equal approximately the risk-free nominal interest rate.
Variations in this value could then be used to investigate sensitivity to
parameter changes induced by short-term market fluctuations”
Reasonable values for r and d range from 4 to 8% p.a.
 By using r = d the risk-neutral drift is zero, which looks
reasonable for a risk-neutral process
