By: Marco Antonio Guimarães Dias Internal Consultant by Petrobras, Brazil

Doctoral Candidate by PUC-Rio http://www.puc-rio.br/marco.ind/

. Investment in Information in Petroleum: Real Options and Revelation

SPE Applied Technology Workshop (ATW)

Risk Analysis Applied to Field Development under Uncertainty

August 29-30, 2002, Rio de Janeiro

E&P As Real Options Process

Delineated but undeveloped reserves Develop? “Wait and See” for better conditions?

RevisedVolume = B’ Appraisal phase: delineation of reserves

Invest in additional information?

Developed reserves Possible but not included: Options to expand the

production, stop temporally, and abandon

Oil/Gas SuccessProbability = p

Expected Volumeof Reserves = B

Drill the wildcat (pioneer)? Wait and See? Technical uncertainty model is required

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:

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)

Given a long-run expectation on oil-prices, how much we shall pay per barrel of developed reserve? The value of one barrel of reserve depends of many variables (permo-porosity 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 value of the developed reserve V is v times the reserve size (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%

E[P] = 18 /bblNPV(t=0) = 50 million $

E[P+] = 19 NPV+ = + 150 million $

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

50%

50%

t = 1

t = 0

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%

E[P] = 18 /bbl NPV(t=0) = 230 million $

E[P+] = 19 NPV = 340 million $

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

50%

50%

t = 1

t = 0

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”

Expiration

Invest Now Region

Wait and See Region

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?

What are the properties of the distribution of scenarios revealed after the new information (revelation distribution)?

E[V]Expected Value of Project (before the investment in information)

Investment inInformation

E[V | bad news]

E[V | neutral news]

E[V | good news]

Revealed Scenarios

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

Don’t confound with 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 unconditional (prior) distribution of X

Proposition 2: The expected value for the revelation distribution is equal the expected value of the original (prior) 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 Var[E[X | I ]] = Var[RX] = Var[X] E[Var[X | I ]] = Expected Variance Reduction (this property reports the revelation power of an alternative)

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

A B

DC

Area A: provedBA = 100 million bbl

Area B: possible50% chances of

BB = 100 million bbl& 50% of nothing

Area D: possible50% chances of

BD = 100 million bbl& 50% of nothing

Area C: possible50% chances of

BC = 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

This is exactly the prior distribution of B (Prop. 1 OK!)

All th

e revelation d

istribu

tions h

ave the sam

e mean

(marin

gale): Prop

. 4 OK

!

(distributions of conditional expectations)

Posterior Distribution x Revelation Distribution Higher volatility, higher option value. Why invest to reduce uncertainty?

Reduction of technical uncertainty

Increase thevariance ofrevelationdistribution(and so the option value)

Why learn?

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)

Development Investment and Reserve Size

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

E[B]

Expected Reserve Size (before the investment in information)

Investment inInformation

E[B | bad news]

E[B | neutral news]

E[B | good news]

Revealed Scenarios Development Decision

Large Platform (large D)

Small Platform (small D)

No Development ( D = 0 )

Non-Optimized System and Penalty Factor Without full information, if the reserve is larger (and/or more productive)

than expected, with the limited process plant capacity the reserves will be produced slowly than in case of full information. This factor 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] + up (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 down = 1 and 0 < up < 1

OBS: Vu = up Vu, i + (1 up) 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; andContinuous-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

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:

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

Combination of Uncertainties in Real Options The simulated sample paths are checked with the threshold (V/D)*

A

Option F(t = 1) = V DF(t = 0) == F(t=1) * exp (r t)

Present Value (t = 0)

B

F(t = 2) = 0ExpiredWorthless

Vt/Dt = (q Pt B)/Dt

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:

Conclusions The 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

APPENDIXSUPPORT 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:

Risk reduction by the investment in information of all firms in the basin(driver is the investment, not the passage of time directly)

Project evaluation with additionalinformation(t = T)

Lower Risk

ExpectedValue

Current project evaluation(t=0)

HigherRisk

ExpectedValue

con

fid

ence

in

terv

al

Lack of Knowledge Trunk of Cone

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

Value withgood revelation

Value withbad revelation

Current project evaluation (t=0)

Investment inInformation

Project valueafter investment

t = T

Value withneutral revelation

E[V]

Geometric Brownian Motion Simulation The real simulation of a GBM uses the real drift . The price P at future time (t + 1), given the current

value Pt is given by:

Pt+1 = Pt exp{ () t + t 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)

The risk-neutral simulation of a GBM uses the risk-neutral drift ’ = r . Why? Because by supressing a risk-premium from the real drift we get r . Proof: Total return = r + (where is the risk-premium, given by CAPM) But total return is also capital gain rate plus dividend yield: = + Hence, + r + = r

So, we use the risk-neutral equation below to simulate P

Pt+1 = Pt exp{ (r ) t + t

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

E[B]Inv

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 x P Chart and the Quality of Reserve

tangent = q . B

D

P ($/bbl)

NP

V (

mil

lion

$) Linear Equation for the NPV:

NPV = q P B D

NPV in function of P

The quality of reserve (q) is relatedwith 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 not exercise the Phase 2 option The oil prices can change the decision for Phased development, but not

for the Overall development alternativeThe 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 V = qPB and NPV = V – D). With

revelation on q and B, the value V jumps.

A

Option F(t = 5.5) = V DF(t = 0) == F(t=5.5) * exp (r*t)

Present Value (t = 0)

B

F(t = 8) = 0Expires 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 pricesWTI Nymex Prices: Spot (First Month) vs. 18 Months

Jul/1996 - Jan/2002

5

10

15

20

25

30

35

407/

22/1

996

10/2

2/19

96

1/22

/199

7

4/22

/199

7

7/22

/199

7

10/2

2/19

97

1/22

/199

8

4/22

/199

8

7/22

/199

8

10/2

2/19

98

1/22

/199

9

4/22

/199

9

7/22

/199

9

10/2

2/19

99

1/22

/200

0

4/22

/200

0

7/22

/200

0

10/2

2/20

00

1/22

/200

1

4/22

/200

1

7/22

/200

1

10/2

2/20

01

1/22

/200

2

WT

I (U

S$/

bb

l)

WTI Nymex Spot (1st Mth) Close (US$/bbl)

WTI Nymex Mth18 Close (US$/bbl)

Brent Oil Prices: Spot x Futures Note that the spot prices reach more extreme values than the long-term

futures pricesBrent Prices: Spot (Dated) vs. IPE 12 Month

Jul/1996 - Jan/2002

5

10

15

20

25

30

35

40

7/22

/199

6

10/2

2/19

96

1/22

/199

7

4/22

/199

7

7/22

/199

7

10/2

2/19

97

1/22

/199

8

4/22

/199

8

7/22

/199

8

10/2

2/19

98

1/22

/199

9

4/22

/199

9

7/22

/199

9

10/2

2/19

99

1/22

/200

0

4/22

/200

0

7/22

/200

0

10/2

2/20

00

1/22

/200

1

4/22

/200

1

7/22

/200

1

10/2

2/20

01

1/22

/200

2

Bre

nt

(US

$/b

bl)

Brent Platt's Dated Mid (US$/bbl)

Brent IPE Mth12 Close (US$/bbl)

Brent Oil Prices Volatility: Spot x Futures Note that the spot prices volatility is much higher than the long-term

futures volatilityBrent Volatility: Spot (Dated) vs. 12 Month (500 last data)

Jul/1996 - Jan/2002

10%

15%

20%

25%

30%

35%

40%

45%

50%7/

18/1

996

10/1

8/19

96

1/18

/199

7

4/18

/199

7

7/18

/199

7

10/1

8/19

97

1/18

/199

8

4/18

/199

8

7/18

/199

8

10/1

8/19

98

1/18

/199

9

4/18

/199

9

7/18

/199

9

10/1

8/19

99

1/18

/200

0

4/18

/200

0

7/18

/200

0

10/1

8/20

00

1/18

/200

1

4/18

/200

1

7/18

/200

1

10/1

8/20

01

1/18

/200

2

Vo

lati

lity

(% p

.a.)

Brent Spot (Dated)

Brent IPE 12 Month

Other Parameters for the Simulation Other important parameters are the risk-free interest rate r

and the dividend yield (or convenience yield for commodities) Even more important is the difference r (the risk-neutral drift) or

the relative value between r and Pickles & Smith (Energy Journal, 1993) suggest for long-run

analysis (real options) to set r = “We suggest that option valuations use, initially, the ‘normal’ value of , 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 range from 4 to 8% p.a. By using r = the risk-neutral drift is zero, which looks reasonable

for a risk-neutral process