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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)

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By: Marco Antonio Guimarães Dias- Internal Consultant by Petrobras, Brazil- Doctoral Candidate by PUC-Riohttp://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

Oil/Gas Success

Probability = p

• Drill the wildcat (pioneer)? Wait and See?

• Technical uncertainty model is required

Expected Volume

of Reserves = B

Revised

Volume = B’

• Appraisal phase: delineation of reserves

• 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

• 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 reserveq (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

t = 1

50%

t = 0

E[P-] = 17  NPV - = - 50 million \$

50%

Rational manager will not exercise

this option  Max (NPV-, 0) = zero

• 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+] = 19  NPV+ = + 150 million \$

E[P] = 18 /bbl

NPV(t=0) = + 50 million \$

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

t = 1

50%

t = 0

E[P-] = 17  NPV = 120 million \$

50%

• 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+] = 19  NPV = 340 million \$

E[P] = 18 /bbl

NPV(t=0) = 230 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)

Invest Now Region

Wait and See Region

Expiration

• 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”

Revealed Scenarios

Investment inInformation

E[V|good news]

E[V|neutral news]

Expected Value of Project

(before the investment

in information)

E[V]

• 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)?

• 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 conditionalto 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]

• 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

• 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 thetruth 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 distributions RX (or distributions of conditional expectations, whereconditioning 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

Area B: possible

50% chances of

BB = 100 million bbl

& 50% of nothing

A

B

Area A: proved

BA = 100 million bbl

C

D

Area D: possible

50% chances of

BD = 100 million bbl

& 50% of nothing

Area C: possible

50% chances of

BC = 100 million bbl

& 50% of nothing

• 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

• 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 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

• 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

• 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 the revelation distributions have the same mean (maringale): Prop. 4 OK!

Posterior Distribution x Revelation Distribution Distributions

Why learn?

Reduction of technical uncertainty

Increase thevariance ofrevelationdistribution

(and so the option value)

(distributions

of conditional

expectations)

• Higher volatility, higher option value. Why invest to reduce uncertainty?

Oilfield Development Option and the NPV Equation Distributions

• 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 Distributions

Development Decision

Revealed Scenarios

Large Platform (large D)

E[B|good news]

Small Platform (small D)

E[B]

E[B|neutral news]

Investment inInformation

Expected Reserve Size

(before the investment

in information)

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

Non-Optimized System and Penalty Factor Distributions

OBS: Vu = gup Vu, i + (1 -gup) E[V]

• 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 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

Dynamic Value of Information Distributions

• 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 Distributions

• 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

• 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:

Combination of Uncertainties in Real Options Distributions

A

B

Present Value (t = 0)

F(t = 2) = 0

Option F(t = 1) = V - D

F(t = 0) =

= F(t=1) * exp (- r t)

ExpiredWorthless

• The simulated sample paths are checked with the threshold (V/D)*

Vt/Dt = (q Pt B)/Dt

Model Results Examples (Paper) Distributions

• 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 Distributions

• 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 Distributions

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 Distributions

HigherRisk

Lower Risk

ExpectedValue

ExpectedValue

confidence interval

Lack of Knowledge Trunk of Cone

Project evaluation with additionalinformation(t = T)

Risk reduction by the investment in information

of all firms in the basin

(driver is the investment, not the passage of time directly)

Current project

evaluation

(t=0)

• 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:

Technical Uncertainty and Revelation Distributions

t = T

Value withgood revelation

Value withneutral revelation

E[V]

Investment in

Information

Project valueafter investment

Current project

evaluation (t=0)

• 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

Geometric Brownian Motion Simulation Distributions

Pt+1 = Pt exp{ (a - 0.5 s2) Dt + s N(0, 1) }

Pt+1 = Pt exp{ (r - d - 0.5 s2) Dt + s N(0, 1) }

• 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:

• 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 a’ = r - d. Why? Because by supressing a risk-premium from the real drift a we get r - d. Proof:

• 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

• Oil Price Process x Revelation Process Distributions

P

Inv

E[B]

Inv

• 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!

Economic Quality of the Developed Reserve Distributions

• 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 Distributions

Linear Equation for the NPV:

NPV = q P B - D

NPV (million \$)

NPV in function of P

tangent q = q . B

P (\$/bbl)

- D

The quality of reserve (q) is relatedwith the inclination of the NPV line

Overall x Phased Development Distributions

• 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 alternative

The valuation is similar to the previously presented

Only by running the simulations is possible to compare the higher NPV versus higher flexibility

A

B

Present Value (t = 0)

Option F(t = 5.5) = V - D

F(t = 0) =

= F(t=5.5) * exp (- r*t)

F(t = 8) = 0

Expires Worthless

• 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.

NYMEX-WTI Oil Prices: Spot x Futures Distributions

• Note that the spot prices reach more extreme values and have more ‘nervous’ movements (more volatile) than the long-term futures prices

Brent Oil Prices: Spot x Futures Distributions

• Note that the spot prices reach more extreme values than the long-term futures prices

Brent Oil Prices Volatility: Spot x Futures Distributions

• Note that the spot prices volatility is much higher than the long-term futures volatility

Other Parameters for the Simulation Distributions

• 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