Decision Analysis & Risk Management in Oil & Gas

Posted on Sep 6, 2024 in Economy

Elements of the Decision Problem: Decisions to be made; Uncertain events; Value of specific outcomes.

Influence Diagrams

Graphical representation of uncertain quantities and decisions that explicitly reveals probabilistic dependence and the flow of information.

Arcs

  • Decision: Information flow & the chronological order.
  • Value & Chance: Conditional and show probabilistic dependence between decision elements.
  • A->B: B is conditioned on the value of A.

Sensitivity Analysis

Relative impact of different variables; explore the impact of changes in probabilities on decisions.

  • Two-way: 2 variables at the same time.
  • Tornado: Length of bar represents sensitivity/importance of each variable.
  • Spider: Percentage deviation from the base case vs. expected NPV.

Risk and Return

  • Expected return: A measure of central tendency.
  • Variance: An average deviation measure of dispersion, obtained by averaging the squares of deviations of individual observations from the mean.
  • Semi-variance: By minimizing standard deviation, the optimization penalizes projects with upside and mainly downside.
  • Normal distribution: Mean = Mode = Median.
  • Lognormal distribution: Skewed to one side, straight line with cumulative frequency.
  • Uniform distribution: Only specify a minimum and a maximum.
  • Triangular distribution: Estimate the minimum, most likely, and maximum.

Independent Event

Event A and B are independent if and only if: P(A) = P(A|B) = P(A ∩ B)/P(B), P(A,B) = P(A)P(B).

Conditional Independence

A and B are conditionally independent if P(A ∩ B|C) = P(A|C)P(B|C).

Marginal Event

Union, unconditional.

Joint Event

Intersection.

Conditional Probability

P(A,B) = P(B)P(A|B).

Bayes’ Theorem

Prior Probability + New Information + Bayes’ Theorem => Posterior Probability (Revised Probability).

Value of Information

Information only has value in a decision problem if it results in a change in some action to be taken by a decision-maker.

  • Perfect Information: Perfectly reliable, EVPI = EV – EV without information.
  • Value of Imperfect Information: EVSI = EV with sample information – EV without information.

Information Can Add Value Along Multiple Dimensions

  • Cost: Avoid non-commercial prospects, fewer wells needed for field appraisal, fewer dry holes, better field development, avoid overcapacity in field development.
  • Reservoir Value: Select the best prospect in a ranking process, make sure topside facilities have sufficient capacity, optimize production and recovery.
  • Uncertainty: Success rates, reservoir areal extent, compartmentalization, reserve size, improve confidence in estimates.

Binomial Approach

Probability of x successes in n independent trials =
n: Number of independent trials.
x: Number of successes in the n trials.
p: Probability of success on any given trial.
: Combination of n things taken x at a time.

Simulation

Objective: Define the distribution of outcomes that could be anticipated for the project. Considers the impact of changes on all variables simultaneously.

Covariance

[Formula]

Correlation Coefficient

[Formula]

Coefficient of Determination: The fraction of the variability in the returns on one investment that can be associated with variability in the returns on the other.

Advantages of Simulation

  1. Capability to define uncertainty as a range and distribution of possible outcomes for each factor.
  2. May be applied to any type of non-deterministic analysis.
  3. No limit to the number of variables that may be modeled.
  4. Distributions of random variables can be of any type.
  5. Integrates both above-ground and below-ground risks into the decision process.
  6. Different individuals can describe uncertainty about different components of the problems.
  7. Lends itself well to sensitivity analysis.
  8. Provides valuable inputs to decision tree modeling.

Deterministic Dominance

Compare outcomes, x-axis.

Conditions:

  1. One alternative dominates the other with certainty.
  2. Probability density functions do not intersect.

Probabilistic/Stochastic Dominance

Compare probability, y-axis.

Conditions:

  1. For all values in the outcome set, alternative A is more likely to exceed that value than alternative B.
  2. When the probability density functions do cross and the cumulative probability distributions of competing alternatives do not cross.

Risk and Return

[Formula]

Beta

The indicator of the degree to which a stock responds to changes in the return produced by the market. [Formula]

Expected Utility Axioms

  1. Orderability & Transitivity.
  2. Reduction of compound uncertain events (probabilities multiplied and added to simplify).
  3. Continuity/Independence.
  4. Substitutability.
  5. Monotonicity.
  6. Invariance.
  7. Finiteness.

Limitations of Expected Value Analysis

  1. The firm doesn’t possess an unlimited pool of exploration capital.
  2. The firm is not risk-neutral.
  3. EMV fails to provide guidance on limiting downside exposure. EMV does not consider the magnitude of money exposed to the chance of loss.

Condition for Risk Neutrality

The firm must be impartial to the magnitudes of potential profits and losses.

Preference or Expected Utility Theory

  1. Dominant approach to the theory of decision making in both economics and finance.
  2. Establishes the process of modeling an individual or firm’s risk propensity.
  3. Enables the decision-maker to incorporate risk attitudes into the decision process.
  4. Provides the firm a technique for determining the appropriate level of diversification.

Certainty Equivalent

That certain value for an uncertain event which a decision-maker is just willing to accept in lieu of the gamble represented by the event.

Risk-Neutral Behavior

Is reflected by a straight line; maximizing EV is equivalent to maximizing EU.

Risk-Averse Behavior

Is reflected by a concave utility function; in this case, the CEQ is less than the expected value of the payoff.

Risk-Seeking Behavior

Is reflected by a convex utility function; it is the opposite of risk aversion in that the CEQ for a gamble is greater than the expected value of the payoff.

CEQ, Expected Value, and Risk Premium All Depend on Two Factors

  1. The decision-maker’s or firm’s utility function.
  2. The probability distribution of payoffs.

Expected Utility Axioms

  • Orderability and Transitivity.
  • Reduction of Compound Uncertain Events.
  • Continuity or Independence.
  • Substitutability (The “Do you really mean it?” axiom).
  • Monotonicity.
  • Invariance.
  • Finiteness.

This Utility Function Has Two Important Properties

  1. The utility of any lottery is the expected utility of its prizes.
  2. If the decision-maker prefers one lottery to another, then it must have the higher utility. (If the attribute of interest is such that more is always better, then the utility curve will always be monotonically increasing.)

Decreasing Risk Aversion

Condition which implies that the degree of risk aversion decreases as the payoffs increase. The decreasing risk premium reflects decreasing risk aversion, which is a property of the logarithmic form of the utility function.

When Constant Risk Aversion Holds and Events Are Independent

Multiple projects can be treated separately. The sum of the CEQs for independent projects is equal to the CEQ of the portfolio of projects.

Exponential Utility Function

U(x) = a – be-x/R

Risk Tolerance (R)

Value represents the sum of money at which the decision-makers are indifferent as a company investment to a 50-50 chance of winning that sum and losing half that sum. It captures in monetary terms the notion of assessing tradeoffs between potential upside gains versus downside losses.

Risk-Sharing Pareto-Optimal

Allocation in which no one firm can be made better off without the other firm being made worse off.

Linear Sharing Rule

When two individuals have exponential utility functions, then they take proportional shares in the ratio of RT1 to RT2.

Measuring Risk Tolerance

Surveys & Interviews.