Michael R. Walls
Strategic Systems Group
Austin
The measurement, management and control of risk are critical to the success of the oil and gas exploration firm in today's competitive and uncertain petroleum markets. Many petroleum exploration companies have utilized the basic expected value rule in making decisions concerning risky investments; however, most analyses of important decision problems have left the incorporation of the firm's risk preferences to informal procedures or decision makers' intuition. The petroleum exploration decision support system discussed in this paper provides a prospect/property evaluation consistent with the risk preferences of the firm as well as the risk characteristics of the exploration venture. The software implements effective and proven decision theory and risk analysis methodologies to (1) provide the firm a technique for determining the right level of prospect diversification; and (2) to enable the firm to exercise more control over the financial risks associated with oil and gas exploration.
RISK
The word "risk" is usually associated with the probability of success or the complementary probability of a dry hole outcome. Many explorationists would say that the "expected value", which weights the financial consequences by their probabilities, adequately takes risk into account. However, to the exploration manager risk is not just a function of the probability distribution of reserve outcomes, but also the magnitude of capital being exposed to the chance of loss. The expected value concept fails to give adequate weight to the exposure to the chance of very large loss. Investment decisions based solely on the expected value rule assume the firm is risk neutral and has unlimited capital. The software addresses these deficiencies by implementing risk discounting based preference theory, also known as utility theory.
Utility theory was first recommended for evaluation of exploration ventures by Grayson (1960). Improvements were made by Pratt (1964). He defined the "certainty equivalent" of a risky venture. The "certainty equivalent" represents 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. The decision maker's or firm's certainty equivalent for the risky venture depends upon such things as the wealth of the firm making the decision, which determines its security against bankruptcy, and the budget level, which represents the liquid assets which it can risk losing. To illustrate, let's assume that Firm X and Firm Y both hold identical exploration prospects with the following parameters:
Probability of success: 50%
Probability of dry hole: 50%
Net present value of success: $10 million
Net present value of dry hole: -$ 2 million
Expected Value = (0.50 x $10MM)+ (0.50 x - $2MM) = $4.0 MM
Assume that Firm X and Y have the option to either retain a 100% working interest and drill the prospect or sell their entire interest to a third party. The cash value which Firm X is just willing to accept in lieu of drilling the prospect is $3 million. This dollar value represents the firm's point of indifference between a certain value and a more lucrative but risky gamble. Assume Firm Y's point of indifference is $2 million. The value designated by each firm for the sale of this "gamble" represents their certainty equivalent and provides valuable information concerning the firm's risk preferences. An individual or firm with a certainty equivalent that is less than the expected value of the payoff, as in the cases of Firms X and Y, is called risk-averse. Risk aversion is the most generally observed attitude toward risk for uncertain events whose consequences are significant.
Utility theory provides us a basis for constructing and using a utility function to predict individual or group (the corporation) choices under conditions of uncertainty. Decisions under conditions of uncertainty such as the example above provide information for assessment of the firm's risk preferences or utility function. While the vast majority of companies do not actually know their utility functions, bounding or estimating their utility functions is a practical approach to obtaining the benefits of utility theory. Cozzolino (1977) has provided us with a measure known as Risk-Adjusted Value (RAV), a term synonymous with "certainty equivalent", which is equal to the expected value less a risk discount. The discount is proportional to the Risk Aversion Level (r) of the firm and the risk characteristics of the venture. A formula for risk adjusted value (RAV), based on the exponential form of utility functions, is derived in the Appendix. For the two outcome scenario as in the example above, the formula reduces to:
[SEE FORMULA (1)]
where,
r = risk aversion level of the firm
p = probability of successful outcome
R = present value of success outcome
C = present value of dry hole outcome
e = exponential function
In - natural logarithm
We now can derive the risk aversion levels (r) of Firm X and Firm Y. The selling prices for the identical prospect, $3 million for firm X and $2 million for firm Y, represent the firms' respective certainty equivalents or RAVs for that gamble. Rearranging Equation 1 and solving for r (risk aversion level) we find that Firm X has a risk aversion level equal to 0.06 while Firm Y has a risk aversion level of 0.12. Firm Y has exhibited a much higher risk aversion level than Firm X. The $2 million dollar dry hole cost may represent a greater proportion of Firm Y's capital budget than Firm X's. A larger risk aversion level (r) represents a greater concern for the downside potential and a lesser concern for the upside potential. Risk aversion level is a key concept for developing a more objective measurement of financial risk.
It is critical to understand that the firm's risk aversion level is neither right nor wrong, but rather descriptive of the firm's attitudes toward risk or financial loss. There is no established theory which tells the decision-maker how risk-averse he ought to be. It remains a subjective parameter of management. The manager who bears the responsibility for decisions should estimate the risk aversion level appropriate for his firm. Consistency of decisions on risk is achieved by evaluating all exploration ventures at the same level of risk aversion. There appears to be some general inverse relationship between capital budget size and risk aversion level. This would imply significant differences in risk aversion levels between independent producers and major oil companies. From this we can draw the conclusion that smaller companies with higher risk aversion levels will desire smaller participation interests to decrease downside exposure.
THE SOFTWARE
The complex nature of decision analysis and utility theory has long prevented its use in the day to day decision making of petroleum exploration firms. However, in this age of microcomputers the merging of powerful decision and risk analysis models with the traditional reserves and economics program is a reality. The ability to measure risk and risk preferences on a sound scientific basis has strong implications for allocating resources across exploration ventures. Exploration companies deal with decisions concerning risky ventures everyday. The primary method of controlling risk is through diversification by taking fractional participation in a relatively large number of projects. The software allows the firm to make this practice more explicit and systematic through formal analysis.
As in traditional reserves and economics packages the user inputs ownership interests, product pricing, capital and operating expenditures, reservoir decline information and other pertinent information concerning the prospect/property. In addition, the user may input reserve and probability information in a variety of ways. The software utilizes a number of different decision tree formats depending on the specific method of reserve inputs selected by the user. Decision tree analysis involves constructing a diagram showing all the decision options and subsequent chance events associated with the decision problem. This allows the user to react to "what-if" scenarios as well as to model a range of outcomes on a particular prospect. An example of one of the many decision trees utilized in the software is shown in Fig. 1.
In order to determine the best share in a given exploration prospect it is necessary to calculate a sample of risk-sharing options available to the firm. The software allows the user to specify the particular terms of the sale or purchase of a partial interest in an exploration prospect. Estimated promotions, premiums, cash considerations and retained overriding royalties are entered by the user. In addition, the user may model the specific terms of a farmout including overrides, payout provisions, back-ins, etc. The user may then elect to calculate the prospect economics and risk analysis across six different risk-sharing options. They are 100%, 75%, 50%, 25% and 12.5% of current or available interest as well as farmout scenario. The software calculates the unrisked and risked scenarios, decision tree analysis and risk-adjusted value analysis (RAV) at 45 different risk aversion levels for each risk-sharing option.
OPTIMAL WORKING INTEREST
Risk measurement cannot be achieved with one number for all firms since different firms have different degrees of risk aversion. However, a more objective measurement of risk can be achieved by reporting a profile of risk-adjusted values. The risk profile curve shows the RAV for many firms since it is a graph of RAV against risk aversion level (r). A zero risk aversion level implies expected value decision-making. The risk profile curve always decreases as the risk aversion level increases, except in the special case of no uncertainty about outcomes. As the risk aversion level increases in infinity the risk profile curve approaches the value of the worst possible outcome of the venture.
If two companies were in agreement on the probability and outcome values of a prospect, then they would also obtain the same risk profile curve, even though they may have different degrees of risk aversion. Fig. 2 shows the software's risk profile comparison for three different working interest levels on the Canyon Ridge Prospect. if the firm's risk aversion level were between 0.125 and 0.275 then the firm should participate at the 40% working interest option since the RAV at that range of risk aversion levels dominates all other risk-sharing options. However, if the risk aversion level of the firm were greater than 0.275 then the firm should reduce to the 10.0% working interest level.
Similarly, if the user wishes to evaluate RAV's at specific risk aversion levels, then RAV's may be compared at user-selected working interest options and risk aversion levels. Fig. 3 shows a prospect where a firm with a risk aversion level of 0.01 would retain a 50% working interest. While in the same prospect a firm with an r value of 0.10 would want to reduce to a 12.5% working interest since the RAV at that interest level dominates all other risk-sharing options.
The software also provides comparative risk-adjusted value analysis on a multiple prospect basis. Fig. 4 shows a risk profile comparison of four different prospects at user-selected working interest levels. Traditional expected value analysis provides information only at the zero risk aversion level (r = 0.0). The software addresses this deficiency by discounting based on the magnitude of capital exposed to a chance of loss. Notice that in Fig. 4 the Bashaw Prospect dominates all others on an expected value (r = 0-0) while it is clearly unacceptable to a firm with a risk aversion level of 0.15 or greater. The Mason Prospect, which was one of the least economic prospects on an expected value basis, dominates all others at the 0.15 risk aversion level with an RAV of $600,000.
PROSPECT RANKING
When investment capital is limited, it is necessary to be able to rank available projects. For this purpose, the software allows the user to rank up to 150 prospects on an RAV basis. The user may select any of 40 different risk aversion levels at which to rank a group of prospects. Table 1 shows a Prospect Ranking Report generated by the software for a group of 14 prospects. The user-selected risk aversion level is 0.50. The report provides a ranking of the 14 prospects on the basis of RAV. In addition it indicates the firm's optimal working interest at that risk aversion level as well as the expected value and unrisked value of the prospect at the optional working interest. By utilizing the RAV Prospect Ranking Report at different risk aversion levels the user is provided additional insight into the risk characteristics of the firm's individual prospects. When exploration capital is limited the RAV Ranking Report provides a useful aid in allocation of resources and development of a balanced prospect portfolio.
CORPORATE RISK POLICY
The author suggests that the firm's risk aversion level (r) is a changing variable, dependent on any number of criteria; for example, the firm's present exploration philosophy, beliefs about product pricing and investment capital availability. Continued monitoring and sensitizing of the firm's level of risk aversion is necessary due to a changing corporate and industry environment. However, over any given budgetary period, utilization of an established risk aversion level will result in consistent and improved decision making with respect to risk.
Now more than ever exploration firms must draw on the available research and technology to aid in the capital budgeting process, Critical to generating long term and consistent returns is the proper allocation of limited resources and capital. Part of this allocation process is determining what level of risk the management or stakeholders are prepared to assume. Independent oil companies, as well as the majors, must evaluate more closely the financial risks associated with petroleum exploration. Though the level of downside exposure taken on by majors and independents may differ, the fundamental issue of identifying and specifying the firm's acceptable level of risk are very much similar. Having established the firm's risk aversion level, the software makes it possible to construct a portfolio of exploration prospects that coincides directly with the firm's risk preferences and capital limitations. Moreover, it provides an effective means of communicating a consistent risk policy throughout the organization.
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