John R. Schuyler
Consultant
Aurora, Colo.
The simulation models described in the previous three papers illustrate ways to analyze transaction and strategy decisions. In all cases the stated objective has been to maximize the expected end net worth of the company.
It is common practice in the petroleum industry to risk-adjust reserve values for categories other than Proved Developed Producing. Usually, the intent is to compensate for downside exposure (rather than the effect of uncertainty in competitive bidding). Reserve category adjustments introduce a risk averse bias into the analysis. Downside exposure is reduced at a cost of forgoing a portion of expected profits. This paper shows how to calculate the cost of a risk-averse attitude. It also presents a more logical and consistent way to incorporate your attitude toward risk into the decision process.
DECISION RULE, RISK ATTITUDE
A decision rule is a procedure for selecting from among decision alternatives. Usually, the rule is to select the alternative which provides the highest value measure.
Value is most often measured in dollars, but this need not be the case. However, a straight dollar measure would be used by someone who is solely trying to maximize a dollar value position. Such a person is risk-neutral about money. To a risk-neutral decision maker, a $10 million gain is as good as a $10 million loss is bad. And a $100 million gain is 10 times as valuable as a $10 million gain.
In reality, few people are neutral about money. Many would greatly prefer an 80% chance of winning $1,000 to a 0.8% chance of winning $100,000 even though both gambles have the same $800 expected value. Also, most persons would try to avoid a situation where there is a 50% chance of winning $10,001 and a 50% chance of losing $10,000, even though the expected value is slightly positive. Companies exhibit the same behavior as individuals, although the dollar amounts may be scaled up several orders of magnitude.
Fig. 1 is an illustration of two investment alternatives. The height of the probability function is proportional to the likelihood of the x-axis value being realized. Alternative B has a higher expected value but also has a greater range of possible outcomes. The width of the curve, usually measured by the standard deviation statistic, represents risk or uncertainty. By definition, the area under a probability curve equals one (100% probability). Many persons would choose A despite its lower expected value rather than face the potential downside of B. This is an example of risk aversion. This means there is a diminishing utility of greater dollars and an amplified negative utility for losses. The author will be showing a meaningful way to be conservative and still perform an objective, risk-neutral analysis.
BEST VALUE MEASURE
In making decisions aimed at optimizing the value of the firm, you need a good way to value alternatives. There are dozens of techniques used by appraisers to determine value. Most techniques involve present value discounting to recognize the time value of money (a time preference). Other approaches include such methods as applying cashflow or production multipliers and summing several years of projected cashflow.
How might we settle the issue of what method is best? To make an appealing and convincing argument, the author developed a simple simulation program which allows one to try various appraisal alternatives. The asset to be appraised is a five-year cashflow with a constant decline rate. Probability distributions are used to represent uncertainty in estimating initial cashflow rate and annual decline rate.
Assume that one pays his full appraised value for an asset. Also assume that the purchase is financed, with debt being repaid from cash flow. If the appraised value, with perfect foresight, equals the actual value, then the net balance will be zero at the end of the cashflow life. You might recognize this as the internal rate of return (IRR) condition. That is, if one buys the asset at actual value, and end up with zero net cash at the end of the transaction, then IRR equals the cost of capital (financing interest rate).
Taxes are not represented in the demonstration model but should be considered in most real analyses. Because interest expense is deductible, the asset value, in the context of what can be paid, is increased with financial leverage. However, paying the higher amount and deducting taxes still maintains the relationships discussed in the preceding paragraph. The best value measure is still the present value of the net cash flow using the after-tax cost of capital as the discount rate.
If there are a limited number of possible outcomes for a decision, the present value of each outcome is multiplied by its probability, and these products are summed. This yields the expected monetary value (EMV) for the outcome. For a continuous range of outcomes, EMV is the mean (or average) of the present value probability distribution.
A run report from the first demonstration program is shown as Fig. 2. Four alternative decision strategies are to be tested. Strategies 2,3, and 4 have their own value measures:
Strategy 0: no value measure; accepting all investments as presented
Strategy 1: present value at the cost of capital rate.
Strategy 2: a factor (.75 shown) times present value at an alternative discount rate (shown rate 2 = .06/year)
Strategy 3: a multiple (1.0 shown) times the sum of several years (3 shown) cashflow.
Part I compares the ending cash position for Strategies 1-3 if the acquisition price equals the respective strategy's value measure. The same 50 hypothetical investments are made for each strategy scenario. Strategy 1 provides the value (-O.478) closest to zero, i.e., closest to the true value. This value approaches zero as the number of investments increases and as the mean deviation of value estimate decreases. Thus, almost by definition, the true value of a cashflow is found to be the present value discounted at the cost of capital.
Part 11 shows the results for the four decision rules. A hypothetical price for the asset was calculated as the average of the three value measures. Except for Strategy 0 which accepts all investments, the decision rule is to accept the investment if the value measure is greater than the price. With the parameters chosen, Strategies 2 and 3 undervalue the proposed investment and, thus, make fewer investments, Strategy 1 is the clear winner here, and, over the long run, will provide a higher value than any other strategy.
In part III, the decision rule is modified to reflect limited capital. In this situation, the ranking criterion is the value measures divided by the investment cost. When the value measure is a PV, the results is called a profitability index (PI). The new decision criteria are used to get "the most bangs for the bucks." The results shown were obtained by ranking 100 investment opportunities and then acquiring as many, in sequence, as the available capital would allow. Note that all three ranking strategies produce about the same result. This is because there is a strong positive correlation between the three strategy value measures. This effect caused me unexpected difficulty when working with the exploration company model described in the second paper: Superior prospects (investments) are always approved, and the clearly undesirable ones are always declined.
IMPACT OF RISK ATTITUDE
When evaluating several alternatives for a single decision, the analysis is very sensitive to value measures. And intentional or unintentional biases, such as introduced by risk adjustments, can have a striking effect on the expected outcome. Achieving the optimum result over a series of investments requires a logical and consistent approach.
Each person has his or her own risk attitude, and this attitude can be encoded as a risk profile curve, also called a preference function or utility curve. There are no right or wrong risk attitudes. This characteristic is based upon the individual's deep-seated values and beliefs. A good decision is simply one which is consistent with the attitudes (values) and judgments (data, beliefs) of the decision maker at the time of the decision.
A person's risk profile can be encoded as a utility function. This is a curve with utility drawn as a function of outcome value. Encoding decision maker's risk attitude is usually done during an interview with a trained decision analyst. The risk profile is determined through a series of questions about potential risks which would be acceptable to the decision maker. For example, a person, representing his or her company, might be asked what potential gain would be necessary to offset a 50% risk of losing $200,000. A series of such hypothetical investments places points on the risk profile curve. When the risk profile represents the attitude to be used throughout a company, it is a succinct and complete statement of risk policy.
Fig. 3 shows an example risk profile curve. Many persons have risk profiles which would have very different shapes from the curve shown here. It is the author's my opinion that as persons learn more about decision analysis, their risk profile curves will approach this shape. The y-axis is in arbitrary units, often called utils. The dashed straight line through the origin is the profile of a risk-neutral decision maker. In reading the curve, for example, a $10 million present value outcome has a value of about .62 utils. In recognizing risk attitude, we will want to maximize utility rather than maximize dollars.
One can see on the graph that a $10 million gain has about the same magnitude utility as does a $5 million loss. Thus, a decision maker with this risk profile would be approximately indifferent to an investment with a 50:50 chance of gaining $10 million or losing $5 million. This is because the expected utility, calculated in the same manner as EMV, is approximately zero.
Now consider a situation where there is a 50% chance of gaining $10 million and 50% chance of zero gain. What is this opportunity worth to the decision maker? The expected utility is .5 x .62 = .31 utils. If you draw a line across from .31 to the risk profile curve, and then down to the x-axis, you get a value of about $3.8 million. This is the certainty equivalent value of the opportunity to the decision maker. He or she has no preference between $3.8 million in hand and a 50% chance of gaining $10 million. Thus, the decision maker is willing to forego $1.2 million of expected value (.5(10) - 3.8) in order to avoid risk. Large companies have much straighter, more risk-neutral curves than individuals and smaller companies; this is what makes the insurance industry possible.
IMPACT OF RISK ADJUSTMENTS
How do we measure the financial impact of a conservative risk policy?
Economic projections for evaluation purposes are traditionally conservative. Nonproducing reserves are usually discounted for risk with factors reflecting performance evidence or reserve category. For example, proved producing might be valued at 100%, while proved undeveloped might be valued at 25%, of the expected value projections. Pricing and other assumptions, also, are frequently conservative. The adjustments are probably in the right direction, but we have no way of knowing whether they are consistent with the decision maker's attitude.
More logical and more consistent results will be obtained if the risk attitude is incorporated only at the last stage of the analysis. The base analysis can then be objective, using the best estimates for all parameters. This allows the decision maker's (or company's) risk policy to be applied consistently.
DEMONSTRATION
A second demonstration program was developed to show the impact of risk attitude in the decision rule. This program operates similar to the first program's Part 11 analysis (see Figure 2). A risk-weighted profitability index (value measure/expected investment) could have been used, but this provides little advantage when the investments are all about the same size. Three decision strategies are compared:
Strategy 0: accept all investments
Strategy 1: accept if Expected Monetary Value 0
Strategy 2: accept if Expected Utility 0
When using the program, your rough-cut risk profile is determined you answer the probability at which you would be indifferent to gamble between a stated gain and a stated loss. This is sufficient to determine parameters for an exponential risk profile function.
Fig. 4 shows the results obtained from a 100-trial simulation of 20 potential investments. This is a cumulative frequency type curve, showing the probability that an outcome will be equal to or greater than the (x-axis) amount. There is a 20% chance of investment success, which is somewhat analogous to oil and gas exploration. The average investment cost is $2 million, and the average success value is $10 million (beyond recouping the $2 million investment). The entire investment is lost if the project fails. Over the long run, Strategy 1, based on PI at the cost of capital, will outperform any other strategy. Strategy 2, based on expected utility, is the most selective and makes the fewest investments. In doing so, it by-pases other investments which are profitable and recognized by the EMV criterion. Reducing the downside is at a high cost: Risk aversion cost this company about $1.5 million, the difference between Strategies 1 and 2.
Fig. 5 shows the results obtained when simulating investments with a high, 80%, success rate. Here, the average investment is $20 million and the average success value (beyond recouping the investment) is $10 million. In this example, the risk-averse Strategy 2 has even poorer results than Strategy 0 which accepted all investments. The expected monetary value criterion yields about $26 million better results than expected utility. If this is too high a price to pay for reducing the downside exposure, then the decision maker should rethink his or her risk policy.
SUMMARY
The author has demonstrated, by experiment, that the best measure or monetary value is PV of the net cash flow discounted at the cost of capital. The risk-weighted PV, EMV, provides a superior decision criterion when net monetary gain is to be maximized and when the situation is unaffected by a capital constraint. EMV divided by the expected investment cost should be used when capital is limited.
Risk considerations can and should be segregated from the fundamental transaction analysis. Then judgments about physical, operating, and financial parameters can be made with complete objectivity. If appropriate, the decision maker's attitude toward risk is incorporated at the end of the decision process. This allows the cost of risk aversion to be measured as the sacrifice in expected monetary value. When applied across many decisions, the impact of risk adjustments can be great, often higher than one expects or desires.
ACKNOWLEDGMENTS
Thanks go to Dr. Paul D. Newendorp and Dr. John A. Pederson for their helpful comments about an early draft of this paper and for their encouragement. We hope these papers will generate some interesting discussions and lead to greater application of decision analysis techniques.
Copyright 1990 Oil & Gas Journal. All Rights Reserved.
