Risk, Uncertainty and Investment Decision-Making in the Upstream Oil and Gas Industry Fiona Macmillan ma hons (University of Aberdeen) October 2000 a thesis presented for the degree of Ph. D. at the University of Aberdeen declaration
Figure 5.5: A preference curve (source: adapted from Newendorp, 1996 p147)
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Figure 5.5: A preference curve (source: adapted from Newendorp, 1996 p147)According to risk consultant Peter Rose (1987), a preference curve shows two things: The pleasure (utility) associated with winning is generally less than the displeasure of losing the same amount (that is, it hurts more to lose than it feels good to win.) People will take a greater chance to avoid a loss than to make a gain of the same amount. People feel more pleasure about gaining $10 going from, say, $10 to $20, than they do about gaining $10 going from $1500 to $1510. Theoretically at least it is possible to draw just such a curve for any individual. Different shaped curves would denote different types of decision-maker. The shape of the curve in the lower left-hand quadrant describes how the individual feels about loss and the one in the upper right quadrant is the individual’s attitude to risk and the levels of profit associated with risk. Many writers have categorised decision-makers according to the shape of their preference curves. In general, these authors perceive there to be three types of decision-maker: risk averters, average players (who would always choose the decision alternative with the maximum EMV) and risk-seekers. Each, they believe, has a distinctive preference curve. These curves are shown in figure 5.6. As indicated above, extensive studies (for example, Newendorp, 1996; Hammond, 1967) have provided strong evidence that the majority of decision-makers are risk averse to some degree, so concave downwards preference curves are the most commonly observed in practice.   1.0
Risk averter Preference Averages player Risk-seeker 0.0 Increasing amounts of money Figure 5.6: Typical preference curves (source: Hammond, 1967) Once the decision-maker’s preference curve has been drawn, von Neumann and Morgenstern showed that it could be used to solve decision problems using an extension of decision tree analysis. The basic principle is if the decision-maker wishes to make the decision consistent with his attitude toward risk, then the decision-maker must choose that course of action that has the highest preference. Preference theory is well illustrated by the following example taken from Hammond (1967). Imagine an oil company executive is facing the decision of whether to drill a well. The decision-maker has three choices: firstly, drill immediately; secondly, pay to acquire and interpret seismic data and then, depending on the result of the test, decide whether to drill or not; or lastly, to let the option expire. The seismic analysis can be performed for a fixed fee of $30,000 and the well can be drilled for a fixed fee of $100,000. A large organisation has promised the decision-maker that if this well discovers oil, it will purchase the company’s rights to the oil for $400,000. The geologists have estimated that there is 0.55 probability that if a well is drilled it will discover oil. Data on the reliability of the seismic analysis indicate that if the analysis is favourable, the probability of finding oil will increase to 0.85, but if the analysis is unfavourable, it will fall to 0.1. The geologists have computed that there is a 0.6 probability that the result will be favourable if seismic interpretation is carried out. Figure 5.7 shows the decision tree for this example. At each terminal fork in the decision tree, the expected value of the decision alternative is noted. (Recall that this is the weighted-average of the numbers at the end positions emanating from the fork). For example, the top-most terminal fork expected value is $340,000 (0.85*$400,000+15*$0). Rolling back the decision tree the decision-maker would end up with the decision tree in figure 5.8 and the decision, according to EMV, would be to drill immediately. Using preference theory, the result is somewhat different. To implement preference theory, assume that the decision-maker’s preference curve has been ascertained. This is shown in figure 5.9. Then: Convert all of the end positions of the decision tree into preferences (ascertained from the decision-maker’s preference curve in figure 5.9). These numbers are red in figure 5.10. Find the decision-maker’s preference for an event fork by taking the mathematical expectation of the preferences values at the end position of the fork. In other words, instead of multiplying the dollar values by probabilities, as in a decision tree analysis using expected values, multiply the preferences by the probabilities. So, at each event fork take a weighted-average of the preferences, where the weights are the probabilities. For example, at the uppermost event fork representing “oil-no oil”, the preference is 0.83 (0.85*0.93+15*0). The preference is written under the fork in green in figure 5.10. For each act fork, the decision-maker or analyst then selects the act with the highest preference. For example, the upper most decision fork in figure 5.10, the choice is between “drill” with a preference of 0.83 and “don’t drill” with a preference of 0.60, so the choice is to drill. The preference of the act chosen is written in pink at the base of each act fork in figure 5.10. The act not chosen is scored off and this is shown by the double bar in figure 5.10. Continue backwards through the tree, repeating steps 2 and 3 until the base of the tree is reached. For instance, the preference of the decision to take the test is 0.74 (0.60*0.83+0.4*0.6), while the preference not to take the test is 0.68. The analysis using preference theory therefore indicates the decision-maker’s best strategy is to take the test and, if it gives a favourable result, drill; if it produces an unfavourable result, do not drill. With EMV, the decision-maker would be advised to drill immediately. The preference theory approach takes into account the executive’s natural conservatism and tells him to take the seismic test first and drill only if it is favourable. The seismic test then is a form of “insurance policy”, which is good for the conservative decision-maker in this case, but not worth its price to the averages-player (who would always choose the decision alternative that would maximise their EMV). 
        
Acquire seismic data $-30,000
Test unfavourable 0.4
Drill No oil 0.9 Don’t acquire seismic data Drill Don’t drill Oil 0.85
$400,000
0.15
Drill Don’t drill Oil 0.55
$400,000 No oil 0.45
$-100,000 $400,000 $0
$100,000 $400,000 $0
$100,000 $430,000 $30,000
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