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
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Table 5.6: Table of the output generated using the base value data and input distributions specified in Table 5.5 (Rec reserves = recoverable reserves) The next section draws on the decision theory and industry literatures to present portfolio theory, a technique that has been used within the finance industry for a number of years but which has only recently been applied to petroleum investment decisions. Therefore, the concepts of portfolio theory will be outlined first before its applicability to upstream investment decision-making is analysed. Portfolio theory In practice, a business will normally invest in a range, or portfolio, of investment projects rather than in a single project. The problem with investing all available funds in a single project is, of course, that an unfavourable outcome could have disastrous consequences for the business. By investing in a spread of projects, an adverse outcome from a single project is unlikely to have major repercussions. Investing in a range of different projects is referred to as diversification, and by holding a diversified portfolio of investment projects, the total risk associated with the business can be reduced (Atrill, 2000 p185). This introduces two concepts. First, asset value is additive. The incremental expected value that an asset adds to the portfolio’s expected value is the asset’s expected value. Second, asset risk is not additive. The amount of risk an asset contributes to the portfolio is not solely dependent on its risk as a stand-alone investment (measured in finance theory by the standard deviation of the expected value probability distribution) (Whiteside, 1997). Atrill (2000 p118) explains this by dividing the total risk relating to a particular project into two elements: diversifiable risk and non-diversifiable risk (figure 5.11): Diversifiable risk is that part of the total risk which is specific to the project, such as reserves, changes in key personnel, legal regulations, the degree of competition and so on. By spreading the available funds between investment projects, it is possible to offset adverse outcomes in occurring in one project against beneficial outcomes in another (Atrill, 2000 p188). Non-diversifiable risk is that part of the total risk that is common to all projects and which, therefore, cannot be diversified away. This element of risk arises from general market conditions and will be affected by such factors as rate of inflation, the general level of interest rates, exchange rate movements and so on (Atrill, 2000 p188). Arguably, the most critical non-diversifiable risk for exploration companies is the oil price. It then follows that the incremental risk an asset adds to the portfolio will always be less than its stand-alone risk. 
Total risk Risk Diversifiable risk Non-diversifiable risk Number of assets Figure 5.11: Reducing risk through diversification (source: Higson, 1995 p120) There are two types of diversification: simple and Markowitz. Simple diversification (commonly referred to as market or systematic diversification in the stock market) occurs by holding many assets. It holds that if a company invests in many independent assets of similar size, the risk will tend asymptotically towards zero. For example, as companies drill more exploration wells, the risk of not finding oil reduces towards zero. Consequently, companies that endorse a strategy of taking a small equity in many wells are adopting a lower risk strategy than those that take a large equity in a small number of wells. However, the economic returns on independent assets are to, a greater or lesser extent, dependent on the general economic conditions and are non-diversifiable. Under these conditions, simple diversification will not reduce the risk to zero but to the non-diversifiable level. Markowitz diversification relies on combining assets that are less than perfectly correlated to each other in order to reduce portfolio risk. The method is named after a 1990 Nobel Prize recipient, a financial theorist, who first introduced the technique in his 1952 paper entitled Portfolio Selection. Markowitz diversification is less intuitive than simple diversification and uses analytical portfolio techniques to maximise portfolio returns for a particular level of risk. This approach also incorporates the fact that assets with low correlation to each other when combined have a much lower risk relative to their return (Whiteside, 1997). Using these principles, portfolio optimisation is a methodology from finance theory for determining the investment program and asset weightings that give the maximum expected value for a given level of risk or the minimum level of risk for a given expected value. This is achieved by varying the level of investment in the available set of assets. The efficient frontier is a line that plots the portfolio, or asset mix, which gives the maximum return for a given level of risk for the available set of assets. Portfolios that do not lie in the efficient frontier are inefficient in that for the level of risk they exhibit there is a feasible combination of assets that result in a higher expected value and another which gives the same return at lower risk. (Note, in reality, due to real world constraints such as the indivisibility of assets, trading costs and the dynamic nature of the world, all practical portfolios are inefficient). To calculate the efficient frontier it is imperative to determine the mean return of each asset (usually the EMV in industrial applications), the variance of this value (defined as risk in finance theory) and each asset’s correlation to the other assets in the available set of investments (Whiteside, 1997). This classification of risk assumes that: Firms’ long run returns are normally distributed and can, consequently, be adequately defined in terms of the mean and variance. In reality, it is likely that the distribution describing long run returns would be “skewed”. Variance is a useful measure of risk. In calculating variance, positive and negative deviations from the mean are equally weighted. In fact, decision-makers are often more pre-occupied with downside risk – the risk of failure. A solution to this problem is to determine the efficient set of portfolios by using another risk measure. A group of suitable risk measures that only takes the dispersions below a certain target into account are the downside risk measures. In the mean downside risk investment models the variance is replaced by a downside risk measure then only outcomes below a certain point contribute to risk. There is enough information to estimate the mean and variance of the distribution of outcomes. This does require a high level of information that, in some cases, is not available (Ross, 1997). However, provided that the assumption that variance is a useful approximation of risk is accepted, the aim is to maximise the expected return under a certain level of variance, which is equivalent to minimising the variance under a certain level of expected return. To determine the variance, Monte Carlo simulation is used. First, information about all the variables that affect the calculation of a cash flow of one of the projects is collected and their probability distributions are estimated. Then for each project, using Monte Carlo simulation, a number of cumulative discounted cash flows and their matching discounted investments can be generated simultaneously. From these points, the EMV of each project, the variance of the EMV of each project and the correlation between the EMVs of the different projects can be calculated. By simulating the cash flows of all projects simultaneously, some of the uncertain variables, which fix the systematic risk and thus provide for the correlation between the different projects, are equal for all projects and therefore the coefficient of correlation between projects can be determined. (The value of this coefficient can range from +1 in the case of perfect correlation, where the two assets move together, to –1 in the case of perfect negative correlation, where the two assets always move in opposite directions. The coefficient is 0 when there is no association between the assets and they are said to be independent.) Then these values, together with any other constraints, are used to generate the efficient frontier. To find the efficient portfolios, Markowitz defined the mean variance model that reduces to a quadratic-programming problem that is easily solved by the many mathematical software packages available. After the efficient set has been determined, a portfolio can be chosen from this group. There are several ways of doing this. For the method advocated by Markowitz (and stochastic dominance) the utility function, or preference curve, of the company would need to be determined, as discussed above in section 5.3, this is particularly difficult. Therefore some finance theorists advocate the use of one of the safety-first criteria (for a full discussion see Ross, 1997). Investment opportunities of the oil industry have a great resemblance to financial assets. As with the financial assets, there is much risk and uncertainty about the profit of the projects. Assets are highly correlated with each other. They all have some variables, such as oil price, that affect the profitability of the project in common. In the stock market paper assets (stocks and shares) are traded and in the oil business companies hold and trade portfolios of real assets by, for instance buying and selling shares in joint ventures. The following simple example from Ball and Savage (1999) shows how the application of the principles of portfolio theory to the oil industry can result in decisions that are counter-intuitive. An oil company has $10 million to invest in exploration and production projects. Only two projects are available and each requires the full $10 million for 100% interest. One project is relatively “safe”; the other relatively “risky”. The chances of success are independent. The facts about the projects are presented in table 5.7.
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