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Efficient-frontier theory is gaining The full-length acceptance as a part of portfolio paper details two analysis. Full stochastic evaluations approaches to project require management of huge quantities evaluation under of data. As a result, several current uncertain conditions solutions use multiple discrete and the effects on the outcomes to represent any given overall portfolio risk project, rather than a complete stochastic measurements. Differences uncertainty-tree approach, between stochastic and discrete outcome in which evaluations are not significant projects are evaluated when price uncertainty is neglected, as distinct outcomes, but inclusion of price leads to significant each with a differences if the resulting differing probability correlation is not accounted for. of occurrence (referred to as simple Introduction stochastic), is compared Usually, all the value) and below (lower risk) are available investments are evaluated, Theory and Definitions more efficient portfolios than those then a subset is selected in which to Three basic principles of efficient frontier that lie to the left or above. Often, this subset is referred to theory should be understood.

SPE-1201-0052-JPT

Artificial Intelligence, asset and portfolio management, correlated price uncertainty, correlation, efficient frontier, efficient portfolio, evaluation, frontier, frontier graph, full monte carlo evaluation, interproject correlation, investment, optimization problem, portfolio, Portfolio analysis, portfolio optimization, Portfolio Optimization Model, Price uncertainty, reserv oir asset management, selection, Significance, Upstream Oil & Gas

SPE Disciplines: Management > Asset and Portfolio Management > Portfolio analysis, management and optimization (1.00)

Technology: Information Technology > Artificial Intelligence > Representation & Reasoning > Optimization (0.42)

Abstract

Efficient frontier portfolio analysis considers the balance between value and risk in the selection of "optimal" portfolios. Efficient frontier theory was originally developed for the realm of securities portfolios, where considering risk and uncertainty as synonymous may be appropriate. However, the appropriateness of this assumption has come to be questioned for petroleum portfolios. By examining the possible portfolios made up of a subset of 30 fictional but realistic projects, the significance of the definition of risk is explored. For each project, several risk profiles were generated based on different measures of value using Monte Carlo simulations. The definitions of risk that are explored include the standard deviation of the portfolio's risk profile, the semi-standard deviation of the risk profile, the tenth percentile of the risk profile, and the probability of the measure of value being less than a specified threshold. The impact of risk being based on measures of value other than that used as the principal value measure is also explored. The conclusion is that the selection of an "optimal" portfolio is strongly dependent on which definition of risk is selected. Consequently, it is important to explore multiple risk definitions in order to more fully understand the quality of a portfolio, and ultimately make wise decisions as to which projects should be pursued.

Introduction

Petroleum companies are continually faced with the decision of where capital should be spent. A subset of projects must be selected from what is generally a much larger selection of possible projects. Portfolio selection is obviously a crucial part of the business cycle, and hence it deserves careful consideration.

Of course, the goal of the portfolio selection process is to identify the "best" portfolio. However, it is generally not clear what the best portfolio is, or even how to define "best" in this context. There are many elements of the portfolio that must be considered:

Does it provide the most value?

Is it affordable?

Does it meet production requirements?

Does it satisfy development constraints?

These considerations and others form the basis for the non-trivial problem of portfolio selection. It is essentially an optimization problem and it can be tackled with a number of methods. However, before leaping into the optimization, the questions that define the problem should be reexamined.

Considering these questions should naturally lead to a whole other category of questions related to risk assessment:

What is the definition of value?

Is the Cost of a project ever precisely known?

Can one know how much a project will produce?

Is value independent of risk?

What is risk?

The last question is a very difficult question to answer, primarily because there is no real answer. Risk assessment is, to a large extent, a matter of personal judgement. Some view risk and uncertainty as synonymous, while others view only the downside of uncertainty as risk. Still others measure risk in terms of probability—the probability of losing money, or the probability of failing to make quotas.

Acknowledging this ambiguity, it seems that it is important to understand how the definition of risk can affect portfolio selection. This paper describes the investigation of this subject using a set of 30 fictional projects and some fairly simple portfolio goals to act as constraints for valid portfolio selection.

Theory and definitions

Harry Markowitz revolutionized the field of portfolio theory with his pioneering work in the 1950s (Markowitz, 1952, 1997). There are three important ideas that should act as starting points for the discussion of his efficient frontier theory:

A rational investor will prefer more value to less value, but will also prefer less risk to more risk.

Artificial Intelligence, asset and portfolio management, constraint, correlation, deviation, efficient frontier graph, efficient portfolio, investment, optimization problem, portfolio, Portfolio analysis, portfolio optimization, Portfolio Selection, probability, quadrant, Risk Definition, risk profile, selection, semi-standard deviation, Significance, spe 62966, Upstream Oil & Gas

SPE Disciplines: Management > Asset and Portfolio Management > Portfolio analysis, management and optimization (1.00)

Technology: Information Technology > Artificial Intelligence > Representation & Reasoning > Optimization (0.34)

Abstract

Efficient frontier theory is gaining acceptance as a part of the portfolio analysis process in the petroleum industry. One of the major difficulties companies encounter in creating corporate efficient frontiers is in representing project level risks in a corporate consolidation of value. Full stochastic evaluations require the management of huge quantities of data. As a result several current solutions use multiple discrete outcomes to represent any given project, rather then a complete stochastic distribution. This paper evaluates the differences resulting from using these two approaches to project risking. By examining the optimized portfolio results and the resultant efficient frontier, we are able to draw direct conclusions about the added value attributable to detailed Monte Carlo based evaluations. Since price is the source of most correlation between projects, the investigation was done with and without price as an input variable. It was discovered that the differences between the stochastic and discrete outcome evaluations are not significant when price uncertainty is neglected, but the inclusion of price leads to significant differences if the resulting correlation is not accounted for.

Introduction

Petroleum managers are constantly faced with the decision of how to invest limited amounts of capital in order to maximize shareholder value or return. This is usually done by evaluating all the available investments, and then selecting a subset in which to invest. This subset is often referred to as the company's portfolio. Selection of this portfolio is critical to a company's success and therefore it requires significant consideration.

The goal of the portfolio selection process is to select the "optimal" set of projects. However, this is not a simple process, and selecting the "optimal" portfolio while staying within the corporate strategy and constraints can become a very daunting exercise. The task of matching project selection to the company strategy and goals is often referred to as Portfolio Management. There are many elements that must be taken into account in portfolio management, including.

Maximizing the value of the portfolio.

Living within the capital spending limits.

Meeting the production requirements.

Achieving both short term and long term cash flow goals.

Matching forecasted net income targets.

Meeting developmental and/or environmental constraints.

This is even more complex in our industry where many projects have significant amounts of uncertainty, or variation in the possible outcomes. In recent years more and more attention has been placed on how to represent these uncertainties within the portfolio evaluation. These uncertainties exist in various forms within the investment projects of a petroleum company, and can include.

Existence of hydrocarbons (probability of success).

Geological reservoir properties.

Timing and extent of the development program.

Capital and operating costs.

Oil and gas prices.

These uncertainties in the input data required to make an economic evaluation of E&P projects lead to uncertainties in the economic results. Acknowledging that these uncertainties exist in the individual projects, naturally leads to the concept that uncertainties exist in the overall portfolio. In recent years a significant amount of effort has been spent in trying to define this portfolio risk and to compare portfolio's by their risk vs. reward relationship.

In light of the importance of portfolio level risk, this paper compares two differing approaches to project evaluation under uncertain conditions, and the effect the differing approaches have on the overall portfolio risk measurements. The two approaches compared will be an uncertainty tree approach where projects are evaluated as distinct outcomes each with a differing probability of occurrence (referred to here as "simple stochastic"), and a full Monte Carlo evaluation approach where the projects are evaluated across the full range of input uncertainties.

Artificial Intelligence, asset and portfolio management, correlation, efficient frontier graph, efficient portfolio, evaluation, Expl, full monte carlo, Monte Carlo, optimization problem, portfolio, Portfolio analysis, portfolio optimization, Price uncertainty, Project Evaluation, selection, simple stochastic evaluation, Upstream Oil & Gas

SPE Disciplines: Management > Asset and Portfolio Management > Portfolio analysis, management and optimization (1.00)

Technology: Information Technology > Artificial Intelligence > Representation & Reasoning > Optimization (0.51)

Costa Lima, G.A. (Institute of Geosciences and Center of Petroleum Studies/State University of Campinas) | Suslick, S.B. (Institute of Geosciences and Center of Petroleum Studies/State University of Campinas) | Schiozer, R.F. (FGV-SP and Center of Petroleum Studies - State University of Campinas) | Repsold, H. (PETROBRAS S/A) | Filho, F. Nepomuceno (PETROBRAS S/A)

The traditional analytical tool for selection of portfolios is the Markowitz's mean-variance model where the focus is purely on financial return. The final product of this model is the efficient frontier. The choice of the optimal portfolio among infinite possibilities is the final problem, but the mean-variance model does not recommend which one is the best portfolio. A set of heavy-oil projects located in deep-waters regions is used as a case-study to test the several alternatives for portfolio selection. This paper proposes an extension of the mean-variance model by including the following steps: First, an estimation of risk and return of each project. Second, a correlation among returns of each pair of selected prospects and third step is the inclusion of corporative goals, oil characteristics, and exploration and production expenditures. Similarly, we find the efficient frontier of portfolios of projects. The selection of optimum portfolio depends on the diversification level of the investor. If the investor is highly diversified the choice must be the portfolio with a maximum return. Contrarily, the decision may be the portfolio less risky. However, in practice, if bonuses of managers are tied to their performance, the choice for portfolio with lower return and risk is possible, which is a classic tradeoff problem found in several projects where heavy oil characteristics demands a certain technology for costs reduction which is not yet completely dominated.

Artificial Intelligence, asset and portfolio management, best portfolio, bitumen, complex reservoir, correlation, deep-water heavy-oil project, Diversification, efficient frontier, equation, exploration, investment, investor, Markowitz, new technology, NPV, oil sand, portfolio, Portfolio Selection, requirement, risk tolerance, selection, Upstream Oil & Gas

SPE Disciplines:

**A New Era in Petroleum E&P Management **

E&P is a risky business because, while a few exploration projects are tremendously successful, most are total failures. This makes management of uncertainty crucial. development of seismic technology in the 1930's and 1940's substantially reduced the risk in finding petroleum. The resulting geology and geophysics (G&G) revolutionized petroleum exploration.

Decision analysis traditionally has been applied to rank projects hole by hole, determining (on an individual basis) whether they should be explored and developed. Today this "hole-istic" approach is being challenged by a holistic one that takes into account the entire portfolio of potential projects as well as current holdings. This portfolio analysis starts with representations of the local uncertainties of the individual projects provided by geology and geophysics. It then takes into account global uncertainties by adding two additional G's: geoeconomics and geopolitics, thereby reducing risks associated with price fluctuations and political events in addition to those addressed by traditional G&G analysis. The holistic approach is based on, but not identical to, the Nobel-prize winning portfolio theory1 that has shaped the financial markets over the past 4 decades. Our approach deals with the following primary differences between investments in stocks and E&P projects.

- Stock portfolios depend only on uncertain returns. E&P projects face both local uncertainties, which involve the discovery and production of oil at a given site, and global uncertainties, which involve prices, politics, and other such factors. Furthermore, uncertainties in stock returns usually follow a bell-shaped curve while E&P uncertainties are highly skewed and stress rare events.
- Historical data exist for stock prices. E&P uncertainties must be modeled by decision trees, Monte Carlo simulation, or other computational means.
- Risk in stock portfolios usually is measured in terms of volatility—i.e., the degree to which the portfolio swings in value. E&P portfolios must specifically track downside risk.
- The stock market is quite efficient, whereas the market for E&P projects may be inefficient. (The term "efficient" is used here in its technical, economic sense. An efficient market is one in which there are no barriers to each item being priced at its actual value as determined by all buyers and sellers; i.e., there are no "bargains").
- Stocks can be bought or sold at will. E&P projects pay out over long time periods.
- A stock portfolio generally contains a small fraction of the outstanding shares of any one company. An E&P portfolio, on the other hand, often contains 100% of its constituent projects, creating budgetary effects.

Ref. 2 provides a more detailed list.

Portfolio thinking in petroleum E&P is based on understanding and exploiting the interplay among both existing and potential projects. It assists in the following areas.

- Selecting a set of E&P projects to fund.
- Illuminating trade-offs between long- and short-term goals.
- Dealing with political and environmental risk.
- Evaluating a project for purchase or sale.
- Determining the risk-related cost of constraints and policies.
- Determining the criteria for projects that would reduce the risk of the portfolio.
- Increasing the value of the firm.

We show that analytical models can help to address directly these and similar issues once decision makers become more comfortable with the holistic perspective. First, we present a simple example that shows how to build intuition into portfolio analysis.

**Retraining Our Intuition **

You are responsible for investing U.S. $10 million in E&P. Only two projects are available, and each requires the full U.S. $10 million for a 100% interest. One is relatively "safe," the other relatively "risky." The chances of success are independent. **Table 1** provides the information. The expected net present value (ENPV), *v _{pE}*, of the two projects, respectively, can be shown to be the same.

Equation 1

Equation 2

If you lose money, you also lose your job. Thus, you have only a 40% chance of unemployment with the safe project, and a 60% chance with the risky one. Both have an ENPV of U.S. $26 million, so you cannot increase ENPV by investing in the risky project. Therefore, if you had to choose between one or the other, you should choose the safe project.

**Diversification Effect **

Suppose, however, that you could split your investment evenly between the two. Intuition cautions against taking 50% out of the safe project and putting it in the risky one. Examine the four possible joint outcomes. Because the projects are independent, the probability of any particular joint outcome is the product of the probabilities of the associated individual outcomes (**Table 2**). Note that the sum of the probability column must be 100% because we have exhausted all possibilities.

This allocation of funds still provides an ENPV of U.S. $26 million. Now the only way you can lose money is with two dry holes, for which the probability is 40%×60%=24%; this cuts your risk of unemployment nearly in half! You can reduce risk by moving money from a safe project to a risky one. Intuition misleads. Although this answer is correct, it is not so obvious.

This is known as the diversification effect, popularly referred to as not putting all your eggs in one basket. This line of reasoning is so fundamental that one wonders how the petroleum industry could do otherwise. However, a recognized authority summarizes the conventional selection process with "Just rank exploration projects by expected present worth."^{3}

Artificial Intelligence, asset and portfolio management, asset interplay management, constraint, correlation, current holdings, dependence, Diversification, efficient frontier, ENPV, environmental risk, exploration, implication, investment, Portfolio analysis, portfolio optimization, safe project, Savage, september 1999, tradeoff, Upstream Oil & Gas

Thank you!