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Selection of overseas oil and gas projects under low oil price
Accepted Manuscript Selection of overseas oil and gas projects under low oil price Bao-Jun Tang, Hui-Ling Zhou, Hong Cao PII:
S0920-4105(17)30500-4
DOI:
10.1016/j.petrol.2017.05.022
Reference:
PETROL 4006
To appear in:
Journal of Petroleum Science and Engineering
Received Date: 24 March 2017 Revised Date:
7 May 2017
Accepted Date: 26 May 2017
Please cite this article as: Tang, B.-J., Zhou, H.-L., Cao, H., Selection of overseas oil and gas projects under low oil price, Journal of Petroleum Science and Engineering (2017), doi: 10.1016/ j.petrol.2017.05.022. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
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Selection of Overseas Oil and Gas Projects under Low Oil
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Price Bao-Jun Tanga,b,c,d,e*, Hui-Ling Zhoua,b,c,d,e, Hong Caoa,f a
Center for Energy and Environmental Policy Research, Beijing Institute of Technology, Beijing 100081,
China b
School of Management and Economics, Beijing Institute of Technology, Beijing 100081, China
c
Beijing Key Lab of Energy Economics and Environmental Management, Beijing 100081, China
d
Sustainable Development Research Institute for Economy and Society of Beijing, Beijing 100081, China
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Collaborative Innovation Center of Electric Vehicles in Beijing, Beijing 100081, China
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School of Finance, Capital University of Economics & Business, Beijing 100083, China
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Abstract
In order to actively resist the risk of falling oil prices, the international oil companies need to
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adjust the business strategy in time. Investment efficiency can be enhanced through effective
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allocation of funds. This work constructs a set of analytical ideas and methods for the
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re-optimization of the oil project portfolio under the constraints of budget and production capacity.
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Based on the quadratic programming model and the preference theory, the optimal portfolio
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decision is made. The case study concludes that the flexibility of contract terms improves the
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optimization efficiency, that is, reduces the portfolio investment risk, optimizes the budget
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allocation, and expands the range of alternative projects. In terms of decision-making, net present
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value should not be the only criterion for project selection. However, the portfolio optimization
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presented in this article, which considers the multiple constraints and inter-projects relationships,
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can achieve the compromise between risk and return.
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Key words: overseas oil project, portfolio, investment, optimization, risk tolerance
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Corresponding author. Tel.: +86 10 68918013.
Email addresses: [email protected] (Bao-Jun Tang)
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1 Introduction
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The low oil price, which continues since the end of 2014, is an important opportunity for
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global oil and gas exploration and development industry. Low cost has become the industry trend
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and oil companies have to tighten the annual budget. Improved efficiency will come from lower
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risk, less investment and fewer new drillings. Accordingly, it is particularly critical to make the
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optimal portfolio of investment projects in the budget and capacity constraints. In the overseas
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resource distributions of China's national oil companies, the variety of regions and conditions
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greatly increases the uncertainty of investment income. Besides, decisions made on such huge
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investment have significant risk characteristics. Therefore, the main task of decision-making is to
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make a balance between profit and risk.
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In 2007-2013, about 40 large and medium-sized projects accomplished Final Investment
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Decisions (FIDs) each year. However, this figure dropped to 8 in 2015, then to 6 by the second
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quarter of 20161. These six projects have at least two common characteristics. Firstly, the average
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capital expenditure reduced by 10-30% after 2014. Secondly, working interests are generally high,
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which can effectively reduce the interference of partners. Nevertheless, differences in reserves,
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investment scale and profits are obvious. For example, the investment of Tengiz oil field
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investment is even higher than the total of the other five. Investors bear the high risk of cost and
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capacity with such high interest ratio. Some projects may have the possibility of selling interests.
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These projects with significant rates of return also have some price-related risks, which lead to
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large volatility ranges in profits. Consequently, the investment budget, cost, production capacity
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and working interest are the must considerations while oil companies build the portfolio in the
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profit-risk dimension.
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Companies' annual investment budgets generally do not support investments in all alternative
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projects. Project selections are required under certain budget constraints. This is the fundamental
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starting point for oil and gas portfolio optimization. Index Ranking is a simple and straightforward
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way to accomplish this task by sorting the project's profitability index (eg, profit to investment
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(P/I) ratio) and picking out the projects by budget ceiling (Orman and Duggan, 1999). With the
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The Wood Mackenzie report shows that these six projects are Zohr (Egypt), KG-DWN-98/2 (India), Atoll
(Egypt), Greater Enfield (Australia), Tangguh Ph.2 (Indonesia) and Tengiz Exp. (Kazakhstan).
ACCEPTED MANUSCRIPT expansion of oil and gas industry, decision-makers tend to consider multiple conditions. Thus,
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Multiple Criteria Decision Making (MCDM) are gradually developing. MCDM is based on
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technologies such as AHP (Analytic Hierarchy Process) and TOPSIS (Technique for Order
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Preference by Similarity to Ideal Solution) to evaluate, sort and select multiple attributes of
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alternative projects. It can provide more information than single-index methods (Lopes and
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Almeida, 2013). However, the weight setting of indexes often needs a large amount of historical
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data or expert opinions. When the data is not completely available, the optimization methods can
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skip the problem of weight setting. Project portfolio is optimized by satisfying certain conditions
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(such as budget, capacity constraints, etc.).
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Modern Portfolio Theory (MPT) (Markowitz, 1952) is one of the classical theories of
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combination optimization. It originally served as the theoretical basis for selection and
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construction of financial portfolio. By selecting assets with different correlation coefficients, a
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portfolio is constructed that reduces the overall portfolio risk at the given expected return and
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respective weights of assets are determined. The idea is also known as the diversification. For oil
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and gas sectors with high risk and high return, each oilfield block can be analogous to a financial
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asset with fluctuations in its earnings. Therefore, MPT has a good applicability to this problem.
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Some subsequent studies attempt to follow the classic MPT model. The objective function is
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minimizing the variance of the portfolio return (Mutaydzic and Maybee, 2015; Walls, 2004; Xue
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et al., 2014). The independent variables are projects investment accounted for the proportions of
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total investment (Mutaydzic and Maybee, 2015; Walls, 2004). In addition, the expected rate of
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portfolio return is imposed a constraint (Walls, 2004).
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However, unlike financial securities, oil projects cannot be replicated. That is, the proportion
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of individual investment to total investment is constrained by the investment ceiling of certain
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project. Relative studies generally require additional constraints and reprocessing of the
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optimization results, thereby translating the investment weights into variables for decision-making
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(i.e., working interests). Therefore, other studies propose an straightforward idea that working
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interests serve as the independent variables (Orman and Duggan, 1999; Al-Harthy and Khurana,
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2008; Xue et al., 2014). It relies on the assumption that the working interest is linear to the
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proportion of project investment to the total investment.
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Another difference between oil projects and financial securities is that, unlike freely traded
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appropriate to add up the internal rate of return (IRR) for different lengths. Some studies constrain
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the expected NPV (net present value) of portfolio (Wood, 2016; Al-Harthy and Khurana, 2008;
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Mutaydzic and Maybee, 2015; Orman and Duggan, 1999). In order to make the measure
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consistent, the objective function should be replaced by minimizing the variance of portfolio NPV,
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otherwise there may be problems with frontier distortions and inconsistent economic implications.
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This model setting not only considers the non-replicability of oil projects, but also solves the
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comparability of income between projects of different lengths.
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The correlation between oil projects is also a key factor in portfolio risk. Walls (2004) set it
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to a fixed constant of +0.2. Moriarty (2001), Aristeguieta (2008), Ball and Savage (1999) argue
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that inter-project relevance mainly includes oil price, politics, location, resource attributes, etc.
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2 Oil Portfolio Optimization Model
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2.1 Assumptions
for oil investment have the following assumptions. i.
Oil company's decision depends only on portfolio return and risk.
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ii.
The expected return of an oil project can be characterized by a probability distribution.
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iii.
The estimation of portfolio risk is related to variations of expected return.
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iv.
Oil company, who is the rational investor, pursues utility maximization.
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v.
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With reference to the MPT model proposed by Markowitz, the portfolio optimization model
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Oil company is risk adverse. While comparing two alternative portfolios with the same
risk, they will value the one that offers higher profits.
This study adopt the idea of directly solving work interests. Based on the proceeding
assumptions (1) - (5), we add (6) and (7).
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vi.
The work interest is linearly related to the project NPV and investment.
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vii.
Signed contract terms (such as working interest, investment scale) can be modified to a
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certain extent. Assumption (6) does not exactly meet with the actual situation. For different host countries
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correlated. However, that will increase the complexity of capital-allocation process. The additional
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assumption (6) can simplify the solution process. The non-linear relationship between profit
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sharing and investment equity is widespread in different types of contracts, but does not fall within
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the scope of this study.
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Assumption (7) reflects the practical significance of this study. That is, oil companies can
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change the investment scale within stipulations, and optimize the capital allocation. Particularly in
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the case of section 3, samples are all operating projects. In the short and medium-term strategic
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development and investment decisions, oil companies also need to adjust the range of equity ratios
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and investment scales.
2.2 Objective function and constraints
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In this study, the objective function and constraints are set as follows.
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The objective is the minimization of portfolio risk, see equation (1). Portfolio risk is
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measured by variance of portfolio NPV, and is composed of the individual risk and the
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inter-project risk. The higher the degree of correlations, the greater the inter-project risk, which
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also reflects the significance of investment diversification.
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min σ = ∑
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i =1
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∑ww σ j =1
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j
num
ij
num
= ∑ w σ + ∑ wi w j ρijσ iσ j i= j
2 i
2 i
（1）
i≠ j
where num is the number of projects and i or j stands for different project. wi is Chinese
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company’s working interest in project i. σ2 is the risk of portfolio and σi2 is the risk of project i. ρij
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is the correlation coefficient between the values of project i and j.
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NPV constraint shows in equation (2). The constant on the right side represents the
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company's requirement for the portfolio profits, indicating that the objective function (portfolio
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risk) is minimized at a given acceptable profitability. num
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∑ w ⋅ npv i =1
i
0i
= NPV
（2）
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where npv0i is the total net present value of project i, and NPV is the net present value of the
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portfolio (constant).
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Budget constraint shows in equation (3). Oil and gas investors are often constrained by
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company's budget when arranging investment plans, thus specifically setting a cap for a particular
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portfolio. As for more detailed budget control, it is often necessary to refine this constraint to each
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year.
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∑w ⋅I
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（3）
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where k is the certain year during the 13th Five-Year Plan of oil company. I0ik is the investment
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ceiling of project i in year k, and Bk is the investment ceiling of portfolio in year k.
Capacity constraint shows in equation (4). The limit production of a specific project is
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difficult to change in the short term. This is determined by its production capacity, and is affected
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by the infrastructure scale, staffing, technical level and other factors.
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∑ w ⋅Q i =1
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i
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（4）
where Qk is the capacity limit in year k, and Q0ik is the capacity limit of project i in year k. Working interest constraints are shown in equation (5) and (6). The constraints directly
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suggest that the oil projects cannot be replicated, that is, the amount of investment for a single
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project cannot exceed the total capital of the project itself. Working interest constraint adjusts due
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to different assumptions of corporate behavior. Assuming that company has no right to follow up
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investment (i.e., increase the work interest) for an established contract, but may choose to sell the
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interest depending on production or market environment, then the contract interest shall be set as
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the upper limit (see equation (5)). Assuming that company has not yet formally signed the contract,
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or contract terms provide a higher degree of freedom, we believe that company own the right to
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sell or acquire the work interest, thus the upper limit is set as 100% (see equation (6)).
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0 ≤ wi ≤ wc , i = 1, 2K, num
（5）
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0 ≤ wi ≤ 1, i = 1, 2K, num
（6）
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where wc is the contract working interest of Chinese company.
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An efficient portfolio defined by MPT suggests that there is no other portfolio with a higher
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value as well as the same or even lower risk, or that there is no other lower-risk portfolio with the
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same or higher value. According to this definition, a set of quadratic programming model is
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established, with the objective function of minimizing portfolio risk (see model I and model II).
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The solution is to keep altering the constant of NPV constraint, and acquire corresponding optimal
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portfolio. Eventually a mean - variance frontier is generated. The points on the frontier are the
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optimal portfolio satisfying the definition of efficient portfolio. In order to compare the results for different degrees of freedom, this article sets the model I
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and model II. Model I assumes that oil company is able to buy or sell its working interest. The
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objective function is equation (1) and constraints include equation (2) - (5). Model II assumes
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that Assume that oil company only has the right to sell its working interest. The objective
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function is equation (1) and constraints include equation (2) - (4) and (6).
2.3 A portfolio selecting method based on preference theory
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In general, oil companies are risk-averse investors. No doubt, they will choose the portfolio
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with lower risk among alternatives of the same NPV. However, if NPV and its variance of one
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portfolio is higher than other alternatives (such as the portfolios at the mean-variance frontier), oil
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company's decision will depend on its degree of risk aversion, i.e. how to weigh the relationship
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between risk and return.
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This study uses the Preference Theory in microeconomics to solve this problem. Risk
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Tolerance (RT) measures the level of risk that an oil company can afford, defined as the maximum
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monetary value that the company has 50% chance to earn or lose. The higher the RT value, the oil
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company is more willing to take risks. Certainty Equivalent (CE) measures the cash equivalent of
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a portfolio in uncertain investment environment in the view of an oil company. It is also the price
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that the oil company is willing to sell the risky portfolio in exchange for a certain return
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(Mutaydzic and Maybee, 2015). The CE function in the mean-variance framework refers to a
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research of Walls (2004), see equation (7).
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CE = µ −
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where µ is the expectation of portfolio value, and σ is the standard deviation of expectation.
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σ2
（7）
2 RT
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Given a RT value, the corresponding CE value can be calculated for any point on the efficient
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frontier. The efficient portfolio with the highest CE value is the option that maximizing company’s
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utility under that RT value.
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In summary, the technical route of this model is shown in Figure 1.
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3 Application to the five-year-plan of a Chinese oil company
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3.1 Data preparations and project economics In this section, 22 operating projects of a certain Chinese oil company are selected as samples.
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The data mainly comes from corporate research and third-party platforms. Due to the availability
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of data, we set a five-year-plan scenario. The project parameters, economics and statistical
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analysis are shown in Table 1, 2 and 3, respectively. The working interests in Table 1 serve as the
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initial values of independent variable w. The standard deviations of NPVs are the exogenous
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parameters of objective function.
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As discussed in Section 1, some studies suggest that IRRs of projects with different lengths is
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not comparable. Here, project economics are evaluated by index ranking method instead of IRR.
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Table 2 ranks the NPVs, investments and P/I ratios of sample projects. Project 10, 8 and 5 rank the
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22rd, 21st and 20th, which are the top-three profitable ones. While considering project investment,
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their rankings for P/I ratio are 11st, 8th, and 22rd. When assessing projects on P/I ratio, a profitable
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project should have relative high NPV and low investment scale. Therefore, project 5 is better than
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project 8 and 10.
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Table 3 shows that the three indicators of the sample data have a large degree of
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discretization. The coefficient of variation shows that the standard deviations of the sample are
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about 2 times the mean values, and that of NPV is the highest. Samples reflect the diversity of
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project size and profit. The series of NPV, planning production and project investment serve as the
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coefficients of constraints 1, 2, and 3, respectively. The constants on the right side of the equations
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are, in order, US$ 14,200 million (model I) / US$ 25560 million (model II), US$ 97835 million,
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5616.08199 mmbbl.
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3.2 Portfolio optimization
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3.2.1 Portfolio optimization mitigates the investment risk
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Results for model I and II are shown in Figure 2. The portfolio before optimization is located
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optimizations. However, given a certain portfolio NPV, the portfolio risk optimized by model II is
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lower than that by model I, even if the difference is rather slight. Model II further looses the
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constraint 4 based on model I, making the work interests vary between 0-100%. Therefore, on the
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one hand, model II generates a longer string of efficient frontier. Portfolios with higher return and
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higher risk work out under certain budget.
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On the other hand, the portfolio risk of model II is slightly lower than that of model I at the
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same portfolio NPV (see Figure 3). Although such relative difference gradually increases with the
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expected NPV, it is generally slight. One possible reason is that the contract working interests are
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at better levels. Therefore, the space for optimization is rather small. Nevertheless, this difference
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also shows that contracts that are more flexible are conducive to portfolio optimization. Risk
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mitigation and capital-allocation optimization can be achieved at the same time.
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3.2.2 Significant differences of working interest exist in model I and II
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Working interests of each point on the portfolio efficient frontier need further discussions.
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Here we adopt 10 optimization points as example. Results of model I and II are shown in Table 4
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and 5, respectively. The different results of Model II compared to Model I are marked in bold in
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Table 5.
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In the case of model I, the working-interest configuration of projects for each optimization
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point is different. For a certain project, the working interest increases monotonically with the
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increasing portfolio NPV. There are four projects not selected for efficient portfolio from
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beginning to end, which are projects 1, 2, 11 and 16. The project data shows that the NPVs of
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projects 1, 2, and 16 are negative, while project 11 falls behind at capacity and P/I ratio (see Table
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2), which suggests a poor economy. Among the selected projects, five of them (projects 4, 7, 8, 15,
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19 and 20) appear in all efficient portfolio. In particular, projects 7, 19 and 20 maintain the
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contract working interests.
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Results in Table 5 show that five projects (No. 1, 2, 6, 9 and 16) remain unselected from
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beginning to end. The additional projects (No. 6 and 9) have the low P/I ratio (see Table 2). In
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model II, less projects have been invested. The possible reason is the interest constraints are
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loosed, so that limited capital is allocated to more risk-return balanced projects. The working interests of projects 7, 8, 19 and 22 increase first and then decrease as portfolio
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NPV increases. The return on investment of project 7 ranks the 7th and its input-output ratio ranks
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the 4th (from low to high order, the same below). The return on investment and input-output ratio
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of project 7 both rank the 5th. When the requirement of return is too high, the budget and capacity
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constraints will restrain investment scale of these two projects further increasing. The planning
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production of project 8 is the highest and the investment quota is among the top. It is extremely
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easy to reach the upper limit of constraints in the optimization iteration, which lead to a decline in
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the working interest. Project 19 has the lowest input-output ratio, which is mainly restricted by
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budget constraint in the optimization iteration and is gradually removed from the frontier
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portfolio.
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3.3 Portfolio selection considering risk appetite
Based on the preceding optimization results, a string of portfolio frontier is formed, each
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point of which represents an optimal combination of oil projects. To further determine the final
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project configurations, the investor’s risk appetite need to be considered. As a rule of thumb, some
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companies use 25% of annual exploration budget as their risk tolerance (Mian, 2011). Here we
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take model II as an example. 25% of the original annual budget constraint is set as the upper limit
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of the risk tolerance for large companies. The range of risk tolerance for small, medium and large
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oil companies is 1000-1500, 1500-3000 and 3000-3500 (million dollar), respectively. In the case
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of RT = $ 1000 million, it means that the oil company would accept a maximum of $ 1000 million
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in cash losses from the portfolio. The certainty equivalents (CEs) at different return requirements
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and portfolio risks are calculated by equation (7), shown in Figure 4.
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Figure 4 shows the certainty equivalent curves for different risk tolerances. The return-risk
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range of the optimal portfolio for small oil companies is (5680MUS $, 5.28x106) - (8529MUS $,
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11.9x106), for medium oil companies is (8529MUS$, 11.9x106) - (19880MUS$, 65x106) and for
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large oil companies is (19880MUS$, 65x106) - (21300MUS$, 74.7x106). It can be seen that the
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degree of risk aversion of large oil companies is lighter than that of small and medium companies,
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so their optimal portfolio tends to high-return and high-risk, which is consistent with the
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connotation of risk tolerance. Oil companies can choose the appropriate risk tolerances according
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to their risk-aversion assessments, and obtain the corresponding certainty equivalence curves, to
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make the final investment decisions based on the portfolio optimization and specific risk appetite.
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3.4 Dual-factor sensitivity analysis of budget and capacity constraints
Suppose that the budget and production constraints are risk variables instead of constants in
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the preceding. Each of them is independent of the normal distribution, and the standard deviation
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is 10% of the mean. Perform Monte Carlo simulations for 1000 times. As can be seen from Figure
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5, model II is more robust than model I. That is, a more flexible contract arrangement is more
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sensitive to the uncertainty of constraints. Therefore, the flexibility of contract rights cannot be
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ignored.
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Table 4 also shows the better robustness of model II. In addition, the work interest is more
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sensitive to the uncertainty of constraints than the portfolio risk. Figure 5 only shows that the
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portfolio risks of the two models are almost indistinguishable, but there is still a probable
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difference in the working interest of each project at different portfolio NPVs. As can be seen in
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Table 6, model II is more likely to enhance the work interests for simulated uncertain constraints
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of budget and capacity, which will be more conducive to optimizing the capital allocation.
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4 Conclusions and policy implications
Based on the tightening-budget low-cost trends of the global oil and gas industry under the
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low oil price, this article constructs a set of ideas and framework for the investment reallocation of
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the oil project portfolio under the constraints of budget, production capacity, return and working
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interest. In addition, with 22 operational oil projects as a case, a series of decision-making analysis
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is carried out from the portfolio optimization to the shutdown timing for individual project. The
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results show the operability of the proposed model in practical decision-making and its robustness
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under uncertain constraints.
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4.1 Portfolio optimization for oil projects can achieve a compromise between risk and return The optimization of the oil project portfolio based on the "return-risk" perspective provides
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an effective framework for oil companies in a dilemma. Risk and return generate form each other.
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Oil companies strive to enhance their profits and lower losses as much as possible, through which
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they can get a compromise without having to face a number of alternatives. The use of preference
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theory at the strategic level can reflect companies’ risk appetites in the current investment
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environment. The portfolio optimization at the tactical level can consider the specifics of projects.
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4.2 NPV should not be the sole criterion for the project selection
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NPV is not the only consideration for whether a project is selected for a company's portfolio.
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According to the optimization results of working interests, the non-selected projects include not
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only those with negative or lower NPV, but also those with some other economic indicators (such
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as P/I ratio). From this point of view, the traditional cash flow evaluation and Index Ranking
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cannot be comprehensive and objective for the project selecting. The idea of portfolio
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optimization need to be adopted, both to analyze the individual features of the project, and the
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inter-project relationships.
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4.3 The flexibility of contract terms improves the optimization efficiency
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Comparing with the results of the two proposed models, the flexibility of contract terms can
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improve the optimization efficiency of the project portfolio. Firstly, it can reduce the portfolio risk
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to some extent. Secondly, the optimal budget allocation can be achieved through the purchase or
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transfer of part of the working interests. Thirdly, while not considering the risk appetite, a more
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high-yield and high-risk portfolio can be formed given the same budget, which expands the scope
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of investment decisions. Furthermore, in the case of uncertain constraints of budget and capacity,
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loose constraint of working interest can enhance the optimized working interests, which will be
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more conducive to optimizing the capital allocation. The higher the freedom for adjustments of
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working interest, the more effectiveness of optimization.
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4.4 The allocation of working interests is critical to mitigate portfolio risk The task of portfolio optimization and re-optimization is not only to choose a better project in
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economics, but also to carefully determine the project's working interest. The looser constraint of
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working interest (model II) not only makes the optimization results more robust, but also makes
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the lower portfolio risk at each expected return. Although the difference of portfolio risk is slight
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under the two kinds of working interest constraints, but the difference in the working interest
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configurations is obvious. Therefore, when negotiating working interest items in the contract
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signing process, oil companies should not only consider a single project of economic, strategic and
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other factors, but also include it into a specific project portfolio. Inter-project relationships
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manipulate project’s final contributions to the portfolio, which need to be fully considered. Even
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for the project with considerable cash flows, its working interest is not the higher the better.
345 346
Acknowledgements
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We gratefully acknowledge the financial support from the National Natural Science
348
Foundation of China (Grant Nos. 71521002, 71573013, 71642004), the Beijing Natural Science
349
Foundation of China (Grant No. 9152014), Key Project of Beijing Social Science Foundation
350
Research Base (Grant No. 15DJA084) and National Key R&D Program (Grant No.
351
2016YFA0602603) and Special Items Fund of Beijing Municipal Commission of Education.
353 354 355 356 357 358 359 360 361 362 363
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References:
Al-Harthy, M.H. and Khurana, A., 2008. Portfolio Optimization: Part 2-An Application of Oil Projects with Inter- and Intra-dependencies. ENERGY SOURCES PART B-ECONOMICS PLANNING AND POLICY, 3(4): 324-330.
Aristeguieta, O., Bratvold, R., Begg, S. and Medaglia, A., 2008. Multi-objective Portfolio Optimisation of Upstream petroleum projects. University of Adelaide. Faculty of Engineering, Computer and Mathematical Science. Australia School of Petroleum. Ball, B.C. and Savage, S.L., 1999. Notes on exploration and production portfolio optimization. available for download from http://www. stanford. edu/~ savage or http://www. ziplink. net/~ benball. Lopes, Y.G. and Almeida, A.T.D., 2013. A multicriteria decision model for selecting a portfolio of oil and gas exploration projects. Pesquisa Operacional, 33(3): 417-441.
ACCEPTED MANUSCRIPT Markowitz, H., 1952. Portfolio selection. The journal of finance, 7(1): 77-91. Mian, M.A., 2011. Project economics and decision analysis: deterministic models, 1. Pennwell Books. Moriarty, N., 2001. Portfolio risk reduction: Optimising selection of resource projects by application of financial industry techniques. Exploration Geophysics, 32(3/4): 352-356. Mutaydzic, M. and Maybee, B., 2015. An extension of portfolio theory in selecting projects to construct a preferred portfolio of petroleum assets. JOURNAL OF PETROLEUM SCIENCE AND ENGINEERING, 133: 518-528.
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Orman, M.M. and Duggan, T.E., 1999. Applying modern portfolio theory to upstream investment decision making. JOURNAL OF PETROLEUM TECHNOLOGY, 51(3): 50-53.
Walls, M.R., 2004. Combining decision analysis and portfolio management to improve project selection in the exploration and production firm. JOURNAL OF PETROLEUM SCIENCE AND ENGINEERING, 44(1-2): 55-65.
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Wood, D.A., 2016. Characterization of gas and oil portfolios of exploration and production assets using a methodology that integrates value, risk and time. JOURNAL OF NATURAL GAS SCIENCE AND ENGINEERING, 30: 305-321.
Xue, Q., Wang, Z., Liu, S. and Zhao, D., 2014. An improved portfolio optimization model for oil and
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gas investment selection. PETROLEUM SCIENCE, 11(1): 181-188.
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364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380
ACCEPTED MANUSCRIPT Table 1 Working interests of Chinese side and NPVs of 22 sample projects
No.
Standard
Working
Project
deviation of
interest
No.
Standard
Working
Project
deviation of
interest
NPV
NPV
Algeria
70
-78.16
12
Kazakhstan D
100
1106.14
2
Brazil
55
-107.52
13
Kazakhstan E
40
263.76
3
Indonesia
45
174.18
14
Niger
4
Iran
100
473.47
15
Oman
5
Iraq A
38
1152.84
16
Peru A
6
Iraq B
33
699.32
17
Peru B
7
Iraq C
45
278.83
18
Peru C
100
317.07
8
Iraq D
46
1735.73
19
Russia
33
85.87
9
Kazakhstan A
25
36.35
20
Tunisia
23
4.65
10
Kazakhstan B
8
8984.73
21
Venezuela A
49
1061.85
11
Kazakhstan C
100
62.70
22
Venezuela B
100
4.84
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1
852.03
100
285.77
100
-30.33
45
92.82
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The project codes reflect the host countries of projects, and the capital letter A to E differentiate projects in the
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same countries. The working interests are the contract interests for the Chinese side. The calculations of standard deviation of NPV are based on historical data. The unit of working interest is % and that of standard deviation of NPV is million US dollar.
Ranking
NPV
Investment
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Project No.
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Table 2 Index rankings of 22 sample projects
P/I
Project No.
Ranking NPV
Investment
P/I
1
2
2
1
12
19
17
15
2
1
16
3
13
11
11
12
3
10
13
10
14
17
14
18
4
15
10
19
15
13
9
21
5
20
8
22
16
3
3
2
6
16
20
6
17
9
4
20
7
12
19
7
18
14
12
13
8
21
21
8
19
8
18
4
ACCEPTED MANUSCRIPT 9
6
7
9
20
4
1
16
10
22
22
11
21
18
15
17
11
7
5
14
22
5
6
5
Table shows the rankings of NPV, investment and P/I ratio for 22 sample projects. The values rank from low to
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high order.
Table 3 Descriptive statistics for cash flow data of 22 sample projects NPV
Planning production
Project investment
Maximum
22060.88
2758.75
108875.00
Minimum
-264.00
2.10
Mean
1948.33
292.77
Standard deviation
4652.74
605.36
26166.44
Coefficient of variation
2.39
2.07
1.95
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Indicator
43.48
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Planning production is the output level required by NPV in the second column. NPV and investment are for the whole project (100% working interest). Coefficient of variation, a non-dimensional indicator, is the ratio of sample
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standard deviation and mean value. It reflects the dispersion of sample data. For primary data, the unit of NPV and project investment is million US dollar, and that of planning production is mmbbl.
Project No.
1420 0.0000
2
2840
4260
5680
Portfolio NPV (MUS$)
Contract working
7100
8520
9940
11360
12780
14200 interest
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.7000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.5500
3
0.0000
0.0000
0.0000
0.2935
0.4500
0.4500
0.4500
0.4500
0.4500
0.4500
0.4500
4
0.5929
1.0000
1.0000
1.0000
1.0000
1.0000
1.0000
1.0000
1.0000
1.0000
1.0000
5
0.0000
0.0000
0.0000
0.1929
0.3800
0.3800
0.3800
0.3800
0.3800
0.3800
0.3800
6
0.0000
0.0000
0.0000
0.0000
0.0289
0.3296
0.3296
0.3296
0.3296
0.3296
0.3296
7
0.4500
0.4500
0.4500
0.4500
0.4500
0.4500
0.4500
0.4500
0.4500
0.4500
0.4500
8
0.0818
0.2455
0.4474
0.4600
0.4600
0.4600
0.4600
0.4600
0.4600
0.4600
0.4600
9
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.2500
0.2500
0.2500
0.2500
0.2500
10
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0097
0.0740
0.0800
11
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
1.0000
12
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.1282
0.6511
1.0000
1.0000
1.0000
13
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.4000
0.4000
0.4000
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Table 4 Optimization results of model I
ACCEPTED MANUSCRIPT 0.0000
0.0000
0.0029
0.1914
0.3130
0.5262
0.6500
0.6500
0.6500
0.6500
0.6500
15
0.0027
0.3578
1.0000
1.0000
1.0000
1.0000
1.0000
1.0000
1.0000
1.0000
1.0000
16
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
1.0000
17
0.0000
0.0000
0.4500
0.4500
0.4500
0.4500
0.4500
0.4500
0.4500
0.4500
0.4500
18
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
1.0000
1.0000
1.0000
1.0000
1.0000
19
0.3300
0.3300
0.3300
0.3300
0.3300
0.3300
0.3300
0.3300
0.3300
0.3300
0.3300
20
0.2300
0.2300
0.2300
0.2300
0.2300
0.2300
0.2300
0.2300
0.2300
0.2300
0.2300
21
0.0000
0.0000
0.0000
0.1153
0.3145
0.4900
0.4900
0.4900
0.4900
0.4900
0.4900
22
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
1.0000
1.0000
1.0000
1.0000
1.0000
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The header numbers represent the defferent portfolio NPVs for constraint 1, forming a differential series from 0 to 14200. Decimals in the table represent the optimal working interests under each NPV constraint. The last column
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shows the original working interests stipulated in the contract as a control portfolio.
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Table 5 Optimization results of model II Portfolio NPV (MUS$) Project No.
1420
2840
4260
5680
7100
8520
9940
11360
Contract working 12780
14200 interest
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.7000
2
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.5500
3
0.0000
0.0000
0.0000
0.1682
1.0000
1.0000
1.0000
1.0000
1.0000
1.0000
0.4500
4
0.5917
1.0000
1.0000
1.0000
1.0000
1.0000
1.0000
1.0000
1.0000
1.0000
1.0000
5
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.1914
0.4750
0.8924
0.3800
6
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.3296
7
0.9439
1.0000
1.0000
1.0000
1.0000
1.0000
1.0000
1.0000
1.0000
1.0000
0.4500
8
0.0000
0.1398
0.3075
0.4979
0.6127
0.7540
0.8953
0.9094
0.8688
0.8297
0.4600
9
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.2500
10
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0800
11
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
1.0000
12
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
1.0000
13
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.4000
14
0.0000
0.0000
0.0000
0.1547
0.2464
0.3742
0.5020
0.6299
0.8120
1.0000
0.6500
15
0.0000
0.2488
1.0000
1.0000
1.0000
1.0000
1.0000
1.0000
1.0000
1.0000
1.0000
16
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
1.0000
17
0.0000
0.0000
0.7829
1.0000
1.0000
1.0000
1.0000
1.0000
1.0000
1.0000
0.4500
18
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
1.0000
19
0.3530
1.0000
1.0000
1.0000
1.0000
1.0000
1.0000
1.0000
1.0000
1.0000
0.3300
20
1.0000
1.0000
1.0000
1.0000
1.0000
1.0000
1.0000
1.0000
1.0000
1.0000
0.2300
21
0.0000
0.0000
0.0000
0.0627
0.2096
0.4208
0.6319
0.8431
1.0000
1.0000
0.4900
22
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
1.0000
1.0000
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The numbers in boldface represent the different working interests of Model II compared to Model I. The numbers in shades of grey represent the monotone changing results.
ACCEPTED MANUSCRIPT
Table 6 Deviations of working interests of model I / II for 10 different portfolio NPVs Deviation range
Model I
30/220
[-27%,5% ]
Model II
18/220
[-12%, 25%]
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Deviation ratio
Deviation ratio is expressed as the ratio of the deviation point value to the sample point value. The sample points represent the 220 values of working interest for 22 sample projects at 10 different portfolio NPVs. The deviation points represents those sample points where the simulated values are different from the original optimization
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results. Deviation range indicates the maximum and minimum values for the relative deviations of the simulated
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values and the original optimization results of the work interests for all projects.
ACCEPTED MANUSCRIPT Dual-factor sensitivity analysis
Objective: minimizing risk
Budget distribution
Constraints: NPV, working interest, budget, capacity
Capacity distribution
Mont Carlo simulation （1000 times）
Required profit 1
Minimum-risk portfolio 1
Interest set 1
Required profit 2
Minimum-risk portfolio 2
Interest set 2 …
Minimum-risk portfolio n
Interest set n
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Oil company's risk tolerance (RT)
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…
… Required profit n
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Efficient portfolio frontier
Judgments on the portfolio value (CE)
Optimal portfolio decision-making considering risk appetite
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Figure 1 Decision-making route for investment portfolio optimization
Figure 2 Optimization results of model I and II
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ACCEPTED MANUSCRIPT
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Figure 3 Relative differences of efficient frontiers of model I and II
Figure 4 Optimal portfolios at different risks
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Figure 5 Efficient portfolio variances of model I / II for 10 different portfolio NPVs
ACCEPTED MANUSCRIPT Highlights Re-optimization and selection of oil projects are integrated in one framework. The working interest serves as the independent variable.
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The model considers inter-project relations and budget and capacity constraints.
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Risk tolerance of oil company is crucial in constructing the optimal portfolio.
S0920-4105(17)30500-4
DOI:
10.1016/j.petrol.2017.05.022
Reference:
PETROL 4006
To appear in:
Journal of Petroleum Science and Engineering
Received Date: 24 March 2017 Revised Date:
7 May 2017
Accepted Date: 26 May 2017
Please cite this article as: Tang, B.-J., Zhou, H.-L., Cao, H., Selection of overseas oil and gas projects under low oil price, Journal of Petroleum Science and Engineering (2017), doi: 10.1016/ j.petrol.2017.05.022. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
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1
Selection of Overseas Oil and Gas Projects under Low Oil
2
Price Bao-Jun Tanga,b,c,d,e*, Hui-Ling Zhoua,b,c,d,e, Hong Caoa,f a
Center for Energy and Environmental Policy Research, Beijing Institute of Technology, Beijing 100081,
China b
School of Management and Economics, Beijing Institute of Technology, Beijing 100081, China
c
Beijing Key Lab of Energy Economics and Environmental Management, Beijing 100081, China
d
Sustainable Development Research Institute for Economy and Society of Beijing, Beijing 100081, China
e
Collaborative Innovation Center of Electric Vehicles in Beijing, Beijing 100081, China
f
School of Finance, Capital University of Economics & Business, Beijing 100083, China
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Abstract
In order to actively resist the risk of falling oil prices, the international oil companies need to
14
adjust the business strategy in time. Investment efficiency can be enhanced through effective
15
allocation of funds. This work constructs a set of analytical ideas and methods for the
16
re-optimization of the oil project portfolio under the constraints of budget and production capacity.
17
Based on the quadratic programming model and the preference theory, the optimal portfolio
18
decision is made. The case study concludes that the flexibility of contract terms improves the
19
optimization efficiency, that is, reduces the portfolio investment risk, optimizes the budget
20
allocation, and expands the range of alternative projects. In terms of decision-making, net present
21
value should not be the only criterion for project selection. However, the portfolio optimization
22
presented in this article, which considers the multiple constraints and inter-projects relationships,
23
can achieve the compromise between risk and return.
24
Key words: overseas oil project, portfolio, investment, optimization, risk tolerance
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*
Corresponding author. Tel.: +86 10 68918013.
Email addresses: [email protected] (Bao-Jun Tang)
ACCEPTED MANUSCRIPT
1 Introduction
27
The low oil price, which continues since the end of 2014, is an important opportunity for
29
global oil and gas exploration and development industry. Low cost has become the industry trend
30
and oil companies have to tighten the annual budget. Improved efficiency will come from lower
31
risk, less investment and fewer new drillings. Accordingly, it is particularly critical to make the
32
optimal portfolio of investment projects in the budget and capacity constraints. In the overseas
33
resource distributions of China's national oil companies, the variety of regions and conditions
34
greatly increases the uncertainty of investment income. Besides, decisions made on such huge
35
investment have significant risk characteristics. Therefore, the main task of decision-making is to
36
make a balance between profit and risk.
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In 2007-2013, about 40 large and medium-sized projects accomplished Final Investment
38
Decisions (FIDs) each year. However, this figure dropped to 8 in 2015, then to 6 by the second
39
quarter of 20161. These six projects have at least two common characteristics. Firstly, the average
40
capital expenditure reduced by 10-30% after 2014. Secondly, working interests are generally high,
41
which can effectively reduce the interference of partners. Nevertheless, differences in reserves,
42
investment scale and profits are obvious. For example, the investment of Tengiz oil field
43
investment is even higher than the total of the other five. Investors bear the high risk of cost and
44
capacity with such high interest ratio. Some projects may have the possibility of selling interests.
45
These projects with significant rates of return also have some price-related risks, which lead to
46
large volatility ranges in profits. Consequently, the investment budget, cost, production capacity
47
and working interest are the must considerations while oil companies build the portfolio in the
48
profit-risk dimension.
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Companies' annual investment budgets generally do not support investments in all alternative
50
projects. Project selections are required under certain budget constraints. This is the fundamental
51
starting point for oil and gas portfolio optimization. Index Ranking is a simple and straightforward
52
way to accomplish this task by sorting the project's profitability index (eg, profit to investment
53
(P/I) ratio) and picking out the projects by budget ceiling (Orman and Duggan, 1999). With the
1
The Wood Mackenzie report shows that these six projects are Zohr (Egypt), KG-DWN-98/2 (India), Atoll
(Egypt), Greater Enfield (Australia), Tangguh Ph.2 (Indonesia) and Tengiz Exp. (Kazakhstan).
ACCEPTED MANUSCRIPT expansion of oil and gas industry, decision-makers tend to consider multiple conditions. Thus,
55
Multiple Criteria Decision Making (MCDM) are gradually developing. MCDM is based on
56
technologies such as AHP (Analytic Hierarchy Process) and TOPSIS (Technique for Order
57
Preference by Similarity to Ideal Solution) to evaluate, sort and select multiple attributes of
58
alternative projects. It can provide more information than single-index methods (Lopes and
59
Almeida, 2013). However, the weight setting of indexes often needs a large amount of historical
60
data or expert opinions. When the data is not completely available, the optimization methods can
61
skip the problem of weight setting. Project portfolio is optimized by satisfying certain conditions
62
(such as budget, capacity constraints, etc.).
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Modern Portfolio Theory (MPT) (Markowitz, 1952) is one of the classical theories of
64
combination optimization. It originally served as the theoretical basis for selection and
65
construction of financial portfolio. By selecting assets with different correlation coefficients, a
66
portfolio is constructed that reduces the overall portfolio risk at the given expected return and
67
respective weights of assets are determined. The idea is also known as the diversification. For oil
68
and gas sectors with high risk and high return, each oilfield block can be analogous to a financial
69
asset with fluctuations in its earnings. Therefore, MPT has a good applicability to this problem.
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Some subsequent studies attempt to follow the classic MPT model. The objective function is
71
minimizing the variance of the portfolio return (Mutaydzic and Maybee, 2015; Walls, 2004; Xue
72
et al., 2014). The independent variables are projects investment accounted for the proportions of
73
total investment (Mutaydzic and Maybee, 2015; Walls, 2004). In addition, the expected rate of
74
portfolio return is imposed a constraint (Walls, 2004).
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However, unlike financial securities, oil projects cannot be replicated. That is, the proportion
76
of individual investment to total investment is constrained by the investment ceiling of certain
77
project. Relative studies generally require additional constraints and reprocessing of the
78
optimization results, thereby translating the investment weights into variables for decision-making
79
(i.e., working interests). Therefore, other studies propose an straightforward idea that working
80
interests serve as the independent variables (Orman and Duggan, 1999; Al-Harthy and Khurana,
81
2008; Xue et al., 2014). It relies on the assumption that the working interest is linear to the
82
proportion of project investment to the total investment.
83
Another difference between oil projects and financial securities is that, unlike freely traded
ACCEPTED MANUSCRIPT securities, oil projects have assorted contract length. There is still controversy over whether it is
85
appropriate to add up the internal rate of return (IRR) for different lengths. Some studies constrain
86
the expected NPV (net present value) of portfolio (Wood, 2016; Al-Harthy and Khurana, 2008;
87
Mutaydzic and Maybee, 2015; Orman and Duggan, 1999). In order to make the measure
88
consistent, the objective function should be replaced by minimizing the variance of portfolio NPV,
89
otherwise there may be problems with frontier distortions and inconsistent economic implications.
90
This model setting not only considers the non-replicability of oil projects, but also solves the
91
comparability of income between projects of different lengths.
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The correlation between oil projects is also a key factor in portfolio risk. Walls (2004) set it
93
to a fixed constant of +0.2. Moriarty (2001), Aristeguieta (2008), Ball and Savage (1999) argue
94
that inter-project relevance mainly includes oil price, politics, location, resource attributes, etc.
95
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2 Oil Portfolio Optimization Model
97
2.1 Assumptions
for oil investment have the following assumptions. i.
Oil company's decision depends only on portfolio return and risk.
101
ii.
The expected return of an oil project can be characterized by a probability distribution.
102
iii.
The estimation of portfolio risk is related to variations of expected return.
103
iv.
Oil company, who is the rational investor, pursues utility maximization.
104 105 106 107
v.
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With reference to the MPT model proposed by Markowitz, the portfolio optimization model
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Oil company is risk adverse. While comparing two alternative portfolios with the same
risk, they will value the one that offers higher profits.
This study adopt the idea of directly solving work interests. Based on the proceeding
assumptions (1) - (5), we add (6) and (7).
108
vi.
The work interest is linearly related to the project NPV and investment.
109
vii.
Signed contract terms (such as working interest, investment scale) can be modified to a
110 111
certain extent. Assumption (6) does not exactly meet with the actual situation. For different host countries
ACCEPTED MANUSCRIPT and contract types, the working interest, profit share ratio and investment scale are not linear
113
correlated. However, that will increase the complexity of capital-allocation process. The additional
114
assumption (6) can simplify the solution process. The non-linear relationship between profit
115
sharing and investment equity is widespread in different types of contracts, but does not fall within
116
the scope of this study.
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Assumption (7) reflects the practical significance of this study. That is, oil companies can
118
change the investment scale within stipulations, and optimize the capital allocation. Particularly in
119
the case of section 3, samples are all operating projects. In the short and medium-term strategic
120
development and investment decisions, oil companies also need to adjust the range of equity ratios
121
and investment scales.
2.2 Objective function and constraints
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In this study, the objective function and constraints are set as follows.
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The objective is the minimization of portfolio risk, see equation (1). Portfolio risk is
125
measured by variance of portfolio NPV, and is composed of the individual risk and the
126
inter-project risk. The higher the degree of correlations, the greater the inter-project risk, which
127
also reflects the significance of investment diversification.
128
min σ = ∑
num
2
i =1
num
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∑ww σ j =1
i
j
num
ij
num
= ∑ w σ + ∑ wi w j ρijσ iσ j i= j
2 i
2 i
（1）
i≠ j
where num is the number of projects and i or j stands for different project. wi is Chinese
130
company’s working interest in project i. σ2 is the risk of portfolio and σi2 is the risk of project i. ρij
131
is the correlation coefficient between the values of project i and j.
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NPV constraint shows in equation (2). The constant on the right side represents the
133
company's requirement for the portfolio profits, indicating that the objective function (portfolio
134
risk) is minimized at a given acceptable profitability. num
135
∑ w ⋅ npv i =1
i
0i
= NPV
（2）
136
where npv0i is the total net present value of project i, and NPV is the net present value of the
137
portfolio (constant).
138
Budget constraint shows in equation (3). Oil and gas investors are often constrained by
ACCEPTED MANUSCRIPT 139
company's budget when arranging investment plans, thus specifically setting a cap for a particular
140
portfolio. As for more detailed budget control, it is often necessary to refine this constraint to each
141
year.
142
∑w ⋅I
num
i
0 ik
≤ Bk , k = 1, 2, K ,5
（3）
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i =1
143
where k is the certain year during the 13th Five-Year Plan of oil company. I0ik is the investment
144
ceiling of project i in year k, and Bk is the investment ceiling of portfolio in year k.
Capacity constraint shows in equation (4). The limit production of a specific project is
146
difficult to change in the short term. This is determined by its production capacity, and is affected
147
by the infrastructure scale, staffing, technical level and other factors.
148
∑ w ⋅Q i =1
149
i
0 ik
≤ Qk , k = 1, 2, K ,5
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（4）
where Qk is the capacity limit in year k, and Q0ik is the capacity limit of project i in year k. Working interest constraints are shown in equation (5) and (6). The constraints directly
151
suggest that the oil projects cannot be replicated, that is, the amount of investment for a single
152
project cannot exceed the total capital of the project itself. Working interest constraint adjusts due
153
to different assumptions of corporate behavior. Assuming that company has no right to follow up
154
investment (i.e., increase the work interest) for an established contract, but may choose to sell the
155
interest depending on production or market environment, then the contract interest shall be set as
156
the upper limit (see equation (5)). Assuming that company has not yet formally signed the contract,
157
or contract terms provide a higher degree of freedom, we believe that company own the right to
158
sell or acquire the work interest, thus the upper limit is set as 100% (see equation (6)).
159
0 ≤ wi ≤ wc , i = 1, 2K, num
（5）
160
0 ≤ wi ≤ 1, i = 1, 2K, num
（6）
161
where wc is the contract working interest of Chinese company.
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An efficient portfolio defined by MPT suggests that there is no other portfolio with a higher
163
value as well as the same or even lower risk, or that there is no other lower-risk portfolio with the
164
same or higher value. According to this definition, a set of quadratic programming model is
165
established, with the objective function of minimizing portfolio risk (see model I and model II).
ACCEPTED MANUSCRIPT 166
The solution is to keep altering the constant of NPV constraint, and acquire corresponding optimal
167
portfolio. Eventually a mean - variance frontier is generated. The points on the frontier are the
168
optimal portfolio satisfying the definition of efficient portfolio. In order to compare the results for different degrees of freedom, this article sets the model I
170
and model II. Model I assumes that oil company is able to buy or sell its working interest. The
171
objective function is equation (1) and constraints include equation (2) - (5). Model II assumes
172
that Assume that oil company only has the right to sell its working interest. The objective
173
function is equation (1) and constraints include equation (2) - (4) and (6).
2.3 A portfolio selecting method based on preference theory
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In general, oil companies are risk-averse investors. No doubt, they will choose the portfolio
176
with lower risk among alternatives of the same NPV. However, if NPV and its variance of one
177
portfolio is higher than other alternatives (such as the portfolios at the mean-variance frontier), oil
178
company's decision will depend on its degree of risk aversion, i.e. how to weigh the relationship
179
between risk and return.
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This study uses the Preference Theory in microeconomics to solve this problem. Risk
181
Tolerance (RT) measures the level of risk that an oil company can afford, defined as the maximum
182
monetary value that the company has 50% chance to earn or lose. The higher the RT value, the oil
183
company is more willing to take risks. Certainty Equivalent (CE) measures the cash equivalent of
184
a portfolio in uncertain investment environment in the view of an oil company. It is also the price
185
that the oil company is willing to sell the risky portfolio in exchange for a certain return
186
(Mutaydzic and Maybee, 2015). The CE function in the mean-variance framework refers to a
187
research of Walls (2004), see equation (7).
188
CE = µ −
189
where µ is the expectation of portfolio value, and σ is the standard deviation of expectation.
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σ2
（7）
2 RT
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Given a RT value, the corresponding CE value can be calculated for any point on the efficient
191
frontier. The efficient portfolio with the highest CE value is the option that maximizing company’s
192
utility under that RT value.
193
In summary, the technical route of this model is shown in Figure 1.
ACCEPTED MANUSCRIPT 194 195
3 Application to the five-year-plan of a Chinese oil company
196
3.1 Data preparations and project economics In this section, 22 operating projects of a certain Chinese oil company are selected as samples.
198
The data mainly comes from corporate research and third-party platforms. Due to the availability
199
of data, we set a five-year-plan scenario. The project parameters, economics and statistical
200
analysis are shown in Table 1, 2 and 3, respectively. The working interests in Table 1 serve as the
201
initial values of independent variable w. The standard deviations of NPVs are the exogenous
202
parameters of objective function.
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As discussed in Section 1, some studies suggest that IRRs of projects with different lengths is
204
not comparable. Here, project economics are evaluated by index ranking method instead of IRR.
205
Table 2 ranks the NPVs, investments and P/I ratios of sample projects. Project 10, 8 and 5 rank the
206
22rd, 21st and 20th, which are the top-three profitable ones. While considering project investment,
207
their rankings for P/I ratio are 11st, 8th, and 22rd. When assessing projects on P/I ratio, a profitable
208
project should have relative high NPV and low investment scale. Therefore, project 5 is better than
209
project 8 and 10.
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Table 3 shows that the three indicators of the sample data have a large degree of
211
discretization. The coefficient of variation shows that the standard deviations of the sample are
212
about 2 times the mean values, and that of NPV is the highest. Samples reflect the diversity of
213
project size and profit. The series of NPV, planning production and project investment serve as the
214
coefficients of constraints 1, 2, and 3, respectively. The constants on the right side of the equations
215
are, in order, US$ 14,200 million (model I) / US$ 25560 million (model II), US$ 97835 million,
216
5616.08199 mmbbl.
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3.2 Portfolio optimization
219
3.2.1 Portfolio optimization mitigates the investment risk
220
Results for model I and II are shown in Figure 2. The portfolio before optimization is located
ACCEPTED MANUSCRIPT above the two efficient frontiers. In general, the portfolio risk is effectively mitigated by
222
optimizations. However, given a certain portfolio NPV, the portfolio risk optimized by model II is
223
lower than that by model I, even if the difference is rather slight. Model II further looses the
224
constraint 4 based on model I, making the work interests vary between 0-100%. Therefore, on the
225
one hand, model II generates a longer string of efficient frontier. Portfolios with higher return and
226
higher risk work out under certain budget.
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221
On the other hand, the portfolio risk of model II is slightly lower than that of model I at the
228
same portfolio NPV (see Figure 3). Although such relative difference gradually increases with the
229
expected NPV, it is generally slight. One possible reason is that the contract working interests are
230
at better levels. Therefore, the space for optimization is rather small. Nevertheless, this difference
231
also shows that contracts that are more flexible are conducive to portfolio optimization. Risk
232
mitigation and capital-allocation optimization can be achieved at the same time.
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3.2.2 Significant differences of working interest exist in model I and II
235
Working interests of each point on the portfolio efficient frontier need further discussions.
236
Here we adopt 10 optimization points as example. Results of model I and II are shown in Table 4
237
and 5, respectively. The different results of Model II compared to Model I are marked in bold in
238
Table 5.
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In the case of model I, the working-interest configuration of projects for each optimization
240
point is different. For a certain project, the working interest increases monotonically with the
241
increasing portfolio NPV. There are four projects not selected for efficient portfolio from
242
beginning to end, which are projects 1, 2, 11 and 16. The project data shows that the NPVs of
243
projects 1, 2, and 16 are negative, while project 11 falls behind at capacity and P/I ratio (see Table
244
2), which suggests a poor economy. Among the selected projects, five of them (projects 4, 7, 8, 15,
245
19 and 20) appear in all efficient portfolio. In particular, projects 7, 19 and 20 maintain the
246
contract working interests.
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Results in Table 5 show that five projects (No. 1, 2, 6, 9 and 16) remain unselected from
248
beginning to end. The additional projects (No. 6 and 9) have the low P/I ratio (see Table 2). In
ACCEPTED MANUSCRIPT 249
model II, less projects have been invested. The possible reason is the interest constraints are
250
loosed, so that limited capital is allocated to more risk-return balanced projects. The working interests of projects 7, 8, 19 and 22 increase first and then decrease as portfolio
252
NPV increases. The return on investment of project 7 ranks the 7th and its input-output ratio ranks
253
the 4th (from low to high order, the same below). The return on investment and input-output ratio
254
of project 7 both rank the 5th. When the requirement of return is too high, the budget and capacity
255
constraints will restrain investment scale of these two projects further increasing. The planning
256
production of project 8 is the highest and the investment quota is among the top. It is extremely
257
easy to reach the upper limit of constraints in the optimization iteration, which lead to a decline in
258
the working interest. Project 19 has the lowest input-output ratio, which is mainly restricted by
259
budget constraint in the optimization iteration and is gradually removed from the frontier
260
portfolio.
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261 262
3.3 Portfolio selection considering risk appetite
Based on the preceding optimization results, a string of portfolio frontier is formed, each
264
point of which represents an optimal combination of oil projects. To further determine the final
265
project configurations, the investor’s risk appetite need to be considered. As a rule of thumb, some
266
companies use 25% of annual exploration budget as their risk tolerance (Mian, 2011). Here we
267
take model II as an example. 25% of the original annual budget constraint is set as the upper limit
268
of the risk tolerance for large companies. The range of risk tolerance for small, medium and large
269
oil companies is 1000-1500, 1500-3000 and 3000-3500 (million dollar), respectively. In the case
270
of RT = $ 1000 million, it means that the oil company would accept a maximum of $ 1000 million
271
in cash losses from the portfolio. The certainty equivalents (CEs) at different return requirements
272
and portfolio risks are calculated by equation (7), shown in Figure 4.
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Figure 4 shows the certainty equivalent curves for different risk tolerances. The return-risk
274
range of the optimal portfolio for small oil companies is (5680MUS $, 5.28x106) - (8529MUS $,
275
11.9x106), for medium oil companies is (8529MUS$, 11.9x106) - (19880MUS$, 65x106) and for
276
large oil companies is (19880MUS$, 65x106) - (21300MUS$, 74.7x106). It can be seen that the
277
degree of risk aversion of large oil companies is lighter than that of small and medium companies,
ACCEPTED MANUSCRIPT 278
so their optimal portfolio tends to high-return and high-risk, which is consistent with the
279
connotation of risk tolerance. Oil companies can choose the appropriate risk tolerances according
280
to their risk-aversion assessments, and obtain the corresponding certainty equivalence curves, to
281
make the final investment decisions based on the portfolio optimization and specific risk appetite.
283 284
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3.4 Dual-factor sensitivity analysis of budget and capacity constraints
Suppose that the budget and production constraints are risk variables instead of constants in
286
the preceding. Each of them is independent of the normal distribution, and the standard deviation
287
is 10% of the mean. Perform Monte Carlo simulations for 1000 times. As can be seen from Figure
288
5, model II is more robust than model I. That is, a more flexible contract arrangement is more
289
sensitive to the uncertainty of constraints. Therefore, the flexibility of contract rights cannot be
290
ignored.
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Table 4 also shows the better robustness of model II. In addition, the work interest is more
292
sensitive to the uncertainty of constraints than the portfolio risk. Figure 5 only shows that the
293
portfolio risks of the two models are almost indistinguishable, but there is still a probable
294
difference in the working interest of each project at different portfolio NPVs. As can be seen in
295
Table 6, model II is more likely to enhance the work interests for simulated uncertain constraints
296
of budget and capacity, which will be more conducive to optimizing the capital allocation.
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4 Conclusions and policy implications
Based on the tightening-budget low-cost trends of the global oil and gas industry under the
300
low oil price, this article constructs a set of ideas and framework for the investment reallocation of
301
the oil project portfolio under the constraints of budget, production capacity, return and working
302
interest. In addition, with 22 operational oil projects as a case, a series of decision-making analysis
303
is carried out from the portfolio optimization to the shutdown timing for individual project. The
304
results show the operability of the proposed model in practical decision-making and its robustness
305
under uncertain constraints.
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4.1 Portfolio optimization for oil projects can achieve a compromise between risk and return The optimization of the oil project portfolio based on the "return-risk" perspective provides
309
an effective framework for oil companies in a dilemma. Risk and return generate form each other.
310
Oil companies strive to enhance their profits and lower losses as much as possible, through which
311
they can get a compromise without having to face a number of alternatives. The use of preference
312
theory at the strategic level can reflect companies’ risk appetites in the current investment
313
environment. The portfolio optimization at the tactical level can consider the specifics of projects.
314
4.2 NPV should not be the sole criterion for the project selection
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NPV is not the only consideration for whether a project is selected for a company's portfolio.
316
According to the optimization results of working interests, the non-selected projects include not
317
only those with negative or lower NPV, but also those with some other economic indicators (such
318
as P/I ratio). From this point of view, the traditional cash flow evaluation and Index Ranking
319
cannot be comprehensive and objective for the project selecting. The idea of portfolio
320
optimization need to be adopted, both to analyze the individual features of the project, and the
321
inter-project relationships.
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Comparing with the results of the two proposed models, the flexibility of contract terms can
325
improve the optimization efficiency of the project portfolio. Firstly, it can reduce the portfolio risk
326
to some extent. Secondly, the optimal budget allocation can be achieved through the purchase or
327
transfer of part of the working interests. Thirdly, while not considering the risk appetite, a more
328
high-yield and high-risk portfolio can be formed given the same budget, which expands the scope
329
of investment decisions. Furthermore, in the case of uncertain constraints of budget and capacity,
330
loose constraint of working interest can enhance the optimized working interests, which will be
331
more conducive to optimizing the capital allocation. The higher the freedom for adjustments of
332
working interest, the more effectiveness of optimization.
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4.4 The allocation of working interests is critical to mitigate portfolio risk The task of portfolio optimization and re-optimization is not only to choose a better project in
336
economics, but also to carefully determine the project's working interest. The looser constraint of
337
working interest (model II) not only makes the optimization results more robust, but also makes
338
the lower portfolio risk at each expected return. Although the difference of portfolio risk is slight
339
under the two kinds of working interest constraints, but the difference in the working interest
340
configurations is obvious. Therefore, when negotiating working interest items in the contract
341
signing process, oil companies should not only consider a single project of economic, strategic and
342
other factors, but also include it into a specific project portfolio. Inter-project relationships
343
manipulate project’s final contributions to the portfolio, which need to be fully considered. Even
344
for the project with considerable cash flows, its working interest is not the higher the better.
345 346
Acknowledgements
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We gratefully acknowledge the financial support from the National Natural Science
348
Foundation of China (Grant Nos. 71521002, 71573013, 71642004), the Beijing Natural Science
349
Foundation of China (Grant No. 9152014), Key Project of Beijing Social Science Foundation
350
Research Base (Grant No. 15DJA084) and National Key R&D Program (Grant No.
351
2016YFA0602603) and Special Items Fund of Beijing Municipal Commission of Education.
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References:
Al-Harthy, M.H. and Khurana, A., 2008. Portfolio Optimization: Part 2-An Application of Oil Projects with Inter- and Intra-dependencies. ENERGY SOURCES PART B-ECONOMICS PLANNING AND POLICY, 3(4): 324-330.
Aristeguieta, O., Bratvold, R., Begg, S. and Medaglia, A., 2008. Multi-objective Portfolio Optimisation of Upstream petroleum projects. University of Adelaide. Faculty of Engineering, Computer and Mathematical Science. Australia School of Petroleum. Ball, B.C. and Savage, S.L., 1999. Notes on exploration and production portfolio optimization. available for download from http://www. stanford. edu/~ savage or http://www. ziplink. net/~ benball. Lopes, Y.G. and Almeida, A.T.D., 2013. A multicriteria decision model for selecting a portfolio of oil and gas exploration projects. Pesquisa Operacional, 33(3): 417-441.
ACCEPTED MANUSCRIPT Markowitz, H., 1952. Portfolio selection. The journal of finance, 7(1): 77-91. Mian, M.A., 2011. Project economics and decision analysis: deterministic models, 1. Pennwell Books. Moriarty, N., 2001. Portfolio risk reduction: Optimising selection of resource projects by application of financial industry techniques. Exploration Geophysics, 32(3/4): 352-356. Mutaydzic, M. and Maybee, B., 2015. An extension of portfolio theory in selecting projects to construct a preferred portfolio of petroleum assets. JOURNAL OF PETROLEUM SCIENCE AND ENGINEERING, 133: 518-528.
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Orman, M.M. and Duggan, T.E., 1999. Applying modern portfolio theory to upstream investment decision making. JOURNAL OF PETROLEUM TECHNOLOGY, 51(3): 50-53.
Walls, M.R., 2004. Combining decision analysis and portfolio management to improve project selection in the exploration and production firm. JOURNAL OF PETROLEUM SCIENCE AND ENGINEERING, 44(1-2): 55-65.
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Wood, D.A., 2016. Characterization of gas and oil portfolios of exploration and production assets using a methodology that integrates value, risk and time. JOURNAL OF NATURAL GAS SCIENCE AND ENGINEERING, 30: 305-321.
Xue, Q., Wang, Z., Liu, S. and Zhao, D., 2014. An improved portfolio optimization model for oil and
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gas investment selection. PETROLEUM SCIENCE, 11(1): 181-188.
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ACCEPTED MANUSCRIPT Table 1 Working interests of Chinese side and NPVs of 22 sample projects
No.
Standard
Working
Project
deviation of
interest
No.
Standard
Working
Project
deviation of
interest
NPV
NPV
Algeria
70
-78.16
12
Kazakhstan D
100
1106.14
2
Brazil
55
-107.52
13
Kazakhstan E
40
263.76
3
Indonesia
45
174.18
14
Niger
4
Iran
100
473.47
15
Oman
5
Iraq A
38
1152.84
16
Peru A
6
Iraq B
33
699.32
17
Peru B
7
Iraq C
45
278.83
18
Peru C
100
317.07
8
Iraq D
46
1735.73
19
Russia
33
85.87
9
Kazakhstan A
25
36.35
20
Tunisia
23
4.65
10
Kazakhstan B
8
8984.73
21
Venezuela A
49
1061.85
11
Kazakhstan C
100
62.70
22
Venezuela B
100
4.84
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1
852.03
100
285.77
100
-30.33
45
92.82
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The project codes reflect the host countries of projects, and the capital letter A to E differentiate projects in the
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same countries. The working interests are the contract interests for the Chinese side. The calculations of standard deviation of NPV are based on historical data. The unit of working interest is % and that of standard deviation of NPV is million US dollar.
Ranking
NPV
Investment
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Project No.
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Table 2 Index rankings of 22 sample projects
P/I
Project No.
Ranking NPV
Investment
P/I
1
2
2
1
12
19
17
15
2
1
16
3
13
11
11
12
3
10
13
10
14
17
14
18
4
15
10
19
15
13
9
21
5
20
8
22
16
3
3
2
6
16
20
6
17
9
4
20
7
12
19
7
18
14
12
13
8
21
21
8
19
8
18
4
ACCEPTED MANUSCRIPT 9
6
7
9
20
4
1
16
10
22
22
11
21
18
15
17
11
7
5
14
22
5
6
5
Table shows the rankings of NPV, investment and P/I ratio for 22 sample projects. The values rank from low to
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high order.
Table 3 Descriptive statistics for cash flow data of 22 sample projects NPV
Planning production
Project investment
Maximum
22060.88
2758.75
108875.00
Minimum
-264.00
2.10
Mean
1948.33
292.77
Standard deviation
4652.74
605.36
26166.44
Coefficient of variation
2.39
2.07
1.95
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Indicator
43.48
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Planning production is the output level required by NPV in the second column. NPV and investment are for the whole project (100% working interest). Coefficient of variation, a non-dimensional indicator, is the ratio of sample
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standard deviation and mean value. It reflects the dispersion of sample data. For primary data, the unit of NPV and project investment is million US dollar, and that of planning production is mmbbl.
Project No.
1420 0.0000
2
2840
4260
5680
Portfolio NPV (MUS$)
Contract working
7100
8520
9940
11360
12780
14200 interest
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.7000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.5500
3
0.0000
0.0000
0.0000
0.2935
0.4500
0.4500
0.4500
0.4500
0.4500
0.4500
0.4500
4
0.5929
1.0000
1.0000
1.0000
1.0000
1.0000
1.0000
1.0000
1.0000
1.0000
1.0000
5
0.0000
0.0000
0.0000
0.1929
0.3800
0.3800
0.3800
0.3800
0.3800
0.3800
0.3800
6
0.0000
0.0000
0.0000
0.0000
0.0289
0.3296
0.3296
0.3296
0.3296
0.3296
0.3296
7
0.4500
0.4500
0.4500
0.4500
0.4500
0.4500
0.4500
0.4500
0.4500
0.4500
0.4500
8
0.0818
0.2455
0.4474
0.4600
0.4600
0.4600
0.4600
0.4600
0.4600
0.4600
0.4600
9
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.2500
0.2500
0.2500
0.2500
0.2500
10
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0097
0.0740
0.0800
11
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
1.0000
12
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.1282
0.6511
1.0000
1.0000
1.0000
13
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.4000
0.4000
0.4000
AC C
1
EP
Table 4 Optimization results of model I
ACCEPTED MANUSCRIPT 0.0000
0.0000
0.0029
0.1914
0.3130
0.5262
0.6500
0.6500
0.6500
0.6500
0.6500
15
0.0027
0.3578
1.0000
1.0000
1.0000
1.0000
1.0000
1.0000
1.0000
1.0000
1.0000
16
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
1.0000
17
0.0000
0.0000
0.4500
0.4500
0.4500
0.4500
0.4500
0.4500
0.4500
0.4500
0.4500
18
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
1.0000
1.0000
1.0000
1.0000
1.0000
19
0.3300
0.3300
0.3300
0.3300
0.3300
0.3300
0.3300
0.3300
0.3300
0.3300
0.3300
20
0.2300
0.2300
0.2300
0.2300
0.2300
0.2300
0.2300
0.2300
0.2300
0.2300
0.2300
21
0.0000
0.0000
0.0000
0.1153
0.3145
0.4900
0.4900
0.4900
0.4900
0.4900
0.4900
22
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
1.0000
1.0000
1.0000
1.0000
1.0000
RI PT
14
The header numbers represent the defferent portfolio NPVs for constraint 1, forming a differential series from 0 to 14200. Decimals in the table represent the optimal working interests under each NPV constraint. The last column
SC
shows the original working interests stipulated in the contract as a control portfolio.
M AN U
Table 5 Optimization results of model II Portfolio NPV (MUS$) Project No.
1420
2840
4260
5680
7100
8520
9940
11360
Contract working 12780
14200 interest
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.7000
2
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.5500
3
0.0000
0.0000
0.0000
0.1682
1.0000
1.0000
1.0000
1.0000
1.0000
1.0000
0.4500
4
0.5917
1.0000
1.0000
1.0000
1.0000
1.0000
1.0000
1.0000
1.0000
1.0000
1.0000
5
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.1914
0.4750
0.8924
0.3800
6
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.3296
7
0.9439
1.0000
1.0000
1.0000
1.0000
1.0000
1.0000
1.0000
1.0000
1.0000
0.4500
8
0.0000
0.1398
0.3075
0.4979
0.6127
0.7540
0.8953
0.9094
0.8688
0.8297
0.4600
9
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.2500
10
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0800
11
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
1.0000
12
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
1.0000
13
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.4000
14
0.0000
0.0000
0.0000
0.1547
0.2464
0.3742
0.5020
0.6299
0.8120
1.0000
0.6500
15
0.0000
0.2488
1.0000
1.0000
1.0000
1.0000
1.0000
1.0000
1.0000
1.0000
1.0000
16
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
1.0000
17
0.0000
0.0000
0.7829
1.0000
1.0000
1.0000
1.0000
1.0000
1.0000
1.0000
0.4500
18
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
1.0000
19
0.3530
1.0000
1.0000
1.0000
1.0000
1.0000
1.0000
1.0000
1.0000
1.0000
0.3300
20
1.0000
1.0000
1.0000
1.0000
1.0000
1.0000
1.0000
1.0000
1.0000
1.0000
0.2300
21
0.0000
0.0000
0.0000
0.0627
0.2096
0.4208
0.6319
0.8431
1.0000
1.0000
0.4900
22
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
1.0000
1.0000
AC C
EP
TE D
1
The numbers in boldface represent the different working interests of Model II compared to Model I. The numbers in shades of grey represent the monotone changing results.
ACCEPTED MANUSCRIPT
Table 6 Deviations of working interests of model I / II for 10 different portfolio NPVs Deviation range
Model I
30/220
[-27%,5% ]
Model II
18/220
[-12%, 25%]
RI PT
Deviation ratio
Deviation ratio is expressed as the ratio of the deviation point value to the sample point value. The sample points represent the 220 values of working interest for 22 sample projects at 10 different portfolio NPVs. The deviation points represents those sample points where the simulated values are different from the original optimization
SC
results. Deviation range indicates the maximum and minimum values for the relative deviations of the simulated
AC C
EP
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M AN U
values and the original optimization results of the work interests for all projects.
ACCEPTED MANUSCRIPT Dual-factor sensitivity analysis
Objective: minimizing risk
Budget distribution
Constraints: NPV, working interest, budget, capacity
Capacity distribution
Mont Carlo simulation （1000 times）
Required profit 1
Minimum-risk portfolio 1
Interest set 1
Required profit 2
Minimum-risk portfolio 2
Interest set 2 …
Minimum-risk portfolio n
Interest set n
M AN U
Oil company's risk tolerance (RT)
SC
…
… Required profit n
RI PT
Efficient portfolio frontier
Judgments on the portfolio value (CE)
Optimal portfolio decision-making considering risk appetite
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TE D
Figure 1 Decision-making route for investment portfolio optimization
Figure 2 Optimization results of model I and II
SC
RI PT
ACCEPTED MANUSCRIPT
AC C
EP
TE D
M AN U
Figure 3 Relative differences of efficient frontiers of model I and II
Figure 4 Optimal portfolios at different risks
SC
RI PT
ACCEPTED MANUSCRIPT
AC C
EP
TE D
M AN U
Figure 5 Efficient portfolio variances of model I / II for 10 different portfolio NPVs
ACCEPTED MANUSCRIPT Highlights Re-optimization and selection of oil projects are integrated in one framework. The working interest serves as the independent variable.
RI PT
The model considers inter-project relations and budget and capacity constraints.
AC C
EP
TE D
M AN U
SC
Risk tolerance of oil company is crucial in constructing the optimal portfolio.