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# Portfolio analysis

Portfolio analysis is based on the Nobel Prize-winning work of Harry Markowitz in the early 1950s^{[1]}^{[2]} in which he showed that the variance in results from a portfolio of stocks could be reduced by choosing stocks with a negative correlation. If two stocks are correlated negatively, when one stock is down the other stock will be up, and the portfolio will grow with very few wild swings. This concept has been introduced into the petroleum literature by several authors^{[3]}^{[4]}^{[5]}^{[6]}^{[7]}^{[8]}^{[9]}^{[10]}^{[11]} with some modifications. The following paragraphs from Brashear, Becker, and Faulder^{[4]} give an overview of the methodology. (Superscripts denoting the references have been added by the current author.)

## Overview

Harry Markowitz (1957)^{[2]} demonstrated in the stock market that risk and return are usually correlated. Achieving higher yields generally necessitates taking greater risks. Further, he pointed out the risk-reducing effects of diversification were reduced if multiple investments are positively correlated but amplified if the investments are negatively correlated. He posited that a rational investor would seek the mix of investments (portfolios) for which no other combination would have a higher return without increased risk or lower risk without loss of return. He coined the phrase "efficient frontier" for the set of portfolios that meets these conditions. The choice of a single portfolio along this frontier depends on the decision-maker’s tolerance for risk.

David Hertz (1968)^{[6]} extended these concepts from investments in financial assets to investments in "real" assets. An efficient frontier could be composed of capital projects that reflected both economic value and risk (measured by standard deviation). Newendorp^{[7]} recognized Hertz’s work and speculated about a 2D display (expected value and expected loss) to illuminate individual project selections but did not propose a full portfolio optimization approach. Ball (1983)^{[8]} applied Hertz’s insights specifically to the upstream oil business. This idea was later proposed also by Hightower and David (1991)^{[9]} and Edwards and Hewitt (1993)^{[10]} and updated by Howell *et al*. (1998),^{[5]} Ball and Savage (1999)^{[11]} and Brashear *et al*. (1999).^{[12]}^{[13]}^{[14]}

While these conceptual advances were being made, increases in the speed of commonly available computers and the efficiency of the required solution algorithms have made the approach practical at field, division, and corporate levels.

The method is conceptually simple but computationally complex. The algorithm is a mathematical programming solution that evaluates all combinations of investments that yield a specific "target" expected value to define the one combination (portfolio) with the lowest risk at a given capital constraint. Other constraints can be added. The process is repeated for all other specific target values, each time finding the specific portfolio with the lowest risk. The locus of the minimum-risk points, the efficient frontier, is the set of all portfolios that satisfies the criterion that no increase in value is possible (given the constraints) without greater risk and no reduction in risk is possible without loss in value. Other algorithms find the maximum value at each risk level; either way the result is the same. </blockquote>

**Fig.1** is an example of the results of a portfolio analysis presented as a graph of reward vs. risk showing the efficient frontier. In some references, the axes are reversed. Reward is often represented by expected monetary value (EMV), while risk has several possible definitions. Markowitz used variance of the expected portfolio return as a metric for risk (or its square root, standard deviation). The petroleum industry is more concerned about downside risk, so oftentimes, semistandard deviation (the downside) or mean loss is used as a measure of risk. Whatever the metrics, the objective is to select a portfolio of projects that maximizes reward for an acceptable level of risk. A quantitative example is used to demonstrate the methodology.

**Table 1** contains the parameters for estimated distributions of net present value (NPV) for nine different projects (labeled A through I), along with the present value cost of each project and the ratio of EMV to investment. Net present value is the result of one possible outcome, while EMV is the expected value or average of all of the possible outcomes. In this example, the NPV is assumed to be normally distributed for each project. Using the ranking criterion from risk analysis for oil and gas property evaluation, the projects are ranked in order of decreasing EMV to investment ratio and chosen until the budget is exhausted. For a budget of $2,500 (which applies throughout the examples that follow), the project mix is I, D, G, and H, which results in an expected value of $1,591. Correlation between the projects, such as those caused by oil price, rig rates, geological concepts, or pipeline constraints, is ignored with this ranking method. Later in this section, correlations are included. While this portfolio has the highest EMV, it also has the highest risk, whether risk is defined as variance or as mean loss. For the purposes of illustration, the projects are assumed to be positively correlated, as shown in **Table 2**. If risk is defined as variance or standard deviation, an analytical solution can be used to calculate the variance of the correlated projects.^{[10]} When the efficient frontier is calculated with the methods shown by Winston,^{[15]} the result is as shown in**Fig.2**. The standard deviation of the expected returns can be reduced from $681 to $300, if the decision maker is willing to accept a reduction in expected results from $1,591 to $1,200. This might be a good trade because the company can still capture 75% (1,200/1,591) of the expected value while reducing its exposure to variance by 56% (381/681). Deviations about the mean for net present value at various levels of risk (defined as standard deviation about EMV) are shown in **Fig.3**. There is about a 16% chance (–1 standard deviation) that the NPV will be less than approximately $900 for risk levels from $300 to $681. Notice that the less risky portfolios are very unlikely (
<

2.3%) to return less than about $575 (–2 standard deviations), while the most aggressive portfolio could return less than $228. Of course, there is a corresponding decrease in the potential upside if a more conservative portfolio is chosen.

The optimal portfolio for each point on the efficient frontier can be calculated. **Fig.4** graphically illustrates the project mix for several points on the efficient frontier. At an expected value of $1,200 (standard deviation of $300), the project mix is 7% of A, 100% of D, 77.7% of E, 100% of F, 15.3% of G, and 100% of I. Project H, selected using EMV/investment, is not selected at all, while 100% of F was taken in which only two projects were ranked lower using EMV/investment. This is because F is almost a sure thing with a standard deviation of 22 about a mean of 147, while the return on H is quite uncertain with a standard deviation that exceeds its expected value.

This analysis assumes that a continuous range of interests from 0 to 100% is available in each project. For those instances in which the available interests are available only in increments such as 15, 25, 35, 50, 75, or 100%, the same methodology can be applied. However, the resulting efficient frontier will be jagged and discontinuous.

## Correlations

The effect of correlation between the projects is shown in **Fig.5**. The highest EMV is independent of the correlation between the projects, but the variance (or standard deviation) for a given NPV is quite dependent on the correlation. If all projects are perfectly correlated (+1), the standard deviation of the NPV at maximum EMV is $950. If the projects are totally independent of each other (unlikely in the oil industry because of price, if nothing else), the standard deviation of NPV at maximum EMV is $519. If the projects are all negatively correlated with correlation coefficients of –0.1, the standard deviation of NPV at maximum EMV is reduced to $454. This illustrates the power of finding projects that are not correlated with each other or that have a negative correlation.

If the metric of risk is mean loss rather than variance, the calculations become more tedious. Ball and Savage^{[11]} discuss the methodology and give an Internet link to a spreadsheet with a sample calculation. When their methodology is applied to the example (with the example correlation matrix), the results are as shown in **Fig.6**. Again, the portfolio with the maximum EMV of $1,591 has the highest risk. In this case, however, the decision maker can reduce the risk from $277 to $48 (83% reduction) with only a 25% reduction in EMV. The project selection, using mean loss as a metric of risk, is somewhat different. Now, we would select 100% of D, 85% of E, 100% of F, 15% of G, and 100% of I. Metrics other than EMV can be managed as shown by Howell *et al*. They give an example of a "generic" E&P portfolio in which the metrics include earnings, production, net cash flow, and reserves.

## Summary

A portfolio analysis has considerable value, but it is not easy to implement. Not only do we have to establish parameters describing the uncertainty on a project-by-project basis, we also have to determine the correlations between the various projects, which requires considerable skill. On a positive note, the computer capabilities currently available can certainly solve the problems once they are formulated. As more decision makers become educated in the methods, it is expected that portfolio analysis will become more common.

## References

- ↑ Markowitz, H.: "Portfolio Selection," J. of Finance (March 1952) 7, No. 1, 77.
- ↑
^{2.0}^{2.1}Markowitz , H.M.: Portfolio Selection and Efficient Diversification of Investments, second edition, Blackwell Publishers, Inc., Malden, Massachusetts (1957). - ↑ Ball, B.C. Jr. and Savage, S.L.: "Holistic vs. Hole-istic E&P Strategies," JPT (September 1999) 74.
- ↑
^{4.0}^{4.1}Brashear, J.P., Becker, A.B, and Faulder, D.D.: "Where Have All the Profits Gone?" JPT (June 2001) 20, 70. - ↑
^{5.0}^{5.1}Howell, J.I. III et al.: "Managing E&P Assets from a Portfolio Perspective," Oil & Gas J. (November 1998) 54. - ↑
^{6.0}^{6.1}Hertz, D. B.: "Investment Policies That Pay Off," Harvard Business Review (January/February 1968) 46, No. 1, 96. - ↑
^{7.0}^{7.1}Newendorp, P. and Schuyler, J.: Decision Analysis for Petroleum Exploration, second edition, Planning Press, Aurora, Colorado (2001) 562–566. - ↑
^{8.0}^{8.1}Ball, B.C.: "Managing Risk in the Real World," European J. of Operational Research (1983) 14, 248. - ↑
^{9.0}^{9.1}Hightower, M.L. and David, A.: "Portfolio Modeling: A Technique for Sophisticated Oil and Gas Investors," paper SPE 22016 presented at the 1991 SPE Hydrocarbon Economics and Evaluation Symposium, Dallas, 11–12 April. - ↑
^{10.0}^{10.1}^{10.2}Edwards, R.A. and Hewett, T.A.: "Applying Financial Portfolio Theory to the Analysis of Producing Properties," paper SPE 26392 presented at the 1993 SPE Annual Technical Conference and Exhibition, Houston, 3–6 October. - ↑
^{11.0}^{11.1}^{11.2}Ball, B.C. and Savage, S.L.: "Portfolio Thinking: Beyond Optimization," Pet. Eng. Intl. (May 1999) 54. - ↑ Brashear, J.P. et al.: "Why Aren’t More U.S. Companies Replacing Oil and Gas Reserves?" Oil & Gas J. (3 March 1997) 85.
- ↑ Brashear, J.P. et al.: "How to Overcome Difficulties With Reserves Replacement," Oil & Gas J. (10 March 1997) 75.
- ↑ Brashear, J.P. et al.: "Analytical Approaches for Reserves Replacement Planning," Oil & Gas J. (17 March 1997) 106.
- ↑ Winston, W.: Financial Models Using Simulation and Optimization, Palisade Corporation, Newfield, New York (1998).

## Noteworthy papers in OnePetro

Allan, P. D. (2011, July 1). Stochastic Analysis of Resource Plays: Maximizing Portfolio Value and Mitigating Risks. Society of Petroleum Engineers. http://dx.doi.org/10.2118/134811-PA

Schuyler, J. R., & Nieman, T. (2008, March 1). Optimizer's Curse: Removing the Effect of this Bias in Portfolio Planning. Society of Petroleum Engineers. http://dx.doi.org/10.2118/107852-PA

Willigers, B. J. A., & Majou, F. (2010, April 1). Creating Efficient Portfolios That Match Competing Corporate Strategies. Society of Petroleum Engineers. http://dx.doi.org/10.2118/129259-PA

## External links

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## See also

Key economic parameters for decision making

## Page champions

Russell S J Krasey - P.Eng