How is quantitative modelling applied to today's risk analysis problems in finance, insurance, oil and gas, manufacturing, and more? Monte Carlo Simulation is the key.  In this blog, we'll discuss the latest tips and techniques to help you judge which risks to take and which to avoid, allowing for the best decision making under uncertainty.

As a regular visitor to Norway, it is hard not to be impressed by the wealth generation in the country. Even more impressive is the discipline of the government and population to accept that the majority of the vast oil windfall of the country should be invested for the future (in a pension fund) and not spent today (high tax rates and price levels being one testament to that).

In this blog I allow myself some raw speculation as to whether holistic risk management thinking is being adequately applied when it comes to the government’s management of the wealth generated by this windfall.

In the spring of 1997, the Ministry of Finance decided that the Government Pension Fund–Global (previously known as the Government Petroleum Fund) should invest parts of its portfolio in equities. In January 1998 the fund consisted of bond investments worth NOK 113 billion (about USD 15 billion at current exchange rates). Since then inflows of new capital into the fund (also boosted by the high oil price) have been significant; in 2007, capital inflows averaged more than USD 300 million per trading day. By January 2008 the fund was worth over NOK 2000 billion (about USD 300 billion) and it is forecast to be worth over NOK 4000 billion (about USD 600 billion) by 2015 (according to the National Budget 2009)—the ultimate in retirement planning. Over time the fund’s investment guidelines have been relaxed, with the fund currently consisting of about 50% equities and 50% bonds, including government, corporate, securitized and inflation linked bonds.

To some extent there is a natural diversification in the fund. For example, to the extent that it is believed that global equities in aggregate are negatively affected by high oil prices, then there is a natural hedge in the portfolio, as increases in the oil price will reduce the equity value but lead to increased capital inflows (although the balance of this will change as the equity portfolio becomes larger). Similarly, oil-related new inflows and the investment in inflation-linked bonds could also provide some protection against long-term inflation (arguably, equities may or may not be a good long term inflation hedge). In addition, the fund of course also uses advanced tools of portfolio management, which are surely applied with rigor. However, as we know from the credit crisis, such tools can lead one to a false sense of confidence if they miss the big picture (deckchairs on the Titanic, etc!).

In this context, I allow myself to speculate (hypothesise?!) as to whether the fund should be devoting far more significant efforts to invest in non-traditional assets. (The fund’s performance is essentially currently measured against a benchmark portfolio of bonds and equities and so such efforts or investments would be hard to justify against these objectives).

The most obvious scenario in which the fund could lose out significantly would be a shift in the world’s energy sources (over the many decades of pension obligations), which could create an environment that is simultaneously largely unfavorable for most asset classes in the fund. Conceivably the potentially massive costs associated with creating a low-carbon global economy could produce a situation that is unfavorable for most global equity investments, that could unleash inflationary forces that reduce the value of many bond investments, and potentially reduce demand for oil (and its price). Such a “nightmare” scenario for the fund does not seem beyond the realms of reality. 

The most obvious strategy to mitigate the effects of this scenario would be for the fund to proactively take very large positions in alternative energy technologies. Such positions would presumably need to be very large (and possibly require the fund to itself create and support the development of new innovative companies in this area, not just to passively invest in existing ones). The costs and risks in doing so would be large (particularly as the scenario may never materialize), but it could be a prudent one, given the already very large fund that already exists for a small population base of about 5m people. Could it be so bad if 5%-10% of that fund were invested in such technologies? (Such investments would arguably support, or at least relate to, some of the fund’s other goals—such as ethical or social investments). A risk assessment would be a good idea. Now, back to the real world!

Dr. Michael Rees
Director of Training and Consulting

This week saw my book "Financial Modelling in Practice: A Concise Guide for Intermediate and Advanced Level" (John Wiley&Sons) being available to a US audience on amazon.com (the original plan was for the launch date to be end December 2008).

I have high hopes for the book in the US market, being one of the most sophisticated markets for financial modelling and its applications. My belief is that many modellers have a reasonable knowledge of core Excel functionality, but desire to increase and consolidate their knowledge in a way that is prioritised, practical, and application-driven. In addition, I felt that there were few if any really good texts out there which help modellers to design, to structure and to build models which are relevant, accurate, and readily understandable. Many texts and training courses in the modelling area put their emphasis either on Excel functionality, or on financial theory, or on mathematical models, but hardly address the modelling process. Finally, most modelling texts either do not adequately treat the topic of risk analysis, or otherwise treat it from a mathematical perspective that is both inaccessible to many modellers and lacking in practical tools.

The book starts with a review of Excel functions that are generally most relevant for building intermediate and advanced level models, including functions relevant to statistical analysis. It then discusses the principles involved in designing, structuring and building relevant, accurate and readily understandable models. Topics covered include the use of sensitivity analysis, best practice modelling principles and related issues, and model auditing tools. A Chapter is devoted to the modelling of financial statements and of cash flow valuation using discounted cash flow analysis. It then moves on to discuss risk assessment and uncertainty modelling. Many practical applications and example models are presented in an intuitive and accessible way and the @RISK Monte Carlo software from Palisade Corporation is used to implement most models. The topic of options and real options modelling is then covered, treating these as a natural extension of risk modelling. Classical option valuation methods are discussed, as well as practical methods of modelling real options, including the implementation of decision trees. Chapter 6 covers VBA for financial modelling applications. The topics selected for inclusion were established by consideration of the core types of financial models that frequently require the use of VBA and provides beginners in this area with a solid base on which to discover the richer possibilities available to modellers by using VBA.

» Buy now at Amazon.com
» Buy now at Amazon.co.uk

Dr. Michael Rees
Director of Training and Consulting

An area gaining traction in the risk analysis world is the application of Monte Carlo simulation to environmental risk. There are numerous uncertainties in the natural world and they affect plans in any number of ways. Think of a typical construction project. What is the impact of weather, specifically inclement weather, on the progress of that project? Are the delays significant enough to trigger penalties? Could a risk assessment help determine that likelihood? Are there mitigating steps to take to better ensure the progress of the job? Could decision trees aid with the consequences and determining the best course of action? Statistical analysis would certainly provide useful data to support a well informed decision.

Specific to the area of renewable energy generation, climate plays a huge role. Variability around forecasting availability of wind or water translates to uncertainty when planning for power generation and delivery. Think of a hydro installation. What capacity should be planned? What is the minimum generation that can be guaranteed? What will long term changes yield in terms of climate shift, and the resulting impact on power generation?

Tools such as @RISK and PrecisionTree add the relevant analytical techniques to spreadsheet models which would allow you to explore these kinds of questions, develop plans around these issues and set policy for future decisions.

Thompson Terry
Palisade Training Team

This week saw Palisade sponsoring the first SMI-organized conference on Financial Modelling in the Oil and Gas Industry, in London (UK). Palisade’s Michael Rees spoke on the use of @RISK, PrecisionTree, Evolver and RISKOptimizer within the industry. The talk included examples of the use of the software to conduct reserves estimation, model exponential decline and production forecasting, model prices, costs and investments and to generate an integrated risk-based decision evaluation process. Other examples included using the software to help make decisions concerning exploration and production, to implement real options valuation, and to optimize production schedules using Evolver’s and RISKOptimizer’s genetic algorithm optimization capabilities.

Palisade recently also offered the first European regional training seminar dedicated solely to Oil and Gas applications. This was held in Oslo, Norway in late October. Due to the success of this event, others are likely to be held in 2009 – watch this space!

DMUU Training Team

Models layered with rules and conditions communicate a sophisticated view of the world. Once enhanced with Monte Carlo software simulation capabilities, these spreadsheet models can extract revealing details about the systems being modeled. All statistical analysis models, regardless of sophistication, have limitations. Do we know what they are? Consider: does the model effectively capture all the relevant risks? When were the assumptions last reviewed for validity? Under what situations do the assumptions fail, producing illogical outcomes?

Sensitivity analysis as performed by @RISK gives a view of a model’s dynamics. With it we can extract some idea of expectations and relationships from the model. More information is accessible using advanced simulation tools such as Stress Analysis. Stress analysis on the model is not a de facto catch all for every possible situation; it highlights the possibilities of imaginable situations. Based on knowledge and assumptions of past data, stress scenarios demonstrate a view of negative consequences and possible opportunities. We know all too well that past data has some degree of obsolescence.

While the model communicates a range of possibilities with associated likelihoods, what the model doesn’t tell us is what to do with the information. If we get certain answers, how do we translate it to some action or decision? Decision evaluation criteria need to be established with courses of action – what do we do if the answer is this, vs. that?

Make informed decisions based on the model intelligence, don’t let the model make the decisions.

Thompson Terry
Palisade Training Team

Risk analysis as a process can be improved by sensitivity analysis. From a given set of output data, we can apply statistical analysis to assess variation. To understand the source of the variation, we can resort to sensitivity analysis. By applying various techniques, among them regression analysis and scenario analysis, we can determine how the variation of the inputs, as defined by probability distribution functions, affects the variation of the output of the model. Once we establish an observed relationship through the results of the model scenarios, the ranking provided by @RISK’s sensitivity analysis can help steer our attention to the factors which most contribute to the output variation. It is these critical inputs which require the greatest attention because of their impact. If they have greater impact in the model, we need to know as much about them as possible. If the inputs have little impact in terms of the relational variation, it may be safe to ignore them in favor of those that do.

Once we establish that certain input variation is critical to the output variation of the simulated Excel model, we know we need to gather as much data pertaining to the inputs as possible. Once gathered, we can apply distribution fitting techniques to establish a suitable representation of the relevant data. These fitted distributions help define the risk variation in the model. As we refine the model with additional data and information from appropriate subject matter experts our simulations become more effective in communicating risks to our decision makers. They can then apply this information to establishing objective criteria for determining which decisions to approve, allowing for the best decision making under uncertainty.

Thompson Terry
Palisade Training Team

The highlight of my week has been the publication of my book "Financial Modelling in Practice: A Concise Guide for Intermediate and Advanced Level" by John Wiley&Sons.

I wrote the book partly as a result of my experiences running training courses, which showed me that many modellers have a reasonable knowledge of core Excel functionality, but desire to increase and consolidate their knowledge in a way that is prioritised, practical, and application-driven. In addition, I felt that there were few if any really good texts out there which help modellers to design, to structure and to build models which are relevant, accurate, and readily understandable.  Many texts and training courses in the modelling area put their emphasis either on Excel functionality, or on financial theory, or on mathematical models, but hardly address the modelling process. Finally, most modelling texts either do not adequately treat the topic of risk analysis, or otherwise treat it from a mathematical perspective that is both inaccessible to many modellers and lacking in practical tools.

The book starts with a review of Excel functions that are generally most relevant for building intermediate and advanced level models, including functions relevant to statistical analysis. It then discusses the principles involved in designing, structuring and building relevant, accurate and readily understandable models.  Topics covered include the use of sensitivity analysis, best practice modelling principles and related issues, and model auditing tools. A Chapter is devoted to the modelling of financial statements and of cash flow valuation using discounted cash flow analysis. It then moves on to discuss risk assessment and uncertainty modelling.  Many practical applications and example models are presented in an intuitive and accessible way and the @RISK Monte Carlo software from Palisade Corporation is used to implement most models. The topic of options and real options modelling is then covered, treating these as a natural extension of risk modelling.  Classical option valuation methods are discussed, as well as practical methods of modelling real options, including the implementation of decision trees. Chapter 6 covers VBA for financial modelling applications.  The topics selected for inclusion were established by consideration of the core types of financial models that frequently require the use of VBA and provides beginners in this area with a solid base on which to discover the richer possibilities available to modellers by using VBA.

» Buy now at Amazon.co.uk
» Buy now at Amazon.com

Dr. Michael Rees
Director of Training and Consulting

The financial crisis had led the media, regulators, even accountants screaming for better “risk management.”  OK, the need seems pretty obvious in 20/20 hindsight.  But what does that really mean?

Lots of very smart people are attempting to answer that question.  A just-released report from Marsh Insurance Brokers outlines “how insurance and risk management strategies can help UK firms improve liquidity, free up cash, strengthen their financial resilience and continue operating profitably during deteriorating economic conditions.”  Everyday bloggers are posting reasonable steps for managing risk.   ZDNet offers three great steps for mitigating your IT risks. And ever-reliable Wikipedia offers its customarily thorough definition and approach.

With so many competing “theories” to risk management, which bullet list do you follow? Which is right for your industry? Wouldn’t you just like to talk to someone else facing problems and ask, “How are you handling this?” There needs to be more forums or meetings of people facing risks to answer these questions. Sure, there is RIMS. The Risk and Insurance Management Society has a huge annual meeting which offers great value to insurance and reinsurance professionals. And, the SRA (Society for Risk Analysis) does great work relating to human health and environmental risk. 


Wilmott magazine founder Paul Wilmott (right) discusses risk with a banking delegate at an earlier Palisade Risk&Decision Analysis conference.

But what if you’re not in those industries? Everyone is facing risk now. The financial crisis means that banks and the money sector are especially hard hit, but the ripple effect includes energy, healthcare, aerospace, manufacturing, and more. The Palisade Risk&Decision Analysis Conference (New York City, November 13-14) is one such forum gathering executives from many industries who face risk. Over 20 case studies provide a learning environment where professionals demonstrate their own unique approaches to risk and uncertainty. Software training using Monte Carlo simulation and other techniques is also available. There is evidence that this approach of learning from each other is particularly valuable for making change quickly.

DMUU Training Team

When using @RISK (risk analysis software for conducting Monte Carlo simulations in Microsoft Excel), one of the output graphs is a tornado graph. Such graphs have their most direct interpretation for linear models with independent input distributions, such as in most typical cost budgeting models. In these cases, the regression coefficients provide a measure of how much the output would change if the input were changed by one standard deviation (the correlation coefficients provide a broadly similar measure, but are slightly different as is covered in another posting). In @RISK5, the “mapped values” feature shows the absolute figures i.e. the absolute change in the output as each input is changed in this way.

For models which have dependencies between the input distributions (e.g. correlation or parameter dependencies) and models where the output behaves in a non-linear way with some of the inputs, these statements hold either with some qualification or may not hold at all. In such cases, the interpretation of the coefficients will in general be specific to the nature of the model. For example, in linear models with correlated input distributions, the regression coefficient will still provide a measure of how much the output would change if the input were changed by one standard deviation, but only assuming that such a change could be implemented independently i.e. without affecting the other variables.

» Watch a video demonstrating Tornado Graphs in @RISK

Dr. Michael Rees
Director of Training and Consulting

The concept of Enterprise Risk Management, or the incorporation of risk assessment in all functional areas of an organization, is not especially new. In 2002, for example, Sarbanes-Oxley required internal controls on financial reports, usually including risk assessment. However, this tidbit from an article on “Smarter Risk Management” from Director of Finance Online caught our attention:

“Standard&Poor’s has recently indicated that they will begin incorporating consideration of the strength of enterprise risk management practices as a component of their credit ratings methodology. This is yet another incentive for ensuring that a company’s approach to risk management is robust, capable of being articulated and will stand up to scrutiny.”

If your S&P score depends, at least in part, on your risk management methods, there may be hope for us yet. There are others signs that enterprise risk management is making a comeback, or at least is remaining in the corporate consciousness. A September piece from Business World Online indicates:

“Risk management has recently come into prominence in the corporate suite. … Risk management exists because a company wants to take advantage of or minimize risks that affect it. These factors include political risks, foreign exchange risks, interest rate risks, liquidity risks, price risks, market risks, operational risks, credit risks, and employee risks.”

And finally, an interesting recent video clip from Bright Cove on how financial services companies are embracing ERM:



What many of these reports miss, however, is the value in learning about ERM directly from others facing risk – and not just in your own industry. The Palisade Risk&Decision Analysis Conference in New York City (Nov 13-14, 2008), is an example of a risk forum bringing together executives from a variety of industries for the purpose of exchanging ideas on risk. Over 20 case studies form a key learning model, along with software training.

DMUU Training Team

When performing a risk analysis using Monte Carlo simulation, there are various measures of dependence; among them, we can name the Pearson correlation coefficient and the non-parametric rank correlation coefficient (Spearman’s correlation coefficient); the later being the most commonly used. The correlation represents the co-movement of two cost components; when one is more expensive, the other tends to cost more (or less for a negative correlation). Both correlation measures range from a value of -1 to 1. The value of 1 indicates perfect correlation while -1 indicates conversely perfect negative dependence. A value of 0 means no correlation.

There is a common agreement that the rank correlation coefficient is a better measure of dependence for construction costs since these costs are frequently not normally distributed; in addition the dependence between two components may be monotonic but not linear in which case the Pearson correlation is not a suitable measure.

An important requirement for including the correlation information in the Monte Carlo simulation (MCS) model is to assure that the coefficients in the correlation matrix are theoretically consistent with a functional relationship, so the variance of the variable derived by the MCS is nonnegative. By definition, the variance is the second moment about the expected value of the derived variable; therefore, it has to be nonnegative. Another way to see this is that if the consistency condition is ignored the determinant of the correlation matrix could be negative and this will lead the decision variable to have a negative variance. A quick way to check for consistency is to test that the Eigen values of the correlation matrix are nonnegative.

Dr. Javier Ordóñez
Palisade Training Team

In a revealing report from the UK, the global Association of Chartered Certified Accountants (ACCA) said that lack of management understanding of risks contributed to the financial crisis. The report recommends that bank risk management departments are strengthened, including better risk management training.

» You can download the full report PDF here.

Risk management training is nothing new. However, from our experience, it tends to come and go as a trend. It will be “hot” for a year or two, then fade as markets boom or attention is otherwise diverted. The ACCA report emphasizes, and we agree with, the need for risk management as a discipline, impervious to market fluctuations or management fads. This does mean failing to incorporate current market data or events into risk forecasts or analyses. It simply means instituting risk management and training as an essential, permanent part of the organizational culture.

When learning about risk, it helps most to see how others do it. Systematic training plays a role, to be sure, but we’ve seen that nothing beats learning from your peers.  This makes risk conferences particularly valuable. Attendees from the 2007 Palisade Risk & Decision Analysis Conference, for example, comment on getting up to speed fast by seeing different approaches to risk. The 2008 Risk & Decision Analysis Conference on November 13-14 in New York City will address these issues and provide a forum for risk professionals to learn from experts and each other.



Many companies have risk management departments, typically related to insurance and loss prevention. Fewer incorporate risk management into daily business operations. There are many other types of risk besides fire, theft, or lawsuits. In addition, if the decision-makers do not understand the risks being faced, then the best risk management techniques will be worthless. For example, Bethesda, MD-based Futron Corporation offers risk assessment and training across hierarchal levels when analyzing project risks. Futron’s Benjamin Juster had this to say about risk analysis training using Monte Carlo simulation that his company received from Palisade Corporation:

“Each of the attendees said that they were able to bring away valuable knowledge from the training, and several have even applied this knowledge to current projects already! It really puts Palisade Corporation on the list of our valued training vendors.”

DMUU Training Team

As we’ve been hearing, the collapse of Lehman Brothers, Merrill Lynch, AIG, Bear Sterns, Washington Mutual, and Wachovia can certainly be blamed on corporate greed, lax oversight, and out of control executive incentive plans. However, what gets lost in the noise is the need for more fundamental quantitative risk analysis at real decision-making levels. Sure, lots of mid-level analysts may have run simulation models showing that many sub-prime mortgage customers wouldn’t be able to make their payments after the low fixed rate expired, but obviously nobody at the top was listening. It’s easy to blame greed, but what top-level exec would have sanctioned these loans if they had known with near-certainty that this would be the result? It’s important to consider the communication process—or lack thereof—within these organizations. Is there an easy way for “quant jocks” to demonstrate to managers who set lending policies that these kinds of risks are real?

Using Monte Carlo simulation, the answer can be “yes.” Surely Monte Carlo simulations were used at Lehman Brothers, WaMu and the rest. But a lot of people, especially managers, especially managers with short-term bonuses on the line, glaze over when presented with reams of figures and endless charts. Instead, the value of Monte Carlo simulation can lie not just in the data it generates or the random number seeds that can be used or the distributions it can incorporate, but rather in its ability to generate simple, easy-to-follow graphs to communicate key points. One large oil company requires every report on a new investment to be accompanied by a single graph from @RISK Monte Carlo software. A single picture like the one below could have shown—at a glance—that the chances of disaster were not trivial (24.6% in the example).

There are thirty-nine distributions on the palette in @RISK for Excel. Sure, a couple are essentially doubles (Lognorm/Lognorm2 etc) and one is a Frequency x Severity concept (Compound) rather than strictly being a particular distribution. But basically there is plenty of choice there! However, what can you do if you have a particular distribution in mind but it isn’t on the list? There are plenty of esoteric risk analysis applications out there that require distributions beyond the realm of the palette.

Thankfully, one of the distributions you can access is the Uniform distribution. This boring rectangle is your key to any distribution you can think of when combined with an inverse CDF.

In a previous life I modelled very heavy-tailed processes (Operational Risk losses) for a large retail bank using Extreme Value Theory. One of the possible limiting distributions (in this case for sample maxima) is the Generalised Extreme Value Distribution (GEV). The Inverse CDF of the GEV is of the form:

σ (μ+(-ln(U(0,1))-ξ-1)/ξ)

Thus sampling from a Uniform(0,1) variable in this function will generate samples from a GEV with parameters μ,σ and ξ. Specific information on the GEV could then be generated by making the cell an output or using the RiskMakeInput function if required. Either way you’ve just created a distribution that isn’t on the standard palette for use in your modeling.

Any distribution can be constructed in the same way, so fear not if the distribution palette at first appears inadequate for your risk assessment needs. It’s not!

Rishi Prabhakar
Palisade Training Team

In this post, we're looking at the components of a risk analysis performed to estimate costs of a construction project. These analyses can be performed in @RISK, Palisade's software for risk analysis using Monte Carlo simulation. @RISK is an add-in to Microsoft Excel.

When dependence exists, the estimated probability density functions (PDFs) of the cost components variables are the marginal PDFs of the joint PDF of the component variables. The PDFs alone are not sufficient for estimating the PDF of total project cost. When positive dependence exists, the effect of assuming independence is underestimation of the variance of the system variables. Under the independence assumption, the single figure estimate of the system variable is almost guaranteed to be exceeded if the summation of the estimates is a large number of small subsystem variables; this seems to contradict the conventional wisdom that subdivision of construction projects into smaller work packages facilitates cost estimation and improves accuracy.

In construction cost estimating the assumption of independence is usually adopted due to the difficulty of modeling dependence. The extent and nature of interdependence does not depend only on the specific project characteristics but also on the number of cost components and the way they are defined. In general, the larger the number of components, the higher the chance that dependence exists. One way to avoid correlation is to divide the system into fewer subsystems or by grouping correlated or independent subsystems into a single subsystem; however this strategy might complicate the estimation of subsystems if they are too large or complex.

» Read about construction consultancy Pantektor's use of @RISK
» Pantektor AB

The Director of the European Offices of the International Monetary Fund, Saleh M. Nsouli, recently gave an address that examined some of the lessons that can be learned from the crisis in today's world financial market. In both the private and public sectors, Nsouli advises taking a harder look at the risk management sector.

For the private sector, Nsouli advises that risk analysis not be ignored, even when profits are up:

"The governance structure of the risk management system needs to be improved in financial firms in which the incentives are biased toward returns rather than the risks involved in attaining them.

"Compensation schemes in many organizations focus on returns and, for the most part, ignore the risk taken to obtain such returns. The risk managers, because they are not profit centers and do not sell products or write trading tickets, tend to be ignored when profits are up. Indeed, many of them apparently did sound the alarm bells before the crisis set in and were often disregarded as too out-of-touch with new structural trends, though not all firms downplayed the advice of their risk managers. The key is to ensure that top management hears both sides at equal volume, choosing the risk-return combination which best represents the risk appetite of the firm."

And in the public sector, Nsouli identifies shortcomings in risk management systems as a key lesson:

"Supervisors and regulators need to have the incentives and resources to look hard and deep at possible flaws in the risk management systems of the institutions they oversee.

"Often, stress tests did not stress the right areas or not enough; funding liquidity risks received inadequate attention; and holistic views across credit, market, and funding risks were not emphasized in part because of the recent and constant attention on Basel II regulations, covering primarily credit risk."

These lessons point to the centrality of risk management, whatever the state of the current market. At many failing banks, there are risk management specialists who have had a frustrating experience in the last few months. Hopefully lessons of this financial crisis will be taken to heart, and credence will be given to proper risk analysis even when profits are up.



To learn about the latest techniques in risk and decision analysis, and network with top-level consultants, industry practicioners and Palisade experts, consider the 2008 Risk & Decision Analysis Conference, November 13th and 14th in New York City.

» More about the Conference

Real options are the flexibilities that are inherent in general business or other decision situations. In general, a real option is present in any decision situation involving a decision-chance-decision sequence; the possibility to (at the second decision) select from a range of different decision possibilities after the occurrence of the chance event may alter the choice of the decision earlier on in the sequence (and/or increase its value). The extra value created by this flexibility is sometimes described as a real options value.

Real options analysis concerns itself with analysing such flexibilities. On some occasions it may be desired to value such flexibilities explicitly. On others, the valuation is not explicitly required and the analysis concerns itself mostly with making the correct decisions and planning risk response or mitigation actions. The topic has links to financial market options, as well as to traditional net present value analysis.

A more detailed description of this topic, with example models using Excel, @RISK (software for risk analysis using Monte Carlo simulation) and PrecisionTree (decision trees in Microsoft Excel) can be found in Chapter 5 of my book Financial Modelling in Practice (John Wiley & Sons, 2008. ISBN-13: 978-0470997444).

Dr. Michael Rees
Director of Training and Consulting

The risk analysis model below examines the familiar production forecasting model for oil and gas wells, the exponential decline curve. The standard equation, q = qie-at (3.3), can be used with random variables for both qi (the initial production rate, sometimes called IP) and a (the constant decline rate). Here the model has an additional parameter, t (time), which makes the output (Rate, STB/YR) more complicated than the volumetric reserves output.

No longer do we just want a distribution of numbers for output. Instead we want a distribution of forecasts or graphs.  The worksheet has two input cells, IP and Decline, and a column of outputs for the Rate of production in STB/YR over 15 years.

After simulation you can generate a summary graph like that shown in the model. This graph shows uncertainty over the 15 year period. The shaded region represents one standard deviation on each side of the mean. The dotted curves represent the 5th and 95th percentiles. Thus, between these dotted curves is a 90% confidence interval. We can think of the band as being made up of numerous decline curves, each of which resulted from choices of qi and a.

» @RISK Example model: Band.xls

This example was taken from Decisions Involving Uncertainty: An @RISK Tutorial for the Petroleum Industry by James Murtha, published by Palisade Corporation, where a detailed, step-by-step explanation can be found.

When building a Monte Carlo simulation model in @RISK for project risk analysis, we can incorporate a risk register through risk factors. Risk factors are more concrete abstractions of risk and define situations that can be individually assessed with a limited amount of information.

Risk factors affect a project through the occurrence of events that disrupt the development of an activity or a group of activities causing variations from the expected duration and cost estimates. This means that risk factors do not affect project activities directly, but do so through conditional consequences given that a risk event has occurred as shown in the figure below. 

The concept of risk factors is similar to one of common causes that is widely used in fault tree analysis in other engineering applications. The fact that a group of activities is affected by a common risk factor will indirectly induce correlation when consequences of that risk materialize. Risk factors are an alternative to deal with correlation between project activities. When a project is affected by several risk factors they are grouped in a risk register.




The main advantage of using risk factors is that we can make use of causal relationships to relate the occurrence of a certain risk event with its consequences on project activities. One example of the application of a risk factor for a construction project is the risk of inclement weather; if inclement weather occurs, it delays not only the execution of open-sky activities that are scheduled at that time but also could affect the productivity of labor and machinery incurring in increased costs.

One of the main problems with risk factor models used in project risk analysis is that risks affecting project performance are considered mutually independent; moreover it examines risk impact of each risk factor separately. In reality, risk factors are very often interdependent and their impact varies simultaneously with a compounding effect. This interdependency can be modeled using event trees.


Dr. Javier Ordóñez
Palisade Training Team