Monte Carlo Simulation

Vertex Pharmaceuticals, Inc. is a global biotechnology company based out of Cambridge, MA. The Company's strategy is to commercialize its products both independently and in collaboration with major pharmaceutical companies. Vertex's product pipeline is focused on viral diseases, cystic fibrosis, inflammation, autoimmune diseases, cancer, and pain.

Given the uncertainty of outcomes in the biotech industry, consideration of variability is an inherent part of the decision process. Often, the mean (average) is not a relevant decision criteria. This is especially true for smaller biotech companies like Vertex – the opportunity costs are extremely high because scarce capital resources would be invested elsewhere, with a higher probability of realistic return. For example, a company may reject a project which is profitable on average (positive Net Present Value) because some of the possible outcomes are unacceptable to the decision maker. Consideration of variability allows a decision maker to bring in their own risk tolerance into the decision. A similar argument applies when estimating a safety margin above a base case (e.g. in cost budgeting).

Vertex’s strategy and analytics group within the corporate finance division seeks to provide the senior management with dynamic revenue and profit forecasting methodology that helps to identify types of drugs that should be developed given a finite amount of cash and resources. A traditional financial view allows the user to identify scenarios and potential outcomes, but lacks the ability to show the range of potential values within each and every outcome. Vertex’s team uses the DecisonTools Suite to establish the average outcome, the variability of outcomes and to pressure-test risk and uncertainty of a particular scenario throughout the decision process.

Vertex’s team built a complex financial risk analysis model using @RISK to enhance its portfolio process. Monte Carlo simulation and optimization are used to analyze and optimize project and portfolio decisions, given short and long-term corporate strategy. @RISK is also frequently used throughout the business development process: simulating across multiple sales forecasts provides BD team with a range of potential outcomes, making it easy to pinpoint a particular scenario on a curve, along with its probability and value. TopRank turns the sensitivity analysis into a quick and seamless exercise, answering multiple what-if questions within minutes. Franchise and program leaders can now see a dollar effect of their program being delayed or advanced, adding supplementary indications to the development plan and even addressing the price uncertainties all at the same time. The simple interface of PrecisionTree along with tornado chart outputs makes it easy to explain the effect and importance of a particular assumption / decision to an audience with no finance background.

As the company continues to grow, adding more drugs and collaborations to its development pipeline, we will see in this free live webcast how the DecisionsTools Suite remains one of Vertex’s analytical tools of choice to enhance and guide the decision making process.

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Abbott suggests a compromise: streamline your plot by masking (Abbott says "removing") fields that contribute to the robustness of the analysis but involve statistical twists and turns that are distracting to decision makers who may not be fascinated with technique and just want to see how the story turns out. This, he explains, allows you to work from a model both you and the decision makers can believe in.

Your thoughts? 

@RISK risk analysis software using Monte Carlo simulation is used for a wide variety of applications. In this model, we have an example of a general usage to address Operational Risk.

In many circumstances one wishes to calculate the aggregate impact of many possible yes/no type events. For example, it is often important to answer questions such as "What is the loss amount that will not be exceeded in 95% of cases?" @RISK simulation can be used to answer such questions.

» Download the example: EventandOperationalRisks.xls

With the New York State primaries coming up September 14 and the general election on November 2, I predict that as soon as summer turns the corner into September, we'll start hearing lots and lots about polls that predict election outcomes.  To find out if there was any early discussion of polls, polling, and outcomes, I returned to my favorite election forecast site from the 2008 presidential elections, FiveThirtyEight: Politics Done Right.

Most people understand that @RISK and Monte Carlo simulation are designed to be an improvement on single-point estimates.  In practice, however, I often see people using @RISK as a forecasting tool to get yet another single-point estimate, such as the 90th percentile, without putting it into the context of the potential range of outcomes.

This is probably the difference between a forecasting and a decision-making.  The former tends to focus on historical or observed trends and developing specific scenarios (e.g. best, most likely, worse) based on expert opinion, while the latter is concerned with confidence ranges and likelihood.

Indeed, it’s not until you add probability, as with @RISK, that you start to measure the quality of your forecasts (i.e. your confidence level) and calculate the margin of error – something that’s crucial in all walks of life!

In my opinion, therefore, @RISK is much more of a decision-making tool than a forecasting tool.  Both involve trying to predict the future but the addition of probability gives decision-makers vital insight to a problem. 

Don’t you just love semantics!

Ian Wallace, ACMA
Palisade Training Team

No matter how good your model, it's still You Play, You Pay.  And Rowland's disclaimer echoed a comment an influential racing veterinarian made to me: "Never invest in something that eats while you sleep."     

In @RISK (risk analysis software using Monte Carlo simulation), you can easily overlay two graphs directly from any graph window.  Just click on a button to identify the variables to overlay, and you’re done. Alternatively, you can drag thumbnails of different simulated results onto the same graph to create overlays. These overlays in the risk analysis models are useful for comparing different strategies, showing trends over time, and more.

A quick video showing how to do this:



» View short videos on recently added @RISK features

@RISK's use of Monte Carlo simulation allows for powerful features, like RiskSimtable.

The RiskSimtable feature can be used to run multiple simulations to test the sensitivity of the risk analysis model, for example to changes in the parameters of a distribution. This model is of a business with a base case expected revenue of 100 and cost of 80, giving a profit of 20.

The risk model assumes that the revenue and cost distributions are determined from a mean and standard deviation. The RiskSimtable feature is used to test the sensitivity of the distribution of profit to changes in the standard deviation of the revenues. Three values are tested of which the first is our original @RISK model. The number of simulations is therefore set at 3. A RiskSimtable can be set up either by directly typing in the required format, or by inserting it as for other Excel functions via the Insert Function menu option. The model also uses some @RISK statistical analysis functions to report the probability for each simulation that the profit exceeds 50.

» Download the example: BasicBusiness.Simtable.xls

Monte Carlo simulation is a very powerful tool for modeling uncertainty. But perhaps the most critical step in any simulation analysis is the meaningful presentation of results to others. Decision makers won’t act on the results of a simulation if they don’t understand what they are seeing. Graphs are the most powerful way to communicate these important insights.

There are lots of ways to make graphs from the data generated by Monte Carlo simulations. But what is the easiest? Microsoft Excel statistics offers its own graphing engine, but you have to tell it which data to use for what. 

@RISK comes with a powerful graphing engine built-in, and you can create meaningful graphs just by dragging and clicking things with your mouse. In this three-part series, we’ll cover the most common ways to get valuable graphical results in @RISK without ever touching your keyboard.

First off, @RISK automatically generates thumbnail graphs of input variables and output results during a simulation. These are accessible in the @RISK Model window (for inputs) and @RISK Results window (for outputs). You can expand any small thumbnail graph from these windows to full size just by dragging it off the window and onto the spreadsheet. 

Here is a quick video showing how easy it is to do this:



» View short videos on recently added @RISK features

@RISK, Palisade's risk analysis software using Monte Carlo simulation, has many features that help you create powerful models for decision making under uncertainty.

This model demonstrates the use of the alternate, percentile parameter formulation. In this case we assume that we have decided to use a Normal distribution to represent the arrival time of someone at work. The use of traditional parameters would require knowledge of the standard deviation of the arrival time, which may be hard to estimate. The use of the alternative parameter formulation allows data to be estimated by others in a more natural way. In the first case, the traditional parameters are used (mean and standard deviation). In the second case, the mean is still used, and the P90 is used in place of the standard deviation, i.e. the time before which the person arrives in 90% of cases. In the second case, the P10 and the P90 is used in place of the standard deviation i.e. the time before which the person arrives in 10% of cases, and in 90% of cases respectively.

» Download the example: AltPars.ArrivalTime.xls

"Everything has to run on the principle of profit.  We'll never let creative decisions rule our business decisions.  If it doesn't fit the model, it doesn't get done."  That doesn't mean, he has explained, that if he really likes a project, he and Wilson can't juggle the variables to make the film project fit the model.  They change the parameters to reveal the path to profit.  And profit he has--the estimated assets of Relativity are about $2 billion.  

So Kavanaugh qualifies as a mogul, a math-for-movies mogul.  When the spotlight falls on him, Monte Carlo simulation isn't far out of it.

  

@RISK, risk analysis software using Monte Carlo simulation, has many powerful features that help you create powerful models for decision making under uncertainty.

For example, you can use the RiskTheo function in @RISK to determine the parameters of a discrete distribution based on a continuous one. In this example, the RiskTheo functions of @RISK work out the P10, P50, and P90 percentiles of a continuous distribution (in this case the LogNormal), and the Mean and Standard Deviation of a RiskDiscrete distribution which has these X-values and some assumed probabilities (or weights). It then uses Excel's Solver to work out the probabilities required so that the discrete distribution based on these percentiles and probabilities would have the same mean and standard deviation as the continuous distribution.

» Download the example: CtsToDiscrete.xls
» See "Uses of the RiskTheo functions in
   @RISK to match distributions"
 » See "DMAIC Failure Rate using RISKTheo" for a
    Six Sigma application of the RISKTheo function

You can save @RISK risk analysis simulation results directly in your Excel workbook. This makes it easy to pass results around to others. Colleagues can see the benefits of risk analysis using Monte Carlo simulation. Just save your workbook like you normally would, then click Yes when prompted if you want to save simulation results. When you reopen the workbook with @RISK running, you will have access to those results again.



» Check out this video to see how

Just after I posted my last blog questioning a recent Investopedia column in the San Francisco Chronicle, I had a congenial note from the author of that column, David Harper.  His column compared Monte Carlo Simulation with two other methods of calculating Value-at-Risk, and I was concerned that its view of risk and risk analysis techniques was overly simplified. David   was surprised to discover that column had just appeared because he wrote it five years ago!

The five-year lag explains a lot--Monte Carlo simulation was not nearly so widely adopted or carried about by so many software tools as it is today--and I should have suspected the article was a vintage piece before I started carping.

So I happily retract my concerns to introduce to you David Harper, CPA and certified Financial Risk Manager.  In response to my comment about the attitudes and techniques that led to last year's collapse of the financial markets, David says that, now that the black swan has flown, "the crisis should implicate both HistoricalSim VaR and parametric VaR (at least multivariate normal!) and point toward Monte Carlo Sim. I've been thinking for a while that all of this [I think he means lack of accuracy in specifying risk] should really boost Monte Carlo."

Investment commentary is only one of David's activities.  He is the founder of Bionic Turtle, a business devoted to e-learning about financial risk and preparation for the certification exam for financial risk managers. This is a worthy enterprise--I was relieved to discover that there are hoops financial risk managers have to got through to be called that--and for anyone who would like to know more about quantitative techniques for risk analysis, its website is worth prowling. 

Thank you, David, for setting me straight.  

Modeling Uncertain Number of Events, Each with Uncertain Parameters
@RISK (risk analysis software using Monte Carlo simulation) is widely used in insurance and reinsurance for premium pricing and loss reserves modeling. A 2006 survey identified @RISK as the third most widely-used software by actuaries, after Microsoft Office and in-house actuarial tools.

@RISK's RiskCompound function allows for the sampling of frequency-severity distributions. This is often required in insurance modelling, as well as in some operations management situations. For example, to determine the total insurance claims payout, one must account for the uncertainty in both the total number of claims (frequency) and the dollar amount of each claim made (severity). 

A powerful feature of the function is that the argument that corresponds to the severity may be a reference to a cell containing a formula (rather than just a single distribution function). 

For example, one could use the function in the form RiskCompound(RiskPoisson(5), A10). The Poisson distribution would describe the frequency (occurrence) of events (e.g. an individual sample may determine that three events occur), and cell A10 would contain a formula that is separately evaluated for each of these three events (before returning the sum of these three as the sampled value of RiskCompound). 

A simple example could be A10 = RiskLognorm(10000,1000)/(1.1^RiskWeibull(2,1)), with the Weibull distribution representing the time to settlement of an insurance claim, which is used to discount the basic claim value sampled from the Lognormal distribution of severity. For example, once a claim is filed for a nominal amount, the actual payment may be delayed due to court actions or disputes, which may reduce the cost of the claim to the insurer.

» Download the model: RiskCompoundCellReferencing.xls

Variance-covariance assumes volatility only in terms of standard deviation, and volatility doesn't come in one flavor or standard deviation.  Neither does risk.   

Developed using the Six Sigma features of @RISK,
software for risk analysis using Monte Carlo simulation

Palisade’s Six Sigma Calculator allows you to create a function that models the performance of a process with uncertain elements. It allows you to include uncertainty around design factors through the use of probability distributions. It was built by Palisade Custom Development using the @RISK Developer’s Kit (RDK) to perform a Monte Carlo simulation so the following process capability metrics can be calculated: Cpk, Cpk Upper, Cpk Lower, Sigma Level, DPM, Cp, Ppk, Pp.

The RDK is Palisade’s widely-used risk analysis programming toolkit. It uses the features and functions of @RISK for Excel - the industry-leading risk analysis tool for spreadsheets. The RDK allows you to build Monte Carlo simulation models in your own applications using Windows and .NET programming languages, such as C, C#, C++, Visual Basic, or Visual Basic .NET. Examples of programs written in Windows and .NET programming languages are provided.

Palisade Custom Development services are used to build tailored applications for individual client needs using @RISK and other technology.

» Six Sigma Calculator
» More about using @RISK for Six Sigma
» More about using @RISK
» Palisade Custom Development

The decisions-by-the-numbers guys certainly had their day in court.  The free advertising wasn't bad either.