1. The AIE Monte Carlo Tool The AIE Monte Carlo tool is an Excel spreadsheet and a set of supporting macros. It is the main tool used in AIE analysis of a risky decision and includes the following worksheets: –Decision Model –Risk Report –Investment Boundary Other worksheets are typically added to maintain a central location for data sources or other calculation tools created for the organization (such as portfolio classification tools, statistical analysis tools, etc.) Copyright HDR 2006 dwhubbard@hubbardresearch.com 1

2. The Decision Model The “Decision Model” worksheet is where the decision model is created, data is input, the Monte Carlo is run, and the Information Values are computed. The variables in your model are stacked vertically. Each variable or such as “productivity improvement” or “revenue” has its own row. The left side is the input area and the right side is the analysis area. Copyright HDR 2006 dwhubbard@hubbardresearch.com 2 Input Area Analysis Area

3. Decision Model Input The variables in your model are stacked vertically. Each variable such as “productivity improvement” or “revenue” has its own row. The left six columns of the “Decision Model” worksheet is the primary area for data input for your models. –Variable Name: This is where you enter the names of variables and the titles you might want to add to organize major parts of your spreadsheet –The range of values for estimates and the type of distribution used –Notes about sources of the estimate or the formula used to compute the value –If a row is a formula (not an estimate), the button “Show Formula Text” pastes the text of a formula in the Source References column Copyright HDR 2006 dwhubbard@hubbardresearch.com 3

4. Basic Monte Carlo Values Value TypeDistribution Type OverviewSource Reference A Distribution Values 1-5These are the uncertain variables in the model. The HDR tool uses 5 basic distribution types Specifies source of the measurement Fixed Value BlankRepresents the fixed value of a numberSpecifies the source of the standard that requires the fixed value Calculation BlankContains the formula for the cell (all calculations refer only to other Best estimate values) Shows the text for the formula The rows in a Decision Model has three basic purposes Each use the columns in the input area differently A row may also be blank or contain only a title or heading for a section of the model 4 Copyright HDR 2007 dwhubbard@hubbardresearch.com

5. Basic Distribution Types What each column contains Distributions*Upper & Lower BoundBest Estimate Dist. Type Normal distribution Represents the "90% confidence interval" Test value only, not used in the distribution calculations 1 Lognormal distribution Represents the "90% confidence interval"; the absolute lower bound of a lognormal is always 0 Test value only, not used in the distribution calculations 2 Uniform distribution Represents the absolute (100% certain) upper and lower bounds Test value only, not used in the distribution calculations 3 Split Triangle distribution Represents the absolute (100% certain) upper and lower bounds Represents the median; the point where there is equal chance of the quantity being higher or lower 4 Binary distribution Not applicable; should be empty Represents the % chance of the event occurring 5 5 65% 35% *A “ ” means a “hard” stop, an “  ” arrow means unbounded Copyright HDR 2007 dwhubbard@hubbardresearch.com If a row does contain an estimate with a distribution, the columns are used differently depending on the distribution type. The AIE Monte Carlo Wizard has five basic types of distributions

6. AIE Calculation Columns Random Scenarios: This is the column that generates random numbers Mean: This column computes the mean based on the distribution type Scenario w/Information: This shows the “expected” result given perfect information about a particular variable or set of variables while the others are held at their mean. This is used in the information value calculation VIA Flag: The macro uses this column to “turn on” individual variables as the one being analyzed for information value. It can also be used manually. By setting it as a “1” during a Monte Carlo simulation of the NPV row in the same column, you can compute EOL given perfect information in those variables. Copyright HDR 2007 dwhubbard@hubbardresearch.com 6

7. AIE Calculation Columns EOL Notes & Calculation: Use this column to place results of selected Monte Carlos for EOL results or for calculations that use them Individual EVPI: This is where the EVPI for a single variable is computed by the “Compute VIA’s” button Individual Threshold: This is the threshold of that value – the point at which this value would begin to make a difference in the decision Threshold probability: This is the probability that a threshold in a range is “violated” – that is, the chance the value could be different enough to affect the decision. Copyright HDR 2007 dwhubbard@hubbardresearch.com 7

8. AIE Calculation Columns Countdown: This shows the number of scenarios remaining when running a Monte Carlo simulation. When the number of scenarios gets to 0, then the Monte Carlo simulation is finished. Opp. Loss: This is the Opportunity Loss for a given scenario (i.e. “the cost of being wrong”) for each scenario run. EOL: The “Expected Opportunity Loss” is the average of all of the values in the Opp. Loss cell in all of the scenarios run in the Monte Carlo. This does not have a formula but is simply a place holder to record the value. When Monte Carlo is run, the choice to compute the average of any value and have it put in a given cell. When this is done for the Opp. Loss cell, the EOL cell is the place to put that value. Copyright HDR 2007 dwhubbard@hubbardresearch.com 8

9. Decision Model Buttons In every row which is a calculation, this automatically pastes the actual texts of formulas in the “Source Notes” column This sets up the random scenario, mean, scenario w/information, and VIA flag columns This opens the Monte Carlo Wizard dialog This clears all columns to the right of the VIA Flag (the VIA calculation columns) This computes the Value of Information Analysis – it places values in the Individual EVPI, Individual Threshold, and Threshold probability columns Copyright HDR 2007 dwhubbard@hubbardresearch.com 9 Show Formula Text Create Monte Carlo Run Monte Carlo Clear VIA’s Compute VIA’s

10. MC Wizard Dialog When the “Run Monte Carlo” button is clicked, the AIE Monte Carlo Wizard dialog box appears Copyright HDR 2006 dwhubbard@hubbardresearch.com 10 Choose whether you want the output of the MC to be an average in a single cell or a histogram showing the distribution of all the values Choose which cell in the model you want to track while the Monte Carlo runs. You can choose from a given list of cells like “NPV” or you can set it to any other cell you like Check this box if you want the model to run faster. Uncheck it if you want see the cells change as the MC runs Enter the number of scenarios you want to run for the MC. Most MC run for actual analysis should be >5,000

11. Risk Report When the user chooses “Histogram to Risk Report page” as the output for the Monte Carlo Wizard, the output is shown on the separate worksheet named Risk Report The header box shows an average of all the values generated, the percentage of them that are negative, the standard deviation and the number of scenarios in this run The histogram table below the header data shows the number of times the value showed up in each of the given “bins” of the histogram Chart titles and axis must be set manually Copyright HDR 2006 dwhubbard@hubbardresearch.com 11

12. Investment Boundary Page Copyright HDR 2007 dwhubbard@hubbardresearch.com 12 The plotted point comes from the values in the “Risk Report” page The thinner investment boundaries represent three benchmark investment sizes The thick investment boundary is interpolated from the other three The “compute CME” calculates a “Certain Monetary Equivalent” based on the relative position of the investment to its boundary Investments sorted by the “CME Ratio” is a very good estimator of much more elaborate methods in MPT