# Getting The Full Picture – Combining Monte Carlo Simulation With Decision Tree Analysis Part I

A very common type of modelling I encounter is the simple NPV-style project profit projection. The standard way to deal with these from a risk analysis point of view is to replace the uncertain “constants” with probability distributions, perhaps in combination with Excel functions or other distributions. Running a Monte Carlo simulation on this model will generate a picture of the exposure to high and low profit outcomes, as well as the actual expected value.

As a quick aside, the step or logic functions/structure of a model (for example, due to a Number of Competitors variable) can mean the spreadsheet itself doesn’t actually show the expected return, even if all variables are set to their true expected values. More on that another time – it sure can freak people out, though!

But there are many real world situations where a standard spreadsheet model doesn’t tell the whole picture. There can be decisions embedded in the process/project being modelled that aren’t easy to represent in these structurally static models. Hence decision trees step in to allow the modelling of these conditional states. They also are helpful in other ways, and I’m sure there’s a blog entry about that around here somewhere! However, classically a decision tree has a static, conditional pay-off calculation that does not include any uncertainty modelling.

The two concepts can be combined using @RISK and PrecisionTree. PrecisionTree allows the creation of a stochastically determined structure, and @RISK provides a simulation engine for use with probability distributions. In this case the model is built using PrecisionTree, with individual node payoffs (or other values) modelled using @RISK distribution functions. Without a simulation being run, an optimal policy will be determined by PrecisionTree. Once those choices have been made, however, there are both uncertain events and uncertain individual payoffs that aren’t being captured specifically. A simulation run on the decision tree will show you what the full range of possible outcomes are for that optimal policy. This gives you an understanding of the exposure you face under that policy in the manner of a standard spreadsheet model simulated using @RISK, but with the flexibility of Decision Tree analysis to allow realistic business applications to be accurately represented.

In Part II we’ll look at what the above process actually looks like and returns by way of charts and information.

Rishi Prabhakar
Trainer/Consultant