Your first Monte Carlo using Crystal Ball

Hi again,

Today we’ll see how to run a simple Monte Carlo simulation using Crystal Ball.
We’ll also see how to interpret some results.

What’s the aim?

Our aim is 2-fold:
- Assess the profitability of a project
- Understand what are the most important variables impacting our profitability

Defining Assumptions – Part 3: Normal Distribution

Now we know we can use the Uniform Distribution in a few cases, how about the Normal Distribution? This distribution is frequently used.
This is mainly due to the result of the Central Limit Theorem which states that the mean of a set of values drawn from the same distribution will be “Normally” described.

Other distributions also tend towards Normal at their limits (e.g. Poisson and Binomial distributions).

What does it look like?

Defining Assumptions – Part 2: Triangular Distribution

The Triangular Distribution is is the most commonly used distribution.
It has no theoretical justification though. However, it is a very simple and clear distribution to use.

Note: It overestimates the size of the tails at the expense of values close to the mean.

Defining Assumptions – Part 1: Uniform Distribution

In our quest for the ultimate model, in our journey towards the “Right Decision” we will have the opportunity of using:

- Expensive in-house developed modelling softwares,
- Off the shelf program like Crystal Ball,
- More “basic” Monte Carlo Excel add-in downloaded from Internet.

All these solutions are meant to turn a deterministic model into a stochastic one. In other words: we need to bring uncertainty into our models. This is done by using probabilities. Our assumptions have to reflect this uncertainty.

What are “assumptions”?

The assumptions are simply the variables of the model. These “factors” are likely to change.
Instead of carving the values of these variables in stone we’ll prefer to consider them “unreliable”, prone to change from one simulation from another.

For instance:

In a financial model you can have:

- Operative Costs = 70% (deterministic)
or
- Operative Costs = Uniform distribution with a minimum value of 65% and a maximum value of 75% (stochastic)

Basically: you will allow your variable to change within a range during the simulation process.
For each iteration in the simulation, the value of this variable will be in between 65% and 75%.

You now understand that we need to be familiar with a Probability Distributions.

The Uniform Distribution

It looks like that:

Defining characteristics:
- Minimum
- Maximum

It is used mainly if the variable is bounded by a known minimum and maximum.
All values in between occur with an equal likelihood.

Example:

- The position of a leak along a pipeline,
- The price at any given point in time of a highly market sensitive commodity
- Growth rates…

Next the Triangular Distribution