USING MONTE CARLO
Michael A. Wallace, CPA, CGMA, MBA
What is Monte Carlo Simulation (MCS)?
• Investopedia Says:
• A problem solving technique used to approximate the probability of
certain outcomes by running multiple trial runs, called
simulations, using random variables. One of the creators was fond
of the casinos in Monte Carlo, hence the name
MCS Is Used In
• Science, engineering, portfolio management, and
business decision making
• MCS was developed at Los Alamos National Labs during nuclear
• Which, as the photo indicates, is another way of saying, MCS
MCS Reduces Uncertainty
• Forecasting anything, tomorrow’s weather, next month’s
sales, commission payouts in Q3, ROI on an investment
is difficult because it is about the FUTURE
For Many Forecasting is an Unweighted
Roll Up of
• Informed and uninformed opinions
• Negotiated compromises
• Incentive compensation sand bagging
• Projection of past performance to the future
And After All That Pain (And Time)
• Organizations often end up with a Single Point Estimate
which is the NUMBER, but that no one believes is the
Typical CFO After Preparing
• MCS improves forecasting so let’s discuss Distributions
• To improve forecasts consider the estimates received as
a distribution of possible outcomes
• You are familiar with some distributions
• Normal Distribution (The Bell Curve) is a distribution
• The Classic Best, Worse, Most Likely Case ( A Triangular
• Binomial Distribution where an event either occurs or it doesn’t
• Don’t focus on a specific number, Focus on getting the
range, probabilities and shape of the distribution
Not This Kind of Range
• Determine the range of possible outcomes I.E. The
• E.G. sales next quarter will not be less Than $1m because next
quarter the Smithson purchase is delivered
• EG sales next quarter will not exceed $2m because $2m is all the
product that can be delivered
• What is the likelihood of a specific outcome?
• Is it possible for outcomes beyond the range to occur?
• Are some outcomes more likely than others?
• Or do all outcomes have the same likelihood of occurring?
• Considering the Range and Probabilities, What is the
Shape of the Distribution?
• Is the Shape Normal or Triangular or Pert or Binomial?
• Examples of each are below
A Simple Example
• The CFO of a Software Reseller is preparing next
quarter’s forecast for 5 products
• After discussions with Sales, Marketing and BizDev The
CFO creates the table on the next slide
Nice Table, But Which Number Do You
Average of Cases
Note that this table indicates the
range, the shape and the
How and What Would You Decide?
• Judgment? Or Average? Or the Most Likely?
• Regardless of choice, what confidence is
there that the choice was rational and
The next slide shows how you could decide…
How About Running 10,000 Simulations and
Getting This Distribution (in Ten Seconds)
The Chart Isn’t Interactive, but Indicates
• 0% Probability of Exceeding Best Case-$245,000
• 67% Probability of Exceeding Most Likely Case-$140,000
• 80% Probability of Exceeding $133,000
• 90% Probability of Exceeding $126,000
• 100% Probability of Exceeding Worse Case-$70,000
• Now Can You Decide What to Forecast?
Yes, You Can!
The Original table with distributions added.
But Wait, There is More!
• What if MCS could also reveal which input had the most
• Hint: It Can
• Go back to prior slide and guess which one that is.
• Then proceed to the next slide
It is the Elasticity Product-As Shown in
This Tornado Chart
• To further increase confidence in the forecast, focus on
tightening the sales forecast for Elasticity
• MCS not only increases confidence in the forecast it helps
prioritizes actions that increase confidence even more!
Forecasting in Real Life Is Complicated
• Much more complicated than the simple model used in
this slide show
• Real life models have thousands of inputs, not five
• Many estimates don’t fit into a Worse, Most Likely, Best Distribution
• Contingencies and Binominal Distributions are common
MCS Is A Powerful Tool
• To improve forecasting
• To identify priorities
• To create more reliable forecasts
• To increase confidence in models
Other Uses of MCS
• Acquisition Modeling
• Optimizing Inventory Stocking Levels
• Portfolio Return Forecasting
• Project Management Timelines
• Pricing Decisions
• And Yes, Building of Nuclear Weapons
Contact For Questions
• MCS concepts are difficult to convey in a slide show so for
more information contact
• Michael Wallace @firstname.lastname@example.org
• The Software tool used in this Slide Show Was @Risk by Palisade.
Learn more at www.palisade.com