USING MONTE CARLO SIMULATION TO INCREASE FORECASTING CONFIDENCEMichael A. Wallace, CPA, CGMA, MBAmichaelawallace@cpa.com

• 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

What is Monte Carlo Simulation (MCS)?

MCS Is Used In• Science, engineering, portfolio management, and

business decision making• MCS was developed at Los Alamos National Labs during nuclear

bomb development• Which, as the photo indicates, is another way of saying, MCS

works

• 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

MCS Reduces Uncertainty

For Many Forecasting is an Unweighted Roll Up of

• Informed and uninformed opinions • Negotiated compromises • Swags • 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 RIGHT number

• MCS improves forecasting so let’s discuss Distributions

Typical CFO After Preparing A Forecast

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

Distribution)• 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 boundaries• 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

Wait….Range?

• 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?

Probabilities?

Shape?• 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

• 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

A Simple Example

Nice Table, But Which Number Do You Forecast?

Software Product Worse Most Likely Best

Ale 15,000 30,000 50,000Bonsai 8,000 22,000 30,000Cataloger 10,000 20,000 25,000Dolphin 12,000 18,000 40,000Elasticity 25,000 50,000 100,000Sum 70,000 140,000 245,000Average of Cases 151,667

Note that this table indicates the range, the shape and the probabilities.

• Judgment? Or Average? Or the Most Likely?• Regardless of choice, what confidence is there that the choice was rational and defensible?

How and What Would You Decide?

• 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.

Software Product Worse

Most Likely Best Distributions

Ale 15,000 30,000 50,000

Bonzai8,000 22,000 30,000

Cataloger10,000 20,000 25,000

Dolphin12,000 18,000 40,000

Elasticity25,000 50,000 100,000

Sum70,000 140,000 245,000

Mean of Cases 151,667

But Wait, There is More!

• What if MCS could also reveal which input had the most uncertainty?

• 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

Which Means?• 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

• To improve forecasting• To identify priorities• To create more reliable forecasts• To increase confidence in models

MCS Is A Powerful Tool

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 @michaelawallace@cpa.com

• The Software tool used in this Slide Show Was @Risk by Palisade. Learn more at www.palisade.com