How To Do Monte Carlo Simulation In Excel

What is Monte Carlo Simulation?

Monte Carlo Simulation is a procedure of using probability curves to make up one's mind the likelihood of an outcome.  You may scratch your head hither and say…  "Hey Rick, a distribution curve has an array of values.  So how exactly do I determine the likelihood of an outcome?"  And improve nevertheless, how do I practice that in Microsoft Excel without whatsoever special add-ins

Thought you would never ask.

This is washed by running the simulation thousands of times and analyzing the distribution of the output.  This is peculiarly important when you are analyzing the output of several distribution curves that feed into one another.

Example:

• # of Units Sold may have a distribution bend
• multiplied by Marketplace price, which may have another distribution curve
• minus variable wages which have another curve
• etc., etc.

In one case all these distributions are intermingled, the output can be quite complex.  Running thousands of iterations (or simulations) of these curve may give you some insights.  This is specially useful in analyzing potential hazard to a decision.

Describe Monte Carlo

When describing Monte Carlo Simulation, I oftentimes refer to the 1980's pic War Games, where a young Mathew Broderick (before Ferris Bueller) is a hacker that uses his punch up modem to hack into the Pentagon computers and starting time World State of war 3.  Kind of.  He then had the Pentagon computers practise many simulations of the games Tic Tac Toe to teach the estimator that no one volition volition a nuclear war – and save the world in the process.

Thanks Ferris. You're a hero.

Hither's a glimpse of the movie to show you big time Monte Carlo in action.  I am assuming that you will overlook the politics, the awkward human hugging and of form, Dabney Coleman.

The Monte Carlo Simulation Formula

Distribution Curves

There are various distribution curves you can utilise to set upwardly your Monte Carlo simulation.  And these curves may be interchanged based on the variable.  Microsoft doesn't have a formula called "Practice Monte Carlo Simulation" in the menu bar 🙂

Uniform Distribution

In a uniform distribution, there is equal likelihood anywhere between the minimum and a maximum.  A uniform distribution looks similar a rectangle.

Normal (Gaussian) Distribution

This is also your standard bong shaped curve.  This Monte Carlo Simulation Formula is characterized by being evenly distributed on each side (median and mean is the same – and no skewness).  The tails of the bend go on to infinity.  And then this may non be the ideal curve for business firm prices, where a few top end houses increase the average (mean) well above the median, or in instances where there is a hard minimum or maximum.  An example of this may be the minimum wage in your locale. Please note that the proper name of the function varies depending on your version.

Lognormal Distribution

A distribution where the logarithm is ordinarily distributed with the mean and standard deviation.  So the setup is similar to the normal distribution, just delight annotation that the mean and standard_dev variables are meant to represent the logarithm.

Poisson Distribution

This is probable the nearly underutilized distribution.  Past default, many people use a normal distribution curve when Poisson is a better fit for their models.  Poisson is all-time described when there is a big distribution near the very showtime that rapidly dissipates to a long tail on one side.  An instance of this would be a call heart, where no calls are answered before second Aught.  Followed by the majority of calls answered in the outset 2 intervals (say xxx and 60 seconds) with a quick drop off in volume and a long tail, with very few calls answered in 20 minutes (allegedly).

The purpose here is not to show yous every distribution possible in Excel, equally that is exterior the scope of this article.  Rather to ensure that you lot know that at that place are many options available for your Monte Carlo Simulation.  Practice not fall into the trap of assuming that a normal distribution bend is the correct fit for all your data modeling.  To find more curves, to go the Statistical Functions within your Excel workbook and investigate.  If you lot have questions, pose them in the comments section beneath.

Building The Model

For this prepare up nosotros volition assume a normal distribution and 1,000 iterations.

Input Variables

The setup assumes a normal distribution. A normal distribution requires three variables; probability, hateful and standard deviation.  We volition tackle the mean and standard departure in our first step.  I assume a finance forecasting trouble that consists of Revenue, Variable and Stock-still Expenses.  Where Revenue minus Variable Expenses minus Fixed Expenses equals Profit.  The Fixed expenses are sunk cost in institute and equipment, so no distribution bend is causeless.  Distribution curves are causeless for Revenue and Variable Expenses.

First Simulation

The instance below indicates the settings for Revenue.  The formula tin can be copy and pasted to cell D6 for variable expenses.  For Acquirement and expenses we you the role NORM.INV() where the parameters are:

• Probability = the function RAND() to elicit a random number based on the other criteria within the distribution.
• Mean = The mean used in the Pace 1.  For Revenue it is C3.
• Standard Difference = The Standard Divergence used in Step ane.  For Revenue it is C4

Since RAND() is used as the probability, a random probability is generated at refresh.  We will employ this to our advantage in the next step.

1,000 Simulations

There are several ways to do 1,000 or more variations.  The simplest option is to have the formula from step #2 and make information technology accented.  Then copy and paste 1,000 times.  That'due south uncomplicated, but not very fancy.  And if Ferris Bueller tin can save the world past showing a new Tic Tac Toe game to a computer, then we tin can spice up this analysis too. Allow'due south venture into the world of tables.

• Showtime nosotros want to create an outline for a table.  We practice this by listing the numbers 1 to one,000 in rows.  In the example epitome below, the number list starts in B12.
• in the next cavalcade, in cell C12, we will reference the first iteration.

• Side by side highlight the area where we desire to house the one,000 iterations
• Select Data > Data Tables
• For Column input jail cell: Select a blank jail cell.  In the download file, prison cell D11 is selected
• Select OK

• Once OK is selected from the previous step, a table is inserted that autopopulates the ane,000 simulations

Summary Statistics

One time the simulations are run, information technology is time to get together summary statistics.  This can be done a number of ways.  In this example I used the COUNTIF() function to determine the percent of simulations that are unprofitable, and the likelihood of a profit greater than $ane Million.  Equally expected, the likelihood of greater than $1M hovers around fifty%.  This is because nosotros used normal distribution curves that are evenly distributed effectually the mean, which was $1M.  The likelihood of losing coin is 4.eight%.  This was gathered by using the COUNTIF() office to count the simulations that were less than null, and dividing by the 1,000 full iterations.

Monte Carlo Simulation Formula

Now What?

In the video above, Oz asks about the diverse uses for Monte Carlo Simulation.  What have you used it for?  Are in that location any specific examples that you tin can share with the grouping?  If so, go out a note below in the comments section.  Also, feel complimentary to sign up for our newsletter, so that you tin can stay up to engagement as new Excel.TV shows are announced.  Leave me a message below to stay in contact.

Source: https://excel.tv/monte-carlo-simulation-excel-tutorial-download/

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