Monte Carlo Sim Primer

Risk Modeling: The Old Way

Single Point Estimates Do you make multi-million dollar decisions based on 1 number?

3-Point Estimates or Scenario Analyses Do you make multi-million dollar decisions based on 3 numbers?

Manual What-if Analyses Will you mandate that your analysts run a hundred scenarios for your million dollar decision? How much will that cost you?!?

What if something changes? What if many things change, and change at different times? Managing risk then becomes cumbersome, time consuming, and error laden.

Probability DistributionsThe direct result of Monte Carlo simulations,which are absolutely necessary for making

defensible business decisions and for managing risk.

Risk Modeling: The New Way

Probability distributions furnish you with the full range of possible outcomes, how likely those outcomes are to occur, and identifies those items that impact your bottom line most

significantly and by how much.

What is Monte Carlo simulation?!?!

At its core, Monte Carlo simulation is a virtual experiment – repeated hundreds, thousands, even millions of times – all the while generating random samples, bound by a set of parameters that you define, from each repetition of that experiment.

It’s really not rocket science.

Those random samples are then collected, organized, and analyzed to help you understand something about the behavior of that process or system.


Let’s use a common example to illustrate . . . rolling a pair of dice . . .

What happens when we roll the dice 48 times . . . and collect the results?

Imagine we have only a vague idea of how 2 dice behave when rolled.

Let’s model it!We define the parameters as: “2 dice” each with “6 possible outcomes”


We get a bunch of numbers . . .

Die 1 Die 2 Total Die 1 Die 2 Total Die 1 Die 2 Total Die 1 Die 2 Total

1 4 5 3 6 9 4 3 7 6 6 12

2 2 4 2 4 6 2 2 4 3 4 7

3 3 6 1 1 2 3 1 4 1 1 2

4 1 5 6 2 8 1 6 7 6 2 8

1 6 7 5 3 8 6 5 11 5 3 8

6 5 11 2 5 7 5 4 9 2 5 7


6 1 7 3 4 7 3 3 6 3 4 7

4 2 6 6 2 8 6 1 7 6 2 8

1 3 4 2 3 5 2 6 8 2 3 5

2 4 6 4 1 5 4 1 5 4 1 5

3 5 8 5 5 10 5 2 7 5 6 11

5 6 11 1 5 6 1 6 7 1 5 6



1 4 5 3 6 9 4 3 7 6 6 12

2 2 4 2 4 6 2 2 4 3 4 7

3 3 6 1 1 2 3 1 4 1 1 2

4 1 5 6 2 8 1 6 7 6 2 8

1 6 7 5 3 8 6 5 11 5 3 8

6 5 11 2 5 7 5 4 9 2 5 7


6 1 7 3 4 7 3 3 6 3 4 7

4 2 6 6 2 8 6 1 7 6 2 8

1 3 4 2 3 5 2 6 8 2 3 5

2 4 6 4 1 5 4 1 5 4 1 5

3 5 8 5 5 10 5 2 7 5 6 11

5 6 11 1 5 6 1 6 7 1 5 6

We then collect those numbers . . .

5 9 7 12

4 6 4 7

6 2 4 2

5 8 7 8

7 8 11 8

11 7 9 7

7 7 6 7

6 8 7 8

4 5 8 5

6 5 5 5

8 10 7 11

11 6 7 6

. . . and then condense the numbers into just the totals . . .


Next . . . we organize the figures . . .

5 9 7 12

4 6 4 7

6 2 4 2

5 8 7 8

7 8 11 8

11 7 9 7

7 7 6 7

6 8 7 8

4 5 8 5

6 5 5 5

8 10 7 11

11 6 7 6

7

7

7

7

7 8

5 6 7 8

5 6 7 8

5 6 7 8

4 5 6 7 8 11

4 5 6 7 8 11

2 4 5 6 7 8 9 11

2 4 5 6 7 8 9 10 11 12


The result is a chart that illustrates something about the behavior of rolling dice.

7

7

7

7

7 8

5 6 7 8

5 6 7 8

5 6 7 8

4 5 6 7 8 11

4 5 6 7 8 11

2 4 5 6 7 8 9 11

2 4 5 6 7 8 9 10 11 12

12

F 10

r

e 8

q

u 6

n

c 4

y

2

0 2 3 4 5 6 7 8 9 10 11 12


Let’s review . . .

Monte Carlo simulation is a virtual experiment that repeats a process or project or situation a large number of times, and generates a large number of random samples bound by a specific set of parameters.

Those random samples are collected and then organized and analyzed to help you understand the behavior of a simple or complex system or process.

Documents

Monte Carlo Sim Primer