1. 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.
2. Probability Distributions
The 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.
3. 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.
4. What is Monte Carlo simulation?!?!
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”
5. What is Monte Carlo simulation?!?!
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
Die 1 Die 2 Total Die 1 Die 2 Total Die 1 Die 2 Total Die 1 Die 2 Total
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
6. What is Monte Carlo simulation?!?!
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
Die 1 Die 2 Total Die 1 Die 2 Total Die 1 Die 2 Total Die 1 Die 2 Total
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 . . .
8. What is Monte Carlo simulation?!?!
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
9. What is Monte Carlo simulation?!?!
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.
