## Monday, October 31, 2016

### Summary of Findings: Monte Carlo Simulation (4 out of 5 Stars)

Note: This post represents the synthesis of the thoughts, procedures and experiences of others as represented in the articles read in advance (see previous posts) and the discussion among the students and instructor during the Advanced Analytic Techniques class at Mercyhurst University in October 2016 regarding Monte Carlo Simulation as an Analytic Technique specifically. This technique was evaluated based on its overall validity, simplicity, flexibility and its ability to effectively use structured data.

Description:

Monte Carlo simulations are a method of assessing risk versus uncertainty. It utilizes a number of different factors in a range that is sampled at random and averaged called an interation. These iterations are generated hundreds or thousands of times. The outcome is then used to generate a distribution that helps to visualize what a potential probability could be via a histogram.

Strengths:

• Flexible in its application
• Has a vast amount of evidence establishing credibility
• Many different free pre-existing formulas that can be used for forecasting
• Can take into account many different variables to increase the level of accuracy
• Proven effectiveness in increasing forecasting accuracy

Weaknesses:

• Complexity can be an issue for decision makers
• Requires mathematical knowledge
• Dependent on the variables which are input into the model (garbage in / garbage out)

How-To:

1. Identify a situation which requires a monte carlo analysis to determine a range of outcome probabilities
2. When creating the model, identify variables which may influence potential outcomes. Be as specific and exhaustive as possible as these variables generate the result figures (many model “shells” are available for free online)
3. Once the variables are included into the model, generate a sample of random outcomes (iterations) via the use of a random number calculator (often included in the free models / excel formats)
4. These iterations produce numerical results which are used to identify whether or not the outcomes are acceptable by decision makers
5. Depending on the decision makers levels of acceptable risk, the variable factors may be adjusted until the point where the likely outcomes are within the range of acceptable risk for the decision maker

Application of Technique:

Two things are required for a successful Monte Carlo simulation: inputs and shape of the data distribution. Ideally, calibrated inputs are used to provide a range of possible outcomes for each variable considered. This range essentially represents an estimator’s 90% confidence interval. Certain types of data lend themselves to different distributions, which must be accounted for in the model. For example, stock prices do not reflect a normal distribution and this should not be used to model the results.

When a range of inputs for all variables are listed, then the computer can be told to randomly sample numbers from each variable and record the output. This is an iteration. In a typical Monte Carlo simulation, hundreds if not thousands of these iterations are run, and then the distribution of the results are visualized with a histogram.

In the class example, a manufacturing company needed to decide if they were going to lease a new piece of equipment, which would cost them \$400,000/ year. There is no option to terminate this contract early, so even if the company loses money on it they must remain in the contract. Ranges were input for the variables of amount of maintenance savings, labor savings, raw materials, and these were added together and multiplied against a range of estimated production per year. It is important to note that some of these ranges include negative values to reflect the possibility of the company losing money on their investment.

These ranges were randomly sampled for each variable, and then an output was recorded to determine if the company would break even on their equipment lease. A normal distribution was used for the shape of this data. Over 400 iterations were run, and the histogram showed that 84% of the time the company would break even, while not doing so 16% of the time. Furthermore, on closer inspection it is possible to see the probability of how much money the company is likely to save. The histogram showed that 27% of the time the company would actually save at least \$600,000, while also revealing that 3% of the time the company would lose up to \$200,000 on the investment.

For Further Information:

Introduction to Monte Carlo Simulation:

Monte Carlo Simulation - Wikipedia:

Monte Carlo Simulation Methods in Finance:

Getguesstimate.com:

Riskamp.com:

Eye in the Sky, movie for decision making:

MathWorks:

Wolfram:

MIT Lecture Series - Sampling and Monte Carlo:

Monte Carlo Simulation Visualization: