# Monte Carlo Simulation

Definition: A Monte Carlo simulation (also known as a Monte Carlo analysis) is a sophisticated computerized technique that applies probability theory to financial analysis. It seeks to measure the possible impacts of random or chance events on, for example, investment returns and business results.The name is derived from that of the famous casino at Monte Carlo in Monaco, and evokes games of chance involving dice, roulette wheels or cards.

In fact, much of modern probability theory is derived from efforts to quantify the odds in such games.

Applications: Typically, securities analysts, project analysts and corporate budgeting departments (to cite just a few examples) develop or scrutinize just a single base case scenario. By applying Monte Carlo analysis, they can create predictive models that offer more information, in the form of ranges of probable outcomes. The more advanced pension consultants and retirement planners are among those financial professionals using this methodology. It also has obvious value for risk managers to use in the quantification of business risks

Methodology: Most commonly developed by management science departments and quants, at the heart of Monte Carlo simulation is the use of a computerized random number generator to vary the inputs in a financial model. Each variable in the model is assigned a likely range of outcomes, based on prior data analysis.

Then, each time the model is run, the computer randomly will assign values to those variables, within the specified ranges. The model is run typically for thousands of iterations, with new randomly-generated input variables each time. The outcomes across all these simulations are tabulated and summarized into a probability distribution.

Form of Results and Output: Rather than just a most likely base case scenario, a Monte Carlo simulation typically produces a range of outcomes that approximates a normal distribution (popularly called a bell-shaped curve), with probabilities attached to each range. For example, using a model built to forecast profits for a company in the next year, a Monte Carlo simulation may produce results of this sort:

• Median or most likely result: \$15 million in profits
• 66% probability of profits between \$13 million and \$17 million
• 95% probability of profits between \$11 million and \$19 million
• 99% probability of profits between \$9 million and \$21 million

Caveats: The results of a Monte Carlo analysis or simulation will be shaped by the assumptions used in designing it. As in any financial model, the accuracy of the assumptions is key. In particular, with a Monte Carlo simulation, the ranges of possible values assigned to each variable constitute a critical set of assumptions on which the whole undertaking rests, along with the methodology for converting random numbers generated by the computer into values within these ranges.