# Using Monte Carlo Analysis to Estimate Risk

The Monte Carlo model makes it possible for researchers from all different kinds of professions to run multiple trials, and thus to define all the potential outcomes of an event or a decision. In the finance industry, the decision is typically related to an investment. When combined, all of the separate trials create a probability distribution or risk assessment for a given investment or event.

Monte Carlo analysis is a kind of multivariate modeling technique. All multivariate models can be thought of as complex illustrations of "what if?" scenarios. Some of the best-known multivariate models are those used to value stock options. Research analysts use them to forecast investment outcomes, to understand the possibilities surrounding their investment exposures, and to better mitigate their risks.

When investors use the Monte Carlo method, the results are compared to various levels of risk tolerance. This can help stakeholders decide whether or not to proceed with an investment.

### Key Takeaways

• The Monte Carlo model makes it possible for researchers from all different kinds of professions to run multiple trials, and thus to define all the potential outcomes of an event or a decision.
• When employing the Monte Carlo model, a user changes the value of multiple variables to ascertain their potential impact on the decision that is being evaluated.
• In the finance industry, the decision is typically related to an investment.
• The probability distributions produced by a Monte Carlo model create a picture of risk.

## Who Uses Multivariate Models

Multivariate models—like the Monte Carlo model—are popular statistical tools that use multiple variables to forecast possible outcomes. When employing a multivariate model, a user changes the value of multiple variables to ascertain their potential impact on the decision that is being evaluated.

Many different types of professions use multivariate models. Financial analysts may use multivariate models to estimate cash flows and new product ideas. Portfolio managers and financial advisors use them to determine the impact of investments on portfolio performance and risk. Insurance companies use them to estimate the potential for claims and to price policies.

The Monte Carlo model is named after the geographic location, Monte Carlo (technically an administrative area of the Principality of Monaco), that has been made famous by its proliferation of casinos.﻿﻿﻿﻿

### Outcomes and Probabilities

With games of chance—like those that are played at casinos—all the possible outcomes and probabilities are known. However, with most investments the set of future outcomes is unknown.

It's up to the analyst to determine the outcomes as well as the probability that they will occur. In Monte Carlo modeling, the analyst runs multiple trials (sometimes even thousands of them) to determine all the possible outcomes and the probability that they will occur.

Monte Carlo analysis is useful because many investment and business decisions are made on the basis of one outcome. In other words, many analysts derive one possible scenario and then compare that outcome to the various impediments to that outcome to decide whether to proceed.

### Pro Forma Estimates

Most pro forma estimates start with a base case. By inputting the highest probability assumption for each factor, an analyst can derive the highest probability outcome. However, making any decisions on the basis of a base case is problematic, and creating a forecast with only one outcome is insufficient because it says nothing about any other possible values that could occur.

It also says nothing about the very real chance that the actual future value will be something other than the base case prediction. It is impossible to hedge against a negative occurrence if the drivers and probabilities of these events are not calculated in advance.

## Creating the Model

Once designed, executing a Monte Carlo model requires a tool that will randomly select factor values that are bound by certain predetermined conditions. By running a number of trials with variables constrained by their own independent probabilities of occurrence, an analyst creates a distribution that includes all the possible outcomes and the probabilities that they will occur.

There are many random number generators in the marketplace. The two most common tools for designing and executing Monte Carlo models are @Risk and Crystal Ball. Both of these can be used as add-ins for spreadsheets and allow random sampling to be incorporated into established spreadsheet models.

### Correct Constraints

The art in developing an appropriate Monte Carlo model is to determine the correct constraints for each variable and the correct relationship between variables. For example, because portfolio diversification is based on the correlation between assets, any model developed to create expected portfolio values must include the correlation between investments.

In order to choose the correct distribution for a variable, one must understand each of the possible distributions available. For example, the most common one is a normal distribution, also known as a bell curve.

### Normal Distribution and Standard Deviation

In a normal distribution, all the occurrences are equally distributed around the mean. The mean is the most probable event. Natural phenomena, people's heights, and inflation are some examples of inputs that are normally distributed.

In the Monte Carlo analysis, a random-number generator picks a random value for each variable within the constraints set by the model. It then produces a probability distribution for all possible outcomes.

The standard deviation of that probability is a statistic that denotes the likelihood that the actual outcome being estimated will be something other than the mean or most probable event. Assuming a probability distribution is normally distributed, approximately 68% of the values will fall within one standard deviation of the mean, about 95% of the values will fall within two standard deviations, and about 99.7% will lie within three standard deviations of the mean.﻿﻿

This is known as the "68-95-99.7 rule" or the "empirical rule."

## Who Uses the Method

Monte Carlo analyses are not only conducted by finance professionals but also by many other businesses. It is a decision-making tool that assumes that every decision will have some impact on overall risk.

Every individual and institution has a different risk tolerance. That makes it important to calculate the risk of any investment and compare it to the individual's risk tolerance.

The probability distributions produced by a Monte Carlo model create a picture of risk. That picture is an effective way to convey the results to others, such as superiors or prospective investors. Today, very complex Monte Carlo models can be designed and executed by anyone with access to a personal computer.

Article Sources
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1. Art B. Owen. "Monte Carlo Theory, Methods and Examples, Chapter 1 End Notes," Page 10. Stanford University.

2. Massachusetts Institute of Technology. "Explained: Monte Carlo Simulations." May 11, 2020.

3. University of Massachusetts Amherst. "Normal Distribution Lab," Page 2.

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