Monte Carlo Method: the key to making decisions in an uncertain market

In the business world, making decisions based on a single probable scenario is risky and increasingly so. The market is volatile and uncertain, and customer behavior is unpredictable. This is where the Monte Carlo method comes into play, a statistical technique that allows for the evaluation of multiple possible scenarios before making a strategic decision.

What is the Monte Carlo Method?

The Monte Carlo simulation is a mathematical technique that allows analyzing uncertainty and variability in difficult situations by generating thousands or millions of possible scenarios. For example, instead of saying "next month we will sell 1,200 units," the Monte Carlo simulation will generate multiple possible scenarios, taking into account different variables and allowing the margin of error to be reduced.

It was developed in 1940, during the Manhattan Project. At that time, it was used to evaluate nuclear reactions, but now it is used in numerous disciplines thanks to its benefits. And its name? It is adopted from the famous Monte Carlo casino in Monaco, referring to the fact that it is based on the use of random numbers, just like games of chance.

In the business context, there are numerous uncertain variables such as future demand, market price, cancellation rate, variable costs, or acquisition cost, among others. With the Monte Carlo method, estimates can be made by incorporating this uncertainty into the model.

In this way, instead of using a single fixed value, ranges and probability distributions are assigned to the variables. Then, the model will execute numerous combinations showing the probability of each scenario.

How does the Monte Carlo Method work?

Before seeing the steps to follow, it is important to fully understand the elements that make up this method:

• Mathematical model. A mathematical representation of the problem to be studied that relates the variables. For example, Profit = (Price x Customers x Average Duration) - Costs.
• Input variables. They are the set of random values that affect the output of the simulation. This can be, for example, the seasonality of a product's sales, or the quality of manufacturing. These variables must be related to the problem being analyzed, for instance, whether launching a new product will be profitable or not.
• Random samples. This method generates random samples to simulate situations and scenarios. These are sets of random values generated from a specific probability distribution.
• Results or output variable. The output variable is the result we want to measure. The model generates a graph and this variable is represented on the X-axis. For example, the useful life of a mobile phone is an output variable expressed as a time value.

Now that you understand each one of the elements, we can explain how the Monte Carlo method works. It can be divided into the following steps.

1. Problem definition. The first step is to define the problem to be analyzed. By doing this, the input variables can be identified.
2. Assignment of probability distributions. This is one of the keys to the Monte Carlo method. For each input variable, instead of setting a fixed number, ranges and probabilistic distributions are assigned to reflect its probable behavior. For example, instead of saying that the price will be €30, it can be said that it will be between €25 to €35. At this point, each variable can follow a different type of distribution (normal, uniform, triangular, etc.).
3. Random number generation. The simulation system used generates thousands of random combinations within these distributions. This will lead to a distribution of possible outcomes, different scenarios created with each combination.
4. Analysis of the results. Now you will have to analyze the distribution of the obtained results to evaluate the risks, opportunities and take informed decisions.

Finally, we are going to look at a fictional example to understand it better. A company is evaluating launching a new project management tool whose development cost is fixed (500.000€). In this context, the profitability of its launchment will depend on these input variables:

• Customer Acquisition Cost (CAC).
• Price that the user is willing to pay
• Client Lifetime Value

Instead of using fixed values, the company establish ranges, meaning that they assign a probability distribution to each variable to be able to use the Monte Carlo system:

• CAC can be between 40€ and 130€ monthly.
• The price can be between 25€ and 35€ monthly.
• The client lifetime can be between 6 and 24 months.

With this, the system executes a thousand fictional launches combining everything in a random way and simulating multiple scenarios. Once this is done, the company analyzes the results to discover how many of these simulations they can lose money. They obtained the next information:

• There is a 72% probability that the project will be profitable within the first 18 months.
• There is a 5% probability that losses will exceed 200,000€ if the CAC rises above 100€ simultaneously with a high churn rate.

To sum up, the Monte Carlo method can be very useful to have in mind the uncertainty in your decision-making process.