Probability and Profits
With: Imran Abdool, Lecturer, Economics and Finance, University of Windsor
The 21st century business environment is complex and rapidly changing. To succeed, requires "telescope and microscope" approach: seeing the big picture but also able to zoom-in on tiny details. Monte Carlo simulations enable businesses by giving them these tools. Monte Carlo techniques were developed during the high-stakes time of World War II. To create atomic weapons, complex mathematics related to probability distributions were used. Several decades later this technology was refined and is now used by the largest corporations and institutions in the world. Monte Carlo techniques allow businesses to view all possible outcomes of a venture through statistical simulations.
The name Monte Carlo stems from the casino town in Monaco. Casinos, being filled with games of chance, were an excellent application of the mathematics for modeling and assessing uncertainty in the outcomes of these games. Monte Carlo simulations work by creating thousands - sometimes millions - of trials or draws and seeing the outcomes that emerge from them. This is in contrast to earlier and simpler method that required very restrictive (often unrealistic) assumptions on its input parameters.
An Everyday Example
As an example, consider modeling the time it takes for a car to travel between two cities. Specifically, our model has two stochastic (random or probability-based) inputs: the weather and time-of-day (i.e., off-peak and peak-demand). In addition to these stochastic variables, two other parameters (known with certainty once a specific route) are distance and average speed. For the weather variable, a probability distribution of various weather states (rain, snow, fog, clear skies, etcetera) and for traffic its own probability distribution (low, medium, high traffic, etcetera). Generation of these probability distributions stem from historical data and/or objective expert measures – meteorologist and civil (highway traffic) engineers, for example. Combining all these inputs, Monte Carlo simulations generates a range of travel times and the corresponding likelihood of each time between the cities.
A Monte Carlo simulation would "run" through various scenarios covering all the different cases. For example, one case would be rainy weather and high traffic. Another case would be rainy weather and medium-level traffic. The travel time from these outcomes and the probability would then be computed. All this information culminates in a full spectrum of possibilities for the decision-maker. More so, any one of these scenarios can be zoomed-in for closer analysis. For example, observing the combination of holiday season and weather may produce unusual results and require closer investigation by the model design team.
Monte Carlo and Your Bottomline
For your business, there are many innovative uses of Monte Carlo simulations to generate additional revenue and differentiate your products in the market. As an example, we developed a Monte Carlo for one of our U.S. health insurance clients to improve the effectiveness of their customer's health coverage.
Our client sells insurance products such as critical illness, long-term disability, medical, dental, and vision coverage through their agent network. One of the most important concerns for critical care coverage is the risk of personal bankruptcy in the event of a sustained medical condition. A customer will have a budget in mind but won't know how much insurance they need to manage their risk.
The system we developed asks simple questions from the customer such as their age, weight, smoking history and other health factors. They also provide their current budget and expenditures with each insurance coverage area. A Monte Carlo simulation is then run that simulates thousands of possible probabilities and paths to determine the potential health outcomes and the associated costs depending on different levels of coverage to determine their risk of bankruptcy. The customer gets an easy-to-understand report that shows them the risks of their current product mix and suggests ways to optimize or increase their coverage to minimize potential financial hardship resulting in increased revenues and lower risks for the insurer.
This simulation must be completed in just a few seconds and requires millions of calculations. Just a few years ago, this type of system would be too costly to implement but with the advent of Cloud Computing platforms, such as Amazon Web Services or Microsoft Azure, high-performance servers can be accessed nearly instantly and the calculations are made quickly with low cost.
Monte Carlo and Medium-sized Business
Consider the following scenarios:
- A change in minimum wage
- A change in corporate tax rate
- A change in depreciation or account rules
- A disruption to your supplier network
The familiar adage, "Failure to plan is planning to fail." Any of the above scenarios could happen, and understanding the full impact on your operations will be imperative to your success.
You don't need a large budget to pursue the use of Monte Carlo technology. If you have an idea and model that will give you a competitive edge and provide your customers with better information, you can quickly develop and offer new products and compete where never possible before.