A Monte Carlo simulation is a mathematical technique used by investors and others to estimate the probability of different outcomes given a situation where multiple variables may come into play.
Monte Carlo simulations are used in such a wide range of industries — e.g., physics, engineering, meteorology, finance, and more — that the term doesn’t refer to a single formula, but rather a type of multivariate modeling technique. Multivariate modeling is a statistical method that uses multiple variables to forecast outcomes. A Monte Carlo simulation is an example of this type of calculation, which provides a range of potential outcomes using a probability distribution.
Keep reading to learn more about the Monte Carlo method and how a Monte Carlo analysis can be used in investing and portfolio management.
What Is Monte Carlo Simulation?
Applying mathematics to investment or business scenarios is difficult precisely because there are so many random variables involved in any single decision or any single investment or portfolio of investments. That’s why a Monte Carlo analysis can be more informative compared with predictive models that use fixed inputs.
A Monte Carlo simulation calculates a probability distribution for any variable that has inherent uncertainty. It then recalculates the results thousands of times over, each time using a different set of random numbers pertaining to each variable, to produce a vast array of outcomes that are then averaged together. In this way, a Monte Carlo analysis enables researchers from many industries to run multiple trials, and thus to define the potential outcome or risk of an event or a decision.
The ability to apply mathematics to situations where many elements are probable, and then rank the likelihood of possible outcomes in order to gauge the potential for risk, is a chief advantage of Monte Carlo simulations. Money managers might use a Monte Carlo analysis to estimate risk levels for different investments when constructing a portfolio. Corporate finance managers might use a Monte Carlo simulation to assess the impact of variables like future sales, commodities prices, interest rates, currency fluctuations, and so on. Brokers might use a Monte Carlo analysis to calculate the risks of stock options.
Monte Carlo Simulation History
Using simulations to solve problems dates back to the 19th century or even earlier, when simulations were an experimental way to test theories, analyze data, or support scientific intuition using statistics. But these simulations typically dealt with established deterministic problems. A modern Monte Carlo analysis, however, inverts that structure by using probabilities to solve the problem.
One of the first known uses of a modern Monte Carlo simulation dates back to the 1930s, when physicist Enrico Fermi experimented with an early form of the method to understand the diffusion of neutrons.
Physicists Stanislaw Ulam and John von Neumann are credited with developing and refining the current Monte Carlo method while working at the Los Alamos National Laboratory on nuclear weapons in the 1940s. Of course the technique needed a code name, and Monte Carlo was chosen because the element of chance also drives the games at a casino (the Monte Carlo region of Monaco is renowned for its gambling).
Soon the simulation method gained traction in the fields of physics, chemistry, and operations research, thanks to its adoption by the Rand Corporation and the U.S. Air Force. From there, it spread to many of the natural sciences, and eventually found its way to finance.
Monte Carlo Simulation Method
The Monte Carlo simulation works by constructing a model of possible outcomes based on an estimated range of possible conditions. It does this by creating a curve of different variables for each unknown variable, and inserting random numbers between the minimum and maximum value for each variable, and running the calculation over and over again. A Monte Carlo experiment will run the calculation thousands upon thousands of times. Along the way, it will produce a large number of possible outcomes.
But even for a simple investment, there are a host of factors that will affect its outcome. There are interest rates, regulations, market swings, as well as factors innate to that investment, such as the sales and revenue of the underlying business, or its competitive landscape, or disruptive technology, and so on. And as an investor seeks to peer further into the future, more possible variables emerge. Using a Monte Carlo simulation to understand those risks requires using a growing number of inputs as the time horizon grows longer.
After an investor runs a Monte Carlo simulation, the calculation will deliver a range of possible outcomes, with a probability score assigned to each outcome. By weighing the probability scores of different outcomes, an investor can proceed with a better sense of the risks and possible rewards of a given investment decision.
Estimating Risk Using the Monte Carlo Method
Using a Monte Carlo simulation is a complicated process that requires a background in mathematics, though some investors have created Monte-Carlo-like models using Excel or a similar spreadsheet program. Some of those homespun programs can be used to try to project possible price trajectories of a given asset.
In Monte Carlo fashion, the user will repeatedly run the equation an arbitrary number of times, to see how often each outcome occurs. The frequency of each outcome will reflect the likelihood of each outcome. The results will most likely form a bell curve, with the most likely result in the middle of the curve. But as with any bell curve, those results also indicate that there is an equal chance that the actual result will be either higher or lower than the number in the middle.
But a Monte Carlo simulation is only as good as the data that’s programmed into it. No matter how well the simulation is run, its predictive powers can easily be undone by factors that haven’t been added into the equation. For example, when using a Monte Carlo simulation to decide whether or not to buy a given stock, the model could seem to deliver a clear picture of the risks and rewards of the investment.
In that example, the problems arise if the programmer or investor leaves out one single factor, such as macro trends, the effectiveness of company leadership, cyclical factors, political changes, and so on. There’s a chance that factor could be the one that completely subverts the simulation. And those variables are potentially without limit.
Who Uses Monte Carlo Simulations and How
Nonetheless, large institutional investors might use Monte Carlo simulations as a tool in their projections and decision making. And its use for investors isn’t limited to hedge fund managers and spreadsheet wizards. There are even online Monte Carlo simulators to help people save for retirement.
Those tools are designed for the average investor to input some basic information like their savings, and years until retirement to help them understand the likelihood that they will be able to reach their financial goals, and whether they will have enough income in retirement. Those calculators use a generic set of parameters for their calculations, with inputs such as interest rates, and a generic portfolio allocation.
The Takeaway
A Monte Carlo simulation is a mathematical technique used to estimate possible outcomes of an uncertain event, such as the movement of securities.
The basis of this analysis is that the probability of different outcomes cannot be determined because random variables cannot be predicted. Therefore, a Monte Carlo simulation will constantly repeat random samples to achieve certain results that can be used to gauge the likelihood of various outcomes, and therefore different risk levels associated with different choices.
So although investing always involves risk and many unknown factors, using a calculator or tool based on the Monte Carlo method can help provide a more sophisticated use of probabilities to make investment choices. You could get started investing today by opening a brokerage account with the SoFi Invest® investment app. SoFi Invest offers an active investing solution that allows you to trade stocks, ETFs, and cryptocurrencies without paying SoFi management fees.
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