The Monte Carlo Simulation – What Is It and How Can It Help You Manage Risk?

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It goes without saying that risk is always part of investing, even if you play it safe. So analyzing your risk level and predicting how it can affect your investments is crucial. One of the more popular ways to do this is what's known as the “Monte Carlo simulation.” But what is it? And can it accurately predict your investing outcomes?

The Monte Carlo simulation was created in the late 1940s by Stanislaw Ulam. He was a brilliant Polish-American mathematician. He worked on the Manhattan Project, which developed the first atomic bomb. And he also discovered cellular automation and planted the seeds for the development of nuclear pulse propulsion.

The story goes that Ulam was recovering from brain surgery and whiling away the hours by playing countless games of solitaire. He became fascinated with plotting the outcome of each game in order to observe the cards' distribution and to determine the probability of winning.

These observations led him to develop the Monte Carlo simulation (or Monte Carlo model, as it is sometimes called) in partnership with his colleague John von Neumann. They named it after the glamorous gambling capital of Monaco, since it deals with chance and random outcomes that are not unlike what you'd find in a game of roulette.

Why Use This Model?

The Monte Carlo simulation lets you see all the possible outcomes of your decisions and assess the impact of risk. This allows for better decision-making in the face of uncertainty.

Essentially, the simulation is a computerized mathematical technique that lets people account for risk in quantitative analysis and decision-making. It provides all possible outcomes for any given choice of action and tells you how likely they are to occur.

Applied to your investment portfolio, this means that you can use the Monte Carlo simulation to help you analyze all of your risk factors. It can show you the outcomes of investing on different extremes, from very conservative to very risky. And of course, it can also show what would happen if you made “middle of the road” decisions. This is particularly useful to investors who want to analyze options plays.

How the Monte Carlo Simulation Works

The Monte Carlo simulation builds models of potential outcomes by substituting a range of values for every uncertain factor. This is known as probability distribution. The simulation then runs through all of the possible results, using a different set of random values every time. This can take tens of thousands of calculations.

During a Monte Carlo simulation, values are sampled at random from the input probability distributions. Each set of samples is defined as an iteration. The resulting outcome from each sample is then recorded.

The Monte Carlo simulation is particularly applicable to the business and finance sectors since they are frequently involved with random variables. It's used to estimate the probability of cost overruns in large projects. It can determine the likelihood that an asset price will change in a certain way. Telecom companies also use it to assess network performance in different scenarios. This helps them to optimize the network.

Additionally, this model can be used to assess the risk that an entity will default and to analyze derivatives such as options. But the Monte Carlo simulation also has many applications outside of business and finance, such as insurance, oil, meteorology, astronomy and particle physics.

How Investors Can Use the Monte Carlo Simulation

But we're investors, so we want to apply the Monte Carlo simulation to see potential outcomes in our portfolios. Sure, we can work out the different possibilities ourselves, but that can be time-consuming (hope you like spreadsheets). Luckily, there are a few online financial services that use this simulation to help you with your account.

One of the handy tools that Vanguard offers its users is its “Retirement Nest Egg Calculator.” With this tool, Vanguard's algorithms determine the possible outcomes for your retirement portfolio using the Monte Carlo simulation. It takes into account your starting balance, annual spending and portfolio asset allocation. Then it runs it through myriad possible market scenarios. The calculator helps you determine the likelihood that your portfolio will last for the duration of your retirement.

Empower also uses the Monte Carlo simulation as the basis for one of its popular portfolio tools. The service calculates your probable annual return and standard deviation for your portfolio's current and target allocations. According to Empower, the median scenario “represents the midpoint of the simulations and can be considered an expected value based on historical results.” It also provides you with a “worst case” outcome in which only 10% of the simulations fared worse. Empower's aim is to demonstrate how poor diversification could fare in a “bad market scenario.”

Ellevest, which was founded as a robo investing tool for women, provides forecasts that reflect a 70% likelihood of reaching the goals that you establish on the platform. The service uses a Monte Carlo simulation to test all possible outcomes to gauge how well your investments would do in different economic situations.

The Shortcomings of the Monte Carlo Simulation

Of course, not everything is perfect — including the Monte Carlo simulation. And unfortunately, there's no such thing as a crystal ball in investing.

Perhaps the biggest strike against the model is that it can be useless in the case of a bear market. The simulation can lull its users into a false sense of security. The simulation depends on constant volatility. But the markets are infamously unpredictable. In fact, a number of Monte Carlo simulations were thrown off by the volatile stock market performance of 2008.


Using a Monte Carlo simulation can be helpful to you as a window into the potential future of your portfolio. But it shouldn't be taken as the absolute truth. It's a great tool to help you make decisions as to your asset allocation, but it's important to remember that the markets can — and likely will — be volatile and unpredictable.

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