(Note: The following article originally appeared on the Optimal Asset Management blog on September 28, 2018. View original post here.)

We can’t predict the future, so where do we put our money?

Every investor understands that investing involves uncertainty. Next year might be choppy or it might be smooth. The market might be up, down, or flat. In short, we do not know. Investments that you consider “safe” such as bonds can lose value because of changes in interest rates. We all know how treacherous the stock market can be, and even cash under your mattress can unexpectedly lose purchasing power if inflation spikes.

In the face of such uncertainty, how do you invest? How do you make plans about what you can afford in the future when you have no idea what the future holds?

The answer, as it turns out, lies in understanding what we do know. And, what we do know is this – stock prices, bond prices and even inflation have a certain randomness built into them. The secret to planning for an uncertain future is to understand randomness. Scientists and mathematicians have studied and obsessed over the nature of this randomness for over a hundred years. 

As far back as 1900 a French mathematician named Louis Bachelier (pictured on the right) published his Theory of Speculation as part of his PhD thesis, where he modeled stock prices as driven by a random process that he referred to as the radiation of probabilities. 

In 1905 a young patent clerk in Bern, Switzerland named Albert Einstein published work that studied the same underlying processes that Bachelier had used in his thesis five years earlier (although Einstein did not know it at the time). 

Both Bachelier and Einstein understood that randomness could be analyzed rigorously, and they were able to apply mathematical techniques to develop a theory and science around random processes.

The Monte Carlo Method is a computerized technique to simulate random processes to estimate the odds of uncertain outcomes

The genius insight of the Monte Carlo simulation method is to take advantage of the mathematical nature of these random processes. It works by using a computerized pseudo-random number generator to simulate the random process to create not just one, but thousands of hypothetical future scenarios. You could think of each generated simulated scenario as just one possible version of the future, but the computer algorithm generates thousands of different possible versions of the future. We then look at the thousands of resulting outcomes from each of the thousands of hypothetical simulated futures and use the range of outcomes to make an educated guess about what to expect and what to plan for.

But wait … Who is Monte Carlo?

Monte Carlo Casino, Monaco

Monte Carlo is not a person. It’s a casino in Monaco towards the south of France.

The story goes that the scientists who developed the technique in 1946 were excited by the possibilities of the “new era of fast computers” while they were working on a highly classified nuclear weapons project at Los Alamos Labs. They needed a secret code name, and the process of generating random numbers seems to have reminded one of the scientists about the Monte Carlo casino in Monaco, where his uncle used to gamble.

The “new era of fast computers” has in fact come a long way since 1946, and it is now possible to generate tens of thousands of simulated futures in fractions of a second, allowing us to better understand the range and frequency of possible outcomes. Modern tools such as Optimal’s Goal Oriented Outcome Shaping Engine (we know that’s a mouthful, so we just call it GOOSE™) can graphically display a histogram of possibilities within seconds, allowing an investor to perform quick, interactive “what-if” experiments in an intuitive web-based control panel to help make well-informed investment decisions.

Using Monte Carlo Simulations with Optimal’s Adaptive Risk Control and the Goal-Optimizing Outcome Shaping Engine

Modern computers have now made it push-button easy to run a Monte Carlo simulation, requiring no more than a standard internet browser and a few clicks of the mouse. The investor first selects an investment horizon between 1 and 25 years within the control panel, and optionally, a downside floor constraint (that the account value should try and stay above) and an upside target account value.

The Monte Carlo simulator generates a histogram of the 10,000 different possible future scenarios, by playing out each different simulated version of the future. Of course, it is important to realize that no simulation is perfectly accurate, and real-world events such as market crashes, political surprises and unexpected interest rate hikes are not easily incorporated in a simulation. Reality is likely to be different from the simulated futures. However, it can still be a powerful planning tool, such as to understand the trade-off between downside risk and upside potential.

Interpreting the Monte Carlo Histogram

The histogram plots the number of simulated scenarios that reach various account levels at the end of the investment horizon. Understanding and interpreting the histogram can assist in keeping you realistic as well as making a more informed trade off between your willingness to weather downside risk versus your potential upside.

For instance, if you set your upside target to doubling your investment in three years, you will likely see that only a very small percentage of the simulated scenarios are likely to reach that target account value under reasonable market return assumptions. On the other hand, setting a very modest upside target (e.g. a total gain of 20% after 5 years) might show that a very large number of the simulated scenarios reach that account value very early and then do not grow any further.

Similarly, if the downside floor constraint is very tight (e.g. lose no more than 5 percent over the next year) it is unlikely that you will have very many scenarios that end up with much more than a modest upside target. Dropping the downside floor will tend to increase the number of simulated scenarios that will end with higher account values by the end of the year.

Since risk control settings (such as the downside floor and upside target) can shape the possible outcomes, we call this form of risk control Outcome Shaping. Optimal’s Goal Optimized Outcome Shaping Engine aims to maximize the likelihood of your hitting your specified upside target while trying to keep you from ending below your specified downside floor. By changing either your investment horizon, your upside target or your downside floor, you can affect the shape of possible outcomes for your investment. You can thank the Monte Carlo method for this revolutionary innovation.

Notes:

A Sad Note: Although Louis Bachelier is widely recognized today as a pioneer of mathematical finance, his work was largely overlooked during his own lifetime and he was forced to endure various professional setbacks during his career.

A Happier Note: Albert Einstein did not have that problem.

An Ironic Note: Louis Bachelier died in 1946 – precisely the same period of time that the military scientists at Los Alamos were developing what is known today as the Monte Carlo method.

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