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From Risk to Resilience: How to Build a Strong Plan for an Uncertain Future

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Monte Carlo simulations are a powerful tool for analyzing complex systems and making predictions about uncertain outcomes. Financial Planners use Monte Carlo simulations to model retirement portfolios, income strategies, and investment outcomes.

By using a large sample of historical market data, Monte Carlo simulations can generate thousands or even millions of hypothetical scenarios, each with slightly different outcomes and paths. These scenarios can then be used to estimate the probability of varying market outcomes, such as the likelihood of your portfolio being able to meet your retirement goals.

This article goes into Monte Carlo simulation in a little more depth. If you’re looking for a more basic explanation, check out my previous article: How Flipping Coins Helps You Make Better Financial Decisions – Gilbert Wealth

Why Use Monte Carlo?

Imagine you would like to invest $100,000 for the next 15 years. You hope to turn this initial investment into $400,000 by the end of the 15 years. You hear that the stock market has returned an average of 12% per year, so you decide to invest in the S&P 500. How likely are you to hit that goal?
 
To answer that, let’s consider the overall returns from the S&P 500, one of the world’s most famous stock market indices, from 1926 to 2022.  Since 1926, there have been 83 full 15-year periods. An entire 15-year period would be 1926 to 1940, 1927 to 1941, and so on, with the last 15-year period being from 2008 to 2022. 

So what was the result? Out of the 83 periods, you only met or exceeded your goal 48 times, or 57.8% of the time.

Well, wait a minute, you might say. Using the Rule of 72 and a 12% rate of return, why did you not consistently achieve your goal? After all, you should have reached it after 12 years, leaving you with 3 years of spare time, right?

The answer is, of course, because of volatility and the fact that certain periods have better overall returns than others. What Monte Carlo does is recognizes this fact and attempt to simulate it so that we can make better decisions about our finances. 

Let’s dig in a little more.

A Deeper Look into Historic Returns

 Below is a projection of what a $100,000 portfolio invested at the beginning of each of those periods would have looked like after 15 years. Here are some quick data points from the chart I’d like to point out.

  1. While the average or mean of the S&P 500 was 12% per year, that return does not factor in volatility which reduces your final return. The true long-term return that factors in volatility is called the Compound Annual Growth Rate or CAGR. Using the CAGR formula, the more critical return is not 12% per year but 10.1% per year.
  2. Every year, returns are different. Some are higher; some are lower than the average. The statistic that seeks to encapsulate this is Standard Deviation which measures how much the actual returns have deviated from the average. The standard deviation from 1926 to 2022 for the S&P 500 was 18.6%. Simply put, this means that 68% of the time, returns might fall between -6.6% and +30.6%. 95% of the time, they will be between -25.2% and +49.2%. Helpful right? Just hang with me. I’ll get back to this.
  3. There was no 15-year period with negative nominal returns… but it was close. The lowest ending balance over a 15-year rolling period was $110,109, which was from 1929 to 1943 and encompassed the whole Great Depression.
  4. The highest 15-year return was from 1985 to 2000, encompassing the entire Dot Com rise without its impending downturn. Interestingly, the 2nd highest ending was from 1942 to 1956, which followed the worst 15-year rolling period. That’s the importance of staying invested. 
  5. The Black Line below shows the initial investment of $100,000. The Red Line marks the 25th percentile (more on this later) of results. The Blue Line marks the 50th percentile. The Green Line marks the 75th percentile.

15-Year Rolling Period Ending Portfolio Values
based on the S&P 500 from 1926 to 2022

Historic S&P Rolling 15 Year Returns
Data from Diminsional's Returns Web
  1.  The portfolio values are in nominal dollars, so they do not reflect purchasing power and the impact of inflation. 
  2.  The portfolio assumes dividends are reinvested. 

Historic analysis is useful but does have its limitations. One of the primary limitations is that we only have one set of historic events. And, in the case of looking at rolling period returns, many of those periods have overlapping returns. For example, the 15 years from 1985 to 2000 share 14 common years of returns with the rolling period from 1984 to 1999, which ended up being the 3rd highest ending period. That is why the above chart has patterns that emerge particularly at the upper end.

Monte Carlo takes the characteristics of investments and creates new scenarios to analyze. It’s based on but not identical to what happened in history. For example, using a simple Monte Carlo projection using the basic inputs of 12% return (yes, Monte Carlo uses average and not CAGR) and an 18.6% standard deviation for just 83 periods at a time, you can create alternate scenarios that, to the eye, could have been historic return.

In the below chart, I’ve done just that. Each varies from the other but inherits the overall shape of the original historic data set. Here are a few things to pay attention to as you look at these:

  1. The percentile returns (Red, Blue, and Green lines) are not all that different from the historic returns. 
  2. While historic returns did not have a negative 15-year period, Monte Carlo can very easily have much lower returns. Several of the snapshots have portfolio ending values below $50,000! 
  3. On the other side of the equation, some scenarios ended significantly higher than historic returns. The scale does cuts off at $1,400,000. To reach that, the annualized return would be 19.2%! 

15-Year Rolling Period Ending Portfolio Values
simulated by Monte Carlo

GIF of Monte Carlo using Market Data

How is Monte Carlo Utilized in Practice

Monte Carlo systems can be simple, as I projected above, using only a basic average and standard deviation, or very complex, using a multitude of variables to create a customized Monte Carlo. 

In practice, most Monte Carlo systems use an overall portfolio return and portfolio standard deviation using forward market estimated returns, standard deviations, and asset correlation. Portfolio return and portfolio standard deviation are beyond the scope of this article but involve detailed calculations. 

 The below chart uses the same standard deviation of 18.6% as the S&P 500 but reduces the average return to 8%. Notice the significant shift in portfolio ending values after 15 years. Remember that these are nominal portfolios. 

 

15-Year Rolling Period Ending Portfolio Values
simulated by Monte Carlo using 8% Returns

Monte Carlo systems run many more scenarios than just 83. Typically, 250 is a minimum with 1,000 being a popular option. Once you get over 1,000 simulations, you begin to get more extreme cases on the positive and negative sides. 

More advanced models of Monte Carlo can factor in so-called Black Swan events, market return skew, and factor in prior simulated returns to generate future returns. Bootstrapping is another method used in Monte Carlo that takes historic data and simply jumbles it up into a new set. For example, it might generate a scenario with the returns from the following years: 1926, 1952, 2003, 1999, 1974, etc. 

The combinations and complexity of the models are endless. The point is that Monte Carlo introduces variation to your retirement portfolios to assess how your plan might respond under different simulations. Armed with this knowledge, you can develop a financial plan that addresses this variability, providing you with the confidence to achieve your financial objectives.

Limitations of Monte Carlo

Monte Carlo is a powerful tool for analysis in a financial plan. However, it does have its limitations that should be understood.
 
  1. Which base statistics you input to simulate future returns has a significant impact on the final results. Using base statistics from the largest 500 stocks in the US that went from a global emerging market in 1900 with ~15% world market capitalization to ~58% of the world market capitalization as of 2022 will give you a different result than if you use return statistics from other global markets or asset classes.
  2. Even within the US, the future economic environment is very different now than it was throughout history. Just check out this video which shows what companies were the largest from 1956 to 2021. Largest US Companies by Revenue 1956 to 2021 – YouTube
  3.  Monte Carlo typically does not factor in changing correlations between assets. 
Steven Gilbert

Steven Gilbert CFP® is the owner and founder of Gilbert Wealth LLC, a financial planning firm located in Fort Wayne, Indiana serving clients locally and nationally. A fixed fee financial planning firm, Gilbert Wealth helps clients optimize their financial strategies to achieve their most important goals through comprehensive advice and unbiased structure.