Monte Carlo Forecasting and Its Limits
Decision-making under uncertainty is a core tenant of investing.
For young investors, asset allocation in a retirement portfolio is fairly straightforward: put a lot of the portfolio in stocks. Maybe put a little in other assets (or maybe not). Set it and forget it for awhile.
For the 60-year-old investor approaching retirement, asset allocation is far more stress-inducing. They want to retire. They want to grow their investments. But they also can’t afford a large drawdown in their portfolio. They might use a rule-of-thumb they find in a book to guide their stock-bond allocation. But what if they want to understand what might the probability of a certain loss might be? They or their financial advisor may create a Monte Carlo forecast of various portfolios to answer this question and similar ones.
A typical Monte Carlo forecast uses the historical returns of a given asset class (stocks, bonds, etc.) as well as historical volatility to create a high number of simulations of possible future returns over a specified duration. For example, a Monte Carlo forecast output might allow someone to say“in 72% of simulations, the portfolio saw a positive return over 10 years” as well as “in just 5% of simulations did the portfolio finish down 10% or more.”1,2
The soon-to-be retiree or their advisor might complete the forecast manually in Excel or an online tool like Portfolio Visualizer.
The tool or advisor might provide some fun visuals for the soon-to-be-retiree to consider:
I believe that Monte Carlo forecasting more-often-than-not helps investors think about the level of risk they’re willing to accept.
Another potential application of Monte Carlo forecasting in investing is option pricing. For example, a trader might use Monte Carlo forecasting to determine the probability a given option trade is likely to be profitable before its expiration date.
However, there are some important flaws with Monte Carlo forecasting.
1. Small sample sizes. A common approach is to use historical returns and volatility of a given security as inputs to the forecast. The challenge is that a financial advisor may want to place their client in a relatively new fund (a covered call fund, for example). The historical returns and volatility of a fund that don’t include key market events (e.g. crashes, recoveries, periods of high/low volatility, etc.) likely will hurt the accuracy of forecasts.
2. Non-normal return distributions. Monte Carlo forecasts are often constructed under the assumption that future returns of a given asset class will follow a normal distribution with a mean and standard deviation equal to the historical mean and standard deviation. However, security returns are often non-normal. A textbook on modern portfolio theory summarizes the research:
Researchers observe nonsymmetric, highly peaked, and longer-tailed(leptokurtic) characteristics in the empirical unconditional distribution of asset returns.
This means that Monte Carlo forecasts, which often fail to account for non-normal distributions, will be inaccurate.
3. Simulation count & “black swans”. Let’s say you run 1,000 Monte Carlo forecasts. At the end, you say, “Wow, there’s not a single simulation where my portfolio went down more than 30%!” This statement is correct. But it would be incorrect to say “My forecast says it's impossible for my portfolio to go down by 30% or more!” There are two reasons for this:
a. 1,000 simulations is a lot. And it’s probably enough to give you a general idea of the relative probabilities of various outcomes. However, if you run 10,000 simulations (or more), you might start to see some simulations where your portfolio does in fact go down by 30% or more.
b. Monte Carlo forecasts do a decent job of taking historical data to extrapolate what might happen in the future. However, they are unable to account for events that will take place in the future that have not occurred in the past. These are so-called “Black Swan” events. If a global pandemic isn’t in your dataset, there’s no way you can expect your Monte Carlo forecast to account for one. The same goes for large scale cyber-attacks and other hard to-anticipate events.
These are just a few of the problems posed by using Monte Carlo forecasting. These are by no means the only problems.
However, Monte Carlo forecasting is often “good enough” to use to understand the relative probabilities of various return scenarios. There are even some techniques to partially overcome some of the method’s shortcomings. However, one must keep in mind its imperfections. Financial advisors should be wary of presenting clients with some of the simulated return graphics shown earlier in this piece. If they do, they should have lengthy written and verbal disclosures of the potential inaccuracies.
As always, please see my own disclosures here.
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1These are purely hypothetical figures. Please work with your financial advisor to discuss your own situation, goals, and optimal asset allocation. Past performance does not predict future performance.
2 There are plenty of other great applications of Monte Carlo forecasting beyond investing. In high school, I ran Monte Carlo forecasts to predict attendance at student group events. This technique would allow me to ask, for example, "What is the probability at least 50 students will be in attendance?"