In January of 1946, a man named Stanislaw Ulam found himself confined to a hospital bed, having suffered an encephalitis attack. A brilliant scientist and a veteran of the Manhattan Project, Ulam wasn’t the type to sit idly while he recuperated. Instead, after playing innumerable games of solitaire to pass the time, Ulam began to examine the statistical aspects of the game. Among the questions he asked: how to accurately estimate the probability of winning a game. To answer this question, Ulam ended up devising a novel statistical technique that he dubbed Monte Carlo analysis. Today, this approach is broadly accepted and widely used in applications ranging from engineering to biology to meteorology—and even basketball. And it is used in financial planning, which is what I would like to discuss here.
How exactly does Monte Carlo analysis work? The idea is this: As long as you know the basic dynamics of how something works—whether it’s weather patterns, card games or anything else—you can use a computer to simulate an experiment thousands of times and then simply count up the frequency of various outcomes. In personal finance, this is how it works: Knowing how the stock market has performed in the past, and the degree to which it varies from year to year, one can simulate the market’s performance over future periods. Instead of focusing on the stock market’s average annual returns, Monte Carlo analysis focuses on average multi-year returns. This allows financial advisors to reassure their clients with confident-sounding statements such as: “I’ve tested ten thousand scenarios and can tell you that your retirement plan has a 90% probability of success.” (To get a better sense of what Monte Carlo simulations look like, you can see an example on Vanguard’s website.)
While Monte Carlo analysis is widely used in financial planning, I would advise caution, for two reasons:
1. Subjective inputs
Monte Carlo simulation works well when forecasting physical or mechanical processes—things that act in predictable ways, or at least within a known set of bounds. A card game, for example, can develop in numerous ways. Still, it’s always played with a fixed set of rules and an identical deck of cards. While you don’t know which card will come up next, you do know there will never be five aces in a deck. As a result, the set of possible outcomes is necessarily limited.
When it comes to the stock market, though, the opposite is true: An infinite combination of political and economic events (and human emotion) drive the market in unpredictable ways. In a card game, it’s difficult to know what will happen next; in the stock market, it’s impossible to know. And it’s not just the stock market. Lots of other variables impact the success of a retirement plan, including inflation, tax rates, interest rates and potential changes to Social Security and Medicare.
Consider this thought experiment: Tomorrow morning, pick up the newspaper and ask yourself how many of the stories you could have predicted five or ten years ago. Not many, I suspect, and yet that is what we are doing when we expect Monte Carlo analysis to help us forecast multi-decade retirement scenarios. To be sure, the past serves as a guide to the future, but it’s just a guide. That’s why any simulation of the stock market rests on shaky ground, simplistically assuming that the future will precisely mirror the past.
2. Less-than-useful output
If the inputs to a Monte Carlo analysis are subjective, the outputs are even more troubling.
First, Monte Carlo output is normally expressed as a percentage—a 90% probability of success, for example—but what exactly does “success” mean? It means simply that one won’t run out of money. While that sounds logical, the problem is that it is defined very literally. If the Monte Carlo determines that there will be even one dollar left at the end of someone’s life, that is defined as success. For a computer, that may make sense, but for a real person seeing their funds rapidly approach zero late in life, that hardly sounds like a pleasant or successful outcome. But because this is the way Monte Carlos work, they carry the potential to lull people into a false sense of security or, alternatively, to scare the daylights out of them, when neither reaction may be warranted.
The second problem with Monte Carlo output is that, if you dig into the results, it provides a range of potential outcomes so wide that it borders on the absurd. Use a typical Monte Carlo to simulate the growth of a $1 million portfolio over a 30-year retirement, for example, and it will unhelpfully project your assets to fall somewhere between zero and $29 million. While statistically this may be accurate, personally I don’t find it very useful.
To be sure, Monte Carlo analysis has its place in scientific disciplines. But when it comes to retirement planning, I would urge you to be skeptical. Always look at the numbers behind the numbers, and never let any one analysis drive your decisions.
